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normalize.f
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! This file is part of std2.
!
! Copyright (C) 2013-2025 Stefan Grimme and Marc de Wergifosse
!
! std2 is free software: you can redistribute it and/or modify it under
! the terms of the GNU Lesser General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! std2 is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU Lesser General Public License for more details.
!
! You should have received a copy of the GNU Lesser General Public License
! along with std2. If not, see <https://www.gnu.org/licenses/>.
!
!! ------------------------------------------------------------------------
ccccccccccccccccccccccccccccccccccc
! optional: Normalization of AOs c
ccccccccccccccccccccccccccccccccccc
! This normalizes the contraction coefficients for each contraction
subroutine normalize(cartbas,nprims,ipao,ipty,exip,cxip)
implicit none
logical, intent ( in ) :: cartbas
integer, intent ( in ) :: ipao(nprims),ipty(nprims)
integer, intent ( in ) :: nprims
real*8, intent( in ) :: exip(nprims)
real*8, intent( inout ) :: cxip(nprims)
integer i,j,k,l,iprimao,iprimtyp,jprimao,jprimtyp
integer ifac,lang,lx,my,nz
real*8 fnorm,summe,dzaehl,dnenn,expon,xlinf
open(unit=11,file='fnorm')
write(*,'(A)',advance='no') 'normalizing...'
j=1
do i=1,nprims+1
if(i.le.nprims) then
iprimao=ipao(i)
iprimtyp=ipty(i)
endif
if(i.gt.1)then
if(i.eq.nprims+1) iprimao=0
if(iprimao.ne.jprimao) then
call deflmna(jprimtyp,lx,my,nz,lang,xlinf)
! we override xlinf here, if a Cartesian basis is present (i.e. selv overlap is 1.0)
if(cartbas) xlinf=1.0d0
fnorm=3.14159265358979323846**1.50d0
fnorm=fnorm/dble(2**lang)
ifac=0
call dblfac(lx,ifac)
fnorm=fnorm*dble(ifac)
call dblfac(my,ifac)
fnorm=fnorm*dble(ifac)
call dblfac(nz,ifac)
fnorm=fnorm*dble(ifac)
fnorm=dsqrt(fnorm)
summe=0.0d0
do k=j,i-1
do l=j,i-1
dzaehl=cxip(k)*cxip(l)
dnenn=exip(k)+exip(l)
expon=dble(lang)+1.50d0
dnenn=dnenn**expon
summe=summe+dzaehl/dnenn
enddo
enddo
summe=dsqrt(summe)
fnorm=fnorm*summe
fnorm=xlinf/fnorm
do k=j,i-1
! write(*,*) k,ipty(k)
! write(*,*) exip(k),cxip(k),fnorm*cxip(k)
cxip(k)=fnorm*cxip(k)
write(11,*)fnorm
! write(*,*)k,jprimao,jprimtyp,cxip(k),cxip(k)**2
enddo
j=i
endif
endif
jprimao=iprimao
jprimtyp=iprimtyp
enddo
close(11)
!!!!!!!!!!!!!!!!!!!!!!!
!! check normalization
! j=1
! do i=1,nprims+1
! iprimao=ipao(i)
! iprimtyp=ipty(i)
! if(i.gt.1)then
! if(i.eq.nprims+1) iprimao=0
! if(iprimao.ne.jprimao) then
! call deflmna(jprimtyp,lx,my,nz,lang,xlinf)
! fnorm=3.14159265358979323846**1.50d0
! fnorm=fnorm/dble(2**lang)
! ifac=0
! call dblfac(lx,ifac)
! fnorm=fnorm*ifac
! call dblfac(my,ifac)
! fnorm=fnorm*ifac
! call dblfac(nz,ifac)
! fnorm=fnorm*ifac
! summe=0.0d0
! do k=j,i-1
! do l=j,i-1
! dzaehl=cxip(k)*cxip(l)
! dnenn=exip(k)+exip(l)
! expon=dble(lang)+1.50d0
! dnenn=dnenn**expon
! summe=summe+dzaehl/dnenn
! enddo
! enddo
! summe=fnorm*summe
! write(*,*) 'self ovlp:', summe
! j=i
! endif
! endif
! jprimao=iprimao
! jprimtyp=iprimtyp
! enddo
!!!
end subroutine normalize
subroutine deflmna(iprtyp,lx,my,nz,lang,xlinf)
implicit none
integer lx,my,nz,lang,iprtyp
real*8 xlinf
xlinf=1.0d0
lx=0
my=0
nz=0
lang=0
c=======================================================================
c cartesian gaussian functions (6d,10f...)
c s,px, py pz, dx**2 dy**2 dz**2 dxy dxz dyz
c 1 2 3 4 5 6 7 8 9 10
c fxxx, fyyy, fzzz, fxxy, fxxz, fyyx, fyyz, fxzz, fyzz, fxyz
c 11 12 13 14 15 16 17 18 19 20
c
c assign for each ipty, the angular momentum (L), and the expinents l,m,n of x,y,z
c linf is the factor to multiply normalized functions that are linearly dependent (e.g. dx**2,dy**2,dz**2)
c=======================================================================
select case(iprtyp)
case(1)
lx=0
my=0
nz=0
lang=0
xlinf=1.0d0
case(2)
lx=1
my=0
nz=0
lang=1
xlinf=1.0d0
case(3)
lx=0
my=1
nz=0
lang=1
xlinf=1.0d0
case(4)
lx=0
my=0
nz=1
lang=1
xlinf=1.0d0
case(5)
lx=2
my=0
nz=0
lang=2
xlinf=dsqrt(3.0d0)
case(6)
lx=0
my=2
nz=0
lang=2
xlinf=dsqrt(3.0d0)
case(7)
lx=0
my=0
nz=2
lang=2
xlinf=dsqrt(3.0d0)
case(8)
lx=1
my=1
nz=0
lang=2
xlinf=dsqrt(3.0d0)
c xlinf=1.0d0
case(9)
lx=1
my=0
nz=1
lang=2
xlinf=dsqrt(3.0d0)
c xlinf=1.0d0
case(10)
lx=0
my=1
nz=1
lang=2
xlinf=dsqrt(3.0d0)
c xlinf=1.0d0
case(11)
lx=3
my=0
nz=0
lang=3
xlinf=dsqrt(15.0d0)
case(12)
lx=0
my=3
nz=0
lang=3
xlinf=dsqrt(15.0d0)
case(13)
lx=0
my=0
nz=3
lang=3
xlinf=dsqrt(15.0d0)
case(14)
lx=2
my=1
nz=0
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(15)
lx=2
my=0
nz=1
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(16)
lx=1
my=2
nz=0
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(17)
lx=0
my=2
nz=1
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(18)
lx=1
my=0
nz=2
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(19)
lx=0
my=1
nz=2
lang=3
! xlinf=dsqrt(3.0d0)
xlinf=dsqrt(15.0d0)
case(20)
lx=1
my=1
nz=1
lang=3
! xlinf=1.0d0
xlinf=dsqrt(15.0d0)
case default
write(*,*)'unrecognized cartesian function/ang. momentum'
write(0,*)'unrecognized cartesian function/ang. momentum'
stop 'normalization impossible! Exiting...'
end select
! for checking - is the factor important??
! xlinf=1.0d0
return
end
subroutine dblfac(iin,iout)
implicit none
integer i,iin,iout,jdem,jnum,jfac
cccccccccccccccccccccccccccccccccccccccccccccc
c
c this calculates the double faculty (2n-1)!!
c i.e. expression in brackets is always odd
c
cccccccccccccccccccccccccccccccccccccccccccccc
jdem=1
do i=1,iin
jdem=jdem*i
enddo
jnum=jdem
do i=iin+1,2*iin
jdem=jdem*i
enddo
jfac=2**iin
jnum=jnum*jfac
iout=jdem/jnum
return
end