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ll_calculate_dipoleg.f90
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ll_calculate_dipoleg.f90
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!
! ParaGauss, a program package for high-performance computations of
! molecular systems
!
! Copyright (C) 2014 T. Belling, T. Grauschopf, S. Krüger,
! F. Nörtemann, M. Staufer, M. Mayer, V. A. Nasluzov, U. Birkenheuer,
! A. Hu, A. V. Matveev, A. V. Shor, M. S. K. Fuchs-Rohr, K. M. Neyman,
! D. I. Ganyushin, T. Kerdcharoen, A. Woiterski, A. B. Gordienko,
! S. Majumder, M. H. i Rotllant, R. Ramakrishnan, G. Dixit,
! A. Nikodem, T. Soini, M. Roderus, N. Rösch
!
! This program is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License version 2 as
! published by the Free Software Foundation [1].
!
! This program 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
! General Public License for more details.
!
! [1] http://www.gnu.org/licenses/gpl-2.0.html
!
! Please see the accompanying LICENSE file for further information.
!
!=====================================================================
!
! Public interface of module
!=====================================================================
subroutine ll_calculate_dipoleg(na,nb,la,lb)
!
! Purpose: calculation of all primitive dipole integrals
! for a given set of indizes
! (unique_atom1,unique_atom2,la,lb).
!
! Author: MS
! Date: 8/96
!
#include <def.h>
use unique_atom_module
use type_module
use solid_harmonics_module, only : solid_harmonics_calc,solid_harmonics_scalar
use int_data_dipole_module
use solhrules_module
use integralpar_module
use options_module, only: options_integral_expmax
implicit none
integer(kind=i4_kind),intent(in) :: na ! number of unique atom a
integer(kind=i4_kind),intent(in) :: nb ! number of unique atom b
integer(kind=i4_kind),intent(in) :: la ! angular momentum of unique atom a
integer(kind=i4_kind),intent(in) :: lb ! angular momentum of unique atom b
!===================================================================
! End of public interface of module
!===================================================================
! constants
real(kind=r8_kind),parameter :: pi=3.14159265358979324_r8_kind
real(kind=r8_kind),parameter :: gam=1.0_r8_kind
real(kind=r8_kind),parameter :: very_small=1.0e-100_r8_kind
real(kind=r8_kind),parameter :: very_big=1.0e100_r8_kind
real(kind=r8_kind),parameter :: zero=0.0_r8_kind
real(kind=r8_kind),parameter,dimension(0:8) :: dfac= (/ &
1.0_r8_kind, 1.0_r8_kind, 3.0_r8_kind, 15.0_r8_kind, 105.0_r8_kind, &
945.0_r8_kind, 10395.0_r8_kind, 135135.0_r8_kind, 2027025.0_r8_kind /)
! variables
integer(kind=i4_kind) :: num,m,alloc_stat,i_xyz,k,i_l,i_lma,i_lmb, &
n_lma,n_lmb,naexps,nbexps,ma,mb,l,iota
integer(kind=i4_kind), dimension(2:4) :: lm2xyz = (/3,1,2/)
! transforms lm-indices 2(z), 3(x), 4(y) into 1(x), 2(y), 3(z)
logical,allocatable :: cutoff(:,:)
real(kind=r8_kind),pointer,dimension(:) :: &
aexps,bexps
real(kind=r8_kind),allocatable,dimension(:) :: &
fact0,fact1,fact2,fact4,fact6,tau,aexp_arr,bexp_arr,clmamb_scalar
real(kind=r8_kind),allocatable,dimension(:,:) :: &
fact0_arr,fact1_arr,fact2_arr,clmamb,diff_arr0, &
grad_clmamb_scalar(:,:)
real(kind=r8_kind),allocatable,dimension(:,:,:) :: &
overlap,diff_arr0_grad,clmamb_grad
real(kind=r8_kind),allocatable,dimension(:,:,:,:) :: &
diff_rule_result,overlap_grad,orbzeeman, corrzeeman
real(kind=r8_kind),allocatable,dimension(:,:,:,:,:) :: &
diff_rule_result_grad,rnabla_primitive
real(kind=r8_kind),dimension(3) :: xa,xb,xd
real(kind=r8_kind) :: arg
integer(kind=i4_kind),parameter:: i1=1,i2=2,i4=4
naexps = unique_atoms(na)%l_ob(la)%n_exponents
nbexps = unique_atoms(nb)%l_ob(lb)%n_exponents
allocate( &
fact0_arr(nbexps,naexps), &
fact1_arr(nbexps,naexps), &
fact2_arr(nbexps,naexps), &
cutoff(nbexps,naexps), &
stat=alloc_stat)
xa = center1
xb = center2
!!$ xb(2) = xb(2)+0.0001
xd =xa-xb
aexps => unique_atoms(na)%l_ob(la)%exponents(:)
bexps => unique_atoms(nb)%l_ob(lb)%exponents(:)
n_lma = (la+1)**2
n_lmb = (lb+1)**2
arg=sum(xd**2)
fact0_arr=(spread(aexps,1,nbexps)+spread(bexps,2,naexps))
fact1_arr=(spread(aexps,1,nbexps)*spread(bexps,2,naexps))
where(fact0_arr>=very_small) ! prevent division by zero
fact2_arr=fact1_arr/fact0_arr
elsewhere
fact2_arr=very_big
end where
where(fact2_arr*arg>options_integral_expmax()) ! cutoff: where almost no overlap
cutoff=.false. ! is present calculation is not necessary
elsewhere
cutoff=.true.
end where
num=count(cutoff)
if(num==0) then ! all integrals are equal zero
prim_int_2cob_dipoleg = 0.0_r8_kind
deallocate( &
fact0_arr, &
fact1_arr, &
fact2_arr, &
cutoff, &
stat=alloc_stat)
return
end if
allocate ( &
fact0(num), &
fact1(num), &
fact2(num), &
fact4(num), &
fact6(num), &
tau(num), &
overlap(num,n_lma,n_lmb), &
overlap_grad(num,n_lma,n_lmb,2:4), &
orbzeeman(num,2*la+1,2*lb+1,3), &
rnabla_primitive(num,2*la+1,2*lb+1,3,3), &
corrzeeman(num,2*la+1,2*lb+1,3), &
diff_rule_result(num,n_lma,n_lmb,3), &
diff_rule_result_grad(num,n_lma,n_lmb,3,2:4), &
aexp_arr(num), &
bexp_arr(num), &
clmamb_scalar((max(la,lb)+1)**2), &
grad_clmamb_scalar(2:4,(la+1)**2), &
clmamb(num,(la+1)**2), &
clmamb_grad(num,(la+1)**2,2:4), &
diff_arr0((la+1)**2,(lb+1)**2), &
diff_arr0_grad((la+1)**2,(lb+1)**2,2:4), &
stat=alloc_stat)
! List of *facts* at the beginning
! fact0 = a + b
! fact1 = a * b
! fact2 = a*b/(a+b)
fact0=pack(fact0_arr,cutoff)
fact1=pack(fact1_arr,cutoff)
fact2=pack(fact2_arr,cutoff)
aexp_arr=pack(spread(aexps,1,nbexps),cutoff)
bexp_arr=pack(spread(bexps,2,naexps),cutoff)
deallocate( &
fact0_arr, &
fact1_arr, &
fact2_arr, &
stat=alloc_stat)
! precalculation of solid harmonics
clmamb_scalar=solid_harmonics_scalar(max(la,lb),xd)
tau=fact2*arg ! a*b/(a+b)*(A-B)**2
! calculate overlap
fact6= exp(-tau) * (4.0_r8_kind*fact2/fact0)**0.75_r8_kind &
/ ( sqrt(aexp_arr**la*dfac(la)) * sqrt(bexp_arr**lb*dfac(lb)) )
i_lmb=1
do i_l=0,lb
do mb=1,2*i_l+1
diff_arr0(:,i_lmb)= &
reshape( &
diff_rule( spread(clmamb_scalar,1,1), 1, n_lma, i_lmb ), &
(/n_lma/) &
)
do i_xyz=2,4
diff_arr0_grad(:,i_lmb,i_xyz)=&
reshape( &
diff_rule_nested(spread(clmamb_scalar,1,1), 1, n_lma, i_xyz,i_lmb), &
(/n_lma/) )
enddo
! do i_lma=1,n_lma
! print*,i_lma,clmamb_scalar(i_lmb),diff_arr0(i_lma,i_lmb),&
! diff_arr0_grad(i_lma,i_lmb,2)
! enddo
i_lmb=i_lmb+1
end do
end do
do i_lma=1,n_lma
grad_clmamb_scalar(2:4,i_lma)=&
reshape(diff_rule(spread(clmamb_scalar,1,1),i2,i4,i_lma),(/3/))
!print*,i_lma,clmamb_scalar(i_lma),grad_clmamb_scalar(2,i_lma)
enddo
fact4=1.0_r8_kind
i_lma=1
do l=0,la
do m=1,2*l+1
clmamb(:,i_lma)=clmamb_scalar(i_lma)*fact4
clmamb_grad(:,i_lma,2)=grad_clmamb_scalar(2,i_lma)*fact4
clmamb_grad(:,i_lma,3)=grad_clmamb_scalar(3,i_lma)*fact4
clmamb_grad(:,i_lma,4)=grad_clmamb_scalar(4,i_lma)*fact4
i_lma=i_lma+1
enddo
fact4=-fact4*fact2*2.0_r8_kind
enddo
i_lmb=1
do i_l=0,lb
do mb=1,2*i_l+1
overlap(:,:,i_lmb)= &
spread( fact6*(2.0_r8_kind*fact2)**i_l, 2, n_lma ) * &
prod_rule( &
spread( diff_arr0(:,i_lmb), 1, num ), &
clmamb(:,:), 1, n_lma &
)
do iota=2,4
overlap_grad(:,:,i_lmb,iota)= &
spread( -xd(lm2xyz(iota))*fact6*(2.0_r8_kind*fact2)**(i_l+1), 2, n_lma ) * &
prod_rule( &
spread( diff_arr0(:,i_lmb), 1, num ), &
clmamb(:,:), 1, n_lma &
)+ &
spread( fact6*(2.0_r8_kind*fact2)**i_l, 2, n_lma ) * ( &
prod_rule( &
spread( diff_arr0(:,i_lmb),1, num ), &
clmamb_grad(:,:,iota), i1, n_lma &
)+ &
prod_rule( &
spread(diff_arr0_grad(:,i_lmb,iota), 1, num ), &
clmamb(:,:), i1, n_lma &
) )
enddo
! print*,overlap(1,1,i_lmb),overlap_grad(1,1,i_lmb,2)
i_lmb = i_lmb+1
end do
enddo
! calculate double differential rule on C(1,m) and multiply all scaling factors
diff_rule_result = 0.0_r8_kind
diff_rule_result_grad = 0.0_r8_kind
diff_rule_result(:,1,1,1) = & !z
pack( &
spread(aexps*xa(3),1,nbexps) + &
spread(bexps*xb(3),2,naexps), &
cutoff &
) / fact0
diff_rule_result_grad(:,1,1,1,2) = bexp_arr / fact0
! diff_rule_result_grad(:,1,1,1,2) = pack(spread(bexps,2,naexps),cutoff)&
! / fact0
! print*,'xb xa',xb(3),xa(3)
diff_rule_result(:,1,1,2) = & !x
pack( &
spread(aexps*xa(1),1,nbexps) + &
spread(bexps*xb(1),2,naexps), &
cutoff &
) / fact0
diff_rule_result_grad(:,1,1,2,3)=bexp_arr / fact0
diff_rule_result(:,1,1,3) = & !y
pack( &
spread(aexps*xa(2),1,nbexps) + &
spread(bexps*xb(2),2,naexps), &
cutoff &
) / fact0
diff_rule_result_grad(:,1,1,3,4)= bexp_arr / fact0
fact6 = aexp_arr / fact0
if(n_lma.ge.4) then
do i_lma = 2, 4
diff_rule_result(:,i_lma,1,i_lma-1) = fact6
enddo
end if
fact6 = bexp_arr / fact0
if(n_lmb.ge.4) then
do i_lmb = 2, 4
diff_rule_result(:,1,i_lmb,i_lmb-1) = fact6
enddo
end if
!!$print*,'diff_rule_result'
! do i_lmb =1, n_lmb
! do i_lma = 1,n_lma
! print*,diff_rule_result(1,i_lma,i_lmb,1), &
! diff_rule_result_grad(1,i_lma,i_lmb,1,2)
! enddo
! enddo
! double product rule with respect to a and b
do i_xyz = 1, 3
do iota=2,4
rnabla_primitive(:,:,:,lm2xyz(i_xyz+1),lm2xyz(iota)) = &
prod_rule_double( &
diff_rule_result_grad(:,:,:,i_xyz,iota), &
overlap, &
la**2+1,la**2+2*la+1, &
lb**2+1,lb**2+2*lb+1 &
)- &
prod_rule_double( &
diff_rule_result(:,:,:,i_xyz), &
overlap_grad(:,:,:,iota), &
la**2+1,la**2+2*la+1, &
lb**2+1,lb**2+2*lb+1 &
)
enddo
enddo
if(.false. .and. la.eq.0.and.lb.eq.2)then
DPRINT 'orbzeeman ll=2,0'
do ma=1,2*la+1
do mb=1,2*lb+1
print*,ma,mb
!!$ print*,rnabla_primitive(1,ma,mb,1,1),rnabla_primitive(1,ma,mb,2,1),&
!!$ rnabla_primitive(1,ma,mb,3,1)
print*,rnabla_primitive(1,ma,mb,1,2),rnabla_primitive(1,ma,mb,2,2),&
rnabla_primitive(1,ma,mb,3,2)
end do
end do
endif
orbzeeman(:,:,:,:)=&
reshape(vec_prod_vector(reshape(rnabla_primitive, & ! the - sign deleted 5.12.99
(/num*(2*la+1)*(2*lb+1),3,3/)))&
,(/num,(2*la+1),(2*lb+1),3/))
corrzeeman(:,:,:,:)=0.0_r8_kind
do ma=1,2*la+1
do mb=1,2*lb+1
do k = 1, 13
select case(k)
case(4) ! Sigma
prim_int_2cob_dipoleg(:,:,mb,ma,4) = &
unpack(overlap(:,la**2+ma,lb**2+mb),cutoff,zero)
case (1:3)
prim_int_2cob_dipoleg(:,:,mb,ma,k) = &
unpack(orbzeeman(:,ma,mb,k),cutoff,zero)
!DG gauge correction----------------------------------------------------
!!$ corrzeeman(:,:,:,:)=&
!!$ reshape(calc_correction_integrals(reshape(rnabla_primitive,&
!!$ (/num*(2*la+1)*(2*lb+1),3,3/)),k)&
!!$ ,(/num,(2*la+1),(2*lb+1),3/))
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,4+(k-1)*3+1) = & !DG 5,8,11
!!$ unpack(corrzeeman(:,ma,mb,1),cutoff,zero)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,4+(k-1)*3+2) = & !6,9,12
!!$ unpack(corrzeeman(:,ma,mb,2),cutoff,zero)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,4+(k-1)*3+3) = & !7,10,13
!!$ unpack(corrzeeman(:,ma,mb,3),cutoff,zero)
!!$ case (5:13)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k) = &
!!$ unpack(overlap(:,la**2+ma,lb**2+mb),cutoff,zero)
!!$ case default
!!$
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k) = &
!!$ unpack(corrzeeman(:,ma,mb,3),cutoff,zero)
!!$ case (5,8,11)
!!$ corrzeeman(:,:,:,:)=&
!!$ reshape(calc_correction_integrals(reshape(rnabla_primitive,&
!!$ (/num*(2*la+1)*(2*lb+1),3,3/)),k)&
!!$ ,(/num,(2*la+1),(2*lb+1),3/))
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k) = &
!!$ unpack(corrzeeman(:,ma,mb,1),cutoff,zero)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k+1) = &
!!$ unpack(corrzeeman(:,ma,mb,2),cutoff,zero)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k+2) = &
!!$ unpack(corrzeeman(:,ma,mb,3),cutoff,zero)
!!$ case (5,9,13)
!!$ prim_int_2cob_dipoleg(:,:,mb,ma,k) = &
!!$ unpack(overlap(:,la**2+ma,lb**2+mb),cutoff,zero)
case default
prim_int_2cob_dipoleg(:,:,mb,ma,k) = 0.0_r8_kind
end select
end do
if(.false..and.la.eq.1.and.lb.eq.1) then
print*,ma,mb
print*,prim_int_2cob_dipoleg(1,1,mb,ma,1), &
prim_int_2cob_dipoleg(1,1,mb,ma,2),&
prim_int_2cob_dipoleg(1,1,mb,ma,3)
end if
end do
end do
deallocate ( &
fact0, &
fact1, &
fact2, &
fact4, &
fact6, &
tau, &
overlap, &
overlap_grad, &
rnabla_primitive, &
orbzeeman, &
corrzeeman,&
diff_rule_result, &
diff_rule_result_grad, &
aexp_arr, &
bexp_arr, &
clmamb_scalar, &
grad_clmamb_scalar, &
clmamb, &
clmamb_grad, &
diff_arr0, &
diff_arr0_grad, &
cutoff, &
stat=alloc_stat)
contains
function vec_prod_vector(r_nabla_elements) result (p)
!
! vector product constartcts
!
!----------------------------------------------------------------
! Modifications
!----------------------------------------------------------------
!
! Modification (Please copy before editing)
! Author: ...DG
! Date: ...11/03/2001
! Description: ...Changed sign in Lz component in finction
!
!
!----------------------------------------------------------------
USE type_module
IMPLICIT NONE
real(kind=r8_kind), intent(in), dimension(:,:,:):: r_nabla_elements
real(kind=r8_kind),dimension(size(r_nabla_elements,1),3)::p
p(:,1)=(r_nabla_elements(:,2,3)-r_nabla_elements(:,3,2))
p(:,2)=(r_nabla_elements(:,3,1)-r_nabla_elements(:,1,3))
!FIXME: sign changed (undo whenever you find and correct the
! reason this change is needed for):
p(:,3)=-(r_nabla_elements(:,1,2)-r_nabla_elements(:,2,1))
end function vec_prod_vector
function calc_correction_integrals (r_nabla_elements,k) result (p)
USE type_module
IMPLICIT NONE
real(kind=r8_kind), intent(in), dimension(:,:,:):: r_nabla_elements
integer(kind=i4_kind), intent (in) :: k
real(kind=r8_kind),dimension(size(r_nabla_elements,1),3)::p
select case (k)
case(5)
p(:,1) = r_nabla_elements(:,2,2)+r_nabla_elements(:,3,3)
p(:,2) = -r_nabla_elements(:,2,1)
p(:,3) = -r_nabla_elements(:,3,1)
case(8)
p(:,1) = -r_nabla_elements(:,1,2)
p(:,2) = r_nabla_elements(:,1,1)+r_nabla_elements(:,3,3)
p(:,3) = -r_nabla_elements(:,3,2)
case(11)
p(:,1) = -r_nabla_elements(:,1,3)
p(:,2) = -r_nabla_elements(:,2,3)
p(:,3) = r_nabla_elements(:,1,1)+r_nabla_elements(:,2,2)
end select
end function calc_correction_integrals
end subroutine ll_calculate_dipoleg