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damping.f
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c
c
c ############################################################
c ## COPYRIGHT (C) 2018 by Joshua Rackers & Jay W. Ponder ##
c ## All Rights Reserved ##
c ############################################################
c
c #################################################################
c ## ##
c ## subroutine dampewald -- find Ewald damping coefficients ##
c ## ##
c #################################################################
c
c
c "dampewald" finds coefficients for error function damping used
c for Ewald real space interactions
c
c
subroutine dampewald (rorder,r,r2,scale,dmpe)
use ewald
use math
implicit none
integer i,niter
integer rorder
real*8 r,r2,scale
real*8 bfac,erfc
real*8 aesq2,afac
real*8 expterm,ra
real*8 bn(0:5)
real*8 dmpe(*)
external erfc
c
c
c initialize the Ewald damping factor coefficients
c
do i = 1, rorder
dmpe(i) = scale
end do
c
c compute the successive Ewald damping factors
c
ra = aewald * r
bn(0) = erfc(ra) / r
dmpe(1) = scale * bn(0)
expterm = exp(-ra*ra)
aesq2 = 2.0d0 * aewald * aewald
afac = 0.0d0
if (aewald .gt. 0.0d0) afac = 1.0d0 / (rootpi*aewald)
niter = (rorder-1) / 2
do i = 1, niter
bfac = dble(2*i-1)
afac = aesq2 * afac
bn(i) = (bfac*bn(i-1)+afac*expterm) / r2
dmpe(2*i+1) = scale * bn(i)
end do
return
end
c
c
c ###############################################################
c ## ##
c ## subroutine dampthole -- original Thole damping values ##
c ## ##
c ###############################################################
c
c
c "dampthole" finds coefficients for the original Thole damping
c function used by AMOEBA and for mutual polarization by AMOEBA+
c
c literature reference:
c
c B. T. Thole, "Molecular Polarizabilities Calculated with a
c Modified Dipole Interaction", Chemical Physics, 59, 341-350 (1981)
c
c
subroutine dampthole (i,k,rorder,r,dmpik)
use atoms
use mpole
use polar
implicit none
integer i,j,k
integer it,kt
integer rorder
real*8 r,damp
real*8 damp2
real*8 damp3
real*8 expdamp
real*8 pgamma
real*8 dmpik(*)
c
c
c initialize the Thole damping factors to a value of one
c
do j = 1, rorder
dmpik(j) = 1.0d0
end do
c
c assign original Thole polarization model damping factors
c
damp = pdamp(i) * pdamp(k)
it = jpolar(ipole(i))
kt = jpolar(ipole(k))
pgamma = thlval(it,kt)
if (damp.ne.0.0d0 .and. pgamma.ne.0.0d0) then
damp = pgamma * (r/damp)**3
if (damp .lt. 50.0d0) then
expdamp = exp(-damp)
dmpik(3) = 1.0d0 - expdamp
dmpik(5) = 1.0d0 - expdamp*(1.0d0+damp)
if (rorder .ge. 7) then
damp2 = damp * damp
dmpik(7) = 1.0d0 - expdamp*(1.0d0+damp+0.6d0*damp2)
if (rorder .ge. 9) then
damp3 = damp * damp2
dmpik(9) = 1.0d0 - expdamp*(1.0d0+damp
& +(18.0d0/35.0d0)*damp2
& +(9.0d0/35.0d0)*damp3)
end if
end if
end if
end if
return
end
c
c
c #################################################################
c ## ##
c ## subroutine damptholed -- alternate Thole damping values ##
c ## ##
c #################################################################
c
c
c "damptholed" finds coefficients for the original Thole damping
c function used by AMOEBA or for the alternate direct polarization
c damping used by AMOEBA+
c
c literature reference:
c
c B. T. Thole, "Molecular Polarizabilities Calculated with a
c Modified Dipole Interaction", Chemical Physics, 59, 341-350 (1981)
c
c
subroutine damptholed (i,k,rorder,r,dmpik)
use atoms
use mpole
use polar
use polpot
implicit none
integer i,j,k
integer it,kt
integer rorder
real*8 r,damp
real*8 damp2
real*8 damp3
real*8 expdamp
real*8 pgamma
real*8 dmpik(*)
c
c
c initialize the Thole damping factors to a value of one
c
do j = 1, rorder
dmpik(j) = 1.0d0
end do
c
c use alternate Thole model for AMOEBA+ direct polarization
c
damp = pdamp(i) * pdamp(k)
if (use_tholed) then
it = jpolar(ipole(i))
kt = jpolar(ipole(k))
pgamma = thdval(it,kt)
if (damp.ne.0.0d0 .and. pgamma.ne.0.0d0) then
damp = pgamma * (r/damp)**(1.5d0)
if (damp .lt. 50.0d0) then
expdamp = exp(-damp)
dmpik(3) = 1.0d0 - expdamp
dmpik(5) = 1.0d0 - expdamp*(1.0d0+0.5d0*damp)
if (rorder .ge. 7) then
damp2 = damp * damp
dmpik(7) = 1.0d0 - expdamp*(1.0d0+0.65d0*damp
& +0.15d0*damp2)
end if
end if
end if
c
c use original AMOEBA Thole polarization damping factors
c
else
it = jpolar(ipole(i))
kt = jpolar(ipole(k))
pgamma = thlval(it,kt)
if (damp.ne.0.0d0 .and. pgamma.ne.0.0d0) then
damp = pgamma * (r/damp)**3
if (damp .lt. 50.0d0) then
expdamp = exp(-damp)
dmpik(3) = 1.0d0 - expdamp
dmpik(5) = 1.0d0 - expdamp*(1.0d0+damp)
if (rorder .ge. 7) then
damp2 = damp * damp
dmpik(7) = 1.0d0 - expdamp*(1.0d0+damp+0.6d0*damp2)
if (rorder .ge. 9) then
damp3 = damp * damp2
dmpik(9) = 1.0d0 - expdamp*(1.0d0+damp
& +(18.0d0/35.0d0)*damp2
& +(9.0d0/35.0d0)*damp3)
end if
end if
end if
end if
end if
return
end
c
c
c ################################################################
c ## ##
c ## subroutine damppole -- penetration damping coefficents ##
c ## ##
c ################################################################
c
c
c "damppole" finds coefficients for two alternative Gordon charge
c penetration damping function
c
c literature references:
c
c L. V. Slipchenko and M. S. Gordon, "Electrostatic Energy in the
c Effective Fragment Potential Method: Theory and Application to
c the Benzene Dimer", Journal of Computational Chemistry, 28,
c 276-291 (2007) [Gordon f1 and f2 models]
c
c J. A. Rackers, Q. Wang, C. Liu, J.-P. Piquemal, P. Ren and
c J. W. Ponder, "An Optimized Charge Penetration Model for Use with
c the AMOEBA Force Field", Physical Chemistry Chemical Physics, 19,
c 276-291 (2017)
c
c
subroutine damppole (r,rorder,alphai,alphak,dmpi,dmpk,dmpik)
use mplpot
implicit none
integer rorder
real*8 termi,termk
real*8 termi2,termk2
real*8 alphai,alphak
real*8 alphai2,alphak2
real*8 r,eps,diff
real*8 expi,expk
real*8 dampi,dampk
real*8 dampi2,dampi3
real*8 dampi4,dampi5
real*8 dampi6,dampi7
real*8 dampi8
real*8 dampk2,dampk3
real*8 dampk4,dampk5
real*8 dampk6
real*8 dmpi(*)
real*8 dmpk(*)
real*8 dmpik(*)
c
c
c compute tolerance and exponential damping factors
c
eps = 0.001d0
diff = abs(alphai-alphak)
dampi = alphai * r
dampk = alphak * r
expi = exp(-dampi)
expk = exp(-dampk)
c
c core-valence charge penetration damping for Gordon f1
c
if (pentyp .eq. 'GORDON1') then
dampi2 = dampi * dampi
dampi3 = dampi * dampi2
dampi4 = dampi2 * dampi2
dampi5 = dampi2 * dampi3
dmpi(1) = 1.0d0 - (1.0d0 + 0.5d0*dampi)*expi
dmpi(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2)*expi
dmpi(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0)*expi
dmpi(7) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/30.0d0)*expi
dmpi(9) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + 4.0d0*dampi4/105.0d0
& + dampi5/210.0d0)*expi
if (diff .lt. eps) then
dmpk(1) = dmpi(1)
dmpk(3) = dmpi(3)
dmpk(5) = dmpi(5)
dmpk(7) = dmpi(7)
dmpk(9) = dmpi(9)
else
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
dampk4 = dampk2 * dampk2
dampk5 = dampk2 * dampk3
dmpk(1) = 1.0d0 - (1.0d0 + 0.5d0*dampk)*expk
dmpk(3) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0)*expk
dmpk(7) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0 + dampk4/30.0d0)*expk
dmpk(9) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0 + 4.0d0*dampk4/105.0d0
& + dampk5/210.0d0)*expk
end if
c
c valence-valence charge penetration damping for Gordon f1
c
if (diff .lt. eps) then
dampi6 = dampi3 * dampi3
dampi7 = dampi3 * dampi4
dmpik(1) = 1.0d0 - (1.0d0 + 11.0d0*dampi/16.0d0
& + 3.0d0*dampi2/16.0d0
& + dampi3/48.0d0)*expi
dmpik(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + 7.0d0*dampi3/48.0d0
& + dampi4/48.0d0)*expi
dmpik(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/24.0d0
& + dampi5/144.0d0)*expi
dmpik(7) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/24.0d0
& + dampi5/120.0d0 + dampi6/720.0d0)*expi
dmpik(9) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/24.0d0
& + dampi5/120.0d0 + dampi6/720.0d0
& + dampi7/5040.0d0)*expi
if (rorder .ge. 11) then
dampi8 = dampi4 * dampi4
dmpik(11) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/24.0d0
& + dampi5/120.0d0 + dampi6/720.0d0
& + dampi7/5040.0d0 + dampi8/45360.0d0)*expi
end if
else
alphai2 = alphai * alphai
alphak2 = alphak * alphak
termi = alphak2 / (alphak2-alphai2)
termk = alphai2 / (alphai2-alphak2)
termi2 = termi * termi
termk2 = termk * termk
dmpik(1) = 1.0d0 - termi2*(1.0d0 + 2.0d0*termk
& + 0.5d0*dampi)*expi
& - termk2*(1.0d0 + 2.0d0*termi
& + 0.5d0*dampk)*expk
dmpik(3) = 1.0d0 - termi2*(1.0d0+dampi+0.5d0*dampi2)*expi
& - termk2*(1.0d0+dampk+0.5d0*dampk2)*expk
& - 2.0d0*termi2*termk*(1.0d0+dampi)*expi
& - 2.0d0*termk2*termi*(1.0d0+dampk)*expk
dmpik(5) = 1.0d0 - termi2*(1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0)*expi
& - termk2*(1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0)*expk
& - 2.0d0*termi2*termk
& *(1.0d0 + dampi + dampi2/3.0d0)*expi
& - 2.0d0*termk2*termi
& *(1.0d0 + dampk + dampk2/3.0d0)*expk
dmpik(7) = 1.0d0 - termi2*(1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/30.0d0)*expi
& - termk2*(1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0 + dampk4/30.0d0)*expk
& - 2.0d0*termi2*termk*(1.0d0 + dampi
& + 2.0d0*dampi2/5.0d0 + dampi3/15.0d0)*expi
& - 2.0d0*termk2*termi*(1.0d0 + dampk
& + 2.0d0*dampk2/5.0d0 + dampk3/15.0d0)*expk
dmpik(9) = 1.0d0 - termi2*(1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + 4.0d0*dampi4/105.0d0
& + dampi5/210.0d0)*expi
& - termk2*(1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0 + 4.0d0*dampk4/105.0d0
& + dampk5/210.0d0)*expk
& - 2.0d0*termi2*termk*(1.0d0 + dampi
& + 3.0d0*dampi2/7.0d0
& + 2.0d0*dampi3/21.0d0
& + dampi4/105.0d0)*expi
& - 2.0d0*termk2*termi*(1.0d0 + dampk
& + 3.0d0*dampk2/7.0d0
& + 2.0d0*dampk3/21.0d0
& + dampk4/105.0d0)*expk
if (rorder .ge. 11) then
dampi6 = dampi3 * dampi3
dampk6 = dampk3 * dampk3
dmpik(11) = 1.0d0 - termi2*(1.0d0 + dampi
& + 0.5d0*dampi2 + dampi3/6.0d0
& + 5.0d0*dampi4/126.0d0
& + 2.0d0*dampi5/315.0d0
& + dampi6/1890.0d0)*expi
& - termk2*(1.0d0 + dampk
& + 0.5d0*dampk2 + dampk3/6.0d0
& + 5.0d0*dampk4/126.0d0
& + 2.0d0*dampk5/315.0d0
& + dampk6/1890.0d0)*expk
& - 2.0d0*termi2*termk*(1.0d0 + dampi
& + 4.0d0*dampi2/9.0d0 + dampi3/9.0d0
& + dampi4/63.0d0 + dampi5/945.0d0)*expi
& - 2.0d0*termk2*termi*(1.0d0 + dampk
& + 4.0d0*dampk2/9.0d0 + dampk3/9.0d0
& + dampk4/63.0d0 + dampk5/945.0d0)*expk
end if
end if
c
c core-valence charge penetration damping for Gordon f2
c
else if (pentyp .eq. 'GORDON2') then
dampi2 = dampi * dampi
dampi3 = dampi * dampi2
dmpi(1) = 1.0d0 - expi
dmpi(3) = 1.0d0 - (1.0d0 + dampi)*expi
dmpi(5) = 1.0d0 - (1.0d0 + dampi + dampi2/3.0d0)*expi
dmpi(7) = 1.0d0 - (1.0d0 + dampi + 0.4d0*dampi2
& + dampi3/15.0d0)*expi
if (diff .lt. eps) then
dmpk(1) = dmpi(1)
dmpk(3) = dmpi(3)
dmpk(5) = dmpi(5)
dmpk(7) = dmpi(7)
else
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
dmpk(1) = 1.0d0 - expk
dmpk(3) = 1.0d0 - (1.0d0 + dampk)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + dampk2/3.0d0)*expk
dmpk(7) = 1.0d0 - (1.0d0 + dampk + 0.4d0*dampk2
& + dampk3/15.0d0)*expk
end if
c
c valence-valence charge penetration damping for Gordon f2
c
dampi4 = dampi2 * dampi2
dampi5 = dampi2 * dampi3
if (diff .lt. eps) then
dampi6 = dampi3 * dampi3
dmpik(1) = 1.0d0 - (1.0d0 + 0.5d0*dampi)*expi
dmpik(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2)*expi
dmpik(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0)*expi
dmpik(7) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/30.0d0)*expi
dmpik(9) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + 4.0d0*dampi4/105.0d0
& + dampi5/210.0d0)*expi
if (rorder .ge. 11) then
dmpik(11) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + 5.0d0*dampi4/126.0d0
& + 2.0d0*dampi5/315.0d0
& + dampi6/1890.0d0)*expi
end if
else
dampk4 = dampk2 * dampk2
dampk5 = dampk2 * dampk3
alphai2 = alphai * alphai
alphak2 = alphak * alphak
termi = alphak2 / (alphak2-alphai2)
termk = alphai2 / (alphai2-alphak2)
dmpik(1) = 1.0d0 - termi*expi - termk*expk
dmpik(3) = 1.0d0 - termi*(1.0d0 + dampi)*expi
& - termk*(1.0d0 + dampk)*expk
dmpik(5) = 1.0d0 - termi*(1.0d0 + dampi + dampi2/3.0d0)*expi
& - termk*(1.0d0 + dampk + dampk2/3.0d0)*expk
dmpik(7) = 1.0d0 - termi*(1.0d0 + dampi + 0.4d0*dampi2
& + dampi3/15.0d0)*expi
& - termk*(1.0d0 + dampk + 0.4d0*dampk2
& + dampk3/15.0d0)*expk
dmpik(9) = 1.0d0 - termi*(1.0d0 + dampi + 3.0d0*dampi2/7.0d0
& + 2.0d0*dampi3/21.0d0 + dampi4/105.0d0)*expi
& - termk*(1.0d0 + dampk + 3.0d0*dampk2/7.0d0
& + 2.0d0*dampk3/21.0d0 + dampk4/105.0d0)*expk
if (rorder .ge. 11) then
dmpik(11) = 1.0d0 - termi*(1.0d0 + dampi
& + 4.0d0*dampi2/9.0d0 + dampi3/9.0d0
& + dampi4/63.0d0 + dampi5/945.0d0)*expi
& - termk*(1.0d0 + dampk
& + 4.0d0*dampk2/9.0d0 + dampk3/9.0d0
& + dampk4/63.0d0 + dampk5/945.0d0)*expk
end if
end if
end if
return
end
c
c
c ################################################################
c ## ##
c ## subroutine dampdir -- direct field damping coefficents ##
c ## ##
c ################################################################
c
c
c "dampdir" finds coefficients for two alternative Gordon direct
c field damping functions
c
c
subroutine dampdir (r,alphai,alphak,dmpi,dmpk)
use mplpot
implicit none
real*8 alphai,alphak
real*8 r,eps,diff
real*8 expi,expk
real*8 dampi,dampk
real*8 dampi2,dampk2
real*8 dampi3,dampk3
real*8 dampi4,dampk4
real*8 dmpi(*)
real*8 dmpk(*)
c
c
c compute tolerance and exponential damping factors
c
eps = 0.001d0
diff = abs(alphai-alphak)
dampi = alphai * r
dampk = alphak * r
expi = exp(-dampi)
expk = exp(-dampk)
c
c core-valence charge penetration damping for Gordon f1
c
if (pentyp .eq. 'GORDON1') then
dampi2 = dampi * dampi
dampi3 = dampi * dampi2
dampi4 = dampi2 * dampi2
dmpi(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2)*expi
dmpi(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0)*expi
dmpi(7) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/30.0d0)*expi
if (diff .lt. eps) then
dmpk(3) = dmpi(3)
dmpk(5) = dmpi(5)
dmpk(7) = dmpi(7)
else
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
dampk4 = dampk2 * dampk2
dmpk(3) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0)*expk
dmpk(7) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0 + dampk4/30.0d0)*expk
end if
c
c core-valence charge penetration damping for Gordon f2
c
else if (pentyp .eq. 'GORDON2') then
dampi2 = dampi * dampi
dampi3 = dampi * dampi2
dmpi(3) = 1.0d0 - (1.0d0 + dampi)*expi
dmpi(5) = 1.0d0 - (1.0d0 + dampi + dampi2/3.0d0)*expi
dmpi(7) = 1.0d0 - (1.0d0 + dampi + 0.4d0*dampi2
& + dampi3/15.0d0)*expi
if (diff .lt. eps) then
dmpk(3) = dmpi(3)
dmpk(5) = dmpi(5)
dmpk(7) = dmpi(7)
else
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
dmpk(3) = 1.0d0 - (1.0d0 + dampk)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + dampk2/3.0d0)*expk
dmpk(7) = 1.0d0 - (1.0d0 + dampk + 0.4d0*dampk2
& + dampk3/15.0d0)*expk
end if
end if
return
end
c
c
c ################################################################
c ## ##
c ## subroutine dampmut -- mutual field damping coefficents ##
c ## ##
c ################################################################
c
c
c "dampmut" finds coefficients for two alternative Gordon mutual
c field damping functions
c
c
subroutine dampmut (r,alphai,alphak,dmpik)
use mplpot
implicit none
real*8 termi,termk
real*8 termi2,termk2
real*8 alphai,alphak
real*8 alphai2,alphak2
real*8 r,eps,diff
real*8 expi,expk
real*8 dampi,dampk
real*8 dampi2,dampi3
real*8 dampi4,dampi5
real*8 dampk2,dampk3
real*8 dmpik(*)
c
c
c compute tolerance and exponential damping factors
c
eps = 0.001d0
diff = abs(alphai-alphak)
dampi = alphai * r
dampk = alphak * r
expi = exp(-dampi)
expk = exp(-dampk)
c
c valence-valence charge penetration damping for Gordon f1
c
if (pentyp .eq. 'GORDON1') then
dampi2 = dampi * dampi
dampi3 = dampi * dampi2
if (diff .lt. eps) then
dampi4 = dampi2 * dampi2
dampi5 = dampi2 * dampi3
dmpik(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + 7.0d0*dampi3/48.0d0
& + dampi4/48.0d0)*expi
dmpik(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0 + dampi4/24.0d0
& + dampi5/144.0d0)*expi
else
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
alphai2 = alphai * alphai
alphak2 = alphak * alphak
termi = alphak2 / (alphak2-alphai2)
termk = alphai2 / (alphai2-alphak2)
termi2 = termi * termi
termk2 = termk * termk
dmpik(3) = 1.0d0 - termi2*(1.0d0+dampi+0.5d0*dampi2)*expi
& - termk2*(1.0d0+dampk+0.5d0*dampk2)*expk
& - 2.0d0*termi2*termk*(1.0d0+dampi)*expi
& - 2.0d0*termk2*termi*(1.0d0+dampk)*expk
dmpik(5) = 1.0d0 - termi2*(1.0d0+dampi+0.5d0*dampi2
& +dampi3/6.0d0)*expi
& - termk2*(1.0d0+dampk+0.5d0*dampk2
& +dampk3/6.00)*expk
& - 2.0d0*termi2*termk
& *(1.0+dampi+dampi2/3.0d0)*expi
& - 2.0d0*termk2*termi
& *(1.0+dampk+dampk2/3.0d0)*expk
end if
c
c valence-valence charge penetration damping for Gordon f2
c
else if (pentyp .eq. 'GORDON2') then
dampi2 = dampi * dampi
if (diff .lt. eps) then
dampi3 = dampi * dampi2
dmpik(3) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2)*expi
dmpik(5) = 1.0d0 - (1.0d0 + dampi + 0.5d0*dampi2
& + dampi3/6.0d0)*expi
else
dampk2 = dampk * dampk
alphai2 = alphai * alphai
alphak2 = alphak * alphak
termi = alphak2 / (alphak2-alphai2)
termk = alphai2 / (alphai2-alphak2)
dmpik(3) = 1.0d0 - termi*(1.0d0 + dampi)*expi
& - termk*(1.0d0 + dampk)*expk
dmpik(5) = 1.0d0 - termi*(1.0d0 + dampi + dampi2/3.0d0)*expi
& - termk*(1.0d0 + dampk + dampk2/3.0d0)*expk
end if
end if
return
end
c
c
c ###############################################################
c ## ##
c ## subroutine damppot -- electrostatic potential damping ##
c ## ##
c ###############################################################
c
c
c "damppot" finds coefficients for two alternative Gordon charge
c penetration damping functions for the electrostatic potential
c
c
subroutine damppot (r,alphak,dmpk)
use mplpot
implicit none
real*8 r,alphak
real*8 expk,dampk
real*8 dampk2,dampk3
real*8 dmpk(*)
c
c
c compute common exponential factors for damping
c
dampk = alphak * r
expk = exp(-dampk)
c
c core-valence charge penetration damping for Gordon f1
c
if (pentyp .eq. 'GORDON1') then
dampk2 = dampk * dampk
dampk3 = dampk * dampk2
dmpk(1) = 1.0d0 - (1.0d0 + 0.5d0*dampk)*expk
dmpk(3) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + 0.5d0*dampk2
& + dampk3/6.0d0)*expk
c
c core-valence charge penetration damping for Gordon f2
c
else if (pentyp .eq. 'GORDON2') then
dampk2 = dampk * dampk
dmpk(1) = 1.0d0 - expk
dmpk(3) = 1.0d0 - (1.0d0 + dampk)*expk
dmpk(5) = 1.0d0 - (1.0d0 + dampk + dampk2/3.0d0)*expk
end if
return
end
c
c
c ################################################################
c ## ##
c ## subroutine damprep -- Pauli exchange repulsion damping ##
c ## ##
c ################################################################
c
c
c "damprep" finds coefficients for the Pauli repulsion damping
c function used by HIPPO
c
c literature reference:
c
c J. A. Rackers and J. W. Ponder, "Classical Pauli Repulsion: An
c Anisotropic, Atomic Multipole Model", Journal of Chemical Physics,
c 150, 084104 (2019)
c
c
subroutine damprep (r,r2,rr1,rr3,rr5,rr7,rr9,rr11,
& rorder,dmpi,dmpk,dmpik)
implicit none
integer rorder
real*8 r,r2,r3,r4
real*8 r5,r6,r7,r8
real*8 rr1,rr3,rr5
real*8 rr7,rr9,rr11
real*8 s,ds,d2s
real*8 d3s,d4s,d5s
real*8 dmpi,dmpk
real*8 dmpi2,dmpk2
real*8 dmpi22,dmpi23
real*8 dmpi24,dmpi25
real*8 dmpi26,dmpi27
real*8 dmpk22,dmpk23
real*8 dmpk24,dmpk25
real*8 dmpk26
real*8 eps,diff
real*8 expi,expk
real*8 dampi,dampk
real*8 pre,term,tmp
real*8 dmpik(*)
c
c
c compute tolerance value for damping exponents
c
eps = 0.001d0
diff = abs(dmpi-dmpk)
c
c treat the case where alpha damping exponents are equal
c
if (diff .lt. eps) then
r3 = r2 * r
r4 = r3 * r
r5 = r4 * r
r6 = r5 * r
dmpi2 = 0.5d0 * dmpi
dampi = dmpi2 * r
expi = exp(-dampi)
dmpi22 = dmpi2 * dmpi2
dmpi23 = dmpi22 * dmpi2
dmpi24 = dmpi23 * dmpi2
dmpi25 = dmpi24 * dmpi2
pre = 2.0d0
s = (r + dmpi2*r2 + dmpi22*r3/3.0d0) * expi
ds = (dmpi22*r3 + dmpi23*r4) * expi / 3.0d0
d2s = dmpi24 * expi * r5 / 9.0d0
d3s = dmpi25 * expi * r6 / 45.0d0
if (rorder .ge. 9) then
r7 = r6 * r
dmpi26 = dmpi25 * dmpi2
d4s = (dmpi25*r6 + dmpi26*r7) * expi / 315.0d0
if (rorder .ge. 11) then
r8 = r7 * r
dmpi27 = dmpi2 * dmpi26
d5s = (dmpi25*r6 + dmpi26*r7 + dmpi27*r8/3.0d0)
& * expi / 945.0d0
end if
end if
c
c treat the case where alpha damping exponents are unequal
c
else
r3 = r2 * r
r4 = r3 * r
dmpi2 = 0.5d0 * dmpi
dmpk2 = 0.5d0 * dmpk
dampi = dmpi2 * r
dampk = dmpk2 * r
expi = exp(-dampi)
expk = exp(-dampk)
dmpi22 = dmpi2 * dmpi2
dmpi23 = dmpi22 * dmpi2
dmpi24 = dmpi23 * dmpi2
dmpk22 = dmpk2 * dmpk2
dmpk23 = dmpk22 * dmpk2
dmpk24 = dmpk23 * dmpk2
term = dmpi22 - dmpk22
pre = 128.0d0 * dmpi23 * dmpk23 / term**4
tmp = 4.0d0 * dmpi2 * dmpk2 / term
s = (dampi-tmp)*expk + (dampk+tmp)*expi
ds = (dmpi2*dmpk2*r2 - 4.0d0*dmpi2*dmpk22*r/term
& - 4.0d0*dmpi2*dmpk2/term) * expk
& + (dmpi2*dmpk2*r2 + 4.0d0*dmpi22*dmpk2*r/term
& + 4.0d0*dmpi2*dmpk2/term) * expi
d2s = (dmpi2*dmpk2*r2/3.0d0
& + dmpi2*dmpk22*r3/3.0d0
& - (4.0d0/3.0d0)*dmpi2*dmpk23*r2/term
& - 4.0d0*dmpi2*dmpk22*r/term
& - 4.0d0*dmpi2*dmpk2/term) * expk
& + (dmpi2*dmpk2*r2/3.0d0
& + dmpi22*dmpk2*r3/3.0d0
& + (4.0d0/3.0d0)*dmpi23*dmpk2*r2/term
& + 4.0d0*dmpi22*dmpk2*r/term
& + 4.0d0*dmpi2*dmpk2/term) * expi
d3s = (dmpi2*dmpk23*r4/15.0d0
& + dmpi2*dmpk22*r3/5.0d0
& + dmpi2*dmpk2*r2/5.0d0
& - (4.0d0/15.0d0)*dmpi2*dmpk24*r3/term
& - (8.0d0/5.0d0)*dmpi2*dmpk23*r2/term
& - 4.0d0*dmpi2*dmpk22*r/term
& - 4.0d0/term*dmpi2*dmpk2) * expk
& + (dmpi23*dmpk2*r4/15.0d0
& + dmpi22*dmpk2*r3/5.0d0
& + dmpi2*dmpk2*r2/5.0d0
& + (4.0d0/15.0d0)*dmpi24*dmpk2*r3/term
& + (8.0d0/5.0d0)*dmpi23*dmpk2*r2/term
& + 4.0d0*dmpi22*dmpk2*r/term
& + 4.0d0/term*dmpi2*dmpk2) * expi
if (rorder .ge. 9) then
r5 = r4 * r
dmpi25 = dmpi24 * dmpi2
dmpk25 = dmpk24 * dmpk2
d4s = (dmpi2*dmpk24*r5/105.0d0
& + (2.0d0/35.0d0)*dmpi2*dmpk23*r4
& + dmpi2*dmpk22*r3/7.0d0
& + dmpi2*dmpk2*r2/7.0d0
& - (4.0d0/105.0d0)*dmpi2*dmpk25*r4/term
& - (8.0d0/21.0d0)*dmpi2*dmpk24*r3/term
& - (12.0d0/7.0d0)*dmpi2*dmpk23*r2/term
& - 4.0d0*dmpi2*dmpk22*r/term
& - 4.0d0*dmpi2*dmpk2/term) * expk
& + (dmpi24*dmpk2*r5/105.0d0
& + (2.0d0/35.0d0)*dmpi23*dmpk2*r4
& + dmpi22*dmpk2*r3/7.0d0
& + dmpi2*dmpk2*r2/7.0d0
& + (4.0d0/105.0d0)*dmpi25*dmpk2*r4/term
& + (8.0d0/21.0d0)*dmpi24*dmpk2*r3/term
& + (12.0d0/7.0d0)*dmpi23*dmpk2*r2/term
& + 4.0d0*dmpi22*dmpk2*r/term
& + 4.0d0*dmpi2*dmpk2/term) * expi
if (rorder .ge. 11) then
r6 = r5 * r
dmpi26 = dmpi25 * dmpi2
dmpk26 = dmpk25 * dmpk2
d5s = (dmpi2*dmpk25*r6/945.0d0
& + (2.0d0/189.0d0)*dmpi2*dmpk24*r5
& + dmpi2*dmpk23*r4/21.0d0
& + dmpi2*dmpk22*r3/9.0d0
& + dmpi2*dmpk2*r2/9.0d0
& - (4.0d0/945.0d0)*dmpi2*dmpk26*r5/term
& - (4.0d0/63.0d0)*dmpi2*dmpk25*r4/term
& - (4.0d0/9.0d0)*dmpi2*dmpk24*r3/term
& - (16.0d0/9.0d0)*dmpi2*dmpk23*r2/term
& - 4.0d0*dmpi2*dmpk22*r/term
& - 4.0d0*dmpi2*dmpk2/term) * expk
& + (dmpi25*dmpk2*r6/945.0d0
& + (2.0d0/189.0d0)*dmpi24*dmpk2*r5
& + dmpi23*dmpk2*r4/21.0d0
& + dmpi22*dmpk2*r3/9.0d0
& + dmpi2*dmpk2*r2/9.0d0
& + (4.0d0/945.0d0)*dmpi26*dmpk2*r5/term
& + (4.0d0/63.0d0)*dmpi25*dmpk2*r4/term
& + (4.0d0/9.0d0)*dmpi24*dmpk2*r3/term
& + (16.0d0/9.0d0)*dmpi23*dmpk2*r2/term
& + 4.0d0*dmpi22*dmpk2*r/term
& + 4.0d0*dmpi2*dmpk2/term) * expi
end if
end if
end if
c
c convert partial derivatives into full derivatives
c
s = s * rr1
ds = ds * rr3
d2s = d2s * rr5
d3s = d3s * rr7
dmpik(1) = 0.5d0 * pre * s * s
dmpik(3) = pre * s * ds
dmpik(5) = pre * (s*d2s + ds*ds)
dmpik(7) = pre * (s*d3s + 3.0d0*ds*d2s)
if (rorder .ge. 9) then
d4s = d4s * rr9
dmpik(9) = pre * (s*d4s + 4.0d0*ds*d3s + 3.0d0*d2s*d2s)
if (rorder .ge. 11) then
d5s = d5s * rr11
dmpik(11) = pre * (s*d5s + 5.0d0*ds*d4s + 10.0d0*d2s*d3s)
end if
end if
return
end
c
c
c ##############################################################
c ## ##
c ## subroutine dampexpl -- exchange polarization damping ##
c ## ##
c ##############################################################
c
c
c "dampexpl" finds the overlap value for exchange polarization
c damping function
c
c
subroutine dampexpl (r,preik,alphai,alphak,s2,ds2)
use polpot
implicit none
real*8 r,s,s2,ds2
real*8 alphai,alphak
real*8 alphaik
real*8 dmpi2,dmpk2
real*8 dmpi22,dmpk22
real*8 dmpik2
real*8 dampik,dampik2
real*8 eps,diff
real*8 expi,expk,expik
real*8 dampi,dampk,dampi2
real*8 pre,term,preik
c
c
if (scrtyp .eq. 'S2U') then
alphaik = sqrt(alphai * alphak)
dmpik2 = 0.5d0 * alphaik
dampik = dmpik2 * r
dampik2 = dampik * dampik
expik = exp(-dampik)
s =(1+dampik+dampik2/3.0d0)*expik
s2 = s*s
ds2 = s * (-alphaik/3.0d0)*(dampik+dampik2)*expik
c
c compute tolerance value for overlap-based damping
c
else if (scrtyp .eq. 'S2 ') then
eps = 0.001d0
diff = abs(alphai-alphak)
c
c treat the case where alpha damping exponents are equal
c
if (diff .lt. eps) then
dmpi2 = 0.5d0 * alphai
dampi = dmpi2 * r
dampi2 = dampi * dampi
expi = exp(-dampi)
s = (1+dampi+dampi2/3.0d0)*expi
ds2 = s * (-alphai/3.0d0)*(dampi+dampi2)*expi
c
c treat the case where alpha damping exponents are unequal
c
else
dmpi2 = 0.5d0 * alphai
dmpk2 = 0.5d0 * alphak
dampi = dmpi2 * r
dampk = dmpk2 * r
expi = exp(-dampi)
expk = exp(-dampk)
dmpi22 = dmpi2 * dmpi2
dmpk22 = dmpk2 * dmpk2
term = dmpi22 - dmpk22
pre = sqrt(alphai**3 * alphak**3) / (r * term**3)
s = pre*(dmpi2*(r*term - 4*dmpk2) * expk
& + dmpk2*(r*term + 4*dmpi2) * expi)
ds2 = 2.0d0*s*pre*dmpi2*dmpk2 *
& ((4.0d0/r-(r*term-4.0d0*dmpk2))*expk
& - ((4.0d0/r+(r*term+4.0d0*dmpi2))*expi))
end if
s2 = s*s
c
c use simple gaussian-based damping functions
c
else if (scrtyp .eq. 'G ') then
alphaik = sqrt(alphai * alphak)
s2 = exp(-alphaik/10.0d0 * r**2)
ds2 = (-alphaik/5.0d0)*r*s2
end if
s2 = preik*s2
ds2 = preik*ds2
return
end