From d4ef2af9f4720c3f491b5aa7bf92820e5b21ae04 Mon Sep 17 00:00:00 2001 From: Pierre Beaujean Date: Tue, 16 Jul 2024 14:54:19 +0200 Subject: [PATCH] typos/reformulations --- Figure12.eps | 505 +++++++++++++++++++----------------- TODO.md | 7 +- analyses/plot_pot_matsui.py | 6 +- im/anion_position.odg | Bin 337281 -> 337465 bytes nitroxides.tex | 125 ++++----- 5 files changed, 348 insertions(+), 295 deletions(-) diff --git a/Figure12.eps b/Figure12.eps index 0aaaec1..b875263 100644 --- a/Figure12.eps +++ b/Figure12.eps @@ -16778,141 +16778,159 @@ pum 248 -253 l 248 -27 l 310 -27 l 310 0 l 151 0 l p ef pom pum -502 1179 t -0.003 0.003 0.003 c 165 176 m 122 114 90 51 71 -11 ct 52 -73 42 -142 42 -220 ct -42 -297 52 -366 71 -428 ct 90 -490 122 -552 165 -614 ct 281 -614 l 238 -551 206 -488 186 -426 ct -167 -364 157 -295 157 -219 ct 157 -144 167 -75 186 -13 ct 206 49 237 112 281 176 ct -165 176 l p ef -447 8 m 403 8 369 -4 345 -27 ct 321 -51 309 -84 309 -127 ct 309 -173 324 -209 354 -233 ct -384 -257 428 -270 485 -270 ct 582 -272 l 582 -295 l 582 -324 577 -345 566 -360 ct -556 -374 540 -381 516 -381 ct 495 -381 479 -376 469 -366 ct 459 -357 453 -340 450 -318 ct -329 -323 l 337 -367 356 -400 389 -423 ct 421 -445 465 -456 521 -456 ct 578 -456 621 -442 652 -415 ct -683 -387 698 -347 698 -296 ct 698 -133 l 698 -108 701 -90 706 -81 ct 712 -71 722 -66 735 -66 ct -744 -66 752 -67 760 -69 ct 760 -6 l 754 -4 747 -3 742 -2 ct 736 0 731 1 725 2 ct -720 3 714 3 708 4 ct 702 4 694 5 686 5 ct 657 5 635 -2 621 -17 ct 607 -31 599 -52 596 -80 ct -594 -80 l 561 -21 512 8 447 8 ct p -582 -208 m 522 -207 l 495 -206 476 -203 465 -198 ct 453 -193 445 -186 439 -176 ct -433 -166 430 -153 430 -136 ct 430 -115 435 -99 445 -89 ct 454 -78 467 -73 484 -73 ct -502 -73 519 -78 534 -88 ct 549 -98 560 -112 569 -129 ct 578 -147 582 -165 582 -185 ct -582 -208 l p ef -755 176 m 799 111 831 48 850 -13 ct 870 -75 879 -144 879 -219 ct 879 -295 869 -364 850 -427 ct -830 -489 798 -552 755 -614 ct 871 -614 l 915 -551 946 -489 965 -427 ct 984 -365 994 -296 994 -220 ct -994 -143 984 -74 965 -11 ct 946 51 915 113 871 176 ct 755 176 l p ef +2090 1150 t +0.003 0.003 0.003 c 158 169 m 117 109 87 50 68 -10 ct 50 -69 40 -136 40 -210 ct +40 -284 50 -350 68 -410 ct 87 -469 117 -529 158 -588 ct 269 -588 l 228 -528 197 -468 178 -408 ct +160 -348 150 -282 150 -210 ct 150 -138 159 -72 178 -12 ct 197 47 227 107 269 169 ct +158 169 l p ef +427 8 m 385 8 353 -3 330 -26 ct 306 -49 295 -80 295 -121 ct 295 -166 309 -200 338 -223 ct +367 -246 409 -258 464 -259 ct 556 -260 l 556 -282 l 556 -310 551 -331 541 -344 ct +532 -358 516 -365 494 -365 ct 473 -365 458 -360 448 -351 ct 439 -341 433 -326 430 -304 ct +314 -310 l 321 -351 340 -383 371 -405 ct 402 -426 445 -437 498 -437 ct 552 -437 594 -424 623 -397 ct +653 -370 667 -332 667 -283 ct 667 -127 l 667 -103 670 -86 676 -77 ct 681 -68 690 -63 703 -63 ct +711 -63 719 -64 727 -66 ct 727 -5 l 721 -4 715 -2 709 -1 ct 704 0 699 1 694 2 ct +688 3 683 3 677 4 ct 671 5 664 5 656 5 ct 628 5 607 -2 594 -16 ct 581 -30 573 -50 570 -76 ct +568 -76 l 536 -20 489 8 427 8 ct p +556 -199 m 499 -198 l 473 -197 455 -194 444 -189 ct 433 -185 425 -178 419 -168 ct +414 -159 411 -146 411 -130 ct 411 -110 415 -95 425 -85 ct 434 -75 447 -70 462 -70 ct +480 -70 496 -74 510 -84 ct 524 -94 536 -107 544 -123 ct 552 -140 556 -158 556 -177 ct +556 -199 l p ef +725 169 m 767 107 797 47 816 -12 ct 835 -72 844 -137 844 -210 ct 844 -282 834 -349 815 -409 ct +796 -468 766 -528 725 -588 ct 836 -588 l 878 -528 908 -468 926 -409 ct 945 -349 954 -283 954 -210 ct +954 -137 945 -70 926 -11 ct 908 49 878 109 836 169 ct 725 169 l p ef pom pum -1776 1179 t -447 0 m 136 -497 l 138 -456 l 140 -387 l 140 0 l 69 0 l 69 -583 l -161 -583 l 476 -83 l 473 -137 471 -176 471 -201 ct 471 -583 l 543 -583 l -543 0 l 447 0 l p ef -724 -208 m 724 -157 735 -117 756 -90 ct 777 -62 808 -48 849 -48 ct 881 -48 907 -54 927 -67 ct -946 -80 959 -97 966 -116 ct 1031 -98 l 1005 -27 944 8 849 8 ct 783 8 732 -12 698 -51 ct -663 -91 646 -149 646 -227 ct 646 -301 663 -357 698 -397 ct 732 -436 782 -456 846 -456 ct -978 -456 1043 -377 1043 -218 ct 1043 -208 l 724 -208 l p -967 -265 m 962 -312 950 -347 931 -368 ct 911 -390 882 -401 845 -401 ct 809 -401 780 -389 759 -365 ct -738 -341 727 -307 725 -265 ct 967 -265 l p ef -1251 8 m 1206 8 1173 -4 1150 -28 ct 1127 -51 1116 -84 1116 -125 ct 1116 -171 1131 -207 1162 -232 ct -1192 -257 1241 -270 1309 -272 ct 1410 -273 l 1410 -298 l 1410 -334 1402 -360 1386 -376 ct -1371 -391 1347 -399 1314 -399 ct 1280 -399 1256 -394 1241 -382 ct 1226 -371 1217 -353 1214 -328 ct -1136 -335 l 1149 -416 1208 -456 1315 -456 ct 1372 -456 1414 -443 1442 -417 ct -1471 -392 1485 -354 1485 -305 ct 1485 -113 l 1485 -91 1488 -74 1494 -63 ct -1499 -52 1510 -46 1527 -46 ct 1534 -46 1542 -47 1551 -49 ct 1551 -3 l 1532 2 1513 4 1494 4 ct -1466 4 1446 -3 1433 -18 ct 1421 -32 1414 -55 1412 -86 ct 1410 -86 l 1391 -52 1368 -28 1343 -13 ct -1318 1 1287 8 1251 8 ct p -1268 -48 m 1295 -48 1320 -54 1341 -66 ct 1362 -79 1379 -96 1391 -118 ct 1403 -139 1410 -161 1410 -184 ct -1410 -221 l 1328 -219 l 1293 -219 1267 -215 1249 -209 ct 1230 -202 1217 -192 1207 -178 ct -1197 -164 1193 -146 1193 -124 ct 1193 -100 1199 -81 1212 -68 ct 1225 -54 1244 -48 1268 -48 ct +3309 1150 t +314 -505 m 252 -505 204 -485 169 -445 ct 135 -406 118 -351 118 -282 ct 118 -213 136 -158 172 -117 ct +207 -75 256 -54 317 -54 ct 395 -54 454 -93 493 -170 ct 555 -140 l 532 -91 500 -55 458 -30 ct +416 -5 368 8 313 8 ct 257 8 208 -4 167 -27 ct 126 -51 95 -84 73 -127 ct 52 -171 41 -222 41 -282 ct +41 -371 65 -441 113 -491 ct 161 -542 228 -567 313 -567 ct 372 -567 422 -555 462 -532 ct +502 -509 531 -474 550 -429 ct 478 -405 l 465 -437 444 -462 416 -479 ct 387 -497 353 -505 314 -505 ct p ef -1608 0 m 1608 -343 l 1608 -375 1607 -410 1605 -448 ct 1676 -448 l 1678 -397 1679 -366 1679 -356 ct -1681 -356 l 1692 -395 1706 -421 1721 -435 ct 1737 -449 1759 -456 1787 -456 ct -1797 -456 1807 -455 1817 -452 ct 1817 -384 l 1807 -386 1794 -388 1777 -388 ct -1746 -388 1723 -374 1707 -348 ct 1690 -321 1682 -283 1682 -233 ct 1682 0 l 1608 0 l +643 1 m 643 -588 l 714 -588 l 714 1 l 643 1 l p ef +1187 -215 m 1187 -140 1170 -84 1137 -47 ct 1104 -10 1057 8 994 8 ct 931 8 884 -11 852 -49 ct +820 -88 804 -143 804 -215 ct 804 -363 868 -437 996 -437 ct 1062 -437 1110 -419 1141 -383 ct +1172 -347 1187 -291 1187 -215 ct p +1112 -215 m 1112 -274 1103 -317 1086 -344 ct 1068 -371 1039 -384 997 -384 ct +956 -384 925 -371 907 -343 ct 888 -316 879 -273 879 -215 ct 879 -158 888 -116 906 -87 ct +925 -59 954 -45 993 -45 ct 1036 -45 1066 -59 1085 -86 ct 1103 -114 1112 -156 1112 -215 ct p ef -2299 -3 m 2275 4 2249 7 2224 7 ct 2164 7 2135 -27 2135 -94 ct 2135 -393 l 2083 -393 l -2083 -447 l 2137 -447 l 2159 -548 l 2209 -548 l 2209 -447 l 2292 -447 l -2292 -393 l 2209 -393 l 2209 -110 l 2209 -89 2212 -74 2220 -65 ct 2227 -57 2239 -52 2256 -52 ct -2266 -52 2280 -54 2299 -58 ct 2299 -3 l p ef -2438 -371 m 2454 -400 2473 -422 2496 -436 ct 2518 -449 2547 -456 2581 -456 ct -2630 -456 2666 -444 2689 -420 ct 2712 -396 2723 -355 2723 -298 ct 2723 0 l 2648 0 l -2648 -284 l 2648 -315 2645 -339 2640 -354 ct 2634 -369 2624 -381 2611 -388 ct -2598 -395 2579 -398 2556 -398 ct 2521 -398 2493 -386 2472 -362 ct 2451 -338 2440 -305 2440 -264 ct -2440 0 l 2366 0 l 2366 -614 l 2440 -614 l 2440 -454 l 2440 -438 2440 -420 2439 -402 ct -2438 -384 2437 -374 2437 -371 ct 2438 -371 l p ef -2891 -208 m 2891 -157 2902 -117 2923 -90 ct 2944 -62 2975 -48 3016 -48 ct 3048 -48 3074 -54 3094 -67 ct -3113 -80 3126 -97 3133 -116 ct 3198 -98 l 3172 -27 3111 8 3016 8 ct 2950 8 2899 -12 2865 -51 ct -2830 -91 2813 -149 2813 -227 ct 2813 -301 2830 -357 2865 -397 ct 2899 -436 2949 -456 3013 -456 ct -3145 -456 3210 -377 3210 -218 ct 3210 -208 l 2891 -208 l p -3134 -265 m 3129 -312 3117 -347 3098 -368 ct 3078 -390 3049 -401 3012 -401 ct -2976 -401 2947 -389 2926 -365 ct 2905 -341 2894 -307 2892 -265 ct 3134 -265 l +1599 -119 m 1599 -78 1584 -47 1553 -25 ct 1523 -3 1480 8 1425 8 ct 1372 8 1331 -1 1302 -18 ct +1273 -36 1254 -63 1246 -101 ct 1309 -113 l 1315 -90 1327 -73 1346 -62 ct 1365 -52 1392 -46 1425 -46 ct +1462 -46 1488 -52 1505 -63 ct 1522 -74 1530 -91 1530 -113 ct 1530 -130 1524 -144 1512 -154 ct +1501 -165 1482 -174 1456 -180 ct 1405 -194 l 1364 -205 1335 -215 1318 -225 ct +1301 -235 1287 -248 1277 -262 ct 1267 -277 1263 -295 1263 -316 ct 1263 -355 1277 -385 1304 -405 ct +1332 -426 1373 -436 1426 -436 ct 1473 -436 1511 -428 1539 -411 ct 1567 -394 1584 -368 1592 -331 ct +1528 -323 l 1524 -342 1513 -357 1496 -367 ct 1478 -377 1455 -382 1426 -382 ct +1394 -382 1370 -377 1355 -367 ct 1340 -358 1332 -343 1332 -323 ct 1332 -311 1335 -301 1341 -293 ct +1348 -285 1357 -278 1370 -273 ct 1382 -267 1408 -259 1448 -249 ct 1486 -240 1513 -231 1530 -223 ct +1546 -215 1559 -206 1569 -196 ct 1579 -187 1586 -175 1591 -162 ct 1597 -150 1599 -135 1599 -119 ct p ef -3543 0 m 3543 -343 l 3543 -375 3542 -410 3540 -448 ct 3611 -448 l 3613 -397 3614 -366 3614 -356 ct -3616 -356 l 3627 -395 3641 -421 3656 -435 ct 3672 -449 3694 -456 3722 -456 ct -3732 -456 3742 -455 3752 -452 ct 3752 -384 l 3742 -386 3729 -388 3712 -388 ct -3681 -388 3658 -374 3642 -348 ct 3625 -321 3617 -283 3617 -233 ct 3617 0 l 3543 0 l +1739 -199 m 1739 -150 1749 -112 1770 -86 ct 1790 -59 1820 -46 1859 -46 ct 1890 -46 1915 -52 1933 -64 ct +1952 -77 1964 -92 1971 -111 ct 2034 -93 l 2008 -26 1950 8 1859 8 ct 1796 8 1747 -11 1714 -49 ct +1681 -87 1664 -143 1664 -217 ct 1664 -288 1681 -342 1714 -380 ct 1747 -418 1795 -437 1856 -437 ct +1982 -437 2045 -361 2045 -209 ct 2045 -199 l 1739 -199 l p +1971 -254 m 1967 -299 1956 -332 1937 -353 ct 1918 -374 1891 -384 1855 -384 ct +1820 -384 1793 -373 1773 -350 ct 1753 -326 1742 -295 1740 -254 ct 1971 -254 l p ef -3882 -208 m 3882 -157 3893 -117 3914 -90 ct 3935 -62 3966 -48 4007 -48 ct 4039 -48 4065 -54 4085 -67 ct -4104 -80 4117 -97 4124 -116 ct 4189 -98 l 4163 -27 4102 8 4007 8 ct 3941 8 3890 -12 3856 -51 ct -3821 -91 3804 -149 3804 -227 ct 3804 -301 3821 -357 3856 -397 ct 3890 -436 3940 -456 4004 -456 ct -4136 -456 4201 -377 4201 -218 ct 4201 -208 l 3882 -208 l p -4125 -265 m 4120 -312 4108 -347 4089 -368 ct 4069 -390 4040 -401 4003 -401 ct -3967 -401 3938 -389 3917 -365 ct 3896 -341 3885 -307 3883 -265 ct 4125 -265 l +2526 -4 m 2503 3 2479 6 2454 6 ct 2397 6 2369 -26 2369 -91 ct 2369 -377 l 2319 -377 l +2319 -429 l 2372 -429 l 2393 -526 l 2440 -526 l 2440 -429 l 2519 -429 l +2519 -377 l 2440 -377 l 2440 -107 l 2440 -86 2443 -72 2450 -63 ct 2457 -55 2469 -51 2485 -51 ct +2495 -51 2508 -53 2526 -56 ct 2526 -4 l p ef +2949 -215 m 2949 -140 2932 -84 2899 -47 ct 2866 -10 2819 8 2756 8 ct 2693 8 2646 -11 2614 -49 ct +2582 -88 2566 -143 2566 -215 ct 2566 -363 2630 -437 2758 -437 ct 2824 -437 2872 -419 2903 -383 ct +2934 -347 2949 -291 2949 -215 ct p +2874 -215 m 2874 -274 2865 -317 2848 -344 ct 2830 -371 2801 -384 2759 -384 ct +2718 -384 2687 -371 2669 -343 ct 2650 -316 2641 -273 2641 -215 ct 2641 -158 2650 -116 2668 -87 ct +2687 -59 2716 -45 2755 -45 ct 2798 -45 2828 -59 2847 -86 ct 2865 -114 2874 -156 2874 -215 ct p ef -4578 -72 m 4564 -43 4545 -23 4523 -10 ct 4500 2 4472 9 4438 9 ct 4382 9 4340 -11 4313 -49 ct -4287 -87 4274 -144 4274 -222 ct 4274 -378 4328 -456 4438 -456 ct 4472 -456 4500 -450 4523 -437 ct -4546 -425 4564 -405 4578 -378 ct 4578 -378 l 4578 -428 l 4578 -614 l 4652 -614 l -4652 -92 l 4652 -45 4653 -15 4654 0 ct 4583 0 l 4583 -4 4582 -14 4581 -30 ct -4580 -46 4579 -60 4579 -72 ct 4578 -72 l p -4352 -224 m 4352 -161 4360 -117 4377 -90 ct 4393 -63 4420 -49 4457 -49 ct 4499 -49 4530 -64 4549 -93 ct -4568 -122 4578 -168 4578 -229 ct 4578 -288 4568 -332 4549 -360 ct 4530 -387 4500 -401 4458 -401 ct -4421 -401 4393 -387 4377 -359 ct 4360 -332 4352 -287 4352 -224 ct p ef -5143 -224 m 5143 -146 5125 -88 5091 -49 ct 5056 -11 5006 8 4941 8 ct 4875 8 4826 -12 4793 -52 ct -4759 -92 4743 -149 4743 -224 ct 4743 -379 4809 -456 4943 -456 ct 5012 -456 5062 -437 5094 -400 ct -5126 -362 5143 -304 5143 -224 ct p -5064 -224 m 5064 -286 5055 -331 5037 -359 ct 5019 -387 4988 -401 4944 -401 ct -4901 -401 4869 -387 4850 -358 ct 4830 -330 4821 -285 4821 -224 ct 4821 -165 4830 -121 4849 -91 ct -4869 -62 4899 -47 4940 -47 ct 4985 -47 5016 -61 5036 -90 ct 5055 -119 5064 -164 5064 -224 ct +3428 -4 m 3405 3 3381 6 3356 6 ct 3299 6 3271 -26 3271 -91 ct 3271 -377 l 3221 -377 l +3221 -429 l 3274 -429 l 3295 -526 l 3342 -526 l 3342 -429 l 3421 -429 l +3421 -377 l 3342 -377 l 3342 -107 l 3342 -86 3345 -72 3352 -63 ct 3359 -55 3371 -51 3387 -51 ct +3397 -51 3410 -53 3428 -56 ct 3428 -4 l p ef +3559 -355 m 3574 -383 3592 -403 3614 -416 ct 3635 -430 3663 -436 3696 -436 ct +3742 -436 3776 -425 3798 -401 ct 3820 -378 3831 -340 3831 -285 ct 3831 1 l 3760 1 l +3760 -271 l 3760 -301 3757 -324 3751 -338 ct 3746 -353 3737 -364 3724 -371 ct +3711 -378 3694 -381 3671 -381 ct 3638 -381 3611 -369 3591 -346 ct 3571 -323 3561 -292 3561 -252 ct +3561 1 l 3489 1 l 3489 -588 l 3561 -588 l 3561 -435 l 3561 -418 3560 -402 3559 -385 ct +3558 -367 3558 -357 3557 -355 ct 3559 -355 l p ef +3995 -199 m 3995 -150 4005 -112 4026 -86 ct 4046 -59 4076 -46 4115 -46 ct 4146 -46 4171 -52 4189 -64 ct +4208 -77 4220 -92 4227 -111 ct 4290 -93 l 4264 -26 4206 8 4115 8 ct 4052 8 4003 -11 3970 -49 ct +3937 -87 3920 -143 3920 -217 ct 3920 -288 3937 -342 3970 -380 ct 4003 -418 4051 -437 4112 -437 ct +4238 -437 4301 -361 4301 -209 ct 4301 -199 l 3995 -199 l p +4227 -254 m 4223 -299 4212 -332 4193 -353 ct 4174 -374 4147 -384 4111 -384 ct +4076 -384 4049 -373 4029 -350 ct 4009 -326 3998 -295 3996 -254 ct 4227 -254 l +p ef +pom +pum +2090 2061 t +56 0 m 56 -329 l 56 -359 55 -393 54 -429 ct 121 -429 l 123 -380 124 -351 124 -341 ct +126 -341 l 137 -378 150 -403 165 -417 ct 180 -430 201 -437 228 -437 ct 237 -437 247 -436 257 -433 ct +257 -368 l 247 -370 234 -372 219 -372 ct 189 -372 166 -359 151 -333 ct 135 -308 128 -271 128 -224 ct +128 0 l 56 0 l p ef +380 -199 m 380 -150 390 -112 411 -86 ct 431 -59 461 -46 500 -46 ct 531 -46 556 -52 574 -64 ct +593 -77 605 -92 612 -111 ct 675 -93 l 649 -26 591 8 500 8 ct 437 8 388 -11 355 -49 ct +322 -87 305 -143 305 -217 ct 305 -288 322 -342 355 -380 ct 388 -418 436 -437 497 -437 ct +623 -437 686 -361 686 -209 ct 686 -199 l 380 -199 l p +612 -254 m 608 -299 597 -332 578 -353 ct 559 -374 532 -384 496 -384 ct 461 -384 434 -373 414 -350 ct +394 -326 383 -295 381 -254 ct 612 -254 l p ef +1049 -69 m 1036 -41 1018 -22 997 -10 ct 975 2 948 8 916 8 ct 862 8 822 -10 796 -47 ct +771 -83 758 -138 758 -212 ct 758 -362 811 -437 916 -437 ct 948 -437 975 -431 997 -419 ct +1018 -407 1036 -388 1049 -362 ct 1050 -362 l 1049 -410 l 1049 -588 l 1120 -588 l +1120 -88 l 1120 -44 1121 -14 1123 0 ct 1055 0 l 1054 -4 1053 -14 1052 -29 ct +1051 -44 1051 -58 1051 -69 ct 1049 -69 l p +833 -215 m 833 -155 841 -112 857 -86 ct 873 -60 898 -47 934 -47 ct 974 -47 1004 -61 1022 -89 ct +1040 -117 1049 -161 1049 -219 ct 1049 -276 1040 -318 1022 -344 ct 1004 -371 975 -384 935 -384 ct +899 -384 873 -371 857 -344 ct 841 -318 833 -274 833 -215 ct p ef +1594 -215 m 1594 -140 1577 -84 1544 -47 ct 1511 -10 1464 8 1401 8 ct 1338 8 1291 -11 1259 -49 ct +1227 -88 1211 -143 1211 -215 ct 1211 -363 1275 -437 1403 -437 ct 1469 -437 1517 -419 1548 -383 ct +1579 -347 1594 -291 1594 -215 ct p +1519 -215 m 1519 -274 1510 -317 1493 -344 ct 1475 -371 1446 -384 1404 -384 ct +1363 -384 1332 -371 1314 -343 ct 1295 -316 1286 -273 1286 -215 ct 1286 -158 1295 -116 1313 -87 ct +1332 -59 1361 -45 1400 -45 ct 1443 -45 1473 -59 1492 -86 ct 1510 -114 1519 -156 1519 -215 ct p ef -5508 0 m 5388 -184 l 5267 0 l 5187 0 l 5346 -230 l 5194 -448 l 5276 -448 l -5388 -274 l 5499 -448 l 5582 -448 l 5430 -231 l 5591 0 l 5508 0 l +1947 0 m 1832 -176 l 1716 0 l 1639 0 l 1792 -220 l 1646 -429 l 1725 -429 l +1832 -262 l 1938 -429 l 2018 -429 l 1872 -221 l 2027 0 l 1947 0 l p ef -5952 -226 m 5952 -167 5961 -123 5980 -94 ct 5999 -65 6027 -51 6065 -51 ct 6091 -51 6113 -58 6131 -72 ct -6149 -87 6160 -109 6164 -139 ct 6239 -134 l 6233 -91 6215 -56 6184 -30 ct 6153 -5 6114 8 6067 8 ct -6004 8 5956 -12 5923 -51 ct 5890 -91 5874 -149 5874 -225 ct 5874 -300 5891 -357 5924 -397 ct -5957 -437 6004 -456 6066 -456 ct 6112 -456 6150 -444 6180 -421 ct 6210 -397 6229 -364 6237 -323 ct -6160 -317 l 6156 -342 6147 -361 6131 -376 ct 6115 -391 6093 -398 6064 -398 ct -6024 -398 5996 -385 5978 -359 ct 5961 -332 5952 -288 5952 -226 ct p ef -6375 -208 m 6375 -157 6386 -117 6407 -90 ct 6428 -62 6459 -48 6500 -48 ct 6532 -48 6558 -54 6578 -67 ct -6597 -80 6610 -97 6617 -116 ct 6682 -98 l 6656 -27 6595 8 6500 8 ct 6434 8 6383 -12 6349 -51 ct -6314 -91 6297 -149 6297 -227 ct 6297 -301 6314 -357 6349 -397 ct 6383 -436 6433 -456 6497 -456 ct -6629 -456 6694 -377 6694 -218 ct 6694 -208 l 6375 -208 l p -6618 -265 m 6613 -312 6601 -347 6582 -368 ct 6562 -390 6533 -401 6496 -401 ct -6460 -401 6431 -389 6410 -365 ct 6389 -341 6378 -307 6376 -265 ct 6618 -265 l +2370 -216 m 2370 -159 2379 -117 2397 -90 ct 2415 -62 2442 -48 2478 -48 ct 2503 -48 2525 -55 2542 -69 ct +2559 -83 2569 -104 2573 -132 ct 2645 -128 l 2640 -86 2622 -53 2592 -29 ct 2563 -4 2525 8 2480 8 ct +2420 8 2374 -11 2343 -49 ct 2311 -87 2295 -142 2295 -215 ct 2295 -287 2311 -342 2343 -380 ct +2375 -418 2420 -437 2479 -437 ct 2523 -437 2559 -426 2588 -403 ct 2617 -380 2635 -349 2643 -309 ct +2569 -303 l 2566 -327 2556 -346 2541 -360 ct 2526 -374 2505 -381 2477 -381 ct +2439 -381 2412 -368 2395 -343 ct 2378 -318 2370 -276 2370 -216 ct p ef +2776 -199 m 2776 -150 2786 -112 2807 -86 ct 2827 -59 2857 -46 2896 -46 ct 2927 -46 2952 -52 2970 -64 ct +2989 -77 3001 -92 3008 -111 ct 3071 -93 l 3045 -26 2987 8 2896 8 ct 2833 8 2784 -11 2751 -49 ct +2718 -87 2701 -143 2701 -217 ct 2701 -288 2718 -342 2751 -380 ct 2784 -418 2832 -437 2893 -437 ct +3019 -437 3082 -361 3082 -209 ct 3082 -199 l 2776 -199 l p +3008 -254 m 3004 -299 2993 -332 2974 -353 ct 2955 -374 2928 -384 2892 -384 ct +2857 -384 2830 -373 2810 -350 ct 2790 -326 2779 -295 2777 -254 ct 3008 -254 l p ef -7072 0 m 7072 -284 l 7072 -313 7069 -336 7064 -353 ct 7058 -369 7048 -381 7036 -388 ct -7023 -395 7005 -398 6980 -398 ct 6944 -398 6916 -386 6895 -362 ct 6875 -337 6864 -303 6864 -259 ct -6864 0 l 6790 0 l 6790 -352 l 6790 -404 6789 -436 6787 -448 ct 6858 -448 l -6858 -446 6858 -443 6858 -437 ct 6859 -430 6859 -424 6859 -416 ct 6860 -408 6860 -393 6861 -371 ct -6862 -371 l 6879 -402 6899 -424 6921 -437 ct 6944 -450 6972 -456 7005 -456 ct -7054 -456 7090 -444 7113 -419 ct 7136 -395 7147 -355 7147 -298 ct 7147 0 l 7072 0 l +3447 0 m 3447 -272 l 3447 -300 3444 -322 3438 -338 ct 3433 -353 3424 -365 3412 -372 ct +3400 -378 3382 -382 3358 -382 ct 3324 -382 3297 -370 3277 -347 ct 3257 -323 3248 -290 3248 -249 ct +3248 0 l 3176 0 l 3176 -337 l 3176 -387 3175 -418 3174 -429 ct 3241 -429 l +3241 -428 3242 -424 3242 -418 ct 3242 -413 3243 -406 3243 -398 ct 3243 -391 3244 -377 3244 -356 ct +3246 -356 l 3262 -385 3281 -406 3302 -419 ct 3324 -431 3351 -437 3383 -437 ct +3430 -437 3464 -425 3486 -402 ct 3507 -379 3518 -340 3518 -286 ct 3518 0 l 3447 0 l p ef -7430 -3 m 7406 4 7380 7 7355 7 ct 7295 7 7266 -27 7266 -94 ct 7266 -393 l 7214 -393 l -7214 -447 l 7268 -447 l 7290 -548 l 7340 -548 l 7340 -447 l 7423 -447 l -7423 -393 l 7340 -393 l 7340 -110 l 7340 -89 7343 -74 7351 -65 ct 7358 -57 7370 -52 7387 -52 ct -7397 -52 7411 -54 7430 -58 ct 7430 -3 l p ef -7552 -208 m 7552 -157 7563 -117 7584 -90 ct 7605 -62 7636 -48 7677 -48 ct 7709 -48 7735 -54 7755 -67 ct -7774 -80 7787 -97 7794 -116 ct 7859 -98 l 7833 -27 7772 8 7677 8 ct 7611 8 7560 -12 7526 -51 ct -7491 -91 7474 -149 7474 -227 ct 7474 -301 7491 -357 7526 -397 ct 7560 -436 7610 -456 7674 -456 ct -7806 -456 7871 -377 7871 -218 ct 7871 -208 l 7552 -208 l p -7795 -265 m 7790 -312 7778 -347 7759 -368 ct 7739 -390 7710 -401 7673 -401 ct -7637 -401 7608 -389 7587 -365 ct 7566 -341 7555 -307 7553 -265 ct 7795 -265 l +3792 -4 m 3769 3 3745 6 3720 6 ct 3663 6 3635 -26 3635 -91 ct 3635 -377 l 3585 -377 l +3585 -429 l 3638 -429 l 3659 -526 l 3706 -526 l 3706 -429 l 3785 -429 l +3785 -377 l 3706 -377 l 3706 -107 l 3706 -86 3709 -72 3716 -63 ct 3723 -55 3735 -51 3751 -51 ct +3761 -51 3774 -53 3792 -56 ct 3792 -4 l p ef +3906 -199 m 3906 -150 3916 -112 3937 -86 ct 3957 -59 3987 -46 4026 -46 ct 4057 -46 4082 -52 4100 -64 ct +4119 -77 4131 -92 4138 -111 ct 4201 -93 l 4175 -26 4117 8 4026 8 ct 3963 8 3914 -11 3881 -49 ct +3848 -87 3831 -143 3831 -217 ct 3831 -288 3848 -342 3881 -380 ct 3914 -418 3962 -437 4023 -437 ct +4149 -437 4212 -361 4212 -209 ct 4212 -199 l 3906 -199 l p +4138 -254 m 4134 -299 4123 -332 4104 -353 ct 4085 -374 4058 -384 4022 -384 ct +3987 -384 3960 -373 3940 -350 ct 3920 -326 3909 -295 3907 -254 ct 4138 -254 l p ef -7967 0 m 7967 -343 l 7967 -375 7966 -410 7964 -448 ct 8035 -448 l 8037 -397 8038 -366 8038 -356 ct -8040 -356 l 8051 -395 8065 -421 8080 -435 ct 8096 -449 8118 -456 8146 -456 ct -8156 -456 8166 -455 8176 -452 ct 8176 -384 l 8166 -386 8153 -388 8136 -388 ct -8105 -388 8082 -374 8066 -348 ct 8049 -321 8041 -283 8041 -233 ct 8041 0 l 7967 0 l +4306 0 m 4306 -329 l 4306 -359 4305 -393 4304 -429 ct 4371 -429 l 4373 -380 4374 -351 4374 -341 ct +4376 -341 l 4387 -378 4400 -403 4415 -417 ct 4430 -430 4451 -437 4478 -437 ct +4487 -437 4497 -436 4507 -433 ct 4507 -368 l 4497 -370 4484 -372 4469 -372 ct +4439 -372 4416 -359 4401 -333 ct 4385 -308 4378 -271 4378 -224 ct 4378 0 l 4306 0 l p ef pom pum -11278 1179 t +13077 1179 t 165 176 m 122 114 90 51 71 -11 ct 52 -73 42 -142 42 -220 ct 42 -297 52 -366 71 -428 ct 90 -490 122 -552 165 -614 ct 281 -614 l 238 -551 206 -488 186 -426 ct 167 -364 157 -295 157 -219 ct 157 -144 167 -75 186 -13 ct 206 49 237 112 281 176 ct 165 176 l p ef @@ -16929,121 +16947,142 @@ p 1040 -143 1030 -74 1011 -11 ct 992 51 961 113 917 176 ct 801 176 l p ef pom pum -12599 1179 t -447 0 m 136 -497 l 138 -456 l 140 -387 l 140 0 l 69 0 l 69 -583 l -161 -583 l 476 -83 l 473 -137 471 -176 471 -201 ct 471 -583 l 543 -583 l -543 0 l 447 0 l p ef -724 -208 m 724 -157 735 -117 756 -90 ct 777 -62 808 -48 849 -48 ct 881 -48 907 -54 927 -67 ct -946 -80 959 -97 966 -116 ct 1031 -98 l 1005 -27 944 8 849 8 ct 783 8 732 -12 698 -51 ct -663 -91 646 -149 646 -227 ct 646 -301 663 -357 698 -397 ct 732 -436 782 -456 846 -456 ct -978 -456 1043 -377 1043 -218 ct 1043 -208 l 724 -208 l p -967 -265 m 962 -312 950 -347 931 -368 ct 911 -390 882 -401 845 -401 ct 809 -401 780 -389 759 -365 ct -738 -341 727 -307 725 -265 ct 967 -265 l p ef -1251 8 m 1206 8 1173 -4 1150 -28 ct 1127 -51 1116 -84 1116 -125 ct 1116 -171 1131 -207 1162 -232 ct -1192 -257 1241 -270 1309 -272 ct 1410 -273 l 1410 -298 l 1410 -334 1402 -360 1386 -376 ct -1371 -391 1347 -399 1314 -399 ct 1280 -399 1256 -394 1241 -382 ct 1226 -371 1217 -353 1214 -328 ct -1136 -335 l 1149 -416 1208 -456 1315 -456 ct 1372 -456 1414 -443 1442 -417 ct -1471 -392 1485 -354 1485 -305 ct 1485 -113 l 1485 -91 1488 -74 1494 -63 ct -1499 -52 1510 -46 1527 -46 ct 1534 -46 1542 -47 1551 -49 ct 1551 -3 l 1532 2 1513 4 1494 4 ct -1466 4 1446 -3 1433 -18 ct 1421 -32 1414 -55 1412 -86 ct 1410 -86 l 1391 -52 1368 -28 1343 -13 ct -1318 1 1287 8 1251 8 ct p -1268 -48 m 1295 -48 1320 -54 1341 -66 ct 1362 -79 1379 -96 1391 -118 ct 1403 -139 1410 -161 1410 -184 ct -1410 -221 l 1328 -219 l 1293 -219 1267 -215 1249 -209 ct 1230 -202 1217 -192 1207 -178 ct -1197 -164 1193 -146 1193 -124 ct 1193 -100 1199 -81 1212 -68 ct 1225 -54 1244 -48 1268 -48 ct +14398 1179 t +328 -527 m 263 -527 213 -507 177 -465 ct 141 -424 123 -367 123 -294 ct 123 -223 142 -166 179 -122 ct +217 -79 267 -57 331 -57 ct 412 -57 474 -97 515 -178 ct 579 -146 l 555 -96 522 -58 478 -31 ct +435 -5 384 8 327 8 ct 268 8 218 -4 175 -29 ct 132 -53 99 -88 77 -133 ct 54 -179 43 -232 43 -294 ct +43 -387 68 -460 118 -513 ct 168 -566 238 -592 327 -592 ct 389 -592 441 -580 482 -556 ct +524 -531 554 -495 574 -448 ct 499 -423 l 486 -457 464 -483 434 -501 ct 404 -518 369 -527 328 -527 ct +p ef +667 0 m 667 -614 l 742 -614 l 742 0 l 667 0 l p ef +1232 -224 m 1232 -146 1214 -88 1180 -49 ct 1145 -11 1095 8 1030 8 ct 964 8 915 -12 882 -52 ct +848 -92 832 -149 832 -224 ct 832 -379 898 -456 1032 -456 ct 1101 -456 1151 -437 1183 -400 ct +1215 -362 1232 -304 1232 -224 ct p +1153 -224 m 1153 -286 1144 -331 1126 -359 ct 1108 -387 1077 -401 1033 -401 ct +990 -401 958 -387 939 -358 ct 919 -330 910 -285 910 -224 ct 910 -165 919 -121 938 -91 ct +958 -62 988 -47 1029 -47 ct 1074 -47 1105 -61 1125 -90 ct 1144 -119 1153 -164 1153 -224 ct p ef -1608 0 m 1608 -343 l 1608 -375 1607 -410 1605 -448 ct 1676 -448 l 1678 -397 1679 -366 1679 -356 ct -1681 -356 l 1692 -395 1706 -421 1721 -435 ct 1737 -449 1759 -456 1787 -456 ct -1797 -456 1807 -455 1817 -452 ct 1817 -384 l 1807 -386 1794 -388 1777 -388 ct -1746 -388 1723 -374 1707 -348 ct 1690 -321 1682 -283 1682 -233 ct 1682 0 l 1608 0 l +1659 -124 m 1659 -82 1643 -49 1611 -26 ct 1579 -3 1535 8 1477 8 ct 1422 8 1379 -1 1349 -20 ct +1318 -38 1299 -66 1290 -105 ct 1355 -118 l 1362 -94 1375 -77 1395 -65 ct 1414 -54 1442 -49 1477 -49 ct +1515 -49 1543 -54 1560 -66 ct 1578 -78 1587 -95 1587 -118 ct 1587 -136 1580 -150 1568 -161 ct +1556 -172 1537 -181 1510 -189 ct 1456 -203 l 1414 -214 1383 -224 1365 -235 ct +1347 -246 1333 -259 1323 -274 ct 1312 -289 1307 -308 1307 -330 ct 1307 -370 1322 -402 1351 -423 ct +1380 -444 1422 -455 1478 -455 ct 1528 -455 1567 -446 1596 -429 ct 1625 -412 1643 -384 1651 -345 ct +1584 -337 l 1580 -357 1569 -372 1551 -383 ct 1533 -393 1508 -399 1478 -399 ct +1445 -399 1420 -394 1404 -383 ct 1388 -373 1380 -358 1380 -337 ct 1380 -324 1383 -314 1390 -306 ct +1396 -297 1406 -290 1419 -285 ct 1432 -279 1459 -271 1501 -261 ct 1540 -251 1569 -241 1586 -233 ct +1603 -225 1617 -215 1627 -205 ct 1637 -195 1645 -183 1651 -170 ct 1656 -156 1659 -141 1659 -124 ct p ef -2299 -3 m 2275 4 2249 7 2224 7 ct 2164 7 2135 -27 2135 -94 ct 2135 -393 l 2083 -393 l -2083 -447 l 2137 -447 l 2159 -548 l 2209 -548 l 2209 -447 l 2292 -447 l -2292 -393 l 2209 -393 l 2209 -110 l 2209 -89 2212 -74 2220 -65 ct 2227 -57 2239 -52 2256 -52 ct -2266 -52 2280 -54 2299 -58 ct 2299 -3 l p ef -2438 -371 m 2454 -400 2473 -422 2496 -436 ct 2518 -449 2547 -456 2581 -456 ct -2630 -456 2666 -444 2689 -420 ct 2712 -396 2723 -355 2723 -298 ct 2723 0 l 2648 0 l -2648 -284 l 2648 -315 2645 -339 2640 -354 ct 2634 -369 2624 -381 2611 -388 ct -2598 -395 2579 -398 2556 -398 ct 2521 -398 2493 -386 2472 -362 ct 2451 -338 2440 -305 2440 -264 ct -2440 0 l 2366 0 l 2366 -614 l 2440 -614 l 2440 -454 l 2440 -438 2440 -420 2439 -402 ct -2438 -384 2437 -374 2437 -371 ct 2438 -371 l p ef -2891 -208 m 2891 -157 2902 -117 2923 -90 ct 2944 -62 2975 -48 3016 -48 ct 3048 -48 3074 -54 3094 -67 ct -3113 -80 3126 -97 3133 -116 ct 3198 -98 l 3172 -27 3111 8 3016 8 ct 2950 8 2899 -12 2865 -51 ct -2830 -91 2813 -149 2813 -227 ct 2813 -301 2830 -357 2865 -397 ct 2899 -436 2949 -456 3013 -456 ct -3145 -456 3210 -377 3210 -218 ct 3210 -208 l 2891 -208 l p -3134 -265 m 3129 -312 3117 -347 3098 -368 ct 3078 -390 3049 -401 3012 -401 ct -2976 -401 2947 -389 2926 -365 ct 2905 -341 2894 -307 2892 -265 ct 3134 -265 l +1803 -208 m 1803 -157 1814 -117 1835 -90 ct 1856 -62 1887 -48 1928 -48 ct 1960 -48 1986 -54 2006 -67 ct +2025 -80 2038 -97 2045 -116 ct 2110 -98 l 2084 -27 2023 8 1928 8 ct 1862 8 1811 -12 1777 -51 ct +1742 -91 1725 -149 1725 -227 ct 1725 -301 1742 -357 1777 -397 ct 1811 -436 1861 -456 1925 -456 ct +2057 -456 2122 -377 2122 -218 ct 2122 -208 l 1803 -208 l p +2046 -265 m 2041 -312 2029 -347 2010 -368 ct 1990 -390 1961 -401 1924 -401 ct +1888 -401 1859 -389 1838 -365 ct 1817 -341 1806 -307 1804 -265 ct 2046 -265 l p ef -3877 -124 m 3877 -82 3861 -49 3829 -26 ct 3797 -3 3753 8 3695 8 ct 3640 8 3597 -1 3567 -20 ct -3536 -38 3517 -66 3508 -105 ct 3573 -118 l 3580 -94 3593 -77 3613 -65 ct 3632 -54 3660 -49 3695 -49 ct -3733 -49 3761 -54 3778 -66 ct 3796 -78 3805 -95 3805 -118 ct 3805 -136 3798 -150 3786 -161 ct -3774 -172 3755 -181 3728 -189 ct 3674 -203 l 3632 -214 3601 -224 3583 -235 ct -3565 -246 3551 -259 3541 -274 ct 3530 -289 3525 -308 3525 -330 ct 3525 -370 3540 -402 3569 -423 ct -3598 -444 3640 -455 3696 -455 ct 3746 -455 3785 -446 3814 -429 ct 3843 -412 3861 -384 3869 -345 ct -3802 -337 l 3798 -357 3787 -372 3769 -383 ct 3751 -393 3726 -399 3696 -399 ct -3663 -399 3638 -394 3622 -383 ct 3606 -373 3598 -358 3598 -337 ct 3598 -324 3601 -314 3608 -306 ct -3614 -297 3624 -290 3637 -285 ct 3650 -279 3677 -271 3719 -261 ct 3758 -251 3787 -241 3804 -233 ct -3821 -225 3835 -215 3845 -205 ct 3855 -195 3863 -183 3869 -170 ct 3874 -156 3877 -141 3877 -124 ct +2625 -3 m 2601 4 2575 7 2550 7 ct 2490 7 2461 -27 2461 -94 ct 2461 -393 l 2409 -393 l +2409 -447 l 2463 -447 l 2485 -548 l 2535 -548 l 2535 -447 l 2618 -447 l +2618 -393 l 2535 -393 l 2535 -110 l 2535 -89 2538 -74 2546 -65 ct 2553 -57 2565 -52 2582 -52 ct +2592 -52 2606 -54 2625 -58 ct 2625 -3 l p ef +3069 -224 m 3069 -146 3051 -88 3017 -49 ct 2982 -11 2932 8 2867 8 ct 2801 8 2752 -12 2719 -52 ct +2685 -92 2669 -149 2669 -224 ct 2669 -379 2735 -456 2869 -456 ct 2938 -456 2988 -437 3020 -400 ct +3052 -362 3069 -304 3069 -224 ct p +2990 -224 m 2990 -286 2981 -331 2963 -359 ct 2945 -387 2914 -401 2870 -401 ct +2827 -401 2795 -387 2776 -358 ct 2756 -330 2747 -285 2747 -224 ct 2747 -165 2756 -121 2775 -91 ct +2795 -62 2825 -47 2866 -47 ct 2911 -47 2942 -61 2962 -90 ct 2981 -119 2990 -164 2990 -224 ct p ef -4037 -448 m 4037 -164 l 4037 -135 4040 -112 4046 -95 ct 4051 -79 4061 -67 4073 -60 ct -4086 -53 4105 -50 4129 -50 ct 4165 -50 4193 -62 4214 -86 ct 4235 -111 4245 -145 4245 -189 ct -4245 -448 l 4319 -448 l 4319 -96 l 4319 -44 4320 -12 4322 0 ct 4252 0 l -4251 -2 4251 -5 4251 -11 ct 4250 -18 4250 -24 4250 -32 ct 4249 -40 4249 -55 4248 -77 ct -4247 -77 l 4230 -46 4210 -24 4188 -11 ct 4165 2 4137 8 4104 8 ct 4055 8 4019 -4 3996 -29 ct -3973 -53 3962 -93 3962 -150 ct 3962 -448 l 4037 -448 l p ef -4813 -226 m 4813 -70 4758 8 4648 8 ct 4614 8 4586 2 4563 -10 ct 4541 -23 4523 -42 4509 -70 ct -4508 -70 l 4508 -61 4507 -48 4506 -31 ct 4505 -13 4504 -3 4504 0 ct 4432 0 l -4433 -15 4434 -46 4434 -92 ct 4434 -614 l 4509 -614 l 4509 -439 l 4509 -421 4508 -400 4507 -376 ct -4509 -376 l 4522 -404 4541 -425 4563 -437 ct 4586 -450 4614 -456 4648 -456 ct -4704 -456 4746 -437 4773 -399 ct 4799 -361 4813 -303 4813 -226 ct p -4734 -224 m 4734 -286 4726 -331 4710 -358 ct 4693 -385 4666 -398 4629 -398 ct -4587 -398 4556 -384 4537 -355 ct 4518 -327 4509 -281 4509 -219 ct 4509 -160 4518 -117 4537 -89 ct -4555 -61 4586 -47 4628 -47 ct 4666 -47 4693 -61 4709 -89 ct 4726 -116 4734 -161 4734 -224 ct +pom +pum +17501 1179 t +466 -3 m 442 4 416 7 391 7 ct 331 7 302 -27 302 -94 ct 302 -393 l 250 -393 l +250 -447 l 304 -447 l 326 -548 l 376 -548 l 376 -447 l 459 -447 l +459 -393 l 376 -393 l 376 -110 l 376 -89 379 -74 387 -65 ct 394 -57 406 -52 423 -52 ct +433 -52 447 -54 466 -58 ct 466 -3 l p ef +605 -371 m 621 -400 640 -422 663 -436 ct 685 -449 714 -456 748 -456 ct 797 -456 833 -444 856 -420 ct +879 -396 890 -355 890 -298 ct 890 0 l 815 0 l 815 -284 l 815 -315 812 -339 807 -354 ct +801 -369 791 -381 778 -388 ct 765 -395 746 -398 723 -398 ct 688 -398 660 -386 639 -362 ct +618 -338 607 -305 607 -264 ct 607 0 l 533 0 l 533 -614 l 607 -614 l 607 -454 l +607 -438 607 -420 606 -402 ct 605 -384 604 -374 604 -371 ct 605 -371 l p ef +1058 -208 m 1058 -157 1069 -117 1090 -90 ct 1111 -62 1142 -48 1183 -48 ct 1215 -48 1241 -54 1261 -67 ct +1280 -80 1293 -97 1300 -116 ct 1365 -98 l 1339 -27 1278 8 1183 8 ct 1117 8 1066 -12 1032 -51 ct +997 -91 980 -149 980 -227 ct 980 -301 997 -357 1032 -397 ct 1066 -436 1116 -456 1180 -456 ct +1312 -456 1377 -377 1377 -218 ct 1377 -208 l 1058 -208 l p +1301 -265 m 1296 -312 1284 -347 1265 -368 ct 1245 -390 1216 -401 1179 -401 ct +1143 -401 1114 -389 1093 -365 ct 1072 -341 1061 -307 1059 -265 ct 1301 -265 l +p ef +pom +pum +13077 2123 t +393 -124 m 393 -82 377 -49 345 -26 ct 313 -3 269 8 211 8 ct 156 8 113 -1 83 -20 ct +52 -38 33 -66 24 -105 ct 89 -118 l 96 -94 109 -77 129 -65 ct 148 -54 176 -49 211 -49 ct +249 -49 277 -54 294 -66 ct 312 -78 321 -95 321 -118 ct 321 -136 314 -150 302 -161 ct +290 -172 271 -181 244 -189 ct 190 -203 l 148 -214 117 -224 99 -235 ct 81 -246 67 -259 57 -274 ct +46 -289 41 -308 41 -330 ct 41 -370 56 -402 85 -423 ct 114 -444 156 -455 212 -455 ct +262 -455 301 -446 330 -429 ct 359 -412 377 -384 385 -345 ct 318 -337 l 314 -357 303 -372 285 -383 ct +267 -393 242 -399 212 -399 ct 179 -399 154 -394 138 -383 ct 122 -373 114 -358 114 -337 ct +114 -324 117 -314 124 -306 ct 130 -297 140 -290 153 -285 ct 166 -279 193 -271 235 -261 ct +274 -251 303 -241 320 -233 ct 337 -225 351 -215 361 -205 ct 371 -195 379 -183 385 -170 ct +390 -156 393 -141 393 -124 ct p ef +553 -448 m 553 -164 l 553 -135 556 -112 562 -95 ct 567 -79 577 -67 589 -60 ct +602 -53 621 -50 645 -50 ct 681 -50 709 -62 730 -86 ct 751 -111 761 -145 761 -189 ct +761 -448 l 835 -448 l 835 -96 l 835 -44 836 -12 838 0 ct 768 0 l 767 -2 767 -5 767 -11 ct +766 -18 766 -24 766 -32 ct 765 -40 765 -55 764 -77 ct 763 -77 l 746 -46 726 -24 704 -11 ct +681 2 653 8 620 8 ct 571 8 535 -4 512 -29 ct 489 -53 478 -93 478 -150 ct 478 -448 l +553 -448 l p ef +1329 -226 m 1329 -70 1274 8 1164 8 ct 1130 8 1102 2 1079 -10 ct 1057 -23 1039 -42 1025 -70 ct +1024 -70 l 1024 -61 1023 -48 1022 -31 ct 1021 -13 1020 -3 1020 0 ct 948 0 l +949 -15 950 -46 950 -92 ct 950 -614 l 1025 -614 l 1025 -439 l 1025 -421 1024 -400 1023 -376 ct +1025 -376 l 1038 -404 1057 -425 1079 -437 ct 1102 -450 1130 -456 1164 -456 ct +1220 -456 1262 -437 1289 -399 ct 1315 -361 1329 -303 1329 -226 ct p +1250 -224 m 1250 -286 1242 -331 1226 -358 ct 1209 -385 1182 -398 1145 -398 ct +1103 -398 1072 -384 1053 -355 ct 1034 -327 1025 -281 1025 -219 ct 1025 -160 1034 -117 1053 -89 ct +1071 -61 1102 -47 1144 -47 ct 1182 -47 1209 -61 1225 -89 ct 1242 -116 1250 -161 1250 -224 ct p ef -5240 -124 m 5240 -82 5224 -49 5192 -26 ct 5160 -3 5116 8 5058 8 ct 5003 8 4960 -1 4930 -20 ct -4899 -38 4880 -66 4871 -105 ct 4936 -118 l 4943 -94 4956 -77 4976 -65 ct 4995 -54 5023 -49 5058 -49 ct -5096 -49 5124 -54 5141 -66 ct 5159 -78 5168 -95 5168 -118 ct 5168 -136 5161 -150 5149 -161 ct -5137 -172 5118 -181 5091 -189 ct 5037 -203 l 4995 -214 4964 -224 4946 -235 ct -4928 -246 4914 -259 4904 -274 ct 4893 -289 4888 -308 4888 -330 ct 4888 -370 4903 -402 4932 -423 ct -4961 -444 5003 -455 5059 -455 ct 5109 -455 5148 -446 5177 -429 ct 5206 -412 5224 -384 5232 -345 ct -5165 -337 l 5161 -357 5150 -372 5132 -383 ct 5114 -393 5089 -399 5059 -399 ct -5026 -399 5001 -394 4985 -383 ct 4969 -373 4961 -358 4961 -337 ct 4961 -324 4964 -314 4971 -306 ct -4977 -297 4987 -290 5000 -285 ct 5013 -279 5040 -271 5082 -261 ct 5121 -251 5150 -241 5167 -233 ct -5184 -225 5198 -215 5208 -205 ct 5218 -195 5226 -183 5232 -170 ct 5237 -156 5240 -141 5240 -124 ct +1756 -124 m 1756 -82 1740 -49 1708 -26 ct 1676 -3 1632 8 1574 8 ct 1519 8 1476 -1 1446 -20 ct +1415 -38 1396 -66 1387 -105 ct 1452 -118 l 1459 -94 1472 -77 1492 -65 ct 1511 -54 1539 -49 1574 -49 ct +1612 -49 1640 -54 1657 -66 ct 1675 -78 1684 -95 1684 -118 ct 1684 -136 1677 -150 1665 -161 ct +1653 -172 1634 -181 1607 -189 ct 1553 -203 l 1511 -214 1480 -224 1462 -235 ct +1444 -246 1430 -259 1420 -274 ct 1409 -289 1404 -308 1404 -330 ct 1404 -370 1419 -402 1448 -423 ct +1477 -444 1519 -455 1575 -455 ct 1625 -455 1664 -446 1693 -429 ct 1722 -412 1740 -384 1748 -345 ct +1681 -337 l 1677 -357 1666 -372 1648 -383 ct 1630 -393 1605 -399 1575 -399 ct +1542 -399 1517 -394 1501 -383 ct 1485 -373 1477 -358 1477 -337 ct 1477 -324 1480 -314 1487 -306 ct +1493 -297 1503 -290 1516 -285 ct 1529 -279 1556 -271 1598 -261 ct 1637 -251 1666 -241 1683 -233 ct +1700 -225 1714 -215 1724 -205 ct 1734 -195 1742 -183 1748 -170 ct 1753 -156 1756 -141 1756 -124 ct p ef -5500 -3 m 5476 4 5450 7 5425 7 ct 5365 7 5336 -27 5336 -94 ct 5336 -393 l 5284 -393 l -5284 -447 l 5338 -447 l 5360 -548 l 5410 -548 l 5410 -447 l 5493 -447 l -5493 -393 l 5410 -393 l 5410 -110 l 5410 -89 5413 -74 5421 -65 ct 5428 -57 5440 -52 5457 -52 ct -5467 -52 5481 -54 5500 -58 ct 5500 -3 l p ef -5565 -543 m 5565 -614 l 5639 -614 l 5639 -543 l 5565 -543 l p -5565 0 m 5565 -448 l 5639 -448 l 5639 0 l 5565 0 l p ef -5923 -3 m 5899 4 5873 7 5848 7 ct 5788 7 5759 -27 5759 -94 ct 5759 -393 l 5707 -393 l -5707 -447 l 5761 -447 l 5783 -548 l 5833 -548 l 5833 -447 l 5916 -447 l -5916 -393 l 5833 -393 l 5833 -110 l 5833 -89 5836 -74 5844 -65 ct 5851 -57 5863 -52 5880 -52 ct -5890 -52 5904 -54 5923 -58 ct 5923 -3 l p ef -6061 -448 m 6061 -164 l 6061 -135 6064 -112 6070 -95 ct 6075 -79 6085 -67 6097 -60 ct -6110 -53 6129 -50 6153 -50 ct 6189 -50 6217 -62 6238 -86 ct 6259 -111 6269 -145 6269 -189 ct -6269 -448 l 6343 -448 l 6343 -96 l 6343 -44 6344 -12 6346 0 ct 6276 0 l -6275 -2 6275 -5 6275 -11 ct 6274 -18 6274 -24 6274 -32 ct 6273 -40 6273 -55 6272 -77 ct -6271 -77 l 6254 -46 6234 -24 6212 -11 ct 6189 2 6161 8 6128 8 ct 6079 8 6043 -4 6020 -29 ct -5997 -53 5986 -93 5986 -150 ct 5986 -448 l 6061 -448 l p ef -6515 -208 m 6515 -157 6526 -117 6547 -90 ct 6568 -62 6599 -48 6640 -48 ct 6672 -48 6698 -54 6718 -67 ct -6737 -80 6750 -97 6757 -116 ct 6822 -98 l 6796 -27 6735 8 6640 8 ct 6574 8 6523 -12 6489 -51 ct -6454 -91 6437 -149 6437 -227 ct 6437 -301 6454 -357 6489 -397 ct 6523 -436 6573 -456 6637 -456 ct -6769 -456 6834 -377 6834 -218 ct 6834 -208 l 6515 -208 l p -6758 -265 m 6753 -312 6741 -347 6722 -368 ct 6702 -390 6673 -401 6636 -401 ct -6600 -401 6571 -389 6550 -365 ct 6529 -341 6518 -307 6516 -265 ct 6758 -265 l +2015 -3 m 1991 4 1965 7 1940 7 ct 1880 7 1851 -27 1851 -94 ct 1851 -393 l 1799 -393 l +1799 -447 l 1853 -447 l 1875 -548 l 1925 -548 l 1925 -447 l 2008 -447 l +2008 -393 l 1925 -393 l 1925 -110 l 1925 -89 1928 -74 1936 -65 ct 1943 -57 1955 -52 1972 -52 ct +1982 -52 1996 -54 2015 -58 ct 2015 -3 l p ef +2081 -543 m 2081 -614 l 2155 -614 l 2155 -543 l 2081 -543 l p +2081 0 m 2081 -448 l 2155 -448 l 2155 0 l 2081 0 l p ef +2439 -3 m 2415 4 2389 7 2364 7 ct 2304 7 2275 -27 2275 -94 ct 2275 -393 l 2223 -393 l +2223 -447 l 2277 -447 l 2299 -548 l 2349 -548 l 2349 -447 l 2432 -447 l +2432 -393 l 2349 -393 l 2349 -110 l 2349 -89 2352 -74 2360 -65 ct 2367 -57 2379 -52 2396 -52 ct +2406 -52 2420 -54 2439 -58 ct 2439 -3 l p ef +2577 -448 m 2577 -164 l 2577 -135 2580 -112 2586 -95 ct 2591 -79 2601 -67 2613 -60 ct +2626 -53 2645 -50 2669 -50 ct 2705 -50 2733 -62 2754 -86 ct 2775 -111 2785 -145 2785 -189 ct +2785 -448 l 2859 -448 l 2859 -96 l 2859 -44 2860 -12 2862 0 ct 2792 0 l +2791 -2 2791 -5 2791 -11 ct 2790 -18 2790 -24 2790 -32 ct 2789 -40 2789 -55 2788 -77 ct +2787 -77 l 2770 -46 2750 -24 2728 -11 ct 2705 2 2677 8 2644 8 ct 2595 8 2559 -4 2536 -29 ct +2513 -53 2502 -93 2502 -150 ct 2502 -448 l 2577 -448 l p ef +3031 -208 m 3031 -157 3042 -117 3063 -90 ct 3084 -62 3115 -48 3156 -48 ct 3188 -48 3214 -54 3234 -67 ct +3253 -80 3266 -97 3273 -116 ct 3338 -98 l 3312 -27 3251 8 3156 8 ct 3090 8 3039 -12 3005 -51 ct +2970 -91 2953 -149 2953 -227 ct 2953 -301 2970 -357 3005 -397 ct 3039 -436 3089 -456 3153 -456 ct +3285 -456 3350 -377 3350 -218 ct 3350 -208 l 3031 -208 l p +3274 -265 m 3269 -312 3257 -347 3238 -368 ct 3218 -390 3189 -401 3152 -401 ct +3116 -401 3087 -389 3066 -365 ct 3045 -341 3034 -307 3032 -265 ct 3274 -265 l p ef -7212 0 m 7212 -284 l 7212 -313 7209 -336 7204 -353 ct 7198 -369 7188 -381 7176 -388 ct -7163 -395 7145 -398 7120 -398 ct 7084 -398 7056 -386 7035 -362 ct 7015 -337 7004 -303 7004 -259 ct -7004 0 l 6930 0 l 6930 -352 l 6930 -404 6929 -436 6927 -448 ct 6998 -448 l -6998 -446 6998 -443 6998 -437 ct 6999 -430 6999 -424 6999 -416 ct 7000 -408 7000 -393 7001 -371 ct -7002 -371 l 7019 -402 7039 -424 7061 -437 ct 7084 -450 7112 -456 7145 -456 ct -7194 -456 7230 -444 7253 -419 ct 7276 -395 7287 -355 7287 -298 ct 7287 0 l 7212 0 l +3728 0 m 3728 -284 l 3728 -313 3725 -336 3720 -353 ct 3714 -369 3704 -381 3692 -388 ct +3679 -395 3661 -398 3636 -398 ct 3600 -398 3572 -386 3551 -362 ct 3531 -337 3520 -303 3520 -259 ct +3520 0 l 3446 0 l 3446 -352 l 3446 -404 3445 -436 3443 -448 ct 3514 -448 l +3514 -446 3514 -443 3514 -437 ct 3515 -430 3515 -424 3515 -416 ct 3516 -408 3516 -393 3517 -371 ct +3518 -371 l 3535 -402 3555 -424 3577 -437 ct 3600 -450 3628 -456 3661 -456 ct +3710 -456 3746 -444 3769 -419 ct 3792 -395 3803 -355 3803 -298 ct 3803 0 l 3728 0 l p ef -7570 -3 m 7546 4 7520 7 7495 7 ct 7435 7 7406 -27 7406 -94 ct 7406 -393 l 7354 -393 l -7354 -447 l 7408 -447 l 7430 -548 l 7480 -548 l 7480 -447 l 7563 -447 l -7563 -393 l 7480 -393 l 7480 -110 l 7480 -89 7483 -74 7491 -65 ct 7498 -57 7510 -52 7527 -52 ct -7537 -52 7551 -54 7570 -58 ct 7570 -3 l p ef +4086 -3 m 4062 4 4036 7 4011 7 ct 3951 7 3922 -27 3922 -94 ct 3922 -393 l 3870 -393 l +3870 -447 l 3924 -447 l 3946 -548 l 3996 -548 l 3996 -447 l 4079 -447 l +4079 -393 l 3996 -393 l 3996 -110 l 3996 -89 3999 -74 4007 -65 ct 4014 -57 4026 -52 4043 -52 ct +4053 -52 4067 -54 4086 -58 ct 4086 -3 l p ef pom pum 8439 6094 t @@ -17181,7 +17220,7 @@ pum 225 -438 235 -442 242 -450 ct 250 -459 254 -469 254 -480 ct p ef pom pum -789 3116 t +789 3416 t 0.003 0.003 0.003 c 53 0 m 53 -86 l 198 -86 l 198 -484 l 58 -397 l 58 -488 l 204 -583 l 314 -583 l 314 -86 l 447 -86 l 447 0 l 53 0 l p ef 471 176 m 515 111 547 48 566 -13 ct 586 -75 595 -144 595 -219 ct 595 -295 585 -364 566 -427 ct @@ -17189,30 +17228,30 @@ pum 710 -143 700 -74 681 -11 ct 662 51 631 113 587 176 ct 471 176 l p ef pom pum -1780 3116 t +1780 3416 t 447 0 m 136 -497 l 138 -456 l 140 -387 l 140 0 l 69 0 l 69 -583 l 161 -583 l 476 -83 l 473 -137 471 -176 471 -201 ct 471 -583 l 543 -583 l 543 0 l 447 0 l p ef pom pum -2390 2836 t +2390 3136 t 161 -146 m 161 -43 l 126 -43 l 126 -146 l 24 -146 l 24 -181 l 126 -181 l 126 -283 l 161 -283 l 161 -181 l 263 -181 l 263 -146 l 161 -146 l p ef pom pum -2678 3116 t +2678 3416 t 483 1 m 416 -170 l 151 -170 l 84 1 l 2 1 l 239 -583 l 329 -583 l 563 1 l 483 1 l p 283 -523 m 280 -511 l 273 -488 262 -459 249 -423 ct 175 -232 l 392 -232 l 318 -424 l 310 -443 302 -465 294 -489 ct 283 -523 l p ef pom pum -3241 2836 t +3241 3136 t 22 -111 m 22 -149 l 142 -149 l 142 -111 l 22 -111 l p ef pom pum -3406 3116 t +3406 3416 t 673 -226 m 673 -70 618 8 508 8 ct 439 8 393 -18 369 -70 ct 367 -70 l 368 -68 369 -44 369 1 ct 369 176 l 294 176 l 294 -356 l 294 -402 293 -433 292 -448 ct 364 -448 l 364 -447 364 -443 365 -436 ct 365 -429 366 -419 367 -405 ct 367 -391 368 -381 368 -376 ct diff --git a/TODO.md b/TODO.md index 19a8ff6..d1a7c7d 100644 --- a/TODO.md +++ b/TODO.md @@ -22,7 +22,10 @@ - [x] Extra explanation solv. (diff of $\varepsilon$ is not enough) - [x] All tables in the SI should be updated (!) -- [ ] Fig. or Figure? -- [ ] PACS code, MSC code? +- [x] Fig. or Figure? → Fig. ;-) +- [x] PACS code, MSC code? → not relevant, also PACS is discontinued - [ ] tries to move labels as much as possible in graphs - [ ] pack the geometries +- [x] Description of the SI? → Nope +- [x] Mat → Matsui +- [ ] Data availability diff --git a/analyses/plot_pot_matsui.py b/analyses/plot_pot_matsui.py index 86cc1e4..c2df423 100644 --- a/analyses/plot_pot_matsui.py +++ b/analyses/plot_pot_matsui.py @@ -99,6 +99,8 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str): plot_exp_vs_matsui(ax1, subdata_wa, 'water', 'Family.P6O', 'tab:blue') plot_exp_vs_matsui(ax1, subdata_wa, 'water', 'Family.P5O', 'black') +plot_exp_vs_matsui(ax1, subdata_wa, 'water', 'Family.IIO', 'tab:green') +plot_exp_vs_matsui(ax1, subdata_wa, 'water', 'Family.APO', 'tab:red') plot_corr(ax1, subdata_wa, 'water') ax1.text(0.75, 0.9, 'Water', fontsize=18) @@ -141,9 +143,9 @@ def plot_corr(ax, data: pandas.DataFrame, solvent: str): positioner.add_labels(ax2) -ax2.legend() +ax1.legend() ax2.xaxis.set_major_formatter('{x:.2f}') -[ax.set_xlabel('Computed $E^P_{rel}(N^+|N^\\bullet)$ (V)') for ax in (ax1, ax2)] +[ax.set_xlabel('Computed $E^{Matsui}_{rel}(N^+|N^\\bullet)$ (V)') for ax in (ax1, ax2)] [ax.set_ylabel('Experimental $E^0_{rel}(N^+|N^\\bullet)$ (V)') for ax in (ax1, ax2)] plt.tight_layout() diff --git a/im/anion_position.odg b/im/anion_position.odg index b23013238f3f676c61666ad93a7f6f50c1fada95..906d865a373003538752376e65a9d4a8783b4eb0 100644 GIT binary patch delta 32533 zcmZ6yV~}RSvNhaxPkY+7&1u`VZQD=Vw%yaVZQHhO>z#A&xe;G{J8DO+$c*}xJ1W=8 ztnEL6+BS&_FE0fOh6)4(1q4*5dm9fg3;G|U%ltnkiR*vN9P58fA~Z1j{{{&Yje(K> z$K~-~*BoKuA~5RzMd3jHH%bWdzZ*3`v_Vg8^AcM@xB*aRL#$&7Q&aX64OXHNMXl4L zA-`9M+D$p9qDEcDq`=@@X-5>JhsY#4T>UzA2iZ6u>&449WTq{Eqv}7Zx7wI&^%NAM zhNkRkg?+C+I<~G2*}L_`uqlUQSJ$m)8>-4E4QQv+1cTp)imy|Tlx!=09fI- zl?|f#7CJg5luJai30LP0{mN8!T zKUihUb6J;~GBBX{9yl@usxm|gqRkHptULG0On{+yIi-jYbYFL*b$d}xC_8v`y)};> z;|&^BCy_m|8>ev;l6d6^9W~EVX-8?y>;vR<9SenXCuQ}^=*g5VA-F?PS80%HyV$xm z`gCmsS6o;R!in~XVQ(Babo`NOni-ME9HrcaEC+*ZhnDlphz^wj>9FM>H`fT`YEN)9 zZUBUx3yf6lpHSen1veq^GpeZ0YU}aoG(;{VPM%gB(~YTs`|0lx(nEb!8kCHTu)5tP z%l@<$%1)BN$-#RoF-?~e((LG7_t*K#cPR+!?*!q+NQcChM zYD<J8|Fz}5PN*U?wh7_Sj9t5~v$ zyP|VA-JdV~z}T8tt76O!j*B@Id%)~51D{ye$gl_JF}9}|Q$0xAFPM}`xhMlpdjL9) zoKgcj&7aa`Y-`_z{-TYgv&SRYO~byms6pt;0MIuXi!Y~yzbts=WL=EG*&L*s&3(4u z%{-KW;P0WupXSJwlPQQ}av~6^tCiwlY4{L*xw!eBFk`A5?;K%glI*k?u?|K+-1K^- zHi3*FzqV;o`2)+qgK?p0wj)H&4;jNlaXb$yM4H}WinKH}_wjGoxy$t6!QTIZyer^; z^1}H3K)=ua9g&DHIqY-NfcW*5hzCIkY?8Jw02uB@>LbF5_UYr4 zKEIm2vIR9S!qz$Pz;y2dVOdV|4!9xmadcpo(r8uNYwBo|ct30JMtO~e*{!EOIu+~^Cl zJ{jv{oentYRxO*fchBm>fQreHNk+1dEK`vKY_T0}`J!4SFt^XEcZwhCES~-m*~In1|U(XuXhd zWGBvDO^2D*q0ffb11{rjz%6ZJ{eDSk5-(@js9DLOH*6{(q$?B799fj=jZ&k2AU!@^ zA6$xPaV#VwFPYL*2--|XLH@SuOVmz|)RvZZ`*Y>HkeidB+$*pV=;THQD?JWig>OpB z@WO>$wpwPUm&dsKD|Qv4OSCGFswm$s%xT2h6yXml2P-5LUg{}x&`U>s8!T94Gn z5TRP}S)K{}%s9FVR18TF@#7ZU9WeK|wY1ZX?N@H^-q#AdRjw&6C8^?@h3+qe6vUHn zov;15kEagXxbBRsYuB@oh5b&Sh22VwgF3vyX?~i zJ^6LgFE*>==ZMJeE=r}js*4Cd2f2ph*EW5NOJ#=lzu)qzKvu_#Y;HwY^- zd*k5yO7M#?E{wI?zbmvd*tO+SxEFp$L+^zc>8VI~!E>~yUtk+=rh)j`&_`7+ z&UZFOR~q$jwlh@B)P6B*XS%da=x1_mNs@rCO`H=tM(stVKB;lg! zs>F07F~|GYz~YqO+;l~k_v{b3eL@$FGJ_QkMR?}%ZA3&g{djAopy1@Zhpq#3a+Gs# zKeb{?bl73&hKXCYxG(WS(bX32J$1beJ(_MI2%a)13j^WkV^|-RO<~X1O^-}Lbwf?| z*J*LLj{9O^OF=qozyge!1uS4BB*8Ee0g+k7m^w4Ux5Amw96^U^J7j*z`plReVoau&agPAnxo+;1 z$P7OL*OVG2{jh!W)b)ukF9ive?+@Vt4hIBuBL@WZzl0eI3hF8_Mv_V zcD{%|rLt7OOA!S@Sb2B~m+>?U%O}eZC&Wz1!oCtA5##`9GeaTE)cP&3-RT&U2Mp&O zK!w3y2dJv)V#2y)Q{umZyx+Pf#<=e_eRD2`j+|9c&xWjB-P}sH�zS8eRbDb)3Zn zFGH0Dx~2k%R|Ufve`it}da1dO*ht*;lyP1vh_=W4wO6w5)-qTS{-lUD^nBeuXZH}* zl>|xXx`zYg*tGi$sx#aL8aQt9Mwl6OkRVyEwJ|AB9bx^J7u#}!E#|a3vNTn}Hrnag z3zI$i=2dYq{xsn0C;Yta*@)0jcHY<)D~W$7NM2lF1m=~_GMesx9FM-_|@Hlwoa%13qr?4FELJ&ry_!c#q$&=k;R(im|{cw!^qAl9;NhLS*iY=A8vd}~%#4{TBWckB=Sn49>$7Jcy> ze#`0LuI?HWme*KVK|Yen#7#dpz5*L}yEW)DWV1-k7v|oG{AO%p-bYp0-`CQ8>FS<; zEa7nL$)HTKpLg7|5!BXh-R5{C>_z?0&ZUQtZP%a{h#mqk`yf8%z|^phJr3Eix%xAr z4a=&j4x|$2brtORxuxFT#UlCdpAAGlafL1oO6T-9%CeTE>h7ubNzKZMNh!5_J@^v) zWq-fVNTM{~jGye+A$s+XBRU$@OXhsQ%%EWy?J|ZwCHv?;C3Qw{k75cDg)S=H-rv zZ?yT}K^8w9jbvPR4S89S3l3@ZEg#M$-K9f`cmXL{iw+QPrVQ{@Jiurb_9QvFs)HW9r^LPP3BTgzx9lk!4z0%8*e1ZDu2K`cv= z*4`y7Dv@V@(Mc)Yd8pEg523m8K9ksYB{YlTTOXO zXi~E_sM#DXg9k~HA^@sf6!zn5>KWd8$^8E=NZ71cR;L1#T@v0 z%31B&OEc6U{u*iV*X@8#rwyIz*C=ySfa|MPKsby*bw`F9kb~M|`rIQw@ zaIK4~8u!Yn>!dB>Uv=>?RZTS_*VRmhLlZ*uW$Hx|eJV0H$0jck#Ev^tIw)|1b;&n? z{%Xf8rAEhtJKEx0k{d0gOr531iCGd{w=Is%=8hoKx|PnW33cj)b%&F>378Jm@~O%h zO;(3CO+b<6$#5Ycj>{lVlUxTOZ;)b2=x(xLzcV9kx?-8MlLSKx^28paNe$)gdn7Wb z&V>RYRAFUid6g^irGM0RSpp4-+G((?`JsDr%~H$01v#iB@WXm*;ibxTjj;8t`Li!b zxIbSKCK65<6~Q_+8>D-h%Z%M55eUX(TJKz1`CSWULlGUIgH8jzb$;}wxmwWv64_{x|IQ5;ssk(7>4358G%IV z^@b5le*`02`ymWAo_vk(1>-R7_XbTKm+)Hi2_6}}k<7mH5p;2rb9OuhNhB^zK}*MD zLu6j#b~Gsf;kHFJ^zqWJionaYrJ*DG(Do|l751TJBsJB{j@#=%eVe25#PxpLUAW8b zdANZ+<|umLy`B6fTC5RtdfWYZxUSP-bt-V7{q7A9{^ISW?H%_w)9!mm>jyDID_Up> z>t*Q30dYq0i7o#OM#n)*_za5CAKz2An1>ZGQ|x!N{MZrLHqD7OMhCG^!|!xoiiYu zTVi{_sM5332B&{Rk}^RSp5VJV6d_tJiQsS;6eoFj94D5bI;$))p%qKeW8&Zl9zrfk z^un|`6ec-V$rch4*A&N;ZDb5s{F?{3rA7N>lUX*sJSF)ti+gELlAUDRdj_BX^mZyy zjtF`i=SR%BnhN(KU&DTlHl-d(e8XQ5Vww|x?P$N2SYlbM zpBi)gORsJ-1itfBdCbOe#SKE%L|qzaQo$X1 zl=Les5xpvA#U9|-mtl6icgWyO&tT}?`f={+_x14i@?iV3rcB~dqcNII9=9=?JZlP| zMtvt_&U1FNV(7DBSKjx~j+bYrXC%QFKL7XJQRv1$eLyj!udg=S$?32+@5hx^Z{kRg8`!L{B?!B;M|1$ zQPc;%3AeH(x}xd=DRFAav_9!PvGM>H4O= zYUHFym~#0iMb{`|h}xAc?;aS*S4)w3FGo_=c%ZtOrZhjJnHDxeTBV@3pEw!-8sMr~ zu}xVvM?9-pYEmiQWZmTuK`0f|Kz9h2PXEQB#|FtUKrwq|i?ntK4; za&KQs9c>ETR_BpJZa8w*diWS6cgLN7T)F!<5q=-#Fuo$LF05J z9#nSuwk)RGg})6L1ANaBOKOBB;ERJ3q%J{}LZ?)=d`B^aEUwNPUo@*2UpCl+-tXV> zLnN=w{HkAI4;mbtSh)oBr3W2W9g9;x%=Y1!l(H^aKR(r38a^;OfWgBN^F5b@INiJi zF8lJBUww0O#u^8fD$(QoBzbg(ugd4=3y}p#CYH(wE9rR2>A0Y z4&;^@ew^N(@RkGEoU2sXB2=c5?2q;$ zHiwZyrP0!-;Pe8c+8yw5>&>F>>dbKFhxrcU$nYIwEG>njORk)k>YtmmotH3K+t~R; z9qGG^_WRU7Df!P-aNqnU*r7~fj~|s&dwILW=?eOHr893 zR(AWXSl_IJ<}Yn#9qm7AAn=MomXp7ZSCh) z?Dw>?%0bCK)Hm=HW{vI6<19V1-;&@*+A)x6HljU_j5FCs55=3uPNp3YjQe_Kf_>vS z5=0YlZ|W(@TFX*;(8+*F5g2uv5gc2HV!6|NAWz%nBVQm2rHGvYFc7IUi~)R@7vCu_ zn$!l&bo_|=^e^A92mo@k_ksbch+d&#WshK)^7xRQUWsq@he0H(Z-1z zo#NzX=lehf_NMp7c>P-{Da^;ZShsa3YuyE0t+p>2hv!3%^n82nN>unFL<5*88v;`e z{Sud7YEapvOtXCFXlnNnFVPqAi$_2t!kze0W6KI<-*p%2suho#paYe~{xbSCz7W|$F+0?M$J6fK|2 zUOCPZjJnBaWI|cc9mK4w@>h88kWy~sE?O}-aJCg?xc-+p9Jly16f(J*d^MtXyHEz} zxWTW-Kdvf5y?{Ic8=KNc&ddC+`XZu*l6-5zV+9&oto)~%PIk09buCu^W8zhd#UPjS zq}L$A;E$|oqb3)9evJ%mMRh9e!`LWKo45EBXcU{PIRUFt?~YgT{fP${2Eyg^OjTze zADn1jVcuYAr89fC@GiZ?(J!p>5nAv)PfNi)9^IoP0Kk~B%c)z0bQL6insp4i)Wy|h zslAf|=PYd?&d`7X_6*1ua?B(31020JKgQTIh;oqg(&9D|q{ZaYUgsK9UPNoz9ZIrV zai7knQ_&^%QfA6xbP%i@cJSDJl>Mk1_@!uYpgwjePHc>ggO7dkj^Hj9nu_fpYytHyOG$C3k~X%>@qHiGv! z0zyeATa%72Y&knTQY^!iPCU^2FaC`kz@3g%M0?<=m{`WF!h1XY(~&HfhCrh$(ucO1^+-s_LATME7H z6AolC%j<#xyDnx`l5Y%BMk*H}PQyDef)2cim3Z#j&gmqPi&Mw-9dE{j649>vOgw0g zkEHk>y5?a5xG*N<_x}2jFSn`4B3|&^$~7F-@#Vj>JcL1}xQZu}CGcMD^6@uQ@71jU zJZ+FyRu~d;>C>4i2c=E&6k4syZ4SkwP<3ONA2Kg~g8u;D9P}_=lp}LS1iQ zc*Ew%uwb~U*Q%?0#kEm=HV%jrO5;Pbpi`(v3GT3q6a^=B)Vk=phGg^bJlplifg9%V zxRg;n3$-zf z#$_CESfP+eE#1V5!)<2yU=Ia#mjpER%WmSW`FZXNYY6%E&+}Lj_?)4%&hl%f1R?fV7Fng=t*#)@7gniv9F^atu74RmFzj*o zP=oNMU2R1WEomidD#Ir+Njqcde`k!YG7}7J-QnC$=&zdc;j~uOD zT+||`2A}gS7w;Ofz*dInpCzG76UK<8B_mo8X^|4l6s<$~^Bg`K30szfyX@ufT_=>g zG8qS>R?|{jH-UdzmJ$;IBhcB)_ei&mS+7FpZ;u~?(>2>ud_o93FzRlyg^KuD$$~YU zyf5bi!7G(JoKp~)QC`5$*-{;x(*qr>qull9UEMs@%EQr$KHSyLp$9{gu98oCyW?2R z!*i$%m!b2Hh7VF7*83}!KhiV2vxdOV_3qL!WgeYpmQtgiA7m;-q?@*F6%eUajdLx5fRN-8I?UpOF8l z#XPS#zKD=OK&@2&SBwAKJ53en1;YW@WicRjzo-$At1;;3{6;JbEe}<$TC7^!h-kvy z|7~rYS^M<@4vL*nUEZ~JaKp%)Ly0%7bJ59A+=faD#f{G)jVRG(E_r)!J2urT^pqbb zCzr(_O^V4y7PY~s^an-7ypvmkQtH-PI+ier2SsWzvD`oZ=ES}&Fj)z9J6Rtf4>F?}z=o>3H{{ zX)2I>UuC`vWj~yv9!5s3HYaG8;##&vf(&<*omUyN}j!%ONciY znuVx`H^v@)HV0k%FIuG}C?ns;9v`7bhzOH-MY)~w*0Hxxo0cT1{Oa8{#?$giW6V#E zxjp8M4xt56B+I&&$qJK<^?+WH=w&A{bORZ>i+ZpUOx24L(06R}L<^?9v4ubd3Q~9vD@97d8!0-zcb6kSti~HV_9% zlU&7q(Irp_1WsB&jm+g6$%!p-o9>?r4(R}=_PsP}ub-A?0?$i`({>6Mz=CZ`sZ*NW z;nO)MSYEdReko>f#=L>PB(zQf{RMST7z$0|m-_XbU=OVvd(dh);zvS2MHNpHE*z`b z_DuAfOuz*K4=Pa>8R+jVq%N^GdAPB+A+($Xg6vQ^O}aFR$gTl7a0$t-ft)R_c=|1W z8!3iV(IjJlUpdSf&>X}j$!D*>L~JG>mBhY~8CRzS;NOTi5}%_z%{dZA7pt|s&dt>2#+$mhJ^wQD-zS-b4hm`3#0R33Hw((fFW^-K??881l*HmQ0TuzQEDu4apslCXlWZO8$|ksoIpmiwu>d@)XAiJg4Aor z5Zpo3S8NR322TJ={5QtT&p6}&oFH9fjsZChrlp?U0+S?>=XNSop+#(RfyqHa%XVA% zD!ui1$=69h~@N&PPIgde!kE-?#CVYuP6-g8)`L-2KdYBC@&?_4 zDC~yHhjS0w2n#kGx|QbE{)WvDu1cQbAVuZ%Sfp+IVYNrG;LxTDriJP)_pXZ+&~=Ra zhsAu~wW_{^bPTF6SQU7df1H(*J^`UiAQ}0Dv*Tf*{&~bTm_(F(Ig3?A`%9p%Tf@w zju*$iDeoK{oCVcohtXDZ^eQ?95DWO%PRxa+uKZj-QYf9|syY%Nq<+Q|zsO|spt~Q{ zy(?6A*sBt2g{e$i7zfUcUIE+gj32`VQKWb^A0m2qi(pJYWUJDeJ+Jp*`__CA&bn^8 zL7X#5)bc;os)zn}J)rLeN?8{Zj~X{60i~#WYKM@(1ex?L;Q$Z9%@H~aV3P<&AYsgu zfGCj~Aacf$jTkZyb{;UoQ!@fu1In#WnUDiH8X9wPmGg1XVOz?=3!b_NNua?ltbJ>a z{%H_SqS{RmP7)9GDkhD3&<16gPt5HnFX#asdjl0WPD0BKrBgrxWX>$bh8XPbLPywf z0M&cwC2wB*J&Sb3Ic}^4*o7xEXHj62pt;0@&{IYfTE^J9NFLz@!@4 zV@qBjwsr*hl|>5mf+EFrhL|EP@F{Q@1Ej%HO3H)tNMbBEeoUlJBwGN)TZ$?=&oMZ{ z>#7a=N9J6Ky)P2!I`}n(#7!X$J^+!6lg*gU(dpA(A zAed3A3SMPGvO={c1eMPfY)D|ols<2qg{jCGM+Oi?2?`3bs96E=V1iDFy}}M}h~%Fa zoag9x58yz^qCRT+8QcZ2kCoU1MyR@YvU4V!tWL_R($TD0%UQ!V+Wicf( zJ?|qAh;w}Nie-NCh;u+W=7WfjFq;|R!2cm^FXZ>#-QT|l5P8V0K>kKg&GoqPI<>LW z?RoaEewjUD=Og&%BXf{nUV>&f-c7&c7_C3H$Lc0#x#O;MM!m+13(iC|`ZZ56R%#R_ zgU8U|uo1 z+!1+&Z>a{*Uw7Ec1y3JsK@=C^$CJ$Ynq_gd@OK z9v>CbJz+~h0DCf{x8;KaUI z0-#!(oc>y2Hk12x*`_lRuhh?3TWx44?GV6cT%HnvV??-mJb!5AKM0-pB6y@}w<7CY zM-l`mtvi0gQuaTf4JuWex#(Xb2lyJK`bU|EK}``%daO;vqdpL!6FkQEfQwfCtKlRz z#V-9zq??n{uu^G6m`1bi^FmAKZI5P0{pC}^2q!b>(|k{Bxj&C|T4oW7e+5zI5|Mgn zq=OM*&lG94DOSggZCK-&o#^r=67$wu%`=nDzL@}`S zJRm=bJei>Pmun?C-j~aEm#)U=u`8CP+p>qFJJfjGGe8s1nr+@uKC)I(i1Y zGh^Mqdh3i8oC32cb!0=@5#?Yif*Rz7B?xF%6ttDk$;jAJ(YoFb6LWno2U@Pjl&b(x zxSAk2aF?R=1dWG znPaz{E~;L#Dr$sga<=l7zEf@%9z73R{SckyB`a6*WYE199z;WoOMwYd_pq z?7|>-8rnvLLl?@nIpWNKR&!xyZtVaLIbH@!Zf(CF>}U;fFu-zBQ<K4% zX_@)`_(qPufuy87X?VDRNV4Hnnzx9!;G`bumsI`-$scvWeJcnY+5L2|sd*HzeqYMX zSp;We(NEJbtHBIkPbxYr&im|6tE9o4D78?uD^gbEDzuu~=B@c;)xKjj)X>T!DLcZYZ&Dy?S)U5+WTo>--IZNi8&=byraJB;|V&*`w9{=BD@4lgrT} zg_1x-kxhHHPYdCAQD4yPbU(E7y?^t)wewvyzw-0=;(M1V)$!Z?K(U*~vA_qUNVDDB z@**TZ@5t`wzUSv1|MMAu|I^3!gInfi7ncy7zM&1_2&nBSECl%InrxySHb13)yi11Sbcr@ye5JRbbtFuj_ zSjFe3$_RE>q18cg8gAGGi32=_0$z7`ZpZMowvTA!5if>G`BVU#_ytp6Nh`D@nT442 z4bys7hMyff?~8I@iTGd1IX}jG&yaENSY|o&6k~b2#wIz%Ya~ZMAG@GGrx$uQ zE(C>OsWKYa^Q=8`el+5;n{jVjTjX!r>7jW{5>A?*b}@XP=r!MGEA%ZGVw457gb9&#~9_ax6OJh=$eN?035sp{}%i*5S4!}2`-_FAW z5O+PFA8HnD7V;<|5>fyonI9|(37Fa&TK%;2$r9i#7gI;?b>U}LagA=0QGN~HKS_YQ zj;OQto?&PkSb|}XVDncWJyo|Py1Q@25%iQjUG-zE>i6;+&?AZa%0rcD_}Fs#(oH>zfuf>+zd8|G&N zl>B>brUoFrq0Qsfy}Djl(27LNncTSYZnb&{xHlp`)8O%+%SR@r_dcT5i|>Fd!qnK2 z4qVOQ@*`mvN^TRcjfED~RdFr5Z8|{s0>r8n+0Eqg0Gf)Q_;J{&BJzVwym9V>t%|7U z-}d_Y`usme*$3taFDGH?J8!Li1h0AHKs-Wm$N}@s;n4Ylj*=<6==!HdRPJ%-)hX#> zu|EqBX81q1mhruB4`wsGYmy?A&=wT$t2fWlf(SP}j)&g@{Em4CPu_H?TDsbu-LLzR zdcJ#YGdvwc4~{KV+rUIo^^K_EB8x6Gv%adHOl?aVj*{I2)wD?K~qA5cYF&rk-4}TknaWU$~$n`kyyF&lUgHOwVh-lb-v|0(E=% zd!;24o$4z%CK-crB*euuUyN%xa+h=C=MM_EV?BO>sbPT}; z!7<&%pWlwI^Atl|uCEayHMh}TwmydWiXu5a_jg)aoY2&BS5Mq*Msu*}GG0Z}DaPK1 z&N;97-&}zYZA#KLLlfW&yQ)dzFE16SW0mp-d zr0n&I_y5Y~Vj{o7yrhee^aWAV_T3$P7eUyhW0g4mb9^M=dJw^RlSnGT%>4E818@jx zmqKB94vf$g7C(#xhh=(gJ~K{ebofDWG^@FucRPF+I=$GgnCtOb=jD4kKszPL6iX%W zrpblZTx`}GwUE`o5Zq3f=KeYe=&GsV%)2;3{(4XD%!E{AOqnXeG9@&ZH|W<{DdW-W zd>p+Kvy_{p@qS-M;G0{QP`_>3dw&_V{3a?@@@Rh?#q9DDnpM(&=nVy8mlsX~r9vYo z0lvNme*30BXikwB4vuUm!Lm$08s#yg%j1k zbR2ckulyDUTVk{KfJ{0E&=w&kCB-;TtctNlwZdq(^soz_khC(XO>xB*7wFv#V8;f7 z!Z+Z4#BGm2y1Ellk(~Nwy`O^lo5`!Cm^vm}HeSWZWIigsCPe)e^EBO$jc~=5fE>E| z0(IAS&nZhU`imM9Wo+PlQ{H16SQ-}mUvJ{^149(Mc(EDESV*)Qu;{nStga>xy8OOZ ztYbz3vNAkjOzE%1doLMnL5oZM71*ELbE(xf14a6o5KewOZ46*Tw9&0Y3c3AiT7DnA zV|UdsqteetkcJzy5cEJLS`i2k*_^HG@I)F&K8USXLVIH;0)v)E`SNQ4BeBV{KQ>o6 znygx)wZq|aFl{*kWW3o6N99njM}_Nj^OudC`rlBLCqnJ;`W`6`frw~fMaK!TUoO;= z5(qh0waITtPgd2j#$I=;E7>Kxj8_Ui$}rNB|81JqH2E2YE>;C0U_J`MMQD>rO0k0$ zpWm{lBhYLTiEy`SceT|mKWqNIcgV@B4IH?eh3q`~@X2rh@VX#lPbGMzXDC-qfVo|_ z-9Ym;^Am>mR0-JeJ1ehRdlm%=+CAno+*;hZoSiF2bI6*%71E8JO8|CU!R%)q`RVr_ z1&eezM0Lw-K9`v!v>A&f2@82}aWF=$d2J~uptCregHI}qNC#5u|E5i@W7_nNP6NA8 zAPr6o{CX(^oEyC;s8M)+^`>3B2&@#2q&_Be3P(HEr!N92T(U4jHy3-8xR#0{;Lx!ky0U!R+m8=ie z@9dfL>yeLwRuh@+BcGZ zthFd!2a)Epl<)*YvOBAJ2^DKDZF;Rp_V%ySxea#4(toyOWNKFe<&ez+zR2kV8kZwbt^;$M5-z8*&m z9*0gvo!5PLV3$(-mONwE$fN$Wm*S5I8zx0&-HN0bG^okF*A6-ZgJ%o^PS~&zJV3?- z%tT@_J{=x?K=M6Dh>?YcUU#AwE{06!rJYPu$`m;ho%^jJ>X$@tIaaFma9VL#LUGPI zNCl>9GyBS0PD$jHRrwmPc98NZBL9qNRFM(D$Uk=3qCAwSpK|EhGxeAC(ohePjv#|* zShiO>jzEsEOWBIyvz`oQT*TuYvvT+VI+K=&O!w(N=I{6S_iZvMr_|n$`i%Szrrg-? z+0pBHC93MuV!3OT$w_`|F|jd8$vQAxPs(^5p>--_Nh#e1V^RsojJDjcLW9f`ohJ9mj*Lyq#t5hl5{)+D8(+$ zfl{m^$Ni3%gX^wzYG^}_P&(`LA1FhIwFt`%Cm;ddZLMM2a5&E>-L*8 zJ69GP#of(?ur;E-LRj`R4{{Yy)VP>BUx@P_MeLri4MCy==hD`02t8~?38b$gDPzWesm z$!?kZA>NtGj@OJkJ7>|7COhVC0wKnha?Jto6JqP^60do;$9_(!9M;xF3(9E;y|&}v z)+HxT)*|M<30|3mAE=-D@6Sp+7|fYR=MLHVlb3Du+}Tg5+@H-8-?KM#J@400AT+$&A^n4J#)IG zqzS7TC}uK7#)cBfL$5YIU6aYy0Y!W|6nM)s|LhXzbT}p^rd`k2spxwT4iwo_ISmMB zvrxQp5Og_9Z=yb8@k?u_=k^nw_oqA6(s%DRPK1t!i3#S`f+q{~)rr{C)mW;YXQe{` zF;ChC({c{a1%BQfkjrq~%u6U^@|$!1$^}wmpBTOK5wBm_MBk(ZV=3U4DM93GxrXN@ zcm{CIW4Ej@aW-G`==|ORRMh8UZBE0}ie^8aC#g%BR-#_}-Y8Dn<9uzV>&EBCO|CwJx(kF)NTkXx2;}@KOo~0P#pgU&Hye#JeP9wLVKrQV$Kl=LcBWZiMHqcaiM0} z*^?|(EVSfNT((3^Y=J9RHr6kL<&);zYT&IZ3!6NOb-FSEC^cQt{d5o4s0a_+-6T+G z=vY0fMrnW+5KBfiO`)YGcjq`8mkZwNNJg32P^JO9UEE@(|GAXH#>RkxAOm}y9DVwJCY*|y|`<$HyU}E$5z}j>smN$(Qv%GpHQD0vET?FSmd8bvn`<>X zD5R14P}+rhs`Ky8KavAJUemL|>hJc!QP%h?X*~niRY}S-EVJ_F205`hGHyu*6JEtr z%y2nr_L1DouFzc9rf>(S1;ZMZ$#7E`r)Io)iOa6OtDk4p$(JbN_AZF zUo+@Cq+5%~mNufP)zv!*9g2Y0z~W4SiML+?!lV|{7bZbL-DRzN?8wIDjc$QgpL7#f zn)XQ+c;b|U7V|-*acOLfHHMzqh=)Kiq0hOBo%ixOnbFoRARL{F{YDF4e$_wstra=gH0r95S<>AOubJ8sU zi3Z-(klqoJ^-$IKcodf`{Jpw)+vWM>ap00QWM${GCO9dUs3HaCu6^OZ;imVn-Z2TW zMcTqIdt~8K2+Ocm0i0(;l;wz4(EO4m=4`)iCqA;-&6+YZ6>T>e3W#jxLff~*Zw4Ix z>Z+rVTG%o18q3E7(;+d}@3xi+Sv>~>c3i0;uBFl|JF(!g z3t7wrTGBEgZ^4a5)#rJNt+d9r%^+cn4fn?g2)=H8`tW7N3Vrqg%DgUc!T^Djk@tH z8hkX0y2Kj0l)L&ER)R|$`K7f8X2=Z;WGW!?mu1QB%5duhh&eH@)8%{5w($)PrxeA( zncoKZ0R}GNXbPW{MWs$zNBJaRRA61C=Y*>>bS&rxe61pV^81dE$EI7=$6EILI`e#~#4zfCQ<44P zEKz!ErFVGfQT);Er5BO(!#u=kfCXH!kB0) zj?Boi_WE&T1$lYoiF0g9Etr?{^$6E?=0ky4p98jyr*XIU{f+mru9pmgb&=CP(^aQOiLu8(;G4Go+Y}Hc zg-fUm8|32axQutPi2O0X63G^M@w&9$B4k;`CRFGnjJqkBOob=p@znIb`Ox)jB=p*r z@sfHn5;+pNP<25Z_d=HZ^rUUq(ZFh(_Oy-r`QHL-pm85_&K^52qwQ2Zc!DFluJgMV z5g^?s{mNP1AIogWv{~Qp%Wzi!jliEe9~~D>{?=04+o-<9$i^~*q&{j5{?^e6Sf6S; zMcG!6O9`rjDzu-<#{750b1=2kEm1=$wwh#fzUfZfA6hkufI*uMs2Vk|m`oqr|H&ml zcE!L{O)1M^5^Y?M8p_(rs~%LXkUGZzl7efQ`!|%JQYoaWk>&yeMPM!DkI$)acu+PE z(M|`i(H~aXOoGAaoMalXrK?UY^z4Juw%0Z0_xUss`CzD6k+=8duF~_;t8CE!z>!~h znh&;F`y{(sUrZ}c2!KuB?oao>V$hu;h2xqZQN~&gS>x7cOGA%m3%$%HT88>z#T=!< za{r;O^CYe^p+W}2hewLr3}l4zw^`Glx0rdNI7l1^yn!)c-mvy0QPxzYsW=BS$hyB2 zQ+>Ru`Mj45b=HUgej>5gyOb<`@_W!1F8xxlAgQRBVg)$Hiv13vjZvI&LM4%;u_3k_ zmBf8y*n*G6@8M)d(>bO5o}O3l7ok<1EBe>&O((7>G6aUWm!Y(3cy~NxZP-e5--V_JN8hMZGbgEE1T-39W^eP3q=P{ z_}+gyM}UXB<6!t54}qWW1zy?nkyV`!fla#ga_evcxWAzWBw5t}2D|y?MWz$9rg9GE zG*iq1y50wkZlIT|ZC1MRl}ctor>kd$_PW%rtcA%jIBrgN9OkKe%3GNv18O7=vWF#z<;m{{@;>BSvM2LoBM6sXn1&pwS@ z@gj0Y#$jfVHg1L}qd%>a3qa(ZWqsoy>S=mKdM~%xMLaUv&>2dY+LGMWBn$XraiHwq zYKYPwWW_F?I4K{t<6UP1fB_k6^h5`#6#eYhSdiFlm8}X7nv7PC z6125C|7^+0hQzyU#A^6`8BcN)?>FM#qqsj9aW%`CU?oF6XDIz|(%&zw=77R@V6d@@ zXXt>lf?{Ugka%76Zbr`KeS?)efnOv9_%lXFHSz5PN>8~{TM2XHs1rpJA;r>wqT&dn z9bSQSlDT}oK}n&b;#cFGk{y4~x)(#E$12IHa=j4-NG^*ESwD{6+r*WSRkuV2HV=5BM)}daz?{-=j;9G=!%{GV_B1&v&F?|_e5}7 z*Yg)Ar{eGZZk@)18MvmVowprLIA?h>p4zvv`-S0V;~i8C#Iobej)`|{e}!l0LbS^S zZsvp2E_yP|OgAZX{P^s~x<3%@`XJftn9ik*>s%T8CI|NNqG@{e{D9h)Et>C5Dp5gI zLBPwb5kDpG2C#r)vs26Y6S;Q%w5Hy!ytnGCIr8q0&OM_E!~3>E*kWYyC-->;I*u?lc%0?BplB3RP&amnj zLeb7mYgMyaRr=$}9iR=FOyv)rh}5yA2799;cVvgJHV&*z6Eirbkk^NgphZ<)8$IZ$ z3rSncR^;7h`*MR?l|-Yuns2eY(=2h96SkHHBt+@+B8g~1vW0TT&~fT5x2lAo22)7C z(ZajiKk+M9DGku9LhQ!zwSaVFln|%Opm5R6Ofl5lX*#0KkGIjY$;U}htV+ZWjrGQ zd7vA&5C;)q24|er5EaxL%{DBS)BO5kTI{Qxj{fUoq0q|*G56 zEfDy)Fw*t3@cH{QNKD@sZRcDKmsZnS6n~2~#@gb7+)gqL$|lN`D969C<+4jBPt)*M zQUz~-=3l=NE$Y&ploO*&_T)MFkXb;46l>)L!O5pu*Gi?+U?_iK-Xf{D!60>kkJ+oj|>AR##bw&;hh^%KN&t_1x_f(G=gQWrj)jnZZ zo-s|^3OJU%W2FlPr6wv#VdQs-bGR zsK%T$C!kbZolozAoQd+6A=T>m;2i64x_!m#T)Il1T=v%}-K%w;FT@~=2$(PKTtgb?8va_3Z^FHu+Kp25j+ zHbAnK{C|=gIpfZz{wulhKfV7XJTf8GEoECnw)ha8p{&&+@4ALAA*54G!#K8aJK8n| z4BC)2eOWrCLiSqYq-+wvI~NI!Gly(B6GktB4UFSEmq3tTR&V2g39U`mL38N#pABgE z-Uz*Zaef#Bgrw&|&+u$vJb}V)%d1(U*m?zrRlYLETLHlWv6- zwCJf5nrc@K8Flt!U28^o{$_y3U10o<&UXmVqu^eQ!X!;S7hCSi0;7cgdWL@CfI(zW zR+wXqDKG@>D4)^QNlKCcVNuu6!s^o+M2X5BmxPuLyQ;j zc`0KKYc59e$HpNIg42-q;1eyES1nLc78lc)q0+@EBZ#+rh1>QbITxdELd+%WCJ#sY zQaJk4;OGacid;<0k|3SY(Uh~^fw+Xx>-Ets5Zt7I6=2Fj-Q*Rs^9<)Pp1!708B9N+ ze^L@#=wt-L%E6kEF&DhGWUAcqo%=gccu0;}ZdRnR>wg41 z7&?KQc3y95%%7wGo`}}&2PnnFWcS@Qbum5Ttr+1>^pH0S0rGt#kgad)sjKooDCd8oRY-uDCs%-90>P z! zLIfWgM64=SaQ=YC+wi=4I{1jqetUgc-w;i&X>PWD@9;9Rp{87^0fvKdoX9$akIcGp z!++Tk3f%sTv!?jonE{W@d>@yPfhtz86!SO^bL)kdly^lkJUwf_;ZlD~4=G98T0gev zzrD`bNq-_J-e+Kio^a0!#7_5vl%x#jr3}ifvk9xogjl(`xi7<4A15~f9}3R}9g)Bg5 zGh#qUs<^8+l?Q|okQ^RfTr_)h#;A2V7PZ*5skamsrIo?;w?Rved2ig8(;ItQdXDBM z_Uyi+upML6US3`ml{aAl*;UKjxSOkP|1qd?_4ks1mYNpM(I?9H66I=n&8ybl~gj^zqwsHOf z7jm(Kg!1g|3|f+1Vc*GSu2JcSj0lXNe$Opu+E#PwXrK0cc`4_vfEO1}y7jy>(MHEW zk5ZN&?mqDB?o~1Eoa6LS$hDntSlgHD{fvzI6-9MNp!EX5Ds6GwCuejRl6jjFh(4W~ zr%e=HG=94htpZ)bj5wyfdZb7Q_r!Q}VJZ_+c_j05&L+}Z(L1!=JZ4Bakl2yrU~23I zQ&8Kjt3Q<-qwaMZEAWjdQ!UW7_3ORRula}i{>)71{U|ett{Vzl;rAc+K7J&;GWh~# zK(3NPkMbQDb<{o(=RbV^M#y174qqYzjt&t95Zf4;t-RUCXXNeMNBs<7?!;Dh;@&CC zzlk*CLW|lf_PiHKmpo*Mj9==k6^Iqb5(PPMr2(2XDHoI34Q7|3qThaq?RKEmK3!6N zotnMq*)%|J!+kF)6QT)l3DVuP5UYW^4~9!ADb3tJb2OP9h@} z_`by~SPJOyAHb&b1$p@+y~!&dFc{#t*l=z&I2R@fKqw&a9sK+NBZAv)xrTvpykAsm z7`I7Ic=8dGBiarOq=YN0Q({t7F7o8^FxL0lj0$(FM_3cNT1|sU+@YKV9mBvV1HCtY z9cu#dw+)hmL1^tRxEy*(Oi~xCf91rvo`;KLge)tXoV%485D(>xUR4422hz_){-eYv zRi)0~u=$JGIwNQ(CT=)E2(?J+=5?jW&F-yVn1eHqgdy(r_G~SOebfB<~wsqa`XW4Q{p?bDM zaL#&ib9;>5+!Ugti$cMb6R0=C3%sq5^E0D$_`a>OZyO{AVFV!hqV!(TnSVwlaVdeP z86({A%J!f?p<#7|_@KYSY<(LW4%T3UQ+yXR00~@scx4(vW5QqQqPe8-(>rkJ4-gPi=GU*^7g1Xh;EzN6E^yPWYf zDu@LSa45?1-Ko`f8uclhdxO=Ri8MfRc8XCAb;0DSO*H`g??zMw`6dJ$I{%sTIk*++BMFRI40){=-tfNxA|lL^BHLOcOk*B zbxTK2^cC&FGpo3CPn}D{$92E|%1*&w)Y;ja5k{`^g6HQxR>vEvvF)Fa^9A5V+e_zi zG1Hp?BtI02UxHeem2{nUfQ{sIK<72+>ciB2@ej_+c3#?uR$aX)K=k|!I29AKu4@h; zIkvHuga#+Xv`hHm0KW?{Fc!qG|01>Hedjh>rddy^th<!KO9RoswyEyF0*hd7Lpk6LbIYu;G34nWYq>r;-`hU6!;1F)-kBE|D%K zC5N>L*9PdA+BE%Iw(zhDMtX(bYYNc3jgH!o#rPhLyz245)YM)y-~$BP8^Kd^(M7)v zV<4=0L!eq5QWf=M7voR6>FbIIcM`4Cn5@Ff#?0 z&P6k4G{|dm;8V3-otkRiyXWbLH)u{$FUl`QU(3}HHwONypveLk4nCPqKsN0kZRu=Q zgdT>viq2jF#gU4avH}|I8GcFq5?{-{)J9QEq7xq0CN8?6yGspl^q6!sl~kiX6c8zN zX85tA8xR}iC-3q@vaC)%inxELrli`g#Ta@Hi6M8UTcstobIr$`<6wc67qBRLt7Dz} zPE|b~Z7ds+qqGR@(_J{CKFtC9i@Pt65%pTsfi(buCF-=oMdm)4*@>_4xS*F z`YeU|vQ)H@w}>uEh3b>S)y-1NLn{vwHZ+D~iN+OO+=$wdr7!mRqdK6!;z7H1zZ7;A z2wq@X6pTTgQG%w3)^7IgxKe+h%bAzKq`z?Y+5pTVk0c5h-&P{_1HwO#f7T#|_Lx3Y z=X)(AL_xgjMsWsWc*)9Aa~dhLnIB*n7X>L!TN7P26KPA1RZnO2BrEg&?6*EbCgEzi z@H#9X&zUw^a1LJZ*i+ba0pESI(o-k&wIfcRo8Sf(FB;^OUTl+pIsGzJVQTVNiC}=w z0&~58Ipr#FxKi9YBB393Ww2<9F03V>lYCGRb{eZVQ~lHZy$Pk8F%riaw}Sc=nmg=W znGke_;yX>n_vvAheUKTGOszx$Hiw#`ZqHnOIlsfB9+g9ql@&~Kr}7oJpaUg|kjSV3 zm=FNk2GP*0=3*SKkD6-D(%_N2`fm-e;IvyxGo68h033FCZm}8tYelF(Asy*O>@xV% z;-G5vl005K0D&mgq2NS-CGKDd6~dn*58zJ_k6C(NJa*kSi_dr%r&~iKYCaN*v$$m& zGBG@oT8o*a%xlZ6up^L26b{_U2}HT*(Q7G|#~jkioHU0lBpDE*K(~(;dhB;}PI5|6 z37#&G<$TX;N-axM9d%p3A(92%2MUDTEmIJByJb`8YH{D1E6(;fd8U9X8I4Qy0TzwX zRIoN97MS2nc$;WRqWBM>+9%rc6#eFe@!`OWOz|@*tmeJ z-HDgGYV8!%XZ(6%qNbKYWLIDN6UbL;6E=NuJQdUMfF4)c9^qrjipo_a)0Vk+b}s43 zxn5@F>HW5E#*oG3b>HBx!zM0H8|vt3O($;3DPXRxAy>>aKGSDpWw3B1Xwh=T8OL%( zV<@{s_@lV^_S6_2v?_@Yk`j@A`I16HnwCj~Kl5~J&RZOMqvG-DgXpg=0b<0#jBI5t zg;d=}wdCK<9-fBPeBa5x{KAzqf;?Vo$iZ7w95N>@HW0-QKslh5xZbf? zgQ?}@7!seEF%T1%6%dNcnglp{Z@TCmgxxj^1c)e7qKV92?jJ zx>q0@&+PPWkKQ3h;%>tF>F8u?vA5Z#Z|q;(amLAc9-o1V1U@$`@Shz^Vng;B-SX$} z2G}-a*DBhOjVMCJNYu+x$;9=K@oJWsz&;QS*{=T}WQj-n^jE6NQYD0o=1AqSUmR1( z62hm~yY)il^-F!LIJxDwmf+kI1_#7T5=bZe-6j;3(^?#lxcA;e0XqAC+i8%5Np7#4 z{m$afDI!l$R$T>>4czioQEK%jY|Cs288FhD^ILSTC3a>?E4l!-D7(P7qGhg(O3jHw+ehBk7Em3af2p1S!BW--bCl-M5?Eb4XQTdxSH091O zw!#gr;kZm`-K5OXvp+R8@rHRNourca6(K z6w6a1{~B;uIUz^IijzjLcX=#bpnD6}-%3lH4 zB1jJN47dj<%i{IqQs@2Po{mu6=$VesOsMATGccyO>`gNWy2_!ZpIHM_KF{`x-@!`P zCS#8PE<(je%z)+2pSCsL0MgGEXzq~{WK7Fgs68g)<03u8y?2#5F8tYTaAhgCKpSp< z*^hZ29Fxyv$QL#q01P}5&HLT~^@pWRSW>ehy@I>sW*d<3>vp@CikG<;XG6DNMd*V0 zx$ql|MFz5rsoe2&<88ADEYD2lr>)gC`qwvsZOFT=Sn+Ty6bYLhYvCO|WZ<+Q-9-%m z1O34~yZW{}$#<68*o^1P*>=GL;|I(*zkF_7^`A6abffB0FD*O?LHUWKx1aLuYlvbW zcM}*1_y}QmB|9KjTAt+5B>D@Sq&Q^+`X1u<(n2d4gDQAPqP7Q*y00;*rsKYjpeG=D z*MTC!)0PF>T~9=S*%nIP3!y}X{hz&7co_QBR_^tQSBr`1v;7e_(3S~K0*s3 z@w1B^jWlfCENg6JXLOU@XSZ;9Q5YLHYxZ3`f1pA47G`<-rTu6&H{}yCjenP>{evepp3zuY?V-!gwTjU5=~@x|YUj>|e7#$s*HV zvcAIecTaVIOJ5Z#a97ajCj{BDT(0|TYLk#dw8XSEV9czIL9j``k=ThjyW4vTQ8Ptl zf9b7&u1Qc)y8r$I+`@?dm#V1n@OhQFYl(5w0%JY|Q1TQ$ZV>0#Nmu)7a4QuUSlurx z-WXf3iy18#6pHndwl2@W3{1QYCiP%SsiLN&SZ;s0*_EwD?2KYMCov< z*YycxaTyPzkx4n>GATNVyY2(DzWmzlV80pT!ko_LV(F~lhjmy`a6+pMC=tIg`@-hBm*<-!=RZOy9 z2a%HnI~NrkSo6Cu{9so;!HOMVyYQL7&;M<5ihRBkK}Gg{aIxRFa$Om?MiUx{vuL-Z z2Z(rf0mK#DA|b<{3;SN?f~`Hbe^M{Z{XD9>wkT#-aAYL;iCcsgO z@^K2OkanN_!k*Y1g?0m3&8;OZ=v<$l|D(3Bd+fZYT_jPT$}jRL*lHCH$JSnTbAcsn zM*BFiPVj_?p=aS6a1Y2QP|b}(PQ{De!FeeSodIp*E3!-sF%4?GEprpV%q+sOTv6A~ zH&;$0M}DhRm3c@~-KCs9RsG9S_U+R<{R=!2W}l}!S)7!w)p1lNAZNcg-VILj%SwL* zFN!^dx7x^tiD9w|0Y%U^N&FvOgAQJSgcDemKkE~!)XGB#NP>Y7)%})!l9I`y%4N{f zsk=TI4ur0jdKpkR>24-v(+u_MfAVm+&&2S*r^QLDOgOAQslTB8o`iS^x=CqKbqcco z@ikWo0=71wO-I>@DoSxRFmTkA%E;<-{}R|e|Dj0W>3v02)9kXYh~4Ua^gJ)E8gerr z6!rJ~Wx>YG1D*tw|EUU71@b9ppm0Qxersr}3kvv{^D=j`BErz_yJEE=l465lP3+Z^ zvW~zsM7B{;33d()Mc!vN zVuTanp&^DGl&_yap6m?FQ#hYsd=)-CTU40kJVUekrGk~33?P9q}fjbqpKxN&?3G5 z))mUS9EwKNKGWZiTm`DM8CwK{YVLW!YdD}xFkxK@UDf_P6qEAJZ{*Gw>3xG&tmyWy zyaAbnJpBG*rOqS4nWCYb)~!H(iLn&GE_(`%Dhvg5?~wb%Yr!bRyiDt_uk5hrmaz1# zxB^83TQ(9Da>+CgPp%Xf#)xSmI!ur)(k#Z5+pd&9zF1{zqB)h04n@Xy{mo?gbS6@z zv9Hl+dO-$Lo&@x5sg;U%9ksn7`6-TO3t z1K$_k#T4mrDExm4F<8{m+p@~jZS|J|Z15$~=R1ocetl7s7G|VTa^7I#deGRWNz1k{ z2=3yzeD+Lc?tcbjObz8S={ZnljLC5iVtWAQ*@}MOxHyB7szR1e!-!qJ+g)#~u#=_MM!hl_iTDZMsM>(1 zZGCz^kF)pwSaj8_!|roW$=@{^{I-&7uTTfklw}o-*uf)C3nPswvtPJgaOcIP{U8>L zs?=SwD8)0+%`y8PAEw| zw~uLic8y0dwL5+5O?JmR0IaDIn*F(S|{8k7w>j@Mx zb;M=Jh9pf0>VP^ttRCCpu094Uf6UH&^36}Pd^(-*K4yhm7*?JLFr|+JTs{+_jz&gs zaRiOzIZv(xoTA>qu|YqeA$0>W9{2DeCjHgMr!1N^=)Q-UQV?&Hsql7dHDb*$zG-|6 z0C~9Wovn8(d;GzJ6zyR6g~Na=>5in-`W#L9kPmY>MIsUe_i9$__10Rvi5wT& zyjMbR6Tpl7q508+5*`R=CU$>H$U0L_BEoE9K3DyY&9))Lj7Pf8RvOBXGR5-o>fIj+ zi@!F>e%jL#4T*F{Dl!1^e~=$)9qeOM(W3XD6&JSZ3{@x@IPI%d)QIsXus9V;b=T4GDPZrIK}l|v$grE_%Q_BJ#i!UGRXofNS9K- z)Dz-`ZL~DM)ciO>E`YbYHH4TIyx!>>+1r-MGnM1~CZs(KAEOZ4WL)YWklFeb{HMHq z{G9`5pp+c0QkNR)Nbv7EOJ zG0h9q55SwxsQMKiR^4!L@!FfxbuF*?JJDlD1(ihTeUef`eWt3v*k4TMsHEq5R8Hwv zF^Bn03qoSkN!Jth9GS!tcOwHqqUg`ERKgig<7F@|i^edZv;w4vk>8NGhCFAD3sInA z8uGAQSF~Q-wO+539RkOX7@?cj$cc|*8=?2APMaRDovo^@mf8aKPpF@dUJ=^K-4dU^ zJ_l)`R9)~sA5jPAQh*2Z2-O5GOd z&@uO`WPlPj+?;jq{t|QuxW&weUgw6ERSetncCrX$Y6Ply&f4N|@m3BEHo+I9f2lgg zz@!zl zeLjjv=5VoN<=oD)-D%lu5`1WR=r|~Z=)q=Du;ft3#Gc6yFm9%g?M^ZqUY2#lu{DJs zZF<(X*!=)7Dm^S!Wob@tuO5-1G|@_cwXXuhNQhx>DsJ*AU7e0 zi8~;JIM=<}Q^z312I!=+?DQ7-F-9cfY6wnm|0%5-E@aLxsfHg+#oBr{P>{++q?QIs zQ}~6IG^i7NZac0;`M9$aC~eRI6YDR{(hvu5|xR(+K~kSCHjE4y2I8) zKHp|_DI3sF=Z$YJz_a1J+}*EU;6?*D);n66ri2wx!RIwe}S1bSe9 z37urBP~6L6(x$2)HFI5R!VP; zR(^u#OZQjvX(L*@&CP2)`2qCn%4EWqf>R&M;(sCJ18vGL{%k@E)mn8N(fx25r4etJ zg}#dB!%aE(g9B0G;=5_yhsrp9Lnqq+<5#GA3X2nO+51`sTL~Z%vu^^PU=HKc`Fijq zFhMDIt)?beQV?=3=;Ytu(V2eXN1ku8S|ifjlbuf31p2-Lk*Z_kcTCtivj=wT`4_4q z$37#18y$q)fEo z3p%|EYFK_D%3Z}L(})70a$ECW=$xap`IIBn!g4#4g$wu;Udm0?9$3xvYwQ5edOHcXx zLM00$Uk<|yw_?+XL&oqk?j8wet87eg;2Xyw!9yeT&UB zT0m)9ynGU#0$Wo#Z7^i`9sfod)0~Xk~XOobtrX zIr0ngb+%=B4A8eB>LM8hYp&WILyX+0M5r!XBmNgFOi2bS{7 z>n;bth?!0Y(RK;IzHlb3u)wiHHIul|VALq`f$7cB8YdS7ME8%s7ca5N_DKi5GcUj5 zjVSX0{afDa^S1JZq2fqFLqnqx<6F8kyF?>JmSeA-uJxJ-a0*SefSdtJvuB8dQ{*}* zIx`KO*SnP>&zmz{!6Z7#LQ8zi_nrGG>M%24`x~P1SdC89#~CZN)>$Ldo-y-E+kEv! zOz!X+&*SRgjfV{xVU!=c5YMN>z6WHTXQ)pIg0V&K$(@vIe6fMlGV0fr9^D2-91|8U z18i|5W)4L~gRUptM8<=)zLXj7)V_1ZalA^1!{_6{9J`K^NTe#ZlF<-Ua#%oWL4ttY zh}NO~U_A6CyZmN=iSS7)$QCWC9jWi}!ev$y&Doy_s`b3e{$F#rc~|NNpG#>L%FsHQ zg{cLnV#nWFYEN>o4{nLje@ME@PL!IQK%P4_*-ej$u35AV_jqsB`nu ziAs^@Z>nacMNN|1R*4I`$cCAyPcO>WE!jy~_$StSXI|;CLRXA2P>U@_%WjT=N%_pY z56mmGkq7pt2g@*0^_wP9=BAYq=U$<&yz5x45HFw)Cs8o02qGH=Q2eaZIX$uTRX&92%4P@J;Z z9vWlR)3+5{{sMF@mL>$wn{j`9thD{cX^N(^l^7!OW)XmE)z)>DOP(Df+b=jd%&AhI zG^2Zhk`hTs>febw+_&cA3P$5yfTCX(+lkKlHNOwaK_EGCga+&Fe|#NcboR zzIc7?dR$?--nx`)5#I8Bgm_bJ%~78^7>I-_mM49(Np zEcyN6c{~3&nB3jwEiw@%ddOhSOXnp*%2xh{!^7jcuN2SLPlD@FDDD;8fIQ3E0qw?} z(5q|R3Ipt_?w*<(iGU3DdEJO*AUbHauuvA2hi2(+DvF@KLVk-M9%jM(fa3I^jpcJ# z9jHH`4Qx>xP;;sEA`8adW-v|crS^&4A(%Fe_BpK7T#SkY(e{L7Bdp_x(Yn5Q{ajH~ zV$7&qwSLFd8sZHt9yArMyu*Fx+UYE*mHg}A0R-x4Hk@m0R%5GARk4&4ULZ)CI6B_( zZ~7-U=Tbl9%CnUR4mb4Q2BUpZ7-5ttkOb>u1TSJOsb96<;}+NXrDl}psFcb%ET*$t ze0V^a9L#1P7O$x`6@Dtb>MUrDhwt`+{(}z9#y*jhvWGmikZVA47r4;r+6WRE7YG~- ziU3j&MtGDQA%O!tK~oFv^87LoT=1#CtFge$!j3`!gRwPDS_KujH_y5$j92#jB)&vq zT~U|PTt||OC7;K+xes&*_>msRkkW63GyY?1Ki$hqAa52q0StbEwb*yy%3hQ4e}w?j zTxg6`WGuQWTRcf#+~oe@`~&^WsA67yqQJr_$~H40g2Roh-)kdN8KoiiDpOK-QiL(M z_Zr4&p~aru(|w(D5_#{Q1wh_*{`wdkKTY2pW>g%PDuymW?slEqdCkZU0WuQ^$~k1s zVPiUT=x64eKm9c_lGK@tGVl~gD%Moi)a^Pp$>!FU-xP|ePyLLfsRW*%p4^xfvVmP* zTIJsyMwDHh>K110LteI@$G)2D$&am^A%UvFl?msmK_DL2NU~F96e1+dGs;eoWC-9I z{?w@A$>#8|l@p9(Ak_-6^&%uKYTOtzp>EY7jXm#KvFhiAW^=^0px~48gpp)2=soNW zO`LWaN zQFLGzPGTC+bfoS5iMa`Vj#89-{o(i!)lNM-2t^=Jrj)WH%A79Jye9WkuCE`75Xvu> z(_&T;pqq%7CD(DeFVjtN95n(9u^Wg_ZxVeis+@`Dm{tuViAKyeg)tCD08|b)>9tsd zun-6NWNT7WyK4tTCdK)?3*(W=or+r+!~aZZU-G z5Aqw{``St{4cWBKn~%lM5oQk#xZGL&f@VYgSO7h(i9}v-L>*dbGn}p`)Gb+RK(=P) zY?EVH(47FokEoX)a;xI$0Yo&WTn2xLcJ~ZW{prWSQB6+}{LEDWLm3O70M*0|54>5E< z_&;?(Qo=}~|E+|c(n$&}@~;Gn3|ji%juIKP*uR}LGH8i^JD)m)Deq*^bpMX%$^TpY zsYsX-Lk`XGAEkNn|5gI0fEGjfr^LvA3QVS`Qb041{v-R}MNIxFE%~1oo{~iYP4KV1 zRtjiB2s@$_03IY>$^`{9CD}hyo362*LX;pe>6UO)+Ep=Q^e3XDOS|bXfP~f(4VsZ2SE9L AfdBvi delta 32317 zcmZVjb8z56vpo*S#>Td>v9+;n+uqopWMkX5ZEtK_8{2mBd!Bpmx9Y8W`=37DGc`3; z(=~nOO#38yzyvy?q6|0$ItU012uQr;bUdOw_;JeUp8s)k?EiI%u%Mj(J4li` zP67#+Xb%eWKY7pp%g>RdYLh}DB<}ogK3<Uw(qQ(sC|sTcciRji<$g+V<<0=UYc`T5Emqh(4*~s!?uLR!^-&%Pk<*sa)+;v@ z``OvyO$>}4Zd-;6lK_17U2SV?h`yMbh7}JKfoBvm9TEo?`d8;X+ z5|prewX!=ON|KI5snk>Z+T5xQ!PHpIQW4Wl{O}yP^%6O$l_@l%)csEd3MBylm95y) zV>c8lAJO6<@MhWZHaYuQre(^QT?5_kL7zXe&VOJZwyN$ z|CsF>|DeBvsTr!HuXogxuhfB8T_t@{F#S0#?)~r0Y+wA&E6KPB0ARjjxHKr6XBDn!>ApkbURM? zao%^ll(;~xdRa?r(&0ZEm9QrNN^TMmSkNYF3GCUkj$Amv_IG6(&lqv4USv>}7)zA2 zyL|E=>ZZUS35Nb57@++awSt?#5{)7GBle!ZevA~*{V&2ikI}SzFaHPNqCzr;hSE3g zB;i3?nz>ywUQ(XuJ;r+k!X}nd=C?KGE8p6ni<03CX+%y_NC*enXg8F6)aht>%mQ_SeHiXHO0 z-C{`l{+_xT56rSE1v-Z}nlOM_Fi874_lGYQ76f1Pzg0=J{K4QB5=l&B5tE+xk(<1E<%k?qC%iA#9&yDMnCL5kS^S0GjeJ z&B%)Xp4f7%CloG0Yudt}T?&$Jcq+HK1?;pPsx332$0p*L49+!{TY~8)eu~{ezDXqN zj<%pDqH77EUCrc?7;nfrVn4UWLhpMONlGrO)(^xZ2ICrdi$*f}8Z4JcOf(Gi@Fs<^ zA0_>}CZKr^(k{@hZ*kAQfN#+Q0B=tEPqlQ_VWles6>O6qLqQ`03&+`sYKHhJl()0l zk)7njueAmDqv&d5(<+q#MqSt>=SF~N{i2Ov)?3AzLU*GKnvf{9d`ipAZi;)zE)C zsYsTA8ReT0b$=vu>d#sbFq`qWqTG@t`8<8w{1lceiZCEh*Ru;!k3}94W(GO`w*yQt z?Q|}Ia3Uc}2ER;DNjC{wM;f0@5QDdft+XKlOS+x(RGx8(w_o;7rBnH_=NvYf_PQg?MLZ&@<|BJESeg4oqQDukh{ zQQJjRaL`YcWDm&{i>9%+-As zcT68j^OGyH3#69h`;jGVuAD{PC#)-^u(nzd3hT{=dqnK}KLU#NW{1#y4oFOyi+pVgTi zcdSS(sZrD%9PwApa0q`(72p@4V9LxPL{V7z4?l4RE(nqq#@gSpD;fDP&2Y(~byUG> zxoKe4yF&0dCut3q=M$7?*AEe~p>~Q^k(3&am6eB?SM&q{8(0WkfuvI2*>X!|ML5}y z-i(g}dje-+-{uJ4!}T`?KlC_AvBl@kz(Lq2K}N7mZT&aF4TruvWexf)RdiMV@#2Ll z?A&~vXEq~u#3Z4Xf3PuzLd%3Xv)B6Fo_w0?b4nV>$-8&D3|RgC*JI_l+;UYP7nWq) zm5QlasE3L`HeHYGArE&F^CU-Ey828&@!x1CjfC65=6g>N#=mh@@pnY4! z_!v#l)gL%%BL_@MJEoa3-~~$G9#hfWrJ*y~o$H6hw)G3jPnKPWa@$I^oIiBy*sfwi z+9`c$akUrhg;x5Usz<`TQZ*vaOB@gFZ_A;qgFCP_9U_;ir!wDD`<|pZ@_UF}Xer-9 z?BS^~BB;d0#{B5%w^hY?1|*1pajO*{=jZReTx4rf0oU1#joP1Ss!}=Fm_I+p;yi2N znhY4ZiFzAdP$v6Byk!DD_zG~1CT(VRL(V4Y?V0&*{}uTHdu5eVyj0z7Z<1FnhFR&| zGopn)zjmo{kFsO_&00<-U`96H9i&SpJ%7iN8vRQ@K@4wsuk9}^ zW?Bl2FMn;P972SaeC4|VsZ>i;eBUW|P3Pi$Lmme$nW0Vh-<&v-nYG31?uVm}xmLQQ$(LP39%=Jd$ii=S(A-qVRM&sfE;<(M ztJZ58OR48akPxXE$k8UYZcnBdXA#|8_L}K2+Pjprf%ok1Nd{@WAwM8knBqspvJzVJ z^kgL>MeX~Fvk)!-45(D^QLKjNq`y06u&0idc*`Pg@8afck2A1WklTF(zS^hbo046} z9O=YOYJW$avXQgC3M2#AJ4@o3nORnv=4IWYrWwzEUX{y*5n!QLgY5(!>zqYb6!Sfi}zaM2!B8R8}9Vlu_uJi8+L zS*cznc>_~S7}X@fFn*EmDaVnb4{}*X5IpUupL8T-Z#1RvlgFrLTEy4YB=nl|` zuS9TU1%Q2KC}f$=uqD!o7ZC7aIlzi+eQx1>LtSdAH8>5xKAk+?P)0y@)RwKqu{ahtwM&YQIn z9#qgydhY5^97Ue1tZW&dm!YlK9~j~M6tZ{yGJsFRE*z3G`yhPAkS8*K&h1qOSKjaI zQNjE;9gwE{=}&su$iDTT0xP z^X5Fme`%~;qHw-@wAN4F668w+w$+uc`$^0MEI!_ZgieaSyF1)K8D$#;4tZpof$ z#)Ov-#V9t!Y=YEhX$TAYIvB#mu8hfMgpQ1D%sa5{jsJ#ba`P*G`r$cSP{fz@I{|77O(T!@8;6El z{}{Y=Ck#B-41cB$+Oao^;m>REQYNkA*=qbt>0+ko%Abr92U8Ke38-az(3b> zGo#bl#!r?mM9@=ZxkPvUgzLD2R(t zy^GCu=cC#X%5WZk za7hjkCi0^!{wUWZOUBa64IAQQXanLQW{H-E(sZ@#?1upB-#c?b8CF9|!4*iA6+?Dt z{ho{nIXIhu?nFu%b5>5XU-yF*?+gfwAb6C&4hivf%joDHfE)@VR$h`D+I?60Uh}UqFuvqan1Tw9tYRPRo=zD$h|9^(x6^ zO-~qogt7pl!=vf06NOu}AxuXX3ELOh@eyxQSu*hEZ;ps~TJYh_#ldt#ON*(LY$kr4 zgt7Y9YTRpM;o95C7@(bxt~qM5SkCZVUMF;4P+ei_ly+7daLUp8y{z^7eG{=fX5Y{2 z${dK%#*-jg8h(u0;bp||san5s4!rJBy&*xhn(5XezJx4v5C9n8e!0tYWu${>GpG|a zfoZ-U2B|f6yPgXgw?$>&=_LJr=`!o1W40?@#S{36J}Wcptd_aV%kNM%G4DoK>$_nm zx2D71_{ZCXSKC#4Ue9;|mlD))3L3lTO1|19N$TM}HmROXdY|4*BeR2#w5w7veStbo z)4KGpM@8||ST+#a`v-qjvVFP324zMHr+)7+KXs8_nCiHq)BV0dXFF{3*_jg}fy?dg zQ(;vt#yLXXp0B4EA@RVM%D7QY?j1pH_V+f%PRkYrTV(eWB!fw{oXrSr=D@iEF>0t6K-C;H`Q_=*OwZkS9BHwg!+*(M68Ui&x4QwO$$Sk$6jL zbYVMw$8`3#hRf@Hr;okXoT-RX&k}lV&Fio_t-cY^nMlk>uxW9g({qiVO7N#MtHo!K z7{#$Hv7Zzi<+X5SNlJ)&n#W?LQVJy4XUyOqpT+_X-^o~~{42t8fcTe#zmZFN}eF#?m@ga-OK-M1IfCZ2_x=^JC-`zVk9 z*6?QjaiwsMXP@VEaT5NZO! zUdKTs*%#e!;w2R>#VK8DK9T&9o~x0E*-@$Mz5Gs_RAC|?7{;Qt}MdUJ75wme9Rtz1ahM4~7O?7ts`g3VElT&Xq)id*Id7DU@q4WdRg+lwa zB2MbHVkA;+*!m?`q*v2|JeTC_p7G15t7SsL7H~HKY>f51t4qe5wCnFo^7u?K6t_}p zSKAT8kIBn2`LNgN{1Yf0$~Ag9DF7rBWdic#y~)+T$%mz~pLkN|j1&b55e&+Rt${V= z>n#hy8qTtydQobohMq3Bc#%M(gYD2(Kw@DUTM~t-%!Gf!rh)sTFd5jJ0iFHNf1=(L;6Gz9nN1)X~c45i> zA`uG9kyY0nPfurwfIP1<+>&*nTEB@54@(z`p<}M6dwDz0=3~r%0?E$ZC^EM1iI5q5 zDQZeSShL|;(<_kXh;d@gUz_9RW+OfW_F2`56wka_ObBtQ$xcbpv;qwBh|miEN7IV- zqrOx$Xuz^Cfr(g!*?F}d0-$A_wup%+iKTA}uXt%FF`LAI7M6%EG;f_LFy;8~fEIT|W4bAb-Bx$L!ffj{gV z`Uhu*-@nsTNZ~{oBFu4Xs5p}Z|7F^I*W$e9gS_VV{A@d%*1<0$KA@k>ZmF)yE;i`0 zk9oa3*1nZ*p1n$me?Izfdx+dr6~)ViOH1N1DA}`J9?AP z^5ClGgRmuCPE74ca&@p80-aaBH=d{teD*YTpc<--pXRK#s4R4Z6{6*-5S=}~AVrfx z(L#CA=|4JWnTA4GIFPmJlr}1bDygJGV;z1&7ajf`lt!*#spgbmS~#M5uEe|~o}D(X zFMk>l4zA385rwOIY#=4hx@VSXEJpe2m4jtePbtOB6X(Vl_asDIZ_V|hD0fgciZUZ7 zr^dKFxExvtx^#Z<>l-`HM>Eu#f*LySVToKZlq9qK7gHt>Jk_jbdcmp=K7Mj5 z2$j4xgVeyvMmjh+v2wxP8FY}{xF|1_AIN=Htvg|>2X2UAa?fl8Iwl^xyBIh9rEh() zqHIFv^lp3>ynhWIyV6l@Oh7Qtqb#@Cku$5h^3S=!S@ZHOu|iLteMP}iS)uT$?-=TR z(cUHI$vumZ7_bfVa#vf}Leo?@_z>h&eb}2preAt3JBE%GFt}d#avhJkm^uY9My9B& zX<>Grybq;>YA|s_KpdVsz6iX}*1yKjcwFT`?OyPo@&wic#ixGOKVDeP?C?hOTg~`q zBD!6gw}R&%VN>}v=WAG;F}}cojT@fdNBr4njruYC8#qru$y7vZ>Cde^%N*=Q07@b* z3kP!F%baGKdDf`a*;RZrht=6-e0D$r;cecnt@T{z(tayQ%n&|9QGM|`#6T5)XkrP8 z;|2{%5PPq@ykJ5HS3UK&az!0PW-Hi4HmXh7+5H|> zjbEF-F<~Dq(@~fge2QWgaEldLf62t3AC#L`lB<5~s;<#q?jgg{a}}4nnu?9zyl12V z*lgcv&a}>P&PzJqh;lHVev$ScFMWgl_c_Ot!Cf|q2m<2x=l?zD{_i)W(FZ@W_rL!a zjc}V$L;nS>>G_}|x&MPqguu#{|BFJAu)$lAup$2D{WnUTYl9#H?40+wP`~_ojU(18 z*Q&pJPd+qxl0`L-z`T(43a8UU^o` zFJMH%89YsCuc|?**6^X=_joB#+HcO7l!%@|HbRJVJhL(~E-i^2y zK}rK0;HHt}KHz!;RVhWUN0~)>rkc?MZ@`-d`N>m)#%5Y)BY%9h%3yO)@7aG5@K(^| z&E++_DMR5u&CazKp|a)$*peM7)BnURxUB8sOs*RRv|R&IOjfNH2hZ53Z(&5>kh!+R z&Ci7c8=BhM>QuRAsG__GUiDMLDb{NxuzCIHg=cPSa86@eBjbk z<`1WFJ9{zX-`Q1jb>R9RH-q}#yM}3iT4S$cpJ?eiNa1XoJv7Bm56`t8E`^L33DBW_ zL(F*q^aC^DKL3f1!BB)k)hmi-ko&^=Mgj6_badBilie^Prs^IfO1E%OYr~@umw`JY zV<9XYVo^Qp=WW>aY7gjh(cqAi|4>-ytxa4UU|l&#FNp5H;5_}U!I2Xem@_%dn27f_J(yuXzo>9xzoWzXGSVd_#9fplt(c}VWRqlYw?J&Ne_w6Yr_sOT@aRki@CE2) z!(QjqX(|%B-J){qfcLxo?GzSHte{jKBEhl&FR;#HHl)&(HElX0doe5!&}OOA#{dJK z*R`p4=t0$j&dO0_6JIoC_cv4$OlqH@8E*;5)k|~hFLA+8P*MP=RSvfwL%plru=gg& zWH>Nj`B<`L9Lz(qtVYN*X8C?E1hR;Y4`i7w1)dD9zq}36WbHRtk z;-x>r+f7{H@y0(D#Un1!Ve83-%#VTj!%+gG1E;i@04-S`ESgR9%|_-IOuo!AM*Dih z_;M&vXVn{{fOumTaPnDYVt^fqZzd^@LwS09+0&EdjF6@tc=u)a;rv)HLVQBR-7XAv z>;uCiy$hsP^nMab(toW^%t%3I$2;~)_eh^m{20cYWG_+Qn-p(nDoIM*V*{+QiKQ2J zW2DhG@_aBy1G*{#oBk?qldk!{jg272KdDWx80OMC#oWcSZ9G;-A=iQ{<3r_9+17$N zO#jHItYL|h@ejqm?>@9xU52P#nLOIxqe?#F$Y1@@y)9#jYF6QQ^BIO3#-lvC+GB;b zGNc4+df;Z+3ny+L{7{m0bp`ZZYeqX+2}>qZmw`puO?uJ}EdL@Fvt+@emN-{p(zoAN5rYwS0iTW;EUpoGq_nzN;lY6*<;}b%=@}3Z5EQ`d$iX(j zz|YA7w71ME$|5hos~}4LLMHvl^{CR2nAcs~Dba3REq*&ycWbo$PM=utbD#IVTB@FX zBl^a{EEyPU1WaP#AOAICJjJ+ow^rp)JhN6XRL3l3$?g2+C(>SCrAt(*Ob76FGI1;I z=RQ6Co@QxcsXW|1D$mbS?wu*^g;~3w6W!MX zI;C5wjiET%EB7QPO*x)qXI>BQlhY3W9vBPW1t6<7q#D<;F@cGIjf|Z3=(%w_c6+L7 z%1pU;fhS5VH=B%5cb&BRRqF@nrzY)ej)~~grgc0y4R~*5`>2rAhiWkoRS45RHXO>2T1_5cI z{eNBe|3uVOyuT3mKx`({kDg}@;tq|vKE9uZ#e@}vE!M>)$_^;?-HSh0M>%BPuHm5? zO!3s(*Y>ZOS#xLzXY|gyn2Ouci}7A&UDJpYoaU0Qo(Citorx;lgMIvtf{bX#W|@t; zV$#>s%Y^q2rKGhwenp=$gEUwehrcPa69+LtPi*ONH}B}30!Y$^S~fNHWxOTzBpxO9 zlrI=MnKb;ijXHli_Ak4^SeMBf&Z&}BCZ1TjjlICMU%d~Xvbxm^sqGl~u}9{J=G1?I zA?7ugcVkTtKjWF$?{(L(x?PKp4OI}S+C)=>R++I%1^z|;8^YhJ`_YrE6?e>CSBv-X zy^Y=dI(+En0KlFjtdTC?+uy|L*r{-=Xk)Y(7o^!Wak|E;ksy#EQxYN|f%a1mz`Vf> zTV;s-*7wJY`h)5thFBo-!vxz1{auL=(h5~r)gQ5?jb(hQ351X!X{n-zaJKZq8Q)h& z?h91+ew1jQMUUhKs%IF>aR4H7Ras5pqi7XNhgb4*&_?0&W;Z-?*XJXiVuaku&EKT< zfKePla%Uhkpmh;mBT=JU?7N}TD@V$k0Lj`>&9k3gnkykUkiIL9SVN1Khx-v4qd zn62dH0ZrHQjYe~h_|&( z{ThJahAp%js&pP|_UupP8HCUv4-E~Cj!ueBNXQHfOim6@O-+r7X-=$4jIXY)kB+Xb zNUE)^O>G;5;6|H?i(86sA1Kb5t*<*zPToyxdQOEHf)D^cW@nC<&Yw?~kN<0*CodJ{1Hzot^rDhbwMp&b)p12C_;64 zBp$>BNKMS&Kc4K7I~!yXjr-a|BXBMgH(#%OcuuPl?XI@88l0z7NheZV=!R~FzK%Jx zY?nKa0UtXz&hSd3B(QpjK~d98{eD$)oY?#aCq0lMTvSs;D0Wu|wHXlBz*jJ)7h-Nm z)U?yntMad(0V?C%ek3I+d5NBWxW3n}%J_v|b!yDbht+zf%f0J!e!Xkd!LVZjjML zqx}*2n-Y=;OIC|r2py@xPt@=t+OC^Pq9AMiA?&P0OId>6Fp;RpSp*v?)$Gg^Fq-|V z181IE&rPywJ&%00MvJi*`Jr2N?)%J+n<3N7#z#h#iUU*(a4W{<(1>HT&4n*OtlKQq zI$C!AtJOdRwF!j0OA$)4Snc%Z%GEw9yy=H{^|ns(gKno#zQI$OtoDv44s-R^QdX!V zP8>bxH5paBV1;D3plzZQriy8jOG3ah-RSR~I2S70<3iB_x?>1xPygy{V=0~>4TOIt zWYh^)Tp(ivBezLcU~d%qLP6v}V$XcPYl0+LsPaoC%|o6?Siz2!+4l2@EA?rp(YT0dF!LJ9FY3Z#9*s378TVZEed*bg88wKAAJ3wOx? zxNt0vu_Kuk3_Q0qFLc{eBGcj#I;!&sC?({k2!7fubvgN;04YO?>;XsC7xEPRoYFzi zD$si$3%I(z2&yzEkkChw0v-vHHpm~uhR9$v?!@(|DyD>%Bea zPca)6h9FlbDi56#3V#9X!2p}nMxMWNlTA#YupiQ>DGUP{s#%Z%7&Fm>57T>vkP&XZ>l_(v8;v4#KwYp zb%FhMz#KQvM*xy8+wVTWDoc2Bmmn`RYO|qMY5T#@7RYVZmDip?XaL@@aB@PfbgQHf zat8u(I-+1qgb=nE_6Iz_MOPDv9P;*|X8yAIiTLnb~lFXYUcX^%93$&jR;|7VF z+@$jdaKo69MKWZv>J5;Q3ympxKnkSRj*pINxz)vggj^a+7qL$TgJX_@m$1%m4M0hn z1q3la#2Y2N;FZXJFY&}Bru0v~1ZL4HMWe8E*@8wjw|M@^;-)nwF5MAX0i(H0#3o3M z%5C~X%720YKz)EMG|pE1l8L{WpkabO@f?^J5~c-FPVa%PUk*7|>T-;T=|sDy=nD12 z2{6@y!@C`i#J4$+_VqKm|(nvt$(ZzU~#3xQ~fdnrpXR zFr`fJw^Se%Cw&m=U|C_#Ahx9-IjZxm8XBxYMjtEctV~QFO}lWY>zCrZK1=dV;B?TO z#EskZIIyUt*e%eYX~_DgeiVmwTa`~Wvw137Xw5&~s7{*v0XGg)JKiNcGwHP`vfBi< z1F9$!D2hyJCh(TlutftQOORI#hegh0yq127D}p~EYm*>+poJbS2!fV9gciqthuwrf z9zy5NR|z4Oo+27(=28V?RSaBv*;x;>!ZaNC#bzi-mw-{!3Kx60YUTk|5>bk6@{qog z!pLCYa}@L3<>u@6n$DZ!b)L?dGPS*udYszE9;oB0dE^W6(&%fQIEf79JY3%<+3cFK24S4RiJuaZ6k zpgE(rr=!buo6*3a+gv|6yGB~};jYkCx7f5Nitn7Qnct$ReFCkR!yW_+XL^!qVyleB zLUidX=jCk5MQDkyajsdMK%1s|`Qo-A#bM9B;?AsQ&qvgWQ9&m72OUp4OVpEZ zlh_;E5ZtqZmUY(|z8DQ-Y1 zE4L(Hn}3-1{|;AbMkG#8JUHi8#pN~^j^YKek5X2oqM3$wsPlKkc=0g06CV$Itg8k; zr9w3q@8s$&?+zN{2}8Zvo@Ng>Mcw98r3$JtwE#F!diPMs%ENzxmuJCHOy;4NnrHtt z?U|xrlW{fX3hIWbQT#0s4A*u|%sO@6PS~2>nU;?SZaEel@RMFdIl>Z5uca27qNfuv zViLoNUUpq9tHD^AT~pc0{{9h3(M}-WjZ&XLa-RAW^fTrjB+k9=O8PAmqqZF$tL91| zh7>4Jb_|(LBE*P#%NbKoLWib_wG~-Aurp3=@XSgf6-kU8M52DNewj5rBye3Ot}8Ex zg(X@;=T8IPvy8-<+i6Ft8*hX4uCw?D`q?^*jVh=zfFm?EUOjP! zna3?tjU&HtgPckTbang_$X&q7@vxOpjW57{wdEW18#j_caD0e6X4;aDNSbP=dd)K{ zusgjSsd&9s-()CXBxj{LTCl$d2$%4CuD_M$&h30V*pL17w0hZkZAwVf#@yy#wr}jZ4_-d= zadus+$`u<62>U!w^ImTnwT2Fz$6!co(Y;ZECr5k(5qPoqzSwu}ObVlms9|?~?EzJ`JKnwT{jLNIK6inxwt`yV6WQ-_ za@;;TcQ6=)!FhGLu}lZ9C?R#t4L$JVbNeF_c$Vn>J_a7}zLl>?sbtYzTo2?g&?1r& zRI*x)7OHn&kAd6VuZvhwX5OT$RZr~kUlH%`-^iR;7NCXGSv5%GSy>sB> z`|D2OijrG+9}r-CA^8#jO_=+Uk3k{I_Q<-c?*Fmy>#Oklst@^+BaSreSWVrhso|Gq z=KB^QYJ!CABp&1Qzf7C&r)PmT`0q0+KbzEQ$YA(gdLPLPWMcN4mScF_n8zgXa|#Q& z`PFatJCW~~8Nb@47=*B_w{3;kqZYgGrqz#lpLvS-YrvINAk{!a$jDjw!$CpdqdK+s z%OX`Lsu10_iy@(ksr_%q>KBMIPIYuPEH@QIq-MSw(lG)jg^%A0-Zyxb+voOYCT67I zkF_!e;R31>(WALfP;$o>Lon{7IT zm#XvcUGJZIr4u*t=oJ&|5m8z++ScEaTE(fIkft%OpcW)~Sj02WBbNDe4N-)Ur9x(? z1IeKRAHZfSIXVcJGEQDU-=haG*%q)_CvP5xE>VCQybVXvx+<`Axe>HGQ#6=E$u;=P;A%aDc8dux4ZoBn-{Mabv-U%*IFh# z0oeDVKruWBj}@XGtBX8r5CI1V|D>Y)cItAR`naF@^&LDjwgs(BJmb8lMUE3dsxt?{x>XJAU21FDF7w;$NUu7fDO?cL<}u(-1*;N#4wvJR^f7d=gkR zrrRE^-#s24Vi|l~9_M~Ou-fo3y2DFO0pP9F`li%Q#xan6*iQVvmY4B5oDOr-($k5| z&bf}9j&psgg45M1a;_OAEAYexPBTs6=NCLbo^r3R&rg0KU4FmyANSt89_#yjtk7m~c&ew;+^}Xo@H2v-+d#e_2|T{|wr;2Y?CEwCGT{F%kM->;226Bh zeoHFGA$W$Ngo-9S7PxzAI$C%(F7~eoQvb@V~Fke5@`&;tTOT-e7{# zhz;VtY!2NXLnOfu(bOgpOW$-EBR*~}`nCc-zUEM(2d`9wy^YCX|s7%ch`JU!I%5HwPuYATw*$1L=8iVTxhoV0Z?Avg_2i?}%Lj#@(hV<8O% z?WSw?8MifEY?e<^2Yk;%IIqLEhmDEgyae&qIGjLbS(;aiD6Azex?$~t>-TgZQF^3D zjWs&WpaUyzIVKGrM@YO5FvFmNo{B4C@5=3XxHzU^^UHl=VLaf4>1Q@5N>iuisFqT0 z$S@^Y&GA>Z3V;}5*3{NlF(cOPs{YSbY>i2E+jBfR)x)2(45in=^C0VAcgyIiDWh?u zxmcKCRApH!Ihr!l_L+oK7sGyv1c}KIwly;=F8)T@5R_-klES4TP<+Jr{50T&BGz6c z!S4{B4xzViKtdWx85A|D{UJMyS!zlWDcwH@mxol-yxC~fX78c2mmr2!r43< zTG}nH3ewhpL=USX$;&9OoEYu077nsf}7 z(h13IJ)yv6H7hXn%DWcDVK0aMbr=)*kC>^Vv-A!sHb-}ko1`Slkp=B;Q38Q?ivDIp znUCc`7-&clFWten0@YO^K+?2S!w^p3~+O+sU=t_U|+;vO&UcDC}CrFGdK5$igah22!@ zYm`tIjmYe#I_zGaCrPS>Dt^yIa1?*e+Neu{aR$v5Yz@;i#(}q70S3`BsWGH0<@G#L za>VD$w8RoK``QIb>$q`nQ0j|DwwS>qip{|Kw(=|)^~s~kV8;iXOEjcVwa+^lvVc!9 zC|pe)6`nj&*pmmJ`uyB}n^iivJR9JBkeS{W5a2DqH46wYJ-A@sVAQe`{w}f&Hf{_E z=)amz@n@?f7`V*{{9CRI=INWJ;WBXW=|P>>bIhInMb54`Zlb1TZ=+V4pOOTWWtE>IV(GFoYj5)fD2x@sLNkPgrXc)l&BSp-`A3e6aAODglzW_psA(qH%sA7NO2ueklnHUAb_wuL?T}zmD(2O0y zLBzJf(ThJfC)K5y=oz+uIRYo~r}=%IznEf_5$`Sk_6Noz7rS7)3fjTo&0AzIS8Qi- z;4?$4ZU5HUaxjTfh1+&s8j2xBap1e6sqG&&p1NQy*`@GN3 z+|LrP;G}_rfu(MS9>@J0;6{sJ)+iHLMX^q4XW%+W>6986fDrag=%ISaF>G_Ff)&39|tjj=NY9~7~zw$uQxw#J5 zeA5IGK36p>d^%VJ>uJE(K+d6lb|?NH$GJV1OV?EE^Zulsyp3> z7v*VE{KBKRrfQklA$bmUxo2-EBKXe$Yo{l~erx*NLZ$@E^Aor);}T+(qGKT~s+PWQ zT}QC_WZGDLHCTDCRdm=_r-ab(BjnC3i zTYK%xsMZU6Yz!ur+|)!$Y69oVO_Qhb%p?G#Z16Lut@3&#*VjmYruSvjc}5*E(L7|q zDsuJI#Y_8GJanO6cMK`YHoW`#TE|xOi-o?~<_@`6TO}`~2WT}TmY^4Ua^2K9M;c$$ zL}<_d&;^y*M+=rvf4TjARt}UYk+vH1iUVE!kyg z9MDEKFIn(1UnR^Xkaq|mP5v_f4i}$SXI`Gv{w2laG={0Ab2=BW8s<^l0&6rNYZx27 zfew=RlMksR9#F8$`2*umGVM?QHo=~9IOB7a+w-#5nCp9Nvvlp@wWw&$(-=2hg4IOW z0D{CACGSAS6t81^D7XOZiNUtGcb8}F9K zlnmA_+%KWE122Q#m;dldf%kNGzrr&tq@mH`&`=2w0RV&rd_Ns$9)3V)@3Ktk618zT zwg3~OuL4cn`)}FCI)s%dH0)mvWJ^n@Yh-VMaOs3L@`g;$GaEKIwcDK!tenrsnXdDZ ze`O>oh{mi|f1Nl!`QeL}3j+&J118l8<>H`v9;DeM#z;E$1T|S=HY3$th2i|Qh$@QwFc$_?`>?LA?#~XUbc8bA^SzAh0o{r{K zuUUUP9HcJQ+bm}dH#o^3iN23f+WW)A;*Q97Dmeq3(sx|{VZ~zD)gWMo#^a;2db@DJs+h;~CDU^>iuj{sTaqJfS~;`_+}uXsG>=$qb92_uw* zg1vuM{l^>HT!vEw)}fFa=+1arp6zgm`A?5uX`GkuI=|f($D6q~+4l9YsiQngu7F^T#B)X;V^3#TkhTnclDz1Qze?}v0m8X z7f0(*X-3IqpQ%)bY`)e+!KVf&;S+?62_P~rgLpiA=uRzOFp<8%MSh4jM1o{E3GKl1 z-DqSx*_n4$#;?0$QBKQx!fT{J(o1_ z4gR|R`p>Vl2Mo02dUX(Xgpx)n zCSDeqVGVV|_i8)+x* z$d8lbp+wcUQa@lhpGIIfH2VS8`%rMXS;{6i70+>LHkD;a-99G4Q8O>17QnfA6E~&E zBzTbQM+`T}U4vBq7%xK@bvrC^CY*XWwQW=pdBC+N|386+RgGF)ZO?i>#|F_Hy)t~o?uzXjZ2+zac2YUZ8j7e`ZRe71VFaDTbFaREL9fm0@dGVawK=zs z4bL{GcU3#WG%AK?HAF4sTmc!NJmb=YGn9!UOxpCoHfr@^)KWb*CMpX3 zAClZPO`O1nMP|WKtpH7=y&S{y0afXNs;6GUMV{QfCiY|&A;)V$;cxMkhn-V?2xTYy zt5$!ptC=s38h)40H{ex49tWZ}#r6N|>KmXVZMt=1+n(6AZBK05<|LhDCRWGJ#J0_e zZCexDy7|6y&OQIVwN|aJcXw6o>b1JoTea~#&SvcPpYlWD-&VMDb_4rP@yguAyA^CyN$;ay=(&IEeWd$!VPeDL`Q_&1=Kja9q_oMQj+#T;2c>`rOdaLbE5n2fSH! zAezyw-V1ThLDf+NMhd;y;14G^2)*ksd_9ZacuL?8FQy*5+7s)dje5D1A)3jpCTvYK z2inQd?N zFy1Jq4zzJ z7U+A^uIb7LMV^;Ey-r?DQ|4`M%_kv-rif=piUh-|WIGh14#)AhoSXWWnssfTWEX8U zcp?UtXekCJ7;j6d!f)p-L1~x}OohA1!T<(>LUVlH9}*yO_}2`FYKJc4&k4yCqb}{@ zdZdb+zQq)xjZ2eR&=`cOOt5c20O)Xs$t!j5WuLm=&d5-a2aI%-`~Gr=+8JeQvbS}U zt7dxrsB|W1yf5l)RWI~VQG>$9-UvA7YbM?zR@J1t%u`PVuiGykrTGwv|A{3KajK1l zxdEJf8A{q6Lj%}@&XgNc*{k-Gc#{J4)6Tj6fOa1VBM)a# zhYKJYDHM&5J~G4WJcF#@!SC7s=I>L+@grEwg{7>$F0RNSf zxT(&M@ww{G`#yX}JNo##-hs9jxD-aFYDRqGoq+*!*Xqc_s@t*h*NMhBxwQvm&Yczd z^3&?>B*RH2LndfaOJg;ZKrR$@fRgyr>tu_zXY)U5PKJ;15Dr;&q08+jHIQOQlZ#x9?a!)bJLN> z4V6un^{kfixZiYNtVq~8fgB@jE7siHtohshS)i;}Jxoa>%2h@MV%07Q0IsAlY%nmv zh&?dQ;AI9oM2r__2q@fBu`B9v2}(9jQiLB71e&e2i{Rcq+*w31D|0|2A4=OBX2eDs z-B~+o+xo^jv7(>-$7#JYX}ypf?0!Bl0psIV842?@lzOm|HqL1|PDtf->H&Rn-Ub~U zlx&gBR@1g=3%M-k@xpvi0PU;jq-;Lsz|3h+j$<>%B>f0kZ~60rDE8p{qR`p?Lph5O zR<*EYZ#5 zvYQqjldylufNvLU6f+n5+3BM(#P__>AuX*pR_Hs5bytG%@F7kl12$QOEds6-WAPqR zWu~-53GtYDe$nzJM&=Tw&E&JqA0wB7RuLIEg!boX zJrs0sIDWss3#PiF4^Dr+E?pKT8-i`ZI*V$Jr8 zu|d+<1n^hRksYI!H+mL5%LqY!-s295#puuGGxrow)?AHg0G>*E6jpDNKX9Xm8ZRG~ zh2gBu$pl^b+fC|V3M}-OqYLWAFj_eUSAwHTt5QZvTIM%{DCQO}r=|d(uh^f5j!~Yi zFI-oH^Xu*0pIi?IimhReomYMEOx;(51JBP(2EMM|n`p^QJ9r3!VK} z7N3E$Z{Udb0QcFq45x#)H~8Dz?Q;Dew|U;5hi?Oy-B(a=`kU@kgJ7@>u=*2FqS?rHtLc$;Lo> zM|iQHSgkF81-+V@sv20$Sg5y!v`hSsWaXq0kC;j!tH7(*%=9{^mIRk#NLP=PKuJ`88XW5^=ILk){?N zPMrCyD|6fPil=szruy2zxO_7BpSW~9k;0Sy07q&*HVnFqFZK4k0_mJY01F+2v!f1yJ*%`T6(AzvkuOTSK7TV$;0G>{DJEpMgHW zbaQQM4N|4ic(W>!`b=xJbF&;;7Ty!_q-hzbGF~0Cra_5^K0s_UWH@2y9+btpr z*xp*~sVEo(5C zg}`?H>M;}sSpwNMo@oB3Be$l&hBIqGYAV(4OGjWaG73Y22Q9g5g?T}^=u2QiA~Djh zI|v{HhcFcEriFd`o)j32O60G!s^Q~&A_8D54uO}s676^P7-YwZUwmZjJPrYOSsrLf z*6hY23E^gOr0&frv4Q*e;S(%v)FSG$JR#_&EVj)_(GV^I1^df{?grmJ)_L9X_BAjRfq*>dcxpBlpzlH z6PIgfolL1bhMoM~{Ga3S)%ux$--ggGdMx#3BRUC@v*S3CoD#_@7MZ3s=~G|Z&W2+$ zQdhszfyz(w_F(jI(H=2SJiLU53@Sj)p7<2!VB)42XdhwM%n7t7UK4K8#UK9vT9y9< z2L2;!o*uUV(5PnxQL<7KXh5jPZxhcZa>%B~To|TlFU`qWt?k*DzYo zv5ccsq#FX)1!YL(t#xgi^I#R%blNGzM~ZdoM%q!Dxq&{%(Hd7xJzAT)!f=AMxF+!( zT4kZ-%NUK9I23PK&?>G?u<>Rwm&k={v*nbP1$s{_a!S#K2={#yt9l zQ56>NoyWH37mztR6KhMq7X`8pL?M_I?JnXx2rNRnr7dxXtAv;8W;Wu&IU~B)$L$H2 zl{GX&K0NytCwARnv(skj9~K6Ph;h zSt%+vYuzHjOIIKWFYoCH31}#Ue%h|4dd%39)cPz~R8JXp4+QQfpyo?%R$kYaPTM${ zHFSg-Oe8N&EG@QK2PP)cSOeKh~U@zo%mA$E7pC6~`E)l0(d#sWI3Q+Ok zfk(l=j0lY20NbH~Ye&8c7a&4>^>g=4j|@PSh%mTH2#MkI^Lv3MiDBd`9CP|zIZ+ib zwG;JWX$}Eao70@ABB@#JEL`01@(i;%Yj<0)(z8FBOof3*Zf%01*>mbh=>%e%P~fiY zS-2bvx${?|79yp&!P>f=@|Gch5C+&No>8{^w3VlbnPWnF=Z+&`S{j`40~|)@!NDI)``)kwXWTK(4l<(@26E7rq0nqa zZHqn9KGF)vim}VQ<~Ca9vs_HT!2sAYvQnH>e)6#LV!3^sJoW+naSu@dor>hL9_Qx( zcDGk4+OT|X08h>H@iD5dqw?`e?{N$3jsh&Xvc9;V9`U3s8Gk`eslINnArw+Hvy1cg zW56M0l$16HI{rPij!Dzu;BtWn*hYCIe5ajAH zO$<4Nmw|zY?f9b|1Hk+-nhgi1<+9M9`;$nfkB8eS|A!bC;!ukask^@wL<9ne{DSMY*R=Ujv5gNu#yI9D9K5T#LL^sfSrD}s?%2omkqNh(dor8Vc?YC!`x+?hQ~_Z z9laCl^g$HOU5SN7l;G&w!ob&E?(=AMf|iWOi>|BIIx6VF1|aU`5^oC4wvVQMQcmCf zyz4skl}`MY=Gj#aTW{gM@=>u_Aq-Z_(taP9*;CRk`6QxeQIeplck;;4{XD?*l@Q&AJhAWC2i(keD~5DPDB@xq4R9lJ(0>|6-B4fJ&}UqUO5(0Ha6b7vm>GR@lzH5 zhpf-%Qt0kNM?g%I06XDV#li4)_?QE?mgKpr?Bo6|c~=FHEACZ-C27KCisSK-9@61@MBtV8T&| zG6xVA=umOQd(XRjcLKeN+@$JETP$AfoxF$)NNGY6A&VMkwPJdsms-EFihTGZB$Lvb)1Uls3Kimpo33}xW zO)YwH00a7GMWC}lv+-&O^+75M$nff^xfvr7OStq^16dxZW>GJGU zX(y~GWa!IYoT{0q$VUMY<8~zZZb8iGC)XY10DBY8`_X1urzpyTLaE8cxoLb_HHLTFlqPJKo@@1Z9_1Wkc5EDSRWM8uC1^AjX$Lj!?l&`$|GhUAnHswupfXr!5>~B{Artuip1i*V0pyqV_9qlD)>@WFH`xl*h~Yj3!vR0! z=zO7j{Ku8*<{u-2sh}Lu5A%0+Jopt5r&By+w6(LGSciJAx}#m4=HRY};HCO~)RBj5 ztY_KOSo0Ry|034}N6dNs=h6O}8$WT&(x%RhH1);nE0fJiCLxVjo(D&BVK`7!qQRj6FLvHZ$4q6DSpA1YCm*QNh zuNLsCGBRj2pwDxqq(cc5*Z4=r&vzzuJ9S$&2WO-TcVN7`L{8@2bCJx=sFaeR4YVXT z3E9KPS5b;z|>WVUjC@G~up%iF* zPL}&?8%#3L8S9SI)Jxw)%8xB-ZaP%VVvTc<%pDw@N5IJ9>6JI;QLO#+;!!E)zCe%s z#-Hn^EiAAua>j`;U467$7T2Rm6X&<_k4X$~j76F@Zq!d{KRLZO_ClH8~x z-0;UoOiapTHb)$x`MGJm8_N3G;2JwM5fP8*n*){6j}fSln|V8|WpUHqPm(Kthh>qgi;a^}&Lv|8 zX)D;Q$S5K=8~`6-^AaPCkQKcQ+HtJP_6y1p%BviGjUpcNDJPg&K+a(R*B&IBi?I%g$2> zC9SQ)^gFo++!xLsMyAAtdd7(8VtKWa^T2$ByC2)RUUd)lwsJu-+#E6KVRMIf(uRgx zy+1Ecg#i9j4H2R(-)X)bE!TF&z;J-g?yrOjAU5V&X@Q-q;DpnxC!FvH)y66_aV9h- zBnH{9L{$->&g5^L48KqaP3#Zz4~rfPqhQLVR!N>X6mP=jInJFanC5Jn zQvr3Uq6>(s)W^=`r; zy~du5hTwx^s1l$j4mlcH)t4lrqbdDMJ%Aa`*|pPR-i@S;aMFpO47^dv%3%pClg;Te zO;srx=~ZBo**bVk;|?_KBTRZnsa88ttpPgaL|on>t;`5DLQS~aXqe2**Nb<@q1e^# zxBN~6+Atpda0)4>bH$qDs?B6A2qb+vj5Cv9*~v021ne~@#V%Iva9AyD6#p65H-Lva z0vRoLOKb;HOvRcNlj2_nF!G_IA1WYl9&9lL`H{k@jZ{B-yr_scMl;SM4-DH?%qAcC zuNqKSqY{l$2}Ec@7vVN513EFKX3bVyYBF%8J6)ntqt+E_bA$!qI(WSq?d;>CfpKjd z0S&Pm{hZB-Nj^lSd>M_Lorro}Zh&%-v^CN2;Av}S?;0X0Hr243#hhUUE()5yf)R56 z`h>YW26XF>q$w7Ac$}5HsIRoU@9kMlNq8?lPnSXRja}pruGpib9FQ`DaFg4 z?|K=ewm8DXcl#!)gH7au)^r(d4U~DAT_mgiTcva2o9bUzuC?DF`#ARCtpGnB>!Kj# zF2wz&XyQSblaa>2^`2Wa)6!gI&k81<6gcHO^;l))Z!Q!ICRYv<6TvdiO`t ze~*jqS2!TIdFQD&%p7WTf}0PSFbO3pV+hICwjgNRQ)KcG?ZI!4CkaOcHp56jiSy}Y z_+e``6in6Zipz>T$kgAf?YLK06Xu><02`oNI-qNA`%_!(OQit2);T(dpu2d`1U&}5 zTm#ux6BubfEs5X})MfU0nktg@M&)wDY9LV;X3f8ArP{cFEC&2q`cohb30t3^I~$51 z5%ZXi++rD)Ok&{zl{mVAC#V?y4&NukxBn;R`nJebc73FpyhYo80jcb&;J=+Y+xAT z*^C5yK6s;jqi3q_i(D{ow|alA?tGrlxV^2`|KZvge!5WC*40*#qIsSXIl6A`ec!hF z$QN|hVwqsLu++LT>E4)!0rV?h+-lPQ|!FRMR}bCX0ixBS<_2ZS2Sjamt*z8V1@ zT&Km218HbnR_zSZamUS|u;zhyxC?AzHq;p-01L@Fdty2ri{UfnHlzXxD`Tf=FkbsW z0@ikiKB|6PMCNoh3rno8dk3w2@m#-0`8q-lcmbEbVjMBSoDYdDHJX+$PKn0xj=WDV z@bXGQB&sq`y3pj6g^xQ+d$=qL)gPXXx1QPR{!v~BS!oKvJjB8zf?XKNyg0NzpA0e` zU=OY>lb%m@tUXOic6@f$u<~`N_8^{oQ~anzW&|93^B?fyT=KWPXYjh_TT1S}iS6p> zcyV1?73SO+r_2}|!`^`o&hfUWh2+v9feBrN=w6}UF>fH-NIG(pcDq08xpkb@7jisoH=upy0J@$)?e-jFNr(tBwX;k(K zAXTiP)!{^wnNz76^Jw-dg^6Ln+ik$D;qOb$`pi;x!EF0|N9iRM2y5ifrIYMPGSPuQPe7~BF*BYI zVSmCNwhn|af*rmV`!6BX&EX(whHQ5H)87&+@K!_u`vZ#b(#`Ckj>Z7Bpp;NW^QgVX zb0+%E!T>du06=L!JZBcm=?}YK?zd>Zy+c<;1TinevAH_XQ&cl==mP?;3c z5Rq18G}Z`MPEd$Ow+hVME?qfE7uj&BWxYQzdpNGW)O!rQ&YA&F$qwaDW1ucB5v)+edxo=vJgdVk*_) z`>&&=tmH4-N$tPq%{LaKb~~c|Al@5_HCusd7TA-p6H_Sr=iOHhlfr4D*(qkP*`x|I z7DXjnS*t1c59HJNd%O(khw=?TU0M$EUg|`Q%X7sucO9H76!&XC$bxtap#ql-L{|n) z(Y#0dJwVv$aPBLtbUnlMx)zNED<0bbj?VU<3u4FD1f8O{cZh066;P#3ufsAgcn9Clx?G@m_lz~DAvzv|>z-1$h(2MZ_M!7d%} zI!eye8Y!jLA*l>#=prGbg6Jobty~Ug8HiCoug92~H2_KD@~Ar0busA;={F8!g&+86 z8Y1ktFwo2luptSQJ2+rNPklS1OS9u3LIqSfqYWx57qHg5qCM*}+xBKZQkshM+&0@! z_v;UyZiqt(%97;BxIAhW`8eR?;IvqhnRrCnd{wNp#L){Wg!XJckChBp{`SimdCN)ttjc%_a6NV$JUrBCK`tGVBU#U#s^#N$o z&WOv2>8{4vbyTI?4uuH4z~lbd+#7o3!=htAjQ|Xa`Sz{qpilptJ>8fs9CsooS<1sY zyQip$wLvaH%v|lPLxlD?mZ3@aQ(l!kZh?-v0c`l)UA>)=vDL>WF1*~UExkV}O zwj0R(JfTG}Gk21|=9rTO)1vPoh%t5v>HMr}WSW8vO82Dw3Ocanl^x5%N7wkiaJB&> zm7Z7y0)l<_4={o1q*a)TKgwND`Q~m3>LtPiHEUDTaj}WO_qe}({k8`1mx%q{2+@$p z8^-b9)}mHwRBu-sG^sC=0Wdfc*6NcQa+C?-%7eeg)8x^L>laoa{-9eRRqFfJg_T%b;tH{*O3Tubpuyq%UzpB?-B<_pWJ8$X#<_s78 z*67nFpF<|=iU&&+VmaAY1Bum2|p!FEj!`X6Wq!0n2zXDfquKmNQ{y zjL$IV9Y4mom+*HFcqmBGWK@8ft=xk>y1%LabcD;aC#$fa)i#zJ__QkMpGyWsrGo;QQT3pa{H z){JiFsHV(zX@M_F2>|;*-{ zdq^3p74}AZ*Izyya9uf9nim;aP(0_X&yIw(M}nWC!pg6AEdYlR53-iKB>uEv)^dw6 z(!1Dye=aiRnh=&o=;nyeEy&F6)N#2P-3%KTSi~vFwR#0Z3NR5gD4tYUO`FA0XD+fE znBQ_HB>Rn2LXtH7X7J|;)CbZyQ1KzP5vo@+UTA!oQ3h%rWju^^_ZC-%p z=*X)q!$(LZLn6EkPTH05a~+->HYkM|XlBr4`+12ovd#T}M@jFo3brT_n?}XmxYbJ~#wILHq{(3SXMUN};63Ot9A^*MH@2-5`tY+uo^Djuv zuwNv&$l$PdK8!buff&>^8W4NtQ@Yc^HX|3amH-)OQ=~rY6GUrbgk$qfW}eS6Ke+=k zGYcZHi0LAG;(?z*YZ$?~mw~%QB~%N?^SHxYzx^KayYEbu>KlK+Z(=&ql$|>`(NzKU zAIP9Shb~6shME#&?^HH-1PQB1Mg~GJJ4t}P zA2QcPsL}w2!QOyT{9v1yPCK}_?q?VHKC3=21W7yCmTt4o?epb{IXhvsq%13qdzaHc zr1RSO{@-xCLZGVnZ>B>5*Vq6e`lqh;3&CrUcKYauKijtK<^t&$Kl7AJgY(Udk{9OQ zss$TN>Y=?l6RN5izpP)9j=C5l5;y>YJdFrntMORu{K~7%QAJujnmw&=*T7i*p>jn8 zx~&geGHgx7_v+8JEx_e<#4|r;utKFzyd;`a{m$}n@XQ{S4bPSUk@c=dW`*Vo?Hf%l zvRA_QN|-ZQF!K4I1Vf{lx&q?1;Tz z`QY!{szm(XjrAZW3SebrnX&Wd#E8vamF87w>R^wgb+F28YZYTB8z7`jH-qL-@OlY- zvSNnF-B=oHBe#lE2w4f?B$ z+J2sgl@(toyUcyNtRA+i-wFUbSAo9Wb?G8upH|2O{6u|fGnlMwfsOc5sG3vYUYa(T zk;{pxtWSR#Wgbi|Y|zoiv1JZGz?Mg(HOaMF@CJz3_?r(JP(=u7n?dOF`}@+|(12ur zBTc3KMRx596(QBh&Ia|V@(c(j5hdcpb~Y{^Zu(-{PF(Kg7m!2EG#G$5dgPpkkw0}h3=WUOnZIrcdE16^XA*!5-^G*Zrpb+TKgU=!mLCc zU_KY@dER9KUslr?pI0skAziA&Y~QDuy2rFMx4?{vLEYlH{D;}#o%qhCrmv9V(u$FN zlog%_44_pd2K&#;e_fl7AA87IyzVy(XysGmlEc*Gg1M%EQ_g074Ftb0o8KS9!oEX> z8)#l$-c8LVkG&r!DiccId|LF%5u*Q;Od**s^h6Qivgon7=)^`jpi5)A&vBf_65TR` z2U;he7oF%eyzSn0Kf@Ob-o?fKu(c0b(eg_T5PcjH-O@8;ci#6J-(8JCr@?#ZIBrog z=$w6&6;P)Ekg2R8crAmps-#knf~|mBg)~nzd5htSMOxIi?A%>VKLm_-%+?oWh)}i% zvTlmPMP>M~CjcH=4L?UbJ0l78g=o@A4TgjD{|pC|EfwUD))v!I4qdIbdDCzv(Eawi z)L-HKP=dH=p>!4Up>?E;2s=LpW4^j-FaYuS)qZjZu(mhP-}vq1<-sS+i11LWQmep_ zRpYQ!`g`Q@rC8{F@|&-ATx~q{P)&HIX^%D$~ao8<3p#~ zP{xz+_TnN}Y_<-|*2R!O77-B$3_4|sfBWCeILD;a8Dlcdo z{5?c3%eO|O6le+UhG+awwiFw`9sY5*iN11aGKh8E&(?4V1oeqjYKcq^#nxm?YLShk;#z}w zYtf8fLj}M1J+0S-@h&+yn(u4mmDYnZt+ZLYHY%4T!CrVzvRmf=cbd-ldwf@-JY+(Gbe;%$%{lYk91Ssw+Ho0U)oGC^DbeQvf;9oHX-;VP~|PIPCF{FqMB}=@WL?(j7@~8yKJ91D2pr z2-sF2`K1XD86eScE(5!uFs$t|ayU-;o-XXM2bCp$cS8v?vWQgjU{^1EXMjLsSNzm3 z^G}_n9xY7f&mwKtyewLONZvK%_X<{u9|39gm)?oH(P3QBukAR_8PGgQFpCMaclA2O zD3$HB4e_i@2d6_cs(|@eqWUZ*11t+g5X8nj1}!P2MxEf1XF##~K0==`TD7cai0U@4 zyGc7+Cz7VG6^ktJbNB7ThHW-LCWy!>7PSrzcH?*MowYiQp0_0hA>1#-6cQ zB`t;OYIUE#(=_;+a%{FZ#)f_hyctCWDnS85cF_n#k5BdG&ph&-`)J zIMzoO_7g*ZTn<9Bx?Rq__bHcl_etJaS$&$Bg{&46B@b)9|B$j-%lga~wxASVkj(S` zg&fMui+cPL2`E<@U8M1l4QPbnyY>W;MpuDdeh5YzzRpb6rFLtdO8f(NE#2hrVr&N{oX~#qOE;7mAd^3b5p?W{E}Ck-b!9 z^3D10JEZ4eBJ!7KZmEei66YRjjS?@wQH5?g0t1wyCNVb3=o`S>-TS`s@r;(i#R!Q= z5jimuU2 zd$k(Gef+4bZ+oe`UaP)P@%8|p*q<4Jd*DN{ThU^Jep{Xi2}`7s*3vcFCdZd#5o!Zl zg*XX|@8-oHGId-B|hK)%`s8bCnjcO%LNoS{(yd5Zy03Ys7?04-7H2h}^ z855+n3{uw#V}N#INSZOu!;Wasg)(Jl4Rn^VI%Rs*LwB7+b)+Bs{@Jz@=oBcp73lCv zLpJV;J7Sf1V77!EAo8-O`z|1>*4Cw3QEW`<01s`+x)WJ#j38iz<&3bRCzJ)UeYC_QW(eO(& zqA4M2ZK29;L^I6SxHQBT7IvY70u<3y61uY6Xt?6 zBluJvUo8IK*gZIDpixmU!)t*d!l?%JeYIdw`u8OhIaf+i4GnQt0S)3oP7M_e`K@i` z1b__59X#4+m!W4u7B55Luge@yU_#yU6!#}xaihMUNFIJ#0D1bUyG+08ORn)en`3Qj!_f3rj_g}2_*|RJuX|oCAi3~-dGpR_FkgBT92tXoq zecludUdJ5bBnfvdZWi3o!$KNt8A73ualjIt1x2(+3Q`8032~>e??ziFjMtHqys+~2 z7tDqV_b7cRsO(7^>*=~l)@G2BW?FbX$Tp`eGdfoRJl+> zgw5^B;?a>E5u|03W_i<5vIi;Ex*WEU`Pz@O18hNPw)}?Lx2`Wd!xp$UZ(}^WJA4SU zGg!gRm;`h$z^F~&@WTwcTjD7V0E(}7_|L`5r=IK1)+-&}gdde%Zw>zE8=f6qFVRdJ zR~DAH!s#~$V`EE46V(R?-jU05hCa{7#amv_2XYD^wLZ??{+Lw;S%w^3y4i+ZFwI|h zW(d_xO=i{#9bh7uoF5hTP%htH+BB})Md8dEWqD`qaM5Q7@9aRPmkcvZG1uxqb6xl@yCK3-O*Vslx-5(I)Inw!8+(SLmQYmwq^%HAi0_?zI$r)T zSd+}-&Q=2iFi}GHbN-!H08rcc(f4QmASApS`s=9mf}NP`u?8Slye_nGoA!3x2#}{v zMYQUPE_$$f@Y@>Ra1+BXPQ zeS^0Bbl`JvA9Cur(s>d?$4Q{ZDbQG9jV zTNe>)nk+qDhNA>ER3Lwv1Ny9~^oT@Rqs%}2oGJW3Q&;&cR&E8p(cl^BQZi3Hy^Rn{ ze{hOMi=0H_azLSBu#<|)i>XcP#|WRt*y|<-OaPTp;eUAD15ABP`8E9!bD22A;Lqwg z@t=vCEAfC%cs?eN$SAv!gD7>QJsy6y@!E&AL?@5`$e6lzeKF$Xd~_0+_1*|7Xu_cJ z;cfFMTQemZG0@}e0Silh*9eHKO&BT z`4%rJAd*Xv4S4r{8SWP9;EwVi=sA5Bd&yLvE62X>?~hckUZIdKFNKVBfh<7hlm{3H zV*XI3OEz$%5SA6A!{VK_=W&HUH2Mh8PPGpHp>|OjTQsG(sqj0i`}HLmv};6v#cJ{B zmVVO7bqU|{Tfb|qDsV*|*z3cceVw_2ISN@ZP+SyI*S=D=lzdhhmz;cdI8j>8l`6)3 zFXI4evho!)<)TU?WEQHBrI4dxn-+Spri0;wmoI;44fjv}M$XWRZU^I=AJ=1+qVa~0 z^Hv<9C!hl;y2q3O;PQe_Zin?-#56#A>r5NfOQfgmS4mFX5amn@wi9=J!rBo1LXgbnrr2V#MOv(gMj=~8UAHdG!u>%<0MvEXI|J46?oOjA^a!CGvb#9V>=_JPi|F3yCaKN!sXel5OwEt23 zpD^iPl#~Baj#?l4;STsLT`VuyZ=XFPl=^~#Qyfr^#6;(4FZDm jA6>pyn=(KFN%imgE-4`K!5Rot5GWz3puE39e)ao56*)~} diff --git a/nitroxides.tex b/nitroxides.tex index 1ba2cff..4e4ddba 100644 --- a/nitroxides.tex +++ b/nitroxides.tex @@ -55,7 +55,7 @@ country={Belgium}} \begin{abstract} - This paper investigates the impact of solute-solvent effects on the redox potentials of nitroxides, with a focus on ionic interactions caused by the presence of electrolytes found in different environment such as batteries. Indeed the Born model highlights the stabilization of charges due to solvent dielectric constant changes, while solute-ion interactions, influenced by electrolyte presence, play a crucial role. The study reveals that moderate electrolyte concentrations stabilize charged compounds through the Debye-Hückel (DH) effect, and higher concentrations lead to ion-pair formation, both affecting redox properties. The analysis of various nitroxide families shows that ion-substituent interactions, especially in aromatic systems, significantly influence complex stability. In particular, in acetonitrile, the hydroxylamine anion and its cation exhibit strong interactions near the nitroxyl moiety, but only if the nitroxyl is well positioned. The study also confirm that an electrostatic interaction model can predict the effects of substituents, aromaticity, and ring size on redox potentials of nitroxides. + This paper investigates the impact of solute-solvent effects on the redox potentials of nitroxides, with a focus on ionic interactions caused by the presence of electrolytes found in different environment such as batteries. The analysis of various nitroxide families shows that ion-substituent interactions, especially in aromatic systems, significantly influence complex stability. In particular, in acetonitrile, the hydroxylamine anion and its cation exhibit strong interactions near the nitroxyl moiety, but only if the nitroxyl is well positioned. The study also confirm that an electrostatic interaction model can predict the effects of substituents, aromaticity, and ring size on redox potentials of nitroxides. Concerning the impact of the environment, solute-ion interactions play a crucial role. This study reveals that moderate electrolyte concentrations stabilize charged compounds as described by the the Debye-Hückel (DH) model, and higher concentrations lead to ion-pair formation, both affecting redox properties. \end{abstract} @@ -112,12 +112,12 @@ \section{Introduction} From a phenomenological perspective, two approaches can be used: at low concentrations in electrolytes, the Debye-Hückel (DH) theory \cite{kontogeorgisDebyeHuckelTheoryIts2018,silvaDerivationsDebyeHuckel2022,silvaImprovingBornEquation2024} provides an initial estimate for interactions within an ionic liquid. While improvements have been proposed over the years to better account for ion-solvent interactions, particularly by including dipole-ion \cite{silvaImprovingBornEquation2024} and quadrupole-ion interactions \cite{slavchovQuadrupoleTermsMaxwell2014,slavchovQuadrupoleTermsMaxwell2014a,coxQuadrupolemediatedDielectricResponse2021}, there have been only a few attempts \cite{matsuiDensityFunctionalTheory2013,xiaoReorganizationEnergyElectron2013,xiaoMolecularDebyeHuckelApproach2014} to incorporate DH theory into the prediction of redox potentials. There is also a limited implementation of DH theory in the polarizable continuum model \cite{cossiInitioStudyIonic1998}. -At high concentrations (such as in ionic liquids), ion-pair formation can be expected \cite{marcusIonPairing2006}. Alongside electrostatic models \cite{krishtalikElectrostaticIonSolvent1991,lundDielectricInterpretationSpecificity2010}, various theoretical calculations of redox potentials have been performed \cite{mehtaTheoreticalInvestigationRedox2007,quAccurateModelingEffect2016,taherkhaniInvestigationIonPairs2022}, indicating that such interactions can be significant. This has also been recently investigated experimentally by Mugisa et al. \cite{mugisaEffectIonparingKinetics2024}, who assessed the impact of complexation on the thermodynamic and kinetics of the reduction of charged metal complexes. +At high concentrations (such as in ionic liquids), ion-pair formation can be expected \cite{marcusIonPairing2006}. Alongside electrostatic models \cite{krishtalikElectrostaticIonSolvent1991,lundDielectricInterpretationSpecificity2010}, various theoretical calculations of redox potentials have been performed \cite{mehtaTheoreticalInvestigationRedox2007,quAccurateModelingEffect2016,taherkhaniInvestigationIonPairs2022}, indicating that such interactions can be significant. This has also been recently investigated experimentally by Mugisa et al. \cite{mugisaEffectIonparingKinetics2024}, who assessed the impact of complexation on the thermodynamics and kinetics of the reduction of charged metal complexes. -Therefore, while seminal studies by Coote and co-workers \cite{hodgsonOneElectronOxidationReduction2007,blincoExperimentalTheoreticalStudies2008} have focused on the impact of substituents on the redox potential of nitroxides, later investigations by other groups have also considered the effect of the nature of the electrolytes and of the various nitroxide-electrolyte interactions between them, including electrostatic interactions. For example, in 2019, Wylie and co-workers \cite{wylieImprovedPerformanceAllOrganic2019a,wylieIncreasedStabilityNitroxide2019b} demonstrated that the interactions between the ionic liquid and the nitroxide can increase the redox potential by more than \SI{3}{\volt} for a well-chosen pair of electrolytes. Prior to this, Zhang \textit{et al.} focused on stabilizing the radical-ion interactions \cite{zhangInteractionsImidazoliumBasedIonic2016,zhangEffectHeteroatomFunctionality2018}, showing that the interactions between a cation and the nitroxyl group are driven by both electrostatic and dispersion effects. +Therefore, while seminal studies by Coote and co-workers \cite{hodgsonOneElectronOxidationReduction2007,blincoExperimentalTheoreticalStudies2008} have focused on the impact of substituents on the redox potential of nitroxides, later investigations by other groups have also considered the effect of the nature of the electrolytes and of the various nitroxide-electrolyte interactions, including electrostatic interactions. For example, in 2019, Wylie and co-workers \cite{wylieImprovedPerformanceAllOrganic2019a,wylieIncreasedStabilityNitroxide2019b} demonstrated that the interactions between the ionic liquid and the nitroxide can increase the redox potential by more than \SI{3}{\volt} for a well-chosen pair of electrolytes. Prior to this, Zhang \textit{et al.} focused on stabilizing the radical-ion interactions \cite{zhangInteractionsImidazoliumBasedIonic2016,zhangEffectHeteroatomFunctionality2018}, showing that the interactions between a cation and the nitroxyl group are driven by both electrostatic and dispersion effects. -In this study, the impact of solvation at low and high concentrations in electrolytes is investigated by using theoretical chemistry methods on the redox potential of various nitroxides. Since the impact of different electrolytes has already been addressed, the focus is on the effects of the skeleton bearing the nitroxyl group, categorized into five families (Fig.~\ref{fig:families}), and of the substituents. To facilitate comparison with experimental data, two solvents are considered: water and acetonitrile, for which experimental results are available \cite{morrisChemicalElectrochemicalReduction1991,goldsteinStructureActivityRelationship2006,blincoExperimentalTheoreticalStudies2008,zhangEffectHeteroatomFunctionality2018}. -Different (semi-)quantitative models are employed at each step to aid in the interpretation of the results. It should be noted that the reduced form (hydroxylamine anion) is generally not found in solution \cite{israeliKineticsMechanismComproportionation2005}, as further proton additions (depending on the pH) are involved to form the hydroxylamine or the hydroxylamonium cation. These species were not considered in this article, and thus only experimental oxidation potentials (first reaction in Fig.~\ref{fig:states}) are compared to the theoretical predictions. +In this study, the impact of solvation at low and high concentrations in electrolytes is investigated on the redox potential of various nitroxides by using theoretical chemistry methods. Since the impact of different electrolytes has already been addressed in previous studies \cite{wylieImprovedPerformanceAllOrganic2019a}, the focus is on the effects of the skeleton bearing the nitroxyl group, categorized into five families (Fig.~\ref{fig:families}), and of the substituents. To facilitate comparison with experimental data, two solvents are considered: water and acetonitrile, for which experimental results are available \cite{morrisChemicalElectrochemicalReduction1991,goldsteinStructureActivityRelationship2006,blincoExperimentalTheoreticalStudies2008,zhangEffectHeteroatomFunctionality2018}. +Different (semi-)quantitative models are employed at each step to aid in the interpretation of the results. It should be noted that the reduced form (hydroxylamine anion) is generally not found in solution \cite{israeliKineticsMechanismComproportionation2005}, as further proton additions (depending on the pH) are involved to form the hydroxylamine or the hydroxylamonium cation. Thus only experimental oxidation potentials (first reaction in Fig.~\ref{fig:states}) are compared to the theoretical predictions. This paper is organized as follows: Section \ref{sec:theory} introduces key concepts and models. The methodology used in this study is detailed in Section \ref{sec:methodo}. The results are then presented in four parts: the impact of substituents on the redox properties is discussed in Section \ref{sec:sar}, followed by an analysis of the effects of solvents in Section \ref{sec:solv}, and the influence of electrolytes in Section \ref{sec:elect}. Finally, a comparison between theoretical predictions and experimental results is provided in Section \ref{sec:exp}. Conclusions and future outlooks are presented in Section \ref{sec:conclusion}. @@ -137,18 +137,18 @@ \subsection{Redox potentials in solution} \end{equation} where $\Delta G_{r}^\star$ is the Gibbs free energy of the reduction reaction in solution, $F$ is the Faraday constant (\SI{9.648533e4}{\coulomb\per\mole}) and $n_e$ the number of electrons involved in the reduction process. Moreover, $G^\star(X^z)$ is the Gibbs free energy of $X^z$ in solution. In the rest of this article, it is considered that $G^\star(e^-) = 0$. -While there is some validity in using the adiabatic ionization/electron affinity potentials instead of the full Gibbs free energy change when the reorganization energy (in the sense of Marcus theory, referring to the geometry relaxation between two redox states) is small, allowing for precise the use of post-Hartree Fock methods \cite{namazianBenchmarkCalculationsAbsolute2010,marenichComputationalElectrochemistryPrediction2014,makosModelingAbsoluteRedox2022}, this condition is not met in the present study, which would require to evaluate geometry reorganization and solvent effects at a different level. Consequently, a coherent treatment at the DFT level is chosen for this article. +While there is some validity in using the adiabatic ionization/electron affinity potentials instead of the full Gibbs free energy change when the reorganization energy (in the sense of Marcus theory, referring to the geometry relaxation between two redox states) is small, allowing for the use of precise post-Hartree Fock methods \cite{namazianBenchmarkCalculationsAbsolute2010,marenichComputationalElectrochemistryPrediction2014,makosModelingAbsoluteRedox2022}, this condition is not met in the present study, which would require to evaluate geometry reorganization and solvent effects at a different levels. Consequently, a coherent treatment at the DFT level is chosen for this article. The comparison between relative (vs SHE) experimental and calculated reduction potential is performed using a common reference:\begin{equation} E^0_{rel}(X^z|X^{z-n_e}) = E^0_{abs}(X^z|X^{z-n_e}) - E^{0}_{abs}(\text{SHE}), \label{eq:ecalc} \end{equation} -with $E^0_{abs}(\text{SHE}) = \SI{4.28}{\volt}$ in water or \SI{4.52}{\volt} in acetonitrile \cite{marenichComputationalElectrochemistryPrediction2014}. +with $E^0_{abs}(\text{SHE}) = \SI{4.28}{\volt}$ in water and \SI{4.52}{\volt} in acetonitrile \cite{marenichComputationalElectrochemistryPrediction2014}. \subsection{Debye-Hückel theory} -From a phenomenological perspective, such $G^\star(X^z)$ values are the sum of the system's energy in vacuum, $G^0(X^z)$, and the change in (free) energy resulting from its transfer to an electrolytic solution, $\Delta G_S^\star(X^z)$. Using the thermodynamic cycle presented in Figure \ref{fig:th}, the latter can be further decomposed int four steps: $\Delta G_d + \Delta G_s$ (``d" means the discharge of in the gas phase followed by, ``c'' charge in a dielectric) accounts for purely electrostatic processes, while $\Delta G_s$ is primarily due to non-electrostatic contributions (cavitation, van der Waals forces, etc.). Finally, $\Delta G^\star_{DH}$ incorporates the effect of the` surrounding ions and is therefore crucial when dealing with electrolytes \cite{silvaImprovingBornEquation2024}. +From a phenomenological perspective, such $G^\star(X^z)$ values are the sum of the system's energy in vacuum, $G^0(X^z)$, and the change in (Gibbs free) energy resulting from its transfer to an electrolytic solution, $\Delta G_S^\star(X^z)$. Using the thermodynamic cycle presented in Figure \ref{fig:th}, the latter can be further decomposed into four steps: $\Delta G_d + \Delta G_s$ (``d" means the discharge process in the gas phase followed by, ``c'' the charging process in a dielectric) accounts for purely electrostatic processes, while $\Delta G_s$ is primarily due to non-electrostatic contributions (cavitation, van der Waals forces, etc.). Finally, $\Delta G^\star_{DH}$ incorporates the effect of the surrounding ions and is therefore crucial when dealing with electrolytes \cite{silvaImprovingBornEquation2024}. \begin{figure}[!h] @@ -183,7 +183,7 @@ \subsection{Debye-Hückel theory} \draw[blue,thick,-latex] (4.5,0) -- +(1.5,0) node[midway,above]{$\Delta G^\star_{DH}$}; \draw[blue,thick,-latex] (7,1) -- ++(0,.75) -- node[midway,above]{$-\Delta G_S^\star(X^z)$} ++(-7,0) -- ++(0,-.75); \end{tikzpicture} - \caption{Thermodynamic cycle to compute the energy of solvation of an ion, $X^z$, in a electrolyte (solvent characterized by a $\varepsilon = \varepsilon_0\,\varepsilon_r$ dielectric constant and by a ``cloud'' of other ions). $\Delta G_d$ is the Gibbs free energy change associated with the discharge of $X^z$ in gas phase, $\Delta G_s$ is the Gibbs free energy change of the solvation of $X$, $\Delta G_c$ is the Gibbs free energy change associated to the charging of $X$ in $\varepsilon$, and $\Delta G^\star_{DH}$ is the Gibbs free energy change due to the addition of the other ions.} + \caption{Thermodynamic cycle to compute the energy of solvation of an ion, $X^z$, in a electrolyte (solvent characterized by a $\varepsilon = \varepsilon_0\,\varepsilon_r$ dielectric constant and by a ``cloud'' of other ions). $\Delta G_d$ is the Gibbs free energy change associated with the discharge of $X^z$ in gas phase, $\Delta G_s$ is the Gibbs free energy change of the solvation of $X^0$, $\Delta G_c$ is the Gibbs free energy change associated to the charging of $X^0$ in $\varepsilon$, and $\Delta G^\star_{DH}$ is the Gibbs free energy change due to the addition of the other ions.} \label{fig:th} \end{figure} @@ -192,52 +192,52 @@ \subsection{Debye-Hückel theory} G^\star_{SCRF}(X) &= \Braket{\Psi(X)|{\hat{H}+\frac{1}{2}\hat{R}}|\Psi(X)} + G_{thermo}[\Psi(X)] + G_{nonelst}(X) \nonumber\\ &= E[\Psi(X)] + G_{thermo}[\Psi(X)] + \underbrace{G_{elst}[\Psi(X)] + G_{nonelst}(X)}_{\Delta G^\star_{S,SCRF}(X)}, \label{eq:scrf} \end{align} -where $\Psi$ is the wavefunction of $X$ (minimized under the application of $\hat R$, so not equal to the gas phase wavefunction), $\hat H$ is the electronic Hamiltonian, leading to the electronic energy, $E[\Psi(x)]$, $\hat R$ is the reaction field operator (generally recognized to give rise to the electrostatic contribution to the solvation energy, $G_{elst}$), $G_{thermo}$ are the thermal contributions to the Gibbs free energy derived from thermostatistic analysis, and $G_{nonelst}$ collects the non-electrostatic contributions (cavitation, dispersion, etc) to the solvation energy. Therefore, using the notation of Figure \ref{fig:th} (and assuming no change in the geometry of $X^z$), $ \Delta G^\star_{S,SCRF}(X^z) = \Delta G_d + \Delta G_s + \Delta G_{c}$. $ \Delta G^\star_{S,SCRF}(X^z)$ is, therefore, an approximation to $\Delta G^\star_S(X^z)$, since $\Delta G^\star_{DH}$ is missing. +where $\Psi(X)$ is the wavefunction of $X$ (minimized under the application of $\hat R$, so not equal to the gas phase wavefunction), $\hat H$ is the electronic Hamiltonian, leading to the electronic energy, $E[\Psi(x)]$, $\hat R$ is the reaction field operator (generally recognized to give rise to the electrostatic contribution to the solvation energy, $G_{elst}$), $G_{thermo}$ are the thermal contributions to the Gibbs free energy derived from thermostatistic analysis, and $G_{nonelst}$ collects the non-electrostatic contributions (cavitation, dispersion, etc) to the solvation energy. Therefore, using the notation of Figure \ref{fig:th} (and assuming no change in the geometry of $X^z$), $ \Delta G^\star_{S,SCRF}(X^z) = \Delta G_d + \Delta G_s + \Delta G_{c}$. $ \Delta G^\star_{S,SCRF}(X^z)$ is, therefore, an approximation to $\Delta G^\star_S(X^z)$, since $\Delta G^\star_{DH}$ is missing. -On the other hand, the Debye-Hückel (DH) theory provides another estimate of $\Delta G_{S}^\star$ \cite{bockrisModernElectrochemistryIonics1998}. Indeed, assuming that a ion $X^z$, bearing a charge $q = z\,e$ ($e$ is the elementary charge), can be approximated by a sphere of radius $a$ and that the ions in the solution are distributed in the solution according to Maxwell-Boltzmann statistics, one obtains the corresponding solvation energy as \cite{kontogeorgisDebyeHuckelTheoryIts2018,silvaTrueHuckelEquation2022,silvaImprovingBornEquation2024}:\begin{align} +On the other hand, the Debye-Hückel (DH) theory provides another estimate of $\Delta G_{S}^\star$ \cite{bockrisModernElectrochemistryIonics1998}. Indeed, assuming that an ion $X^z$, bearing a charge $q = z\,e$ ($e$ is the elementary charge), can be approximated by a sphere of radius $a$ and that the ions in the solution are distributed according to Maxwell-Boltzmann statistics, one obtains the corresponding solvation energy as \cite{kontogeorgisDebyeHuckelTheoryIts2018,silvaTrueHuckelEquation2022,silvaImprovingBornEquation2024}:\begin{align} \Delta G^\star_{S,DH}(X^z) - &= \Delta G^\star_{Born}(X^z) + \Delta G^\star_{DH}(X^z)\label{eq:adh} + &= \Delta G^\star_{Born}(X^z) + \Delta G^\star_{DH}(X^z).\label{eq:adh} \end{align} -where: +$\Delta G^\star_{Born}$ accounts for the solvation Gibbs free energy of a charged species while $ \Delta G^\star_{DH}$ describes the effect of the surrounding ions. In this theory, \begin{align} &\Delta G^\star_{DH}(X^z) = -\frac{q^2}{4\pi\varepsilon_0\varepsilon_r}\,\frac{\kappa}{(\kappa\,a)^3}\,\left[\ln(1+\kappa\,a)-\kappa\,a+\frac{1}{2}(\kappa\,a)^2\right],\label{eq:dh} \end{align} in which $\kappa$ is the inverse of the Debye screening length, defined from:\begin{equation} \kappa^2 = \sum_i^{\text{electrolytes}} \frac{n_i\,q_i^2}{\varepsilon_0\varepsilon_r\,k_B\,T}, \label{eq:kappa2} \end{equation} -where $n_i$ is the number density of ion of type $i$ ($n_i = N_i / V = c_i\,\mathcal{N}_a$ where $\mathcal{N}_a$ is the Avogadro number and $c_i$ is the concentration in ion $i$), $k_B$ is the Boltzmann constant (\SI{1.380649e-23}{\joule\per\kelvin}), and $T$ is the temperature (assumed to be \SI{298.15}{\kelvin}). $\kappa$ is proportional to the ionic strength of the solution, $I = \frac{1}{2}\sum_i c_i\,z_i^2$. -Furthermore: +$n_i$ is the number density of ion of type $i$ ($n_i = N_i / V = c_i\,\mathcal{N}_a$ where $\mathcal{N}_a$ is the Avogadro number and $c_i$ is the concentration in ion $i$), $k_B$ is the Boltzmann constant (\SI{1.380649e-23}{\joule\per\kelvin}), and $T$ is the temperature (assumed to be \SI{298.15}{\kelvin}). $\kappa$ is proportional to the ionic strength of the solution, $I = \frac{1}{2}\sum_i c_i\,z_i^2$. +Furthermore, \begin{equation} \Delta G^\star_{Born}(X^z) =\frac{q^2}{8\pi\varepsilon_0\,a}\,\left[\frac{1}{\varepsilon_r}-1\right], \label{eq:born}\\ \end{equation} The Born part [Eq.~\eqref{eq:born}] is generally dominant in solvation energies predicted by this model (Fig.~S1). - While the SCRF approach neglect $\Delta G^\star_{DH}$, the DH approach approximate $\Delta G_{d}$ and $\Delta G_{c}$ (with the Born model) and neglect $\Delta G_{s}$. Therefore, by combining Eqs.~\eqref{eq:scrf} and \eqref{eq:adh}, one defines:\begin{equation} + While the SCRF approach neglects $\Delta G^\star_{DH}$, the DH approach approximates $\Delta G_{d}$ and $\Delta G_{c}$ (with the Born model) and neglects $\Delta G_{s}$. Therefore, by combining Eqs.~\eqref{eq:scrf} and \eqref{eq:adh}, one defines:\begin{equation} G^\star(X^z) = G^\star_{SCRF}(X^z) + \Delta G^\star_{DH}(X^z), \label{eq:gtot} \end{equation} to be used in Eq.~\eqref{eq:nernst}. \subsection{Modeling the effect of the substituents on the nitroxides and its reduction potential}\label{sec:eleczhang} -The effect of the substituent(s) on the nitroxide can be described using an electrostatic model. Within this model, the interaction occurs between the dipole moment of the non-charged substituent and the charge of the nitroxide (when oxidized or reduced). Specifically, the charge-dipole interactions stabilize the oxoammonium ($>$\ce{N+=O}) if the dipole is aligned with the charge, while they destabilize the hydroxylamine ($>$\ce{N-O-}), both resulting in a decrease in the redox potential (see Fig.~\ref{fig:dipole}). Within this framework, it is therefore expected that compounds with donor substituents have lower redox potentials than acceptor substituents. +The effect of the substituent(s) on the nitroxide can be described using an electrostatic model. Within this model, the interaction occurs between the dipole moment of the non-charged substituent and the charge of the nitroxide (when oxidized or reduced). Specifically, the charge-dipole interactions stabilize the oxoammonium ($>$\ce{N+=O}) if the dipole is points outward with respect to the charge, while they destabilize the hydroxylamine ($>$\ce{N-O-}), both resulting in a decrease in the redox potential (see Fig.~\ref{fig:dipole}). Within this framework, it is therefore expected that compounds with donor substituents have lower redox potentials than those with acceptor substituents. \begin{figure}[!h] \centering \includegraphics[width=\linewidth]{Figure4} - \caption{Impact of the dipole orientation of the \ce{R} substituent on the redox potential when the dipole is oriented in the positive $x$ direction (acceptor substituent, left) or not (donor substituent, right).} + \caption{Impact of the dipole orientation of the \ce{R} substituent on the redox potential when the dipole is oriented in the positive $x$ direction (acceptor substituent, left) or in the reverse direction (donor substituent, right).} \label{fig:dipole} \end{figure} -In 2018, building upon previous work by Gryn'ova and co-workers \cite{grynovaOriginScopeLongRange2013,grynovaSwitchingRadicalStability2013}, Zhang \textit{et al.} extended and applied this model to the oxidation potential of nitroxides \cite{zhangEffectHeteroatomFunctionality2018}. They further expanded the electrostatic interaction as multipoles, truncated after the third order, to incorporate the large quadrupole moment of aromatic compounds. The following formula is used in this article: +In 2018, building upon previous work by Gryn'ova and co-workers \cite{grynovaOriginScopeLongRange2013,grynovaSwitchingRadicalStability2013}, Zhang \textit{et al.} extended and applied this model to the oxidation potential of nitroxides \cite{zhangEffectHeteroatomFunctionality2018}. So, the electrostatic interactions were not restricted to the dipolar term, but included as well the quadrupole-based third-order term to account for the large quadrupole moment of aromatic compounds. The following formula is used here: \begin{equation} U_q(r) =\frac{q}{4\pi\varepsilon_0} \left[\frac{\mu_x}{r^2} + \frac{Q_{xx}}{r^3}\right], \label{eq:Er} \end{equation} -where $q$ is the charge of the redox center, assuming a non-charged substituent. The different quantities (dipole moment, $\mu_x$, and traceless quadrupole moment, $Q_{xx}$) are evaluated through a single-point calculation on a simplified structure, using the geometry of the radical where the \ce{N-O^.} moiety is substituted by \ce{CH2}. Since the alignment of the dipole with the charge needs to be accounted for, this geometry is oriented such that the $x$-axis passes through the the carbon bearing the substituent (set as the origin) and the nitrogen. This definition differs from the original model, as Zhang and co-workers \cite{zhangEffectHeteroatomFunctionality2018} did not consider multiple positions for a given substituent. They also only focused on the oxidation, while both redox processes are considered here. +where $q \in \{-1, 1\}$ is the charge of the redox center, assuming a non-charged substituent. The different quantities (dipole moment, $\mu_x$, and traceless quadrupole moment, $Q_{xx}$) are evaluated through a single-point calculation on a simplified structure, using the geometry of the radical where the \ce{N-O^.} moiety is substituted by \ce{CH2}. Since the alignment of the dipole with the charge needs to be accounted for, this geometry is oriented such that the $x$-axis passes through the the carbon bearing the substituent (set as the origin) and the nitrogen. This definition differs from the original model, as Zhang and co-workers \cite{zhangEffectHeteroatomFunctionality2018} did not consider multiple positions for a given substituent. They also only focused on the oxidation, while both redox processes are considered here. \subsection{Impact of ion-pair formation on redox potentials} -At high concentrations of electrolytes, the formation of ion pairs in solution is expected (further insights are provided in the subsequent subsection). In this study, the electrolyte consists of a pair, \ce{AC}, of counterions, where \ce{A-} and \ce{C+} represent the anion and cation, respectively. Furthermore, two possibilities of complexation are considered: \begin{inparaenum}[(i)] +At high concentrations of electrolytes, the formation of ion pairs in solution is expected (further insights are provided in the subsequent subsection). In this study, the electrolyte consists of a pair, \ce{AC}, of counterions, where \ce{A-} and \ce{C+} represent the anion and cation, respectively. Furthermore, two possible degree of of complexation are considered: \begin{inparaenum}[(i)] \item the pairs \ce{N+A-}, \ce{N^.C+}, and \ce{N^-C+} between the oxidized, neutral and reduced states of the nitroxide (with a complexation equilibrium constant $K_{x1}$, $x=0$, 1, and 2 for oxidized, radical, and reduced states, respectively), with their corresponding counterions (\ce{A-} and \ce{C+}, respectively), and then \item complexation with the \ce{AC} pair (with an equilibrium constant $K_{x2}$), which occurs when the concentration of electrolyte becomes large \cite{wylieImprovedPerformanceAllOrganic2019a}. \end{inparaenum} @@ -275,13 +275,13 @@ \subsection{Impact of ion-pair formation on redox potentials} \node[below of=N2cc] (N3cc) {\ce{N^-AC}}; \arrwy{N3cc.east}{N3.west}{$K_{22}$} \end{tikzpicture} - \caption{Scheme illustrating the different possible reactions: \ce{N+} and \ce{N-} are the oxidized and reduced forms of a given nitroxide, \ce{N^.}, and \ce{C+} and \ce{A-} are the countercation and anion coming from electrolyte, respectively. Horizontal arrows are ion-pairing reactions (with the \ce{AC} pair in left, with a single counterion in right), while vertical arrows are electrochemical reactions.} + \caption{Scheme illustrating the different reactions: \ce{N+} and \ce{N-} are the oxidized and reduced forms of a given nitroxide, \ce{N^.}, and \ce{C+} and \ce{A-} are the countercation and anion coming from electrolyte, respectively. Horizontal arrows are ion-pairing reactions (with the \ce{AC} pair in left, with a single counterion in right), while vertical arrows are electrochemical reactions.} \label{fig:cip} \end{figure} Following Mugisa and co-workers \cite{mugisaEffectIonparingKinetics2024}, a quantitative model is derived from Fig.~\ref{fig:cip}, owing that: \begin{inparaenum}[(i)] \item the total concentrations of the redox-active species are given by $c_{ox} = [\ce{N+}] + [\ce{N+A-}] + [\ce{N+AC}]$, $c_{rad} = [\ce{N^.}] + [\ce{N^.C+}] + [\ce{N^.AC}]$, and $c_{red} = [\ce{N-}] + [\ce{N^-C+}] + [\ce{N^-AC}]$, - \item due to electroneutrality, $ [\ce{C+}] = [\ce{A-}] $, + \item due to electroneutrality, $ [\ce{C+}] = [\ce{A-}]$ initially, \item the electrolyte is present in large amounts compared to redox-active species, hence $[X] = [\ce{C+}] = [\ce{A-}] $ is constant ($[X]$ represents the electrolyte concentration), \item at the equilibrium of redox reactions, $c_{ox} = c_{rad}$ (for $K_1$) and $c_{red} = c_{rad}$ (for $K_2$), and \item the redox potentials of the ion-pair complexes are smaller than the one of the free species. @@ -290,7 +290,7 @@ \subsection{Impact of ion-pair formation on redox potentials} E^f_{abs}(\ce{N+|N^.}) &= E^0_ {abs}(\ce{N+|N^.})+\frac{RT}{F}\,\ln\left[\frac{1+K_{11}\,[X]+K_{12}\,[X]^2}{1+K_{01}\,[X]+K_{02}\,[X]^2}\right],\label{eq:ef1}\\ E^f_{abs}(\ce{N^.|N-}) &= E^0_ {abs}(\ce{N^.|N-})+\frac{RT}{F}\,\ln\left[\frac{1+K_{21}\,[X]+K_{22}\,[X]^2}{1+K_{11}\,[X]+K_{12}\,[X]^2}\right],\label{eq:ef2} \end{align} -in which $K_{ij}= \exp\left[-\frac{\Delta G_{cplx}^\star}{RT}\right]$, where $\Delta G_{cplx}^\star$ is the Gibbs free energy change [computed with Eq.~\eqref{eq:gtot}] for a given complexation reaction. +in which $K_{ix}= \exp\left[-\frac{\Delta G_{cplx}^\star}{RT}\right]$, where $\Delta G_{cplx}^\star$ is the Gibbs free energy change [computed with Eq.~\eqref{eq:gtot}] for a given complexation reaction. An example of the impact of the electrolytes on $E^f_{abs}$ is provided in Fig.~S2: to have a significant impact ($>\SI{0.1}{\volt}$), two conditions must be met: \begin{inparaenum}[(i)] \item the complexation constant must be large, and @@ -361,8 +361,8 @@ \subsection{Model for the ion-pair formation} \subsection{Counterion as a fictitious particle} -Alternatively, Matsui et al. \cite{matsuiDensityFunctionalTheory2013} proposed that the impact of counterions on the redox potential of $X^z$ could be described using a single fictitious particle, $P^{-z}$, with a radius $a=fa_0$ proportional to that of the redox species, $a_0$ (considered constant for all oxidation states of $X$), and bearing the appropriate counter-charge, $-q$. They suggested evaluating the energy of this particle using a modified Born approach [Eq.~\eqref{eq:born}]:\begin{align} - &\Delta G^\star_{Mat}(P^z) = \frac{1}{4\pi\epsilon_0}\, \frac{q^2}{2fa_0}\,\left[\frac{1}{\varepsilon_r}-1\right]\,\erf(\mu\,a_0\,|q|), +Alternatively, Matsui et al. \cite{matsuiDensityFunctionalTheory2013} proposed that the impact of counterions on the redox potential of $X^z$ could be described using a single fictitious particle, $P^{-z}$, with a radius $a=fa_0$ proportional to that of the redox species, $a_0$ (considered constant for all oxidation states of $X$), and bearing the appropriate counter-charge, $-q$. They suggested evaluating the Gibbs free energy of this particle using a modified Born approach [Eq.~\eqref{eq:born}]:\begin{align} + &\Delta G^\star_{Matsui}(P^z) = \frac{1}{4\pi\epsilon_0}\, \frac{q^2}{2fa_0}\,\left[\frac{1}{\varepsilon_r}-1\right]\,\erf(\mu\,a_0\,|q|), \end{align} where $f$ and $\mu$ are method-dependent factors, the latter being described in Ref.~\citenum{matsuiDensityFunctionalTheory2013} as a parameter to induce a screening effect near the redox center. @@ -376,14 +376,15 @@ \subsection{Counterion as a fictitious particle} \end{array} \label{eq:corr} \end{equation*} and therefore,\begin{align} - E^{Mat}_{abs}(X^z|X^{z-n_e}) &= E_{abs}^0(X^{z}|X^{z-n_e}) -\frac{1}{n_e\,F}\,[\Delta G^\star_{Mat}(P^{n_e-z}) - \Delta G^\star_{Mat}(P^{-z})] \nonumber\\ - &= E_{abs}^0(X^{z}|X^{z-n_e}) -\frac{\Delta\Delta G^\star_P}{n_e\,F}, \label{eq:matsui} + E^{Matsui}_{abs}(X^z|X^{z-n_e}) &= E_{abs}^0(X^{z}|X^{z-n_e})\nonumber\\ + &\hspace{2em}-\frac{1}{n_e\,F}\,[\Delta G^\star_{Matsui}(P^{n_e-z}) - \Delta G^\star_{Matsui}(P^{-z})] \nonumber\\ + &= E_{abs}^0(X^{z}|X^{z-n_e}) -\frac{\Delta\Delta G^\star_{Matsui}}{n_e\,F}, \label{eq:matsui} \end{align} where:\begin{align*} - \Delta\Delta G^\star_{Mat}&=\frac{1}{4\pi\epsilon_0}\frac{1}{2fa_0}\,\left[\frac{1}{\varepsilon_r}-1\right]\times\nonumber\\ - &\left[ (n_e-q)^2\,\erf(\mu\,a_0\,|n_e-q|)-q^2\,\erf(\mu\,a_0\,|q|)\right]. + \Delta\Delta G^\star_{Matsui}&=\frac{1}{4\pi\epsilon_0}\frac{1}{2fa_0}\,\left[\frac{1}{\varepsilon_r}-1\right]\times\nonumber\\ + &\hspace{2em}\left[ (n_e-q)^2\,\erf(\mu\,a_0\,|n_e-q|)-q^2\,\erf(\mu\,a_0\,|q|)\right]. \end{align*} -Matsui and co-workers proposed to find the parameter $f$ and $\mu$ so that they minimize the difference between $E^{Mat}_{rel}(X^z|X^{z-n_e})$ [from Eq.~\eqref{eq:ecalc}] and experimental $E^0_{rel}(X^z|X^{z-n_e})$ values. Note that therefore they consider that $ E^{0}_{abs}(\text{SHE})$ is a third fitting parameter. +Matsui and co-workers proposed to find the parameters $f$ and $\mu$ so that they minimize the difference between $E^{Matsui}_{rel}(X^z|X^{z-n_e})$ [from Eq.~\eqref{eq:ecalc}] and experimental $E^0_{rel}(X^z|X^{z-n_e})$ values. Note that therefore they consider that $ E^{0}_{abs}(\text{SHE})$ is a third fitting parameter. \section{Compounds and computational chemistry aspects} \label{sec:methodo} @@ -396,12 +397,11 @@ \section{Compounds and computational chemistry aspects} \label{sec:methodo} \label{fig:nitroxides} \end{figure} -Geometry optimizations and subsequent vibrational frequency calculations were performed at the density functional theory (DFT) level with the $\omega$B97X-D exchange-correlation functional (XCF), with the 6-311+G(d) basis set. The solvent effects are included using the SMD approach \cite{marenichUniversalSolvationModel2009} approach. All calculations were performed with Gaussian 16 C02 \cite{g16}. With other possible candidates, this XCF have been demonstrated to provide reliable geometries (see Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}) and redox potentials \cite{flores-leonarFurtherInsightsDFT2017,maierG4AccuracyDFT2020} (see also Fig.~S4). For compound \textbf{1}-\textbf{54}, the geometries obtained by Hodgson et al.~\cite{hodgsonOneElectronOxidationReduction2007} have been used as a starting point, taking advantage of their extensive conformational search. All radical forms are considered to have a doublet ground state [$\braket{S^2}=\frac{3}{4}$]. Then, the same calculations were performed in acetonitrile for the subset of compounds for which experimental redox potentials are available (Fig.~\ref{fig:nitroxides}). The geometries of the complexes (Fig.~\ref{fig:cip}) were then optimized at the same level of approximation, for which different positions of the counterions have been assessed (\textit{vide infra}). Finally, to study the influence of the substituent on the redox potential with the model presented in Section \ref{sec:eleczhang}, single point calculation are performed at the $\omega$B97X-D/6-311+G(d) level in gas phase, using the optimized geometries of the radical states of each nitroxides (in water) in which the $>$\ce{N-O^.} moiety is substituted by \ce{CH_2} (the rest of the geometry is kept fixed). +Geometry optimizations and subsequent vibrational frequency calculations were performed at the density functional theory (DFT) level with the $\omega$B97X-D exchange-correlation functional (XCF), and with the 6-311+G(d) basis set. The solvent effects are included using the SMD approach \cite{marenichUniversalSolvationModel2009} approach. All calculations were performed with Gaussian 16 C02 \cite{g16}. With other possible candidates, this XCF has been demonstrated to provide reliable geometries (Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}) and redox potentials \cite{flores-leonarFurtherInsightsDFT2017,maierG4AccuracyDFT2020} (see also Fig.~S4). For compound \textbf{1}-\textbf{54}, the geometries obtained by Hodgson et al.~\cite{hodgsonOneElectronOxidationReduction2007} have been used as starting point, taking advantage of their extensive conformational search. All radical forms are considered to have a doublet ground state [$\braket{S^2}=\frac{3}{4}$]. Then, the same calculations were performed in acetonitrile for the subset of compounds for which experimental redox potentials are available (Fig.~\ref{fig:nitroxides}). The geometries of the different complexes (Fig.~\ref{fig:cip}) were then optimized at the same level of approximation, for which different positions of the counterions have been assessed (\textit{vide infra}). Finally, to study the influence of the substituent on the redox potential with the model presented in Section \ref{sec:eleczhang}, single point calculations are performed at the $\omega$B97X-D/6-311+G(d) level in gas phase, using the optimized geometries of the radical states of each nitroxides (in water) in which the $>$\ce{N-O^.} moiety is substituted by \ce{CH_2} (the rest of the geometry is kept fixed). -Since all thermochemical quantities are $\kappa$-dependent, analyses were performed using custom Python scripts. When required (e.g., in Eq.~\eqref{eq:dh}), the value of $a$ (the radius of the solute cavity) is taken as half the largest distance between any pair of two atoms in the molecule. Although this is an approximation, it provides a consistent method to treat all molecules proportionally to their size and it is consistent with other publications \cite{matsuiDensityFunctionalTheory2013}. Furthermore, a value of $\varepsilon_{r,water}=80$ for water and $\varepsilon_{r,acetonitrile}=35$ for acetonitrile is used. These relative permittivities correspond to those of the pure solvents and are known to be lower for the respective electrolyte solutions \cite{silvaTrueHuckelEquation2022}. These variations can be substantial; for example, $\varepsilon_r \approx 70$ for a solution containing \SI{1}{\mol\per\kilo\gram} of \ce{NaCl} in water \cite{kontogeorgisDebyeHuckelTheoryIts2018, silvaTrueHuckelEquation2022}, but they depend on the nature of the electrolyte, so it was not considered here. +Since all thermochemical quantities are $\kappa$-dependent, analyses were performed using custom Python scripts. When required (e.g., in Eq.~\eqref{eq:dh}), the value of $a$ (the radius of the solute cavity) is taken as half the largest distance between any pair of two atoms in the molecule. Although this is an approximation, it provides a consistent method to treat all molecules proportionally to their size and this approach is consistent with other publications \cite{matsuiDensityFunctionalTheory2013}. Furthermore, a value of $\varepsilon_{r,water}=80$ for water and $\varepsilon_{r,acetonitrile}=35$ for acetonitrile is used. These relative permittivities correspond to those of the pure solvents and are known to be lower for the respective electrolyte solutions \cite{silvaTrueHuckelEquation2022}. These variations can be substantial; for example, $\varepsilon_r \approx 70$ for a solution containing \SI{1}{\mol\per\kilo\gram} of \ce{NaCl} in water \cite{kontogeorgisDebyeHuckelTheoryIts2018, silvaTrueHuckelEquation2022}, but they depend on the nature of the electrolyte, so it was not considered here. - -Unless otherwise mentioned, the value of $\kappa^2$ is obtained assuming $c_{ox} = c_{rad} = c_ {red} = \SI{e-3}{\mole\per\liter}$, a prototypical concentration in measurements. +The value of $\kappa^2$ [Eq.~\eqref{eq:kappa2}] is obtained assuming $c_{ox} = c_{rad} = c_ {red} = \SI{e-3}{\mole\per\liter}$, a prototypical concentration in measurements. \section{Results and discussion} \label{sec:results} @@ -414,7 +414,7 @@ \subsection{Structure-activity relationships} \label{sec:sar} \begin{figure}[!h] \centering \includegraphics[width=.9\linewidth]{Figure8} - \caption{Relationship between the absolute oxidation and reduction potentials of nitroxides, as computed at the $\omega$B97X-D/6-311+G(d) level in water (SMD), with a concentration in electrolyte, $[\ce{X}]=\SI{0}{\mole\per\liter}$. The color indicates the family (Fig.~\ref{fig:families}). For each of them, an ellipse is drawn, centered on the mean potential value among the family, whom width and height are given by the standard deviations.} + \caption{Relationship between the absolute oxidation and reduction potentials of nitroxides, as computed at the $\omega$B97X-D/6-311+G(d) level in water (SMD), with a concentration in electrolyte, $[\ce{X}]=\SI{0}{\mole\per\liter}$. The color indicates the family (Fig.~\ref{fig:families}). For each of them, an ellipse is drawn, centered on the mean potential value among the family, which width and height are given by the standard deviations.} \label{fig:family} \end{figure} @@ -429,17 +429,17 @@ \subsection{Structure-activity relationships} \label{sec:sar} To elucidate these effects, attempts are made to correlate both potentials with Hammett constants for P5O and P6O, but the correlations are found to be very weak, especially for reduction (Fig.~S5). -The electrostatic interaction model [Eq.~\eqref{eq:Er}] provides more insights. Results are presented in Fig.~\ref{fig:corr} (see also Table S4). It should be noted that this model fails to account for the effect of substituting methyl groups with ethyl groups. Moreover, including the disubstituted compounds (e.g., \textbf{9}, \textbf{10}, \textbf{20}, ...) worsens the correlation ($R^2 \sim 0.5$ and 0.3 for oxidation and reduction, respectively). Compounds \textbf{56} and \textbf{58} remain outliers for reduction. Therefore, all three sets of compounds are treated as outliers in the following discussion. -Though the correlation is poorer for reduction than for oxidation (probably because the electron delocalization means nitrogen is not the atom that should be used to define the origin in that case), this model helps explain the general trends. For instance, the increase in oxidation (and reduction) potential for aromatic compounds correlates with an increase in quadrupole moment ($Q_{xx} > \SI{5}{\elementarycharge\bohr\squared}$ for most members of IIO or APO). Additionally, modifications due to donor/acceptor substituents are linked to changes in the dipole moment. For example, aromatic compounds with \ce{NH2} as a substituent (\textit{e.g.}, \textbf{51}) are characterized by $\mu_{x} < 0$, which increases for compounds with \ce{COOH} (\textit{e.g.}, \textbf{39}) or \ce{NO2} (\textit{e.g.}, \textbf{54}). Furthermore, members of P5O generally present a smaller value of $U_r$ than P6O (\textit{e.g.}, \textbf{17} versus \textbf{5}), which correlates with the increase in oxidation potential observed between these two families. The same trend is observed between APO and IIO. +The electrostatic interaction model [Eq.~\eqref{eq:Er}] provides more insights. Results are presented in Fig.~\ref{fig:corr} (see also Table S4). It should be noted that this model fails to account for the effect of substituting methyl groups with ethyl groups. Moreover, including the disubstituted compounds (e.g., \textbf{9}, \textbf{10}, \textbf{20}, ...) worsens the correlation ($R^2 \sim 0.5$ and 0.3 for oxidation and reduction, respectively). Compounds \textbf{56} and \textbf{58} remain outliers for reduction. Therefore, all these sets of compounds are treated as outliers in the following discussion. +Though the correlation is poorer for reduction than for oxidation (probably because the electron delocalization means that the nitrogen atom is not the atom that should be used to define the origin in that case), this model helps explaining the general trends. For instance, the increase in oxidation (and reduction) potential for aromatic compounds correlates with an increase in quadrupole moment ($Q_{xx} > \SI{5}{\elementarycharge\bohr\squared}$ for most members of IIO or APO). Additionally, modifications due to donor/acceptor substituents are linked to changes in the dipole moment. For example, aromatic compounds with \ce{NH2} as a substituent (\textit{e.g.}, \textbf{51}) are characterized by $\mu_{x} < 0$, which increases for compounds with \ce{COOH} (\textit{e.g.}, \textbf{39}) or \ce{NO2} (\textit{e.g.}, \textbf{54}). Furthermore, members of P5O generally present a smaller value of $U_q$ than P6O (\textit{e.g.}, \textbf{17} versus \textbf{5}), which correlates with the increase in oxidation potential observed between these two families. The same trend is observed between APO and IIO. This model also accounts for some effects due to the position of the substituent (see, e.g., \textbf{49}-\textbf{51}), which was not the case with the original model by Zhang and co-workers (resulting in weak correlations, $R^2 \leq 0.3$). -Finally, although this model is not directly applicable to positively charged substituents (\textbf{11}, \textbf{21}, and \textbf{35}), for which the dipole and higher multipole moments are ill-defined, the only term of Eq.~\eqref{eq:Er} would be $(q\,q')/r$ (where $q'$ is the charge of the substituent), resulting in a destabilizing interaction with \ce{N+} and \ce{N^.}, while stabilizing \ce{N-} (see Fig.~\ref{fig:dipole}), which correlates well with the increase in oxidation and reduction potentials for these compounds. +Finally, although this model is not directly applicable to positively charged substituents (\textbf{11}, \textbf{21}, and \textbf{35}), for which the dipole and higher multipole moments are ill-defined, the only term of Eq.~\eqref{eq:Er} would be $(q\,q')/r$ (where $q'$ is the charge of the substituent), resulting in a destabilizing interaction with \ce{N+} and \ce{N^.}, while stabilizing \ce{N-} (Fig.~\ref{fig:dipole}), which correlates well with the increase in oxidation and reduction potentials for these compounds. \begin{figure}[!h] \centering \includegraphics[width=\linewidth]{Figure9} -\caption{Relationship between absolute oxidation (top) and reduction (bottom) potentials of nitroxides and the electrostatic potential between the redox center ($>$\ce{N-O^.}) and the substituent, as computed using \eqref{eq:Er} at the $\omega$B97X-D/6-311+G(d) level in water (SMD), in the limit of $[\ce{X}]=\SI{0}{\mole\per\liter}$. Triangular marker ($\blacktriangle$) indicates results that are excluded from the correlation (see text).} +\caption{Relationship between absolute oxidation (top) and reduction (bottom) potentials of nitroxides and the electrostatic potential between the redox center ($>$\ce{N-O^.}) and the substituent, as computed using Eq.~\eqref{eq:Er} at the $\omega$B97X-D/6-311+G(d) level in water (SMD), in the limit of $[\ce{X}]=\SI{0}{\mole\per\liter}$. Triangular marker ($\blacktriangle$) indicates results that are excluded from the correlation (see text).} \label{fig:corr} \end{figure} @@ -447,9 +447,12 @@ \subsection{Structure-activity relationships} \label{sec:sar} \subsection{Impact of the solvent} \label{sec:solv} -The solvent exerts a significant stabilizing effect on the charge. In the gas phase (Table S2), $E^0_{abs}(\ce{N+}|\ce{N^.})$ values are around \SI{7}{\volt} (and up to \SI{10}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}), while $E^0_{abs}(\ce{N^.}|\ce{N-})$ values are approximately \SI{0.3}{\volt} (around \SI{3}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}). The modifications due to the solvent, primarily resulting from the stabilization of the charges (as indicated by the Born model), but also including moderate geometry changes, amount to about \SI{2}{\volt} (\SI{200}{\kilo\joule\per\mole}). +The solvent exerts a significant stabilizing effect on the charge. In the gas phase (Table S2), $E^0_{abs}(\ce{N+}|\ce{N^.})$ values are around \SI{7}{\volt} (and up to \SI{10}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}), while $E^0_{abs}(\ce{N^.}|\ce{N-})$ values are approximately \SI{0.3}{\volt} (around \SI{3}{\volt} for \textbf{11}, \textbf{21}, and \textbf{35}). The modifications due to the solvent, primarily resulting from the stabilization of the charges (as indicated by the Born model), but also including moderate geometry changes, amount to about \SI{2}{\volt} (which corresponds to an free Gibbs energy change of \SI{200}{\kilo\joule\per\mole}). + +The difference between redox potentials computed in water and acetonitrile is reported in Fig.~\ref{fig:watvsac} (see also Table S3). The oxidation potential is minimally affected, while the reduction potentials show a disparity greater than \SI{0.5}{\volt}. Indeed, while the linear regressions are similar in both case (in particular, the slope is of 1.2), the lower values for the reduction potential results in large differences. + +In a first approximation, the Born model [Eq.~\eqref{eq:born}] can explain the electrostatic contribution to these changes. For oxidation, the change in potentials between the two solvents, $E^0_{\text{acetonitrile}} - E^0_{\text{water}}$, is proportional to $\varepsilon_{r,\text{acetonitrile}}^{-1} - \varepsilon_{r,\text{water}}^{-1}$ (about \SI{0.1}{\volt} for $a = \SI{3}{\angstrom}$ using Eq.~\eqref{eq:born}), which is positive (assuming \ce{N^.} is neutral, which is valid for the subset of compounds considered). For reduction, it is proportional to $\varepsilon_{r,\text{water}}^{-1} - \varepsilon_{r,\text{acetonitrile}}^{-1}$, having the same magnitude but opposite sign. However, the non-electrostatic contribution to the solvation energies must also be considered. The cavitation term is expected to be larger in water due to hydrogen bonding than in acetonitrile \cite{marenichUniversalSolvationModel2009}. In this case, both effects are of the same order of magnitude and they counterbalance each other in the case of oxidation, while they add together in the case of reduction. -The difference between redox potentials computed in water and acetonitrile is reported in Fig.~\ref{fig:watvsac} (see also Table S3). The oxidation potential is minimally affected, while the reduction potentials show a disparity greater than \SI{0.5}{\volt}. In a first approximation, the Born model [Eq.~\eqref{eq:born}] can account for these findings: for oxidation, the change in potentials in the two solvents, $E^0_{acetonitrile} - E^0_{water}$, is proportional to $\varepsilon_{r,acetonitrile}^{-1} - \varepsilon_{r,water}^{-1}$ (about \SI{0.1}{\volt} for $a = \SI{3}{\angstrom}$ using Eq.~\eqref{eq:born}), which is positive (assuming \ce{N^.} is neutral, which is valid for the subset of compounds considered). For reduction, it is proportional to $\varepsilon_{r,water}^{-1} - \varepsilon_{r,acetonitrile}^{-1}$, having the same magnitude but opposite sign. However, the non-electrostatic contribution to the solvation energies must also be considered: the cavitation term is expected to be larger in water (due to hydrogen bonding) than in acetonitrile \cite{marenichUniversalSolvationModel2009}. This effect seems to dominate. Since the impact of both corrections (to which changes in geometry should be added) is nearly systematic for the set of compounds considered here, similar trends (in terms of the impact of substituents) between redox potentials in water and acetonitrile are observed. @@ -465,7 +468,7 @@ \subsection{Impact of the solvent} \label{sec:solv} \clearpage \subsection{Impact of the electrolytes} \label{sec:elect} -So far, the concentration of electrolyte, $[X]$, has been maintained at zero. To evaluate its impact on the redox potentials, the DH correction itself, Eq.~\eqref{eq:dh}, is initially examined in Fig.~\ref{fig:DH}. As anticipated due to the amplitude of the charges involved ($z=\pm 1$), it remains small within the concentration range considered here (a few tenths of millivolts for $[X] \leq \SI{1}{\mole\per\liter}$ and larger in acetonitrile), increasing with $[X]$. Its sign differs between oxidation and reduction potentials, since it only affects the charged species, and while \ce{N+} is a reactant, \ce{N-} a product. Additionally, it decrease for compounds belonging to the IIO and APO families (as they are larger molecules with larger $a$), while it is amplified for species with a net positive charge (\textbf{11}, \textbf{21}, \textbf{35}), for which the correction for oxidation and reduction potentials is negative. +So far, the concentration of electrolyte, $[X]$, has been maintained at zero. To evaluate its impact on the redox potentials, the DH correction itself, Eq.~\eqref{eq:dh}, is initially examined in Fig.~\ref{fig:DH}. As anticipated due to the amplitude of the charges involved ($z=\pm 1$), it remains small within the concentration range considered here (a few tenths of millivolts for $[X] \leq \SI{1}{\mole\per\liter}$ and larger in acetonitrile), increasing with $[X]$. Its sign differs between oxidation and reduction potentials, since it only affects the charged species, and while \ce{N+} is a reactant, \ce{N-} a product. Additionally, it decreases for compounds belonging to the IIO and APO families (as they are larger molecules with larger $a$), while it is amplified for species with a net positive charge (\textbf{11}, \textbf{21}, \textbf{35}), for which the correction for oxidation and reduction potentials is negative. \begin{figure}[!b] @@ -486,11 +489,11 @@ \subsection{Impact of the electrolytes} \label{sec:elect} \begin{figure}[!h] \centering \includegraphics[width=.8\linewidth]{Figure12} -\caption{$\Delta G^\star_{cplx}$ of compound \textbf{4} as a function of counterion poisition. The distance between the redox center (the nitrogen in the oxidized form, $>$\ce{N+=O}, or the oxygen in the reduced form, $>$\ce{N-O-}) and the counterion are also given. Calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water (black) and acetonitrile (blue) using SMD, in the limit of $[X]=\SI{0}{\mole\per\liter}$.} +\caption{$\Delta G^\star_{cplx}$ of compound \textbf{4} as a function of counterion position. The distance between the redox center (the nitrogen in the oxidized form, $>$\ce{N+=O}, or the oxygen in the reduced form, $>$\ce{N-O-}) and the counterion are also given. Calculations were performed at the $\omega$B97X-D/6-311+G(d) level in water (black) and acetonitrile (blue) using SMD, in the limit of $[X]=\SI{0}{\mole\per\liter}$.} \label{fig:pos-anion} \end{figure} -In both solvents, the radical (\ce{N^.}) interacts with \ce{C+} (\textit{i.e.}, \ce{NMe4+}) in the first position, near $>$\ce{N-O^.} \cite{zhangEffectHeteroatomFunctionality2018}. Then, in water, the complexation energies for the \ce{N+A-} and \ce{N^-C+} pairs are positive and significant. The difference in complexation energies between the two positions is generally small (a few \si{\kilo\joule\per\mole}), but the second position is favored in most of the case. Interestingly, this type of interaction corresponds to a larger nitroxide-to-counterion distance, indicating a smaller electrostatic interaction between the redox center and the counterion and suggesting that the substituent also plays a role in lowering the complexation energy. Another contributing factor is the quadrupole-ion interaction due to the aromatic moieties present in compounds from the IIO and APO families, which is particularly important in the \ce{N^-C+} pair. Here, the difference in energy between the two positions is more pronounced. +In both solvents, the radical (\ce{N^.}) interacts with \ce{C+} (\textit{i.e.}, \ce{NMe4+}) in the first position, near $>$\ce{N-O^.} \cite{zhangEffectHeteroatomFunctionality2018}. Then, in water, the complexation energies for the \ce{N+A-} and \ce{N^-C+} pairs are positive and significant. The difference in complexation energies between the two positions is generally small (a few \si{\kilo\joule\per\mole}), but the second position is favored in most of the cases. Interestingly, this type of interaction corresponds to a larger nitroxide-to-counterion distance, indicating a smaller electrostatic interaction between the redox center and the counterion and suggesting that the substituent also plays a role in lowering the complexation energy. Another contributing factor is the quadrupole-ion interaction due to the aromatic moieties present in compounds from the IIO and APO families, which is particularly important in the \ce{N^-C+} pair. Here, the difference in energy between the two positions is more pronounced. In acetonitrile, however, the lower dielectric constant leads to a reduced charge screening. A significant decrease of the complexation energy (10 to \SI{20}{\kilo\joule\per\mole}) is observed for the \ce{N^-C+} pair when \ce{C+} is near the nitroxyl group (first position). This aligns with the model for ion pair formation [Eq.~\eqref{eq:pair}], particularly when considering the impact of the ratio between the radii of the cavities. Since \ce{NMe4+} has a larger radius (\SI{2.1}{\angstrom}) than \ce{BF4-} (\SI{1.5}{\angstrom}), the former is closer in size to nitroxides ($>$\SI{3}{\angstrom}). The second position remains generally favored in the \ce{N+A-} pair, though only by a few \si{\kilo\joule\per\mole}. @@ -500,7 +503,7 @@ \subsection{Impact of the electrolytes} \label{sec:elect} \begin{figure}[!h] \centering \includegraphics[width=\linewidth]{Figure13} - \caption{Value of the cologarithm ($pK = -\log_{10}K$) of the complexation equilibrium constants: $pK_{01}$ (triangular markers, $\bullet$), $pK_{11}$ (round markers, $\blacktriangle$), and $pK_{21}$ (square markers, $\blacksquare$), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is for visualization purposes.} + \caption{Value of the cologarithm ($pK = -\log_{10}K$) of the complexation equilibrium constants: $pK_{01}$ (round markers, $\bullet$), $pK_{11}$ (triangular markers, $\blacktriangle$), and $pK_{21}$ (square markers, $\blacksquare$), as computed at the $\omega$B97X-D/6-311+G(d) level in water (top) and acetonitrile (bottom) using SMD and $[X]=\SI{1}{\mole\per\liter}$. The dashed line is for visualization purposes.} \label{fig:Kx1} \end{figure} @@ -535,13 +538,13 @@ \subsection{Impact of the electrolytes} \label{sec:elect} \label{fig:Kx2} \end{figure} -As expected, the equilibrium constants are smaller by about four orders of magnitude ($\Delta G^\star_{cplx} \sim \SI{40}{\kilo\joule\per\mole}$) than those previously discussed. In water, the general order is $K_{22} \leq K_{02} < K_{12}$. However, for many compounds in the IIO and APO families, $K_{02}$ is larger than $K_{22}$, attributed to the interaction between the \ce{NMe4+} cation and the aromatic moiety present in these compounds. In acetonitrile, the \ce{NAC^-} complexes are again more stable than the others, consistent with previous observations \cite{wylieImprovedPerformanceAllOrganic2019a}. Thus, the dielectric constant significantly impacts the equilibrium constants of these ion-triplets. This is further confirmed by the observation that the stabilization of \ce{N^.AC} is less pronounced in this study than in Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}, which employed a solvent with an even lower dielectric constant. +As expected, the equilibrium constants are smaller by about four orders of magnitude ($\Delta G^\star_{cplx} \sim \SI{40}{\kilo\joule\per\mole}$) than those previously discussed. In water, the general order is $K_{22} \leq K_{02} < K_{12}$. However, for many compounds in the IIO and APO families, $K_{02}$ is larger than $K_{22}$, which is attributed to the interaction between the \ce{NMe4+} cation and the aromatic moiety present in these compounds. In acetonitrile, the \ce{NAC^-} complexes are again more stable than the others, consistently with previous observations \cite{wylieImprovedPerformanceAllOrganic2019a}. Thus, the dielectric constant significantly impacts the equilibrium constants of these ion-triplets. This is further confirmed by the observation that the stabilization of \ce{N^.AC} is less pronounced in this study than in Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}, which employed a solvent with an even lower dielectric constant. \clearpage \subsection{Comparison to experiment} \label{sec:exp} -A comparison between theoretical (including all corrections discussed above) and experimental oxidation potentials is shown in Fig.~\ref{fig:expvstheo}. Excluding compounds bearing an \ce{NH2} group (so, \textbf{57} in water, and \textbf{4}, \textbf{51}, and \textbf{59} in acetontrile) results in an excellent linear correlation ($R^2 \sim 0.9$). The fit indicates that the method used in this paper tends to overestimate the oxidation potentials in water and systematically underestimate them in acetonitrile, with a large mean average error (MAE). This suggests that the value for $E^0_{abs}(\text{SHE})$ might not be appropriate in this solvent. +A comparison between theoretical (including all corrections discussed above) and experimental oxidation potentials is shown in Fig.~\ref{fig:expvstheo}. Excluding compounds bearing a \ce{NH2} group (so, \textbf{57} in water, and \textbf{4}, \textbf{51}, and \textbf{59} in acetonitrile) results in an excellent linear correlation ($R^2 \sim 0.9$). The fit indicates that the method used in this paper tends to slightly overestimate the oxidation potentials (by 0.05 to \SI{0.1}{\volt}) in water and systematically underestimate them in acetonitrile (by 0.3 to \SI{0.45}{\volt}), with a larger mean average error (MAE). This suggests that the value for $E^0_{abs}(\text{SHE})$ might not be appropriate in this solvent. \begin{figure}[!h] \centering @@ -550,11 +553,11 @@ \subsection{Comparison to experiment} \label{sec:exp} \label{fig:expvstheo} \end{figure} -Note that the computed potentials for compounds with \ce{NH2} are higher (by more than $\SI{0.1}{\volt}$) than the fit line, suggesting that the amine group might be protonated under the experimental measurement conditions. This is indeed consistent with the other cases (\textit{e.g.}, \textbf{25} vs \textbf{35}) discussed in Section \ref{sec:sar}. +Note that the computed potentials for compounds with the \ce{NH2} substituent are higher (by more than $\SI{0.1}{\volt}$) than the fit line, suggesting that the amine group might be protonated under the experimental measurement conditions. This is indeed consistent with the other cases (\textit{e.g.}, \textbf{25} vs \textbf{35}) discussed in Section \ref{sec:sar}. The impact of the different corrections (see Fig.~S7) is to decrease the potential, mainly due to the DH correction (given the value of the complexation equilibrium constants for the oxidation reaction, see Table \ref{tab:Kx1}), as seen in Fig.~\ref{fig:DH}. While this improves the slope and MAE in water, the opposite effect is observed in acetonitrile. -For comparison, the model by Matsui and co-workers \cite{matsuiDensityFunctionalTheory2013} is used in Fig.~\ref{fig:matsui}. The different parameters are determined by fitting the experimental data. It should be noted that for such an oxidation process (\ce{N+ + e- -> N^.}), the $\Delta\Delta G^\star_P$ correction [Eq.~\eqref{eq:matsui}] can only be positive. As a consequence of this limitation, while the corrected $E^0_{abs}(\text{SHE)}$ predicted by this model is slightly larger than the recommended value in water, it is lower in acetonitrile but this value being smaller than in water is not in agreement with experimental data \cite{marenichComputationalElectrochemistryPrediction2014}. Interestingly, this correction is similar to the value of the MAE reported in Fig.~\ref{fig:expvstheo}. Furthermore, while the slope of the linear regression improves in water, it remains the same in acetonitrile. Finally, both $f$ and $\mu$ are smaller than those reported by Matsui and colleagues, though they treated systems bearing larger charges. Therefore, this model is not well-suited for this case. +For comparison, the model by Matsui and co-workers \cite{matsuiDensityFunctionalTheory2013} is used in Fig.~\ref{fig:matsui}. The different parameters are determined by fitting the experimental data. It should be noted that for such an oxidation process (\ce{N+ + e- -> N^.}), the $\Delta\Delta G^\star_{Matsui}$ correction [Eq.~\eqref{eq:matsui}] can only be positive. As a consequence of this limitation, while the corrected $E^0_{abs}(\text{SHE)}$ predicted by this model is slightly larger than the recommended value in water, it is lower in acetonitrile. Interestingly, this correction is similar to the value of the MAE reported in Fig.~\ref{fig:expvstheo}. Furthermore, while the slope of the linear regression improves in water, it remains the same in acetonitrile. Finally, both $f$ and $\mu$ are smaller than those reported by Matsui and colleagues, though they treated systems bearing larger charges. \begin{figure}[!h] @@ -565,20 +568,22 @@ \subsection{Comparison to experiment} \label{sec:exp} \end{figure} \clearpage -\section{Conclusion} \label{sec:conclusion} +\section{Conclusions and outlooks} \label{sec:conclusion} + +In this paper, the impact of different solute-solvent effects on the redox potentials of nitroxides has been assessed using quantum chemistry approaches, with a particular emphasis on ionic interactions. The calculation have been performed at the DFT level ($\omega$B97X-D/6-311+G*), with implicit solvation (SMD) to account for the impact of the solvent. -In this paper, the impact of different solute-solvent effects on the redox potentials of nitroxides has been assessed, with a particular emphasis on ionic interactions. While the Born model [Eq.~\eqref{eq:born}] shows that the solvent tends to stabilize charges due to changes in the dielectric constant (especially in polar solvents), other, more subtle effects arise from solute-ion interactions caused by the presence of electrolytes. These electrolytes are found in moderate concentrations (\textit{i.e.,} \SI{0.1}{\mole\per\liter}) during the experimental measurement of redox potentials and in higher concentrations (>$\SI{1}{\mole\per\liter}$) in ionic liquids used for batteries. +Different families of nitroxides have been considered: 5- (P6O, APO) and 6-membered rings (P5O, IIO) containing the nitroxyl moiety, and with (IIO, APO) or without an aromatic system (P5O, P6O) in close vicinity. The impact of such structural changes as well as of substituent, on the redox potentials is largely explained by the electrostatic interaction model (Fig.~\ref{fig:dipole}) developed by Zhang and co-workers \cite{zhangEffectHeteroatomFunctionality2018}: thought the dipole interaction between the substituent and the redox center can explain, in first approximation, the variation that are observed, the inclusion of the quadrupole moment is necessary to explain the increases of both the oxidation and reduction potentials of aromatic nitroxides. Furthermore, acceptor substituents (such as \ce{NO2}) further increase both potentials. While the impact remains moderate (+\SI{0.4}{\volt}), it is hoped that this will provide design rules for future investigations. -The impact of electrolytes is twofold: +While the Born model [Eq.~\eqref{eq:born}] shows that the solvent tends to stabilize charges due to changes in the dielectric constant (especially in polar solvents), other, more subtle effects arise from solute-ion interactions caused by the presence of electrolytes. These electrolytes are found in moderate concentrations (\textit{i.e.,} \SI{0.1}{\mole\per\liter}) during the experimental measurement of redox potentials and in higher concentrations (>$\SI{1}{\mole\per\liter}$) in ionic liquids used for batteries. +Their impact is twofold: \begin{inparaenum}[(i)] - \item at any concentration, the background of charge further stabilizes charged compounds, as described by the Debye-Hückel (DH) model [Eq.~\eqref{eq:dh}], and + \item at any concentration, the background of charge stabilizes charged compounds, and \item at high concentrations, the formation of ion-pairs modifies the redox properties of nitroxides. \end{inparaenum} -Both effects have been examined: when the charge of the compound and of the electrolyte constituents is moderate, the DH correction is small. However, the formation of pairs depends on the redox state of the nitroxide and the nature of the intermolecular interactions, which goes beyond a simple pair formation model (Fig.~\ref{fig:ionpair}). Two positions are possible for the ion: near the redox center of the nitroxide, and near its substituent, if any. The ion-substituent interaction (in the second position) generally leads to more favorable complexes (especially when the molecule contains aromatic moieties). However, in acetonitrile, the interaction between the reduced form (hydroxylamine anion) and its cation, positioned near the $>$\ce{N-O-} moiety, is the strongest. This seems to be the case in other low-dielectric environments, as noted by others in an even less polar solvent ($\varepsilon_r$ = 25) \cite{wylieImprovedPerformanceAllOrganic2019a}. +Both effects have been examined: when the charge of the compound and of the electrolyte constituents is moderate the correction proposed by the Debye-Hückel model is sufficient. However, the formation of pairs depends on the redox state of the nitroxide and the nature of the intermolecular interactions, which goes beyond a simple pair formation model (such as the one found in Fig.~\ref{fig:ionpair}). Indeed, two positions are possible for the ion: near the redox center of the nitroxide, and closer to its substituent, if any. The ion-substituent interaction (in the second position) generally leads to more favorable complexes (especially when the molecule contains aromatic moieties). However, in acetonitrile, the interaction between the reduced form (hydroxylamine anion) and its cation, positioned near the $>$\ce{N-O-} moiety, is the strongest. This seems to be the case in other low-dielectric environments, as noted by others in an even less polar solvent (using methanol, $\varepsilon_r$ = 25, in Ref.~\citenum{wylieImprovedPerformanceAllOrganic2019a}). +It was, however, not possible to correlate the impact of the substitution on the formation of ion-pairs, but it was noticed that the favorable interactions between \ce{N-} and \ce{C+} was systematically hampered by the nitroxyl in an axial position in P6O. This is another important design rule for future applications. -In this work, different families of nitroxides have been considered: 5- (P6O, APO) and 6-membered rings (P5O, IIO) containing the nitroxyl moiety, and with (IIO, APO) or without an aromatic system (P5O, P6O) in close vicinity. The impact of such changes, and of substituents, on the redox potentials is largely explained by the electrostatic interaction model (Fig.~\ref{fig:dipole}) developed by Zhang and co-workers \cite{zhangEffectHeteroatomFunctionality2018}: a large quadrupole moment increases both the oxidation and reduction potentials of nitroxides, while increasing the size of the ring (and thus the distance between the substituent and the nitroxyl) mostly affects the reduction potential. Furthermore, acceptor substituents (such as \ce{NO2}) further increase both potentials. While the impact remains moderate (+\SI{0.4}{\volt}), it is hoped that this will provide design rules for future investigations. It was, however, not possible to correlate the impact of the substitution on the formation of ion-pairs, but it was noticed that the favorable interaction between \ce{N-} and \ce{C+} mentioned was systematically hampered by the nitroxyl in an axial position in P6O. This is another important design rule for future applications. - -Finally, a comparison with experiment has been performed. It results in an excellent correlation, but the impact of the corrections presented above is minimal in the solvents considered here (water and acetonitrile) and with the concentrations of electrolytes used experimentally. It would be interesting to compare redox potentials measured under different conditions (such as in ionic liquids). Another factor that should be investigated is the temperature, which would affect both the DH correction (through $\kappa$, Eq.~\eqref{eq:kappa2}) and the complexation equilibrium constant (though the entropic contribution). For example, conventional lithium-ion batteries can operate up to \SI{60}{\degreeCelsius} \cite{maTemperatureEffectThermal2018}, but ionic liquids are stable over extended temperature ranges. The modification of the dielectric constant of the solution with increasing electrolyte concentration \cite{kontogeorgisDebyeHuckelTheoryIts2018, silvaTrueHuckelEquation2022}, is another point that should be considered in future studies. +Finally, a comparison with experiment has been performed. It results in an excellent correlation, but the impact of the corrections presented above is small in the solvents considered here (water and acetonitrile) and with the concentrations of electrolytes used experimentally. As a matter of fact, it would be interesting to compare redox potentials measured under different conditions (such as in ionic liquids). Another factor that should be investigated is the temperature, which would affect both the DH correction (through $\kappa$, Eq.~\eqref{eq:kappa2}) and the complexation equilibrium constant (though the entropic contribution). For example, conventional lithium-ion batteries can operate up to \SI{60}{\degreeCelsius} \cite{maTemperatureEffectThermal2018}, and ionic liquids are stable over extended temperature ranges. The modification of the dielectric constant of the solution with increasing electrolyte concentration \cite{kontogeorgisDebyeHuckelTheoryIts2018, silvaTrueHuckelEquation2022}, is another point that should be considered in future studies. \section*{Notes} The author declare no competing financial interest. @@ -589,6 +594,10 @@ \section*{Acknowledgements} \item the computers of the Consortium des \'{E}quipements de Calcul Intensif (C\'{E}CI, \url{http://www.ceci-hpc.be}) and particularly those of the Technological Platform of High-Performance Computing, for which the author gratefully acknowledge the financial support of the F.R.S-FNRS, of the Walloon Region, and of the University of Namur (Conventions No. 2.5020.11, U.G006.15, U.G018.19, U.G011.22, 1610468, and RW/GEQ2016), and \item on Lucia, the Tier-1 supercomputer of the Walloon Region, infrastructure funded by the Walloon Region (grant agreement No. 1910247). \end{inparaenum} + +\section{Data availability} + +xxx. \bibliographystyle{elsarticle-num-names}