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linear_response.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/>.
!
!! ------------------------------------------------------------------------
! written by Marc de Wegifosse 2017-2020
SUBROUTINE lresp(nci,apb,amb,iconf,maxconf,xl,yl,zl,moci,no,nv)
use commonresp
use commonlogicals
use omp_lib
IMPLICIT NONE
integer ::i,j,k,ii,jj,kk,ij,jk,ab,io,iv,idum1,idum2,nci
integer ::io1,io2,iv1,iv2,iwrk,jwrk
integer ::maxconf,moci,no,nv
integer ::iconf(maxconf,2)
integer*8 ::lin8
real*8 ::xl(moci*(moci+1)/2)
real*8 ::yl(moci*(moci+1)/2)
real*8 ::zl(moci*(moci+1)/2)
real*8 ::mu(moci*(moci+1)/2,3)
real*4 ::mu_x(nci)
real*4 ::mu_y(nci)
real*4 ::mu_z(nci)
real*4 ::apb(nci*(nci+1)/2)
real*4 ::amb(nci*(nci+1)/2)
real*4, allocatable ::inv_amb(:)
real*4, allocatable ::inv_resp(:)
real*4, allocatable ::XpY(:,:)
real*4 ::omega
real*4 ::freq(num_freq+1)
real*4 ::alpha_xx,alpha_xy,alpha_xz
real*4 ::alpha_yy,alpha_yz
real*4 ::alpha_zz
character*1 ::uplo
integer ::info
integer, allocatable ::ipiv(:)
real*4, allocatable ::work (:)
integer ::ix,iy,iz
real*4 ::start_time,end_time
character(len=14):: dummy
mu=0.0
mu(:,1)=xl(:)
mu(:,2)=yl(:)
mu(:,3)=zl(:)
open(unit=101,file='wavelength',form='formatted',status='old')
freq(1)=0.0
write(*,*)
write(*,*)'====================================================
.=================='
write(*,*)' Welcome in nonlinear response sTD-DFT
. program'
write(*,*)'====================================================
.=================='
write(*,*)
write(*,*) 'Wavelengths (nm)'
write(*,*) ' infinity'
Do i=1, num_freq
read(101,*)freq(i+1)
write(*,*)freq(i+1)
freq(i+1)=45.56335/freq(i+1)
enddo
close(101)
allocate(inv_amb(nci*(nci+1)/2))
inv_amb=amb
uplo='U'
allocate(ipiv(1:nci),work(1:nci))
call ssptrf(uplo,nci,inv_amb,ipiv,info)
call ssptri(uplo,nci,inv_amb,ipiv,work,info)
deallocate(ipiv,work)
allocate( XpY(nci,3))
! the dipole moment matrix mu_ai
mu_x=0.0
mu_y=0.0
mu_z=0.0
!$omp parallel private(j,io,iv,idum1,idum2,ij)
!$omp do
Do j=1, nci
io=iconf(j,1)
iv=iconf(j,2)
idum1=max(io,iv)
idum2=min(io,iv)
ij=idum2+idum1*(idum1-1)/2
mu_x(j)=-2.0*xl(ij)
mu_y(j)=-2.0*yl(ij)
mu_z(j)=-2.0*zl(ij)
enddo
!$omp end do
!$omp end parallel
Do ii=1, num_freq+1
omega=freq(ii)
XpY(:,:)=0.0
call cpu_time(start_time)
allocate(inv_resp(nci*(nci+1)/2))
inv_resp=apb-omega**2.0*inv_amb
uplo='U'
XpY(:,1)=mu_x(:)
XpY(:,2)=mu_y(:)
XpY(:,3)=mu_z(:)
allocate(ipiv(1:nci))
call ssptrf(uplo,nci,inv_resp,ipiv,info)
call ssptrs(uplo,nci,3,inv_resp,ipiv,XpY,nci,info)
deallocate(ipiv)
if(nto)then
write(dummy,'(a,i0)')'1-',ii
open(unit=14,file=dummy)
write(14,*)XpY(:,1)
close(14)
write(dummy,'(a,i0)')'2-',ii
open(unit=14,file=dummy)
write(14,*)XpY(:,2)
close(14)
write(dummy,'(a,i0)')'3-',ii
open(unit=14,file=dummy)
write(14,*)XpY(:,3)
close(14)
endif
alpha_xx=0.0
alpha_xy=0.0
alpha_xz=0.0
alpha_yy=0.0
alpha_yz=0.0
alpha_zz=0.0
!$omp parallel private(i,io,iv,idum1,idum2,ij)
!$omp& reduction(+:alpha_xx,alpha_xy
!$omp& ,alpha_xz,alpha_yy,alpha_yz
!$omp& ,alpha_zz)
!$omp do
Do j=1, nci
io=iconf(j,1)
iv=iconf(j,2)
idum1=max(io,iv)
idum2=min(io,iv)
ij=idum2+idum1*(idum1-1)/2
alpha_xx=alpha_xx-(xl(ij)*XpY(j,1))*2.0
alpha_xy=alpha_xy-(xl(ij)*XpY(j,2))*2.0
alpha_xz=alpha_xz-(xl(ij)*XpY(j,3))*2.0
alpha_yy=alpha_yy-(yl(ij)*XpY(j,2))*2.0
alpha_yz=alpha_yz-(yl(ij)*XpY(j,3))*2.0
alpha_zz=alpha_zz-(zl(ij)*XpY(j,3))*2.0
enddo
!$omp end do
!$omp end parallel
write(*,*)
write(*,3333) 'Polarizability (',-45.56335/omega,
. ';',45.56335/omega,')'
write(*,*)
write(*,1111)'x','y','z'
write(*,2222)'x',alpha_xx,alpha_xy,alpha_xz
write(*,2222)'y',alpha_xy,alpha_yy,alpha_yz
write(*,2222)'z',alpha_xz,alpha_yz,alpha_zz
write(*,*)
write(*,111) 'Mean of alpha',(alpha_xx+alpha_yy+alpha_zz)/3.0
write(*,*)
deallocate(inv_resp)
enddo
deallocate(XpY)
deallocate(inv_amb)
111 format(A15,F20.6)
1111 format(A22,2A20)
2222 format(A2,3F20.6)
3333 format(A16,F7.1,A1,F7.1,A1)
end subroutine lresp
SUBROUTINE lresp1(nci,apb,amb,iconf,maxconf,xl,yl,zl,moci,no,nv)
use commonresp
use omp_lib
IMPLICIT NONE
integer ::i,j,k,ii,jj,kk,ij,jk,ab,io,iv,idum1,idum2,nci
integer ::io1,io2,iv1,iv2,iwrk,jwrk
integer ::maxconf,moci,no,nv
integer ::iconf(maxconf,2)
integer, allocatable :: A_list(:,:)
integer ::counter_A
integer, allocatable :: B_list(:,:)
integer ::counter_B
integer*8 ::lin8
real*8 ::xl(moci*(moci+1)/2)
real*8 ::yl(moci*(moci+1)/2)
real*8 ::zl(moci*(moci+1)/2)
real*8 ::mu(moci*(moci+1)/2,3)
real*4 ::mu_x(nci)
real*4 ::mu_y(nci)
real*4 ::mu_z(nci)
real*4 ::XpY_int(nci,3)
real*4 ::apb(nci*(nci+1)/2)
real*4 ::amb(nci*(nci+1)/2)
real*4, allocatable ::inv_amb(:)
real*4, allocatable ::inv_resp(:)
real*8, allocatable ::XpY(:,:,:,:)
real*4 ::omega
real*4 ::freq(num_freq+1)
real*8 ::alpha_xx,alpha_xy,alpha_xz
real*8 ::alpha_yy,alpha_yz
real*8 ::alpha_zz
real*8, allocatable ::XmY(:,:,:,:)
real*8, allocatable ::X(:,:,:,:)
real*8, allocatable ::Y(:,:,:,:)
character*1 ::uplo
integer ::info
integer, allocatable ::ipiv(:)
real*4, allocatable ::work (:)
integer ::ix,iy,iz
real*8 ::beta(3,3,3),A,B
real*8 ::beta2_ZZZ, beta2_XZZ, beta_HRS, DR
real*8 ::betaVEC_X, betaVEC_Y, betaVEC_Z
real*4 ::start_time,end_time
mu=0.0
mu(:,1)=xl(:)
mu(:,2)=yl(:)
mu(:,3)=zl(:)
open(unit=555,file='beta_HRS',form='formatted',status='replace')
open(unit=556,file='beta_tensor',form='formatted',
. status='replace')
open(unit=101,file='wavelength',form='formatted',status='old')
freq(1)=0.0
write(*,*)
write(*,*)'====================================================
.=================='
write(*,*)' Welcome in nonlinear response sTD-DFT
. program'
write(*,*)'====================================================
.=================='
write(*,*)
write(*,*) 'Wavelengths (nm)'
write(*,*) ' infinity'
Do i=1, num_freq
read(101,*)freq(i+1)
write(*,*)freq(i+1)
freq(i+1)=45.56335/freq(i+1)
enddo
close(101)
allocate(inv_amb(nci*(nci+1)/2))
inv_amb=amb
uplo='U'
allocate(ipiv(1:nci),work(1:nci))
call ssptrf(uplo,nci,inv_amb,ipiv,info)
call ssptri(uplo,nci,inv_amb,ipiv,work,info)
deallocate(ipiv,work)
allocate( XpY(nci,num_freq+1,2,3))
allocate( XmY(nci,num_freq+1,2,3))
allocate( X(nci,num_freq+1,2,3),
. Y(nci,num_freq+1,2,3))
XpY(:,:,:,:)=0.0
XmY(:,:,:,:)=0.0
X(:,:,:,:)=0.0
Y(:,:,:,:)=0.0
! the dipole moment matrix mu_ai
mu_x=0.0
mu_y=0.0
mu_z=0.0
!$omp parallel private(j,io,iv,idum1,idum2,ij)
!$omp do
Do j=1, nci
io=iconf(j,1)
iv=iconf(j,2)
idum1=max(io,iv)
idum2=min(io,iv)
ij=idum2+idum1*(idum1-1)/2
mu_x(j)=-2.0*xl(ij)
mu_y(j)=-2.0*yl(ij)
mu_z(j)=-2.0*zl(ij)
enddo
!$omp end do
!$omp end parallel
Do ii=1, num_freq+1
Do jj=1, 2 !2*omega
omega=freq(ii)*jj
if(jj==2) omega=-omega ! from GAMESS implementation, this is what seems to be!
call cpu_time(start_time)
allocate(inv_resp(nci*(nci+1)/2))
inv_resp=apb-omega**2.0*inv_amb
uplo='U'
XpY_int(:,1)=mu_x(:)
XpY_int(:,2)=mu_y(:)
XpY_int(:,3)=mu_z(:)
allocate(ipiv(1:nci))
call ssptrf(uplo,nci,inv_resp,ipiv,info)
call ssptrs(uplo,nci,3,inv_resp,ipiv,XpY_int,nci,info)
deallocate(ipiv)
XpY(:,ii,jj,1)=dble(XpY_int(:,1))
XpY(:,ii,jj,2)=dble(XpY_int(:,2))
XpY(:,ii,jj,3)=dble(XpY_int(:,3))
if(jj==1)then !print alpha only for omega and not -2*omega
alpha_xx=0.0
alpha_xy=0.0
alpha_xz=0.0
alpha_yy=0.0
alpha_yz=0.0
alpha_zz=0.0
!$omp parallel private(i,io,iv,idum1,idum2,ij)
!$omp& reduction(+:alpha_xx,alpha_xy
!$omp& ,alpha_xz,alpha_yy,alpha_yz
!$omp& ,alpha_zz)
!$omp do
Do j=1, nci
io=iconf(j,1)
iv=iconf(j,2)
idum1=max(io,iv)
idum2=min(io,iv)
ij=idum2+idum1*(idum1-1)/2
alpha_xx=alpha_xx-(xl(ij)*XpY(j,ii,jj,1))*2.0
alpha_xy=alpha_xy-(xl(ij)*XpY(j,ii,jj,2))*2.0
alpha_xz=alpha_xz-(xl(ij)*XpY(j,ii,jj,3))*2.0
alpha_yy=alpha_yy-(yl(ij)*XpY(j,ii,jj,2))*2.0
alpha_yz=alpha_yz-(yl(ij)*XpY(j,ii,jj,3))*2.0
alpha_zz=alpha_zz-(zl(ij)*XpY(j,ii,jj,3))*2.0
enddo
!$omp end do
!$omp end parallel
write(*,*)
write(*,3333) 'Polarizability (',-45.56335/omega,
. ';',45.56335/omega,')'
write(*,*)
write(*,1111)'x','y','z'
write(*,2222)'x',alpha_xx,alpha_xy,alpha_xz
write(*,2222)'y',alpha_xy,alpha_yy,alpha_yz
write(*,2222)'z',alpha_xz,alpha_yz,alpha_zz
write(*,*)
write(*,111) 'Mean of alpha',(alpha_xx+alpha_yy+alpha_zz)/3.0
write(*,*)
endif
c frequency-dependent first hyperpolarizability (beta) SHG only
! extract X and Y from XpY
! (X-Y)=omega*(A-B)^-1 (X+Y)
! X=((X+Y)+(X-Y))/2
! Y=(X+Y)-X
!$omp parallel private(i,j,ij,ix)
!$omp& reduction (+:XmY)
!$omp do
Do i=1,nci
Do j=1,nci
ij=lin8(i,j)
Do ix=1,3
XmY(i,ii,jj,ix)=XmY(i,ii,jj,ix)+ dble(omega)
. *dble(inv_amb(ij))*XpY(j,ii,jj,ix)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
!$omp parallel private(ix,j)
!$omp& reduction(+:X,Y)
!$omp do
Do ix=1,3
Do j=1,nci
X(j,ii,jj,ix)=(XpY(j,ii,jj,ix)+XmY(j,ii,jj,ix))/2.0
Y(j,ii,jj,ix)=XpY(j,ii,jj,ix)-X(j,ii,jj,ix)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(inv_resp)
call cpu_time(end_time)
print '("alpha Time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
enddo !jjdo
c beta beta = A - B + C (here C=0 since no derivative of g^XC)
call cpu_time(start_time)
if(ii==1)then
!
! Genarating a list of indexes used in A and B formula to save a great bunch of time
!
counter_A=0
!$omp parallel private(j,i,kk)
!$omp& reduction(+:counter_A)
!$omp do
Do i=1,nci
Do j=1,no
Do kk=1,nci
if(iconf(kk,1)==j .and. iconf(kk,2)==iconf(i,2))then
counter_A=counter_A+1
endif
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(A_list(1:counter_A,1:3))
A_list=-9999
call List_A(maxconf,no,nci,iconf,A_list,counter_A)
!Do i=1,counter_A
!write(*,*)i,A_list(i,1:3)
!enddo
counter_B=0
!$omp parallel private(j,i,kk)
!$omp& reduction(+:counter_B)
!$omp do
Do i=1,nci
Do j=1,nv
Do kk=1,nci
if(iconf(kk,1)==iconf(i,1) .and. iconf(kk,2)==j+no)then
counter_B=counter_B+1
endif
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(B_list(1:counter_B,1:3))
B_list=-9999
call List_B(maxconf,no,nv,nci,iconf,B_list,counter_B)
!Do i=1,counter_B
!write(*,*)i,B_list(i,1:3)
!enddo
call cpu_time(end_time)
print '("A & B indexes list Time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
endif
!
!Fast version
!
beta(:,:,:)=0.0
! Let's save time applying symmetry conditions
if(ii==1)then !static case Kleinman condition applied ijk = kij = jki
! only 10 tensor components computed
!Diagonal
call beta_resp_fast(1,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,1,1)=A-B
call beta_resp_fast(2,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,2,2)=A-B
call beta_resp_fast(3,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,3,3)=A-B
!Off-diagonal
!ijj
call beta_resp_fast(1,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,2,2)=A-B
beta(2,1,2)=beta(1,2,2)
beta(2,2,1)=beta(1,2,2)
call beta_resp_fast(1,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,3,3)=A-B
beta(3,1,3)=beta(1,3,3)
beta(3,3,1)=beta(1,3,3)
call beta_resp_fast(2,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,1,1)=A-B
beta(1,2,1)=beta(2,1,1)
beta(1,1,2)=beta(2,1,1)
call beta_resp_fast(2,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,3,3)=A-B
beta(3,2,3)=beta(2,3,3)
beta(3,3,2)=beta(2,3,3)
call beta_resp_fast(3,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,2,2)=A-B
beta(2,3,2)=beta(3,2,2)
beta(2,2,3)=beta(3,2,2)
call beta_resp_fast(3,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,1,1)=A-B
beta(1,3,1)=beta(3,1,1)
beta(1,1,3)=beta(3,1,1)
!ijk
call beta_resp_fast(1,2,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,2,3)=A-B
beta(1,3,2)=beta(1,2,3)
beta(3,1,2)=beta(1,2,3)
beta(3,2,1)=beta(1,2,3)
beta(2,3,1)=beta(1,2,3)
beta(2,1,3)=beta(1,2,3)
else ! ijk=ikj because SHG (2 identical frequencies)
!Diagonal
call beta_resp_fast(1,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,1,1)=A-B
call beta_resp_fast(2,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,2,2)=A-B
call beta_resp_fast(3,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,3,3)=A-B
!Off-diagonal
!ijj
call beta_resp_fast(1,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,2,2)=A-B
call beta_resp_fast(2,1,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,1,2)=A-B
beta(2,2,1)=beta(2,1,2)
call beta_resp_fast(1,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,3,3)=A-B
call beta_resp_fast(3,1,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,1,3)=A-B
beta(3,3,1)=beta(3,1,3)
call beta_resp_fast(2,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,1,1)=A-B
call beta_resp_fast(1,2,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,2,1)=A-B
beta(1,1,2)=beta(1,2,1)
call beta_resp_fast(2,3,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,3,3)=A-B
call beta_resp_fast(3,2,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,2,3)=A-B
beta(3,3,2)=beta(3,2,3)
call beta_resp_fast(3,2,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,2,2)=A-B
call beta_resp_fast(2,3,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,3,2)=A-B
beta(2,2,3)=beta(2,3,2)
call beta_resp_fast(3,1,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,1,1)=A-B
call beta_resp_fast(1,3,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,3,1)=A-B
beta(1,1,3)=beta(1,3,1)
!ijk
call beta_resp_fast(1,2,3,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(1,2,3)=A-B
beta(1,3,2)=beta(1,2,3)
call beta_resp_fast(3,1,2,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(3,1,2)=A-B
beta(3,2,1)=beta(3,1,2)
call beta_resp_fast(2,3,1,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
beta(2,3,1)=A-B
beta(2,1,3)=beta(2,3,1)
endif
call cpu_time(end_time)
print '("beta Time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
betaVec_X=0.0
betaVec_Y=0.0
betaVec_Z=0.0
Do k=1,3
betaVec_X=betaVec_X+beta(1,k,k)+beta(k,1,k)+beta(k,k,1)
betaVec_Y=betaVec_Y+beta(2,k,k)+beta(k,2,k)+beta(k,k,2)
betaVec_Z=betaVec_Z+beta(3,k,k)+beta(k,3,k)+beta(k,k,3)
enddo
betaVec_X=betaVec_X/5.0
betaVec_Y=betaVec_Y/5.0
betaVec_Z=betaVec_Z/5.0
write(*,*) '_____________________________________________
.________'
write(*,*)
write(*,5555) 'SHG first hyperpolarizability ('
.,-45.56335/(freq(ii)*2.0),';',45.56335/freq(ii),','
.,45.56335/freq(ii),')'
write(*,*)
write(556,5555) 'SHG first hyperpolarizability ('
.,-45.56335/(freq(ii)*2.0),';',45.56335/freq(ii),','
.,45.56335/freq(ii),')'
write(*,*)
call PrintBeta(beta,556)
write(*,*)
write(*,6666) 'beta_VEC_X',betaVec_X
write(*,6666) 'beta_VEC_Y',betaVec_Y
write(*,6666) 'beta_VEC_Z',betaVec_Z
write(*,*)
call HRS(beta,beta2_ZZZ, beta2_XZZ, beta_HRS, DR)
write(*,9007) 6.0*beta2_ZZZ - 9.0*beta2_XZZ,
. sqrt(6.0*beta2_ZZZ - 9.0*beta2_XZZ),
. 63.0/2.0*beta2_XZZ - 7.0/2.0*beta2_ZZZ,
. sqrt(63.0/2.0*beta2_XZZ - 7.0/2.0*beta2_ZZZ),
. sqrt(63.0/2.0*beta2_XZZ - 7.0/2.0*beta2_ZZZ)/
. sqrt(6.0*beta2_ZZZ - 9.0*beta2_XZZ)
write(*,4444) 'beta**2_ZZZ',beta2_ZZZ, 'beta**2_XZZ', beta2_XZZ
write(*,4444) 'beta_HRS',beta_HRS,' DR', DR
write(*,*) '_____________________________________________
.________'
write(555,*)freq(ii)*27.21139,beta_HRS
! beta(:,:,:)=0.0
! ! Let's save time applying symmetry conditions
! if(ii==1)then !static case Kleinman condition applied ijk = kij = jki
! ! only 10 tensor components computed
! !Diagonal
! call beta_resp(1,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,1,1)=A-B
! call beta_resp(2,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,2,2)=A-B
! call beta_resp(3,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,3,3)=A-B
! !Off-diagonal
! !ijj
! call beta_resp(1,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,2,2)=A-B
! beta(2,1,2)=beta(1,2,2)
! beta(2,2,1)=beta(1,2,2)
! call beta_resp(1,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,3,3)=A-B
! beta(3,1,3)=beta(1,3,3)
! beta(3,3,1)=beta(1,3,3)
! call beta_resp(2,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,1,1)=A-B
! beta(1,2,1)=beta(2,1,1)
! beta(1,1,2)=beta(2,1,1)
! call beta_resp(2,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,3,3)=A-B
! beta(3,2,3)=beta(2,3,3)
! beta(3,3,2)=beta(2,3,3)
! call beta_resp(3,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,2,2)=A-B
! beta(2,3,2)=beta(3,2,2)
! beta(2,2,3)=beta(3,2,2)
! call beta_resp(3,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,1,1)=A-B
! beta(1,3,1)=beta(3,1,1)
! beta(1,1,3)=beta(3,1,1)
! !ijk
! call beta_resp(1,2,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,2,3)=A-B
! beta(1,3,2)=beta(1,2,3)
! beta(3,1,2)=beta(1,2,3)
! beta(3,2,1)=beta(1,2,3)
! beta(2,3,1)=beta(1,2,3)
! beta(2,1,3)=beta(1,2,3)
!
! else ! ijk=ikj because SHG (2 identical frequencies)
! !Diagonal
! call beta_resp(1,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,1,1)=A-B
! call beta_resp(2,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,2,2)=A-B
! call beta_resp(3,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,3,3)=A-B
! !Off-diagonal
! !ijj
! call beta_resp(1,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,2,2)=A-B
! call beta_resp(2,1,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,1,2)=A-B
! beta(2,2,1)=beta(2,1,2)
!
! call beta_resp(1,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,3,3)=A-B
! call beta_resp(3,1,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,1,3)=A-B
! beta(3,3,1)=beta(3,1,3)
! call beta_resp(2,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,1,1)=A-B
! call beta_resp(1,2,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,2,1)=A-B
! beta(1,1,2)=beta(1,2,1)
! call beta_resp(2,3,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,3,3)=A-B
! call beta_resp(3,2,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,2,3)=A-B
! beta(3,3,2)=beta(3,2,3)
! call beta_resp(3,2,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,2,2)=A-B
! call beta_resp(2,3,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,3,2)=A-B
! beta(2,2,3)=beta(2,3,2)
! call beta_resp(3,1,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,1,1)=A-B
! call beta_resp(1,3,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,3,1)=A-B
! beta(1,1,3)=beta(1,3,1)
! !ijk
! call beta_resp(1,2,3,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(1,2,3)=A-B
! beta(1,3,2)=beta(1,2,3)
! call beta_resp(3,1,2,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(3,1,2)=A-B
! beta(3,2,1)=beta(3,1,2)
! call beta_resp(2,3,1,X,Y,
! . mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
!
! beta(2,3,1)=A-B
! beta(2,1,3)=beta(2,3,1)
!
! endif
!
! call cpu_time(end_time)
! print '("beta Time = ",f12.2," minutes.")'
! . ,(end_time-start_time)/60.0
!
! betaVec_X=0.0
! betaVec_Y=0.0
! betaVec_Z=0.0
! Do k=1,3
! betaVec_X=betaVec_X+beta(1,k,k)+beta(k,1,k)+beta(k,k,1)
! betaVec_Y=betaVec_Y+beta(2,k,k)+beta(k,2,k)+beta(k,k,2)
! betaVec_Z=betaVec_Z+beta(3,k,k)+beta(k,3,k)+beta(k,k,3)
! enddo
! betaVec_X=betaVec_X/5.0
! betaVec_Y=betaVec_Y/5.0
! betaVec_Z=betaVec_Z/5.0
!
!
! write(*,*) '_____________________________________________
! .________'
! write(*,*)
! write(*,5555) 'SHG first hyperpolarizability ('
! .,-45.56335/(freq(ii)*2.0),';',45.56335/freq(ii),','
! .,45.56335/freq(ii),')'
! write(*,*)
! call PrintBeta(beta)
! write(*,*)
! write(*,6666) 'beta_VEC_X',betaVec_X
! write(*,6666) 'beta_VEC_Y',betaVec_Y
! write(*,6666) 'beta_VEC_Z',betaVec_Z
! write(*,*)
! call HRS(beta,beta2_ZZZ, beta2_XZZ, beta_HRS, DR)
! write(*,4444) 'beta**2_ZZZ',beta2_ZZZ, 'beta**2_XZZ', beta2_XZZ
! write(*,4444) 'beta_HRS',beta_HRS,' DR', DR
! write(*,*) '_____________________________________________
! .________'
enddo
deallocate(XpY)
deallocate(XmY)
deallocate(X,Y)
deallocate(inv_amb)
111 format(A15,F20.6)
1111 format(A22,2A20)
2222 format(A2,3F20.6)
3333 format(A16,F7.1,A1,F7.1,A1)
4444 format(A12,F20.3,A12,F20.3)
5555 format(A31,F7.1,A1,F7.1,A1,F7.1,A1)
6666 format(A12,F20.3)
9007 format(2X,'|Bj=1|^2 :', F15.4,' |Bj=1| :', F15.4,
. /,2X,'|Bj=3|^2 :', F15.4,' |Bj=3| :', F15.4,
. /,2X,'rho=|Bj=3|/|Bj=1| :', F15.4,/)
end subroutine lresp1
SUBROUTINE beta_resp_fast(ix,iy,iz,X,Y,
. A_list,B_list,counter_A,counter_B,
. mu,maxconf,no,nv,nci,moci,ii,iconf,A,B)
use commonresp
use omp_lib
implicit none
integer ::xx,yy,zz
integer ::ix,iy,iz,wx,wy,wz,no,nv,nci,ii,maxconf,moci
integer ::iconf(maxconf,2)
real*8 ::mu(moci*(moci+1)/2,3)
real*8 ::X(nci,num_freq+1,2,3)
real*8 ::Y(nci,num_freq+1,2,3)
real*8 ::A,B
real*8 ::A1,A2,A3,A4,A5,A6
real*8 ::B1,B2,B3,B4,B5,B6
integer ::counter_A,counter_B
integer :: A_list(1:counter_A,1:3)
integer :: B_list(1:counter_B,1:3)
A=0.0
B=0.0
A1=0.0
A2=0.0
A3=0.0
A4=0.0
A5=0.0
A6=0.0
B1=0.0
B2=0.0
B3=0.0
B4=0.0
B5=0.0
B6=0.0
c A1 ix iy iz
xx=ix
wx=2
yy=iy
wy=1
zz=iz
wz=1
call A_beta_fast(xx,yy,zz,wx,wy,wz,X,Y,
. mu,nci,moci,ii,A1,A_list,counter_A)
c A2 ix iz iy
xx=ix
wx=2
yy=iz
wy=1
zz=iy
wz=1
call A_beta_fast(xx,yy,zz,wx,wy,wz,X,Y,
. mu,nci,moci,ii,A2,A_list,counter_A)
c A3 iy iz ix
xx=iy
wx=1
yy=iz
wy=1
zz=ix
wz=2
call A_beta_fast(xx,yy,zz,wx,wy,wz,X,Y,
. mu,nci,moci,ii,A3,A_list,counter_A)
c A4 iy ix iz
xx=iy
wx=1
yy=ix
wy=2
zz=iz
wz=1
call A_beta_fast(xx,yy,zz,wx,wy,wz,X,Y,
. mu,nci,moci,ii,A4,A_list,counter_A)
c A5 iz ix iy
xx=iz
wx=1
yy=ix
wy=2
zz=iy
wz=1
call A_beta_fast(xx,yy,zz,wx,wy,wz,X,Y,
. mu,nci,moci,ii,A5,A_list,counter_A)
c A6 iz iy ix
xx=iz
wx=1
yy=iy