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ll_calculate_hfc.f90
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ll_calculate_hfc.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
!=====================================================================
#define FPP_DEBUG
#include <def.h>
Subroutine ll_calculate_hfc (na, nb, la, lb)
!
! Purpose: calculation of all primitive 2 center orbital
! for hfc
!
!
! Author: DG
! Date: 1/2003
!
!== Interrupt of public interface of module ========================
!-------------------------------------------------------------------
! Modifications
!-------------------------------------------------------------------
!
! Modification (Please copy before editing)
! Author: ...
! Date: ...
! Description: ...
!-------------------------------------------------------------------
Use unique_atom_module
Use gamma_module
Use type_module
Use datatype
Use solid_harmonics_module, Only: solid_harmonics_calc, &
& solid_harmonics_scalar
Use solhrules_module
Use integralpar_module
Use options_module, Only: options_integral_expmax, options_finite_nucleus
Use int_data_dipole_module, Only: prim_int_2cob_hfc, center1,center2
Implicit None
!
!== Interrupt end of public interface of module ====================
!
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
!===================================================================
!
Integer (Kind=i4_kind) :: naexps, nbexps
Real (Kind=r8_kind), Pointer :: aexps (:), bexps (:)
Integer (Kind=i4_kind) :: max_order
!
! constants
Real (Kind=r8_kind), Parameter :: pi = &
& 3.14159265358979324_r8_kind, very_small = 1.0e-100_r8_kind, &
& very_big = 1.0e100_r8_kind, zero = 0.0_r8_kind, one = &
& 1.0_r8_kind, two = 2.0_r8_kind, four = 4.0_r8_kind, six = &
& 6.0_r8_kind
Real (Kind=r8_kind), 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 /)
Integer (Kind=i4_kind) :: one_i, zero_i
Integer (Kind=i4_kind) :: num, counter, m, ma, mb, alloc_stat
!
Logical, Allocatable :: cutoff (:, :)
!
! help factors
Real (Kind=r8_kind), Allocatable, Dimension (:, :) :: fact0_arr, &
& fact1_arr, fact2_arr, fact10
Real (Kind=r8_kind), Allocatable, Dimension (:) :: fact0, fact1, &
& fact2, fact4, fact5, fact6, fact7, fact8,fact81, rcsabc, tau
!
! help arrays for gamma-function
Real (Kind=r8_kind), Allocatable, Dimension (:, :) :: gamma_arg, &
& gamma_help, gamma_arg_fin_a,gamma_arg_fin_b
Real (Kind=r8_kind), Allocatable, Dimension (:) :: gamma_arg2
!arrays of some derivatives
Real (Kind=r8_kind), Allocatable, Dimension (:, :, :) :: &
& gamma_first_der
Real (Kind=r8_kind), Allocatable, Dimension (:, :, :) :: &
& gamma_second_der
! help arrays for solid harmincs
Real (Kind=r8_kind), Allocatable :: yl_arr (:, :), yl_arr2 (:, &
& :),yl_arr_fin_a (:, :),yl_arr_fin_b (:, :), clmamb (:, :), clmamb2 (:, :), clmamb_scalar (:),&
clmamb_scalar_xyz (:,:), clmamb_xyz(:,:,:)
!
! help arrays for product_rule and diff_rule
Real (Kind=r8_kind), Allocatable :: prod_arr (:, :, :, :, :), prod_arr1 (:, :, :, :, :), &
& diff_arr (:, :, :),diff_arr_a (:, :, :), diff_arr0 (:, :), diff_arr0_xyz(:,:,:), diff_arr_fin(:,:,:)
!
! help arrays for product rule
Real (Kind=r8_kind), Allocatable :: help_arr0 (:, :)
Real (Kind=r8_kind) :: arg
! cartesian coordinates
Real (Kind=r8_kind), Dimension (3) :: xa, xb, xc, xd
!
Integer (Kind=i4_kind) :: i_ua, j_ua, i_l, k, l
Integer (Kind=i4_kind) :: ly_max
Integer (Kind=i4_kind) :: n_equals
Real (Kind=r8_kind), Allocatable :: aexp_arr (:), bexp_arr (:)
Type (unique_atom_type), Pointer :: ua_pointer
!
Real (Kind=r8_kind), Allocatable :: diff_arr_xyz (:, :, :, :),diff_arr_axyz(:,:,:,:), diff_arr_xyz_a(:,:,:,:), &
& yl_arr_xyz (:, :, :),yl_arr_axyz(:,:,:), yl_arr_2xyz (:, :, :),yl_arr_2axyz(:,:,:), diff_arr_2xyz (:, &
& :, :, :), diff_arr_2axyz(:,:,:,:)!second derivatives
!
Real (Kind=r8_kind), Allocatable :: overlap (:, :, :), overlap_xyz (:, :, :, :),&
help_mat(:,:,:)
!
!
!
!
Real (Kind=r8_kind), Allocatable :: nuc_second_der (:, :, :, :), &
& aqapb (:, :), nuc_2grad_ac(:,:,:,:)
Real (Kind=r8_kind), Allocatable :: finite_nuc_iso (:, :, :)
Integer (Kind=i4_kind) :: k_gr, nm_la, nm_lb, lasq, lbsq, laposq, &
& lbposq, l2pm
Integer (Kind=i4_kind), Dimension (6, 2) :: meta2xyz, meta2xyzL
Integer (Kind=i4_kind), Dimension (3) :: xyz_map
Real (Kind=r8_kind):: cexp
Intrinsic Max
!
!
!--------------------- Initialisation-----------------------
! using mapping x=1 , y=2, z=3 for two indecses use metaindex
! Integrals type1 type2
! x y z x y z
!x 1 4 5 x 4 5
!y 2 6 y 1 6
!z 3 z 2 3
! meta2xyz(k_gr,{1,2})
xyz_map (1) = 3_i4_kind
xyz_map (2) = 4_i4_kind
xyz_map (3) = 2_i4_kind
meta2xyz (1, 1) = 1_i4_kind ; meta2xyz (1, 2) = 1_i4_kind
meta2xyz (2, 1) = 2_i4_kind ; meta2xyz (2, 2) = 2_i4_kind
meta2xyz (3, 1) = 3_i4_kind ; meta2xyz (3, 2) = 3_i4_kind
meta2xyz (4, 1) = 1_i4_kind ; meta2xyz (4, 2) = 2_i4_kind
meta2xyz (5, 1) = 1_i4_kind ; meta2xyz (5, 2) = 3_i4_kind
meta2xyz (6, 1) = 2_i4_kind ; meta2xyz (6, 2) = 3_i4_kind
!---------------------------------
meta2xyzL (1, 1) = 2_i4_kind ; meta2xyzL (1, 2) = 1_i4_kind
meta2xyzL (2, 1) = 3_i4_kind ; meta2xyzL (2, 2) = 1_i4_kind
meta2xyzL (3, 1) = 3_i4_kind ; meta2xyzL (3, 2) = 2_i4_kind
meta2xyzL (4, 1) = 1_i4_kind ; meta2xyzL (4, 2) = 2_i4_kind
meta2xyzL (5, 1) = 1_i4_kind ; meta2xyzL (5, 2) = 3_i4_kind
meta2xyzL (6, 1) = 2_i4_kind ; meta2xyzL (6, 2) = 3_i4_kind
nm_la = 2 * la + 1
nm_lb = 2 * lb + 1
lasq = la ** 2
lbsq = lb ** 2
laposq = (la+1) ** 2
lbposq = (lb+1) ** 2
one_i = 1_i4_kind
zero_i = 0_i4_kind
ly_max = Max (la, lb)
max_order = 3 + la + lb
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)
If (alloc_stat .Ne. 0) Call error_handler ("LL_CALCULATE_HFC: allocat&
&ion (1) failed")
!
!
xa = center1
xb = center2
xd = xa - xb
aexps => unique_atoms(na)%l_ob(la)%exponents(:)
bexps => unique_atoms(nb)%l_ob(lb)%exponents(:)
!
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_hfc = 0.0_r8_kind
Deallocate (fact0_arr, fact1_arr, fact2_arr, cutoff, &
& Stat=alloc_stat)
If (alloc_stat .Ne. 0) Call error_handler ("LL_CALCULATE_HFC: deal&
&location (1) failed")
Return
End If
!
Allocate (fact0(num),rcsabc(num),&
& fact1(num), fact2(num), fact4(num), &
& fact5(num), fact6(num), fact7(num), &
& fact8(num),fact81(num), &
& tau(num), gamma_arg_fin_a(num, 3),gamma_arg_fin_b(num, 3),gamma_arg(num, 3),&
& aexp_arr(num), bexp_arr(num), &
& overlap(num, (la+1)**2, (lb+1)**2),&
& overlap_xyz(num,laposq,lbposq,3),&
& help_mat(num,laposq,lbposq),&
& clmamb_scalar((Max(la,lb)+1)**2),&
& clmamb_scalar_xyz((Max(la,lb)+1)**2,3),&
& clmamb(num, (la+1)**2),&
& clmamb_xyz(num,laposq,3),&
& clmamb2(num, (la+1)**2), &
& diff_arr_a(num,laposq,lbposq),&
& diff_arr_xyz_a(num,laposq,lbposq,3),&
& diff_arr0((la+1)**2,(lb+1)**2),&
& diff_arr0_xyz((la+1)**2,(lb+1)**2,3),&
& aqapb(num, 0:ly_max+2),fact10(num,(ly_max+1)**2),&
& Stat=alloc_stat)
If (alloc_stat .Ne. 0) Call error_handler&
("LL_CALCULATE_HFC: allocation (2) failed")
!
!-----------array allocation---------------------
!------------------------------------------------
! List of *facts* at the beginning
! fact0 = a + b
! fact1 = a * b
! fact2 = a*b/(a+b)
! fact7= 1/sqrt(a**l*(2l-1)!!)
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)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (2) failed")
!
! gamma_arg = (a*vec_a + b*vec_b)/(a + b)
gamma_arg (:, 1) = (pack(spread(aexps*xa(1), 1, &
& nbexps)+spread(bexps*xb(1), 2, naexps), cutoff)) / fact0
!
gamma_arg (:, 2) = (pack(spread(aexps*xa(2), 1, &
& nbexps)+spread(bexps*xb(2), 2, naexps), cutoff)) / fact0
!
gamma_arg (:, 3) = (pack(spread(aexps*xa(3), 1, &
& nbexps)+spread(bexps*xb(3), 2, naexps), cutoff)) / fact0
!
!
! precalculation of solid harmonics
clmamb_scalar = solid_harmonics_scalar (Max(la, lb), xd)
clmamb_scalar_xyz=0.0_r8_kind
do l=1,(ly_max+1)**2
do k_gr=1,3
do k=1,solhrules_differential(xyz_map(k_gr),l)%n_summands
clmamb_scalar_xyz(l,k_gr)=clmamb_scalar_xyz(l,k_gr)+&
solhrules_differential(xyz_map(k_gr),l)%coef(k)*&
clmamb_scalar(solhrules_differential(xyz_map(k_gr),l)%lm_sh(k))
end do
end do
end do!loop over l
fact4 = 1.0_r8_kind
counter = 1
tau = fact2 * arg ! a*b/(a+b)*(A-B)**2
Do l = 0, la
Do m = 1, 2 * l + 1
clmamb (:, counter) = clmamb_scalar (counter) * fact4
clmamb2 (:, counter) = clmamb_scalar (counter) * fact4 * &
& (tau-real(l, kind=r8_kind))
do k_gr=1,3
clmamb_xyz(:,counter,k_gr)=clmamb_scalar_xyz(counter,k_gr)*fact4
end do
counter = counter + 1
End Do
fact4 = - fact4 * fact2 * 2.0_r8_kind
End Do
! calculate derivatives of solid harmonics
! first calculating 2-center integrals----------------
! fact5=fact2*(3.0_r8_kind-2.0_r8_kind*tau+2.0_r8_kind*la)
! a*b/(a+b)(3-2*tau+2*l)
fact6 = 1.0_r8_kind / Sqrt (aexp_arr**la*dfac(la)) / Sqrt &
& (bexp_arr**lb*dfac(lb)) * Exp (-tau) * (4.0_r8_kind*fact2/fact0) &
& ** 0.75_r8_kind
fact5 = fact2 * fact6
fact7 = (fact2*2.0_r8_kind) ** lb
counter = 1
Do i_l = 0, lb
Do mb = 1, 2 * i_l + 1
! calculate C1m(grad a(i))Clm(a-b)
diff_arr0 (:, counter) = reshape &
& (diff_rule(spread(clmamb_scalar, 1, 1), 1, (la+1)**2, counter), (/ (la+1)**2 /))
! now calculate derivatives of diff_arr0
do k_gr=1,3
diff_arr0_xyz(:,counter,k_gr)=reshape(diff_rule(&
spread(clmamb_scalar_xyz(:,k_gr),1,1),1,laposq,counter),(/laposq/))
end do
counter = counter + 1
End Do
End Do
counter=1
help_mat(:,:,1)= 0.0_r8_kind
diff_arr_xyz_a=spread(diff_arr0_xyz(:,:,:),1,num)
diff_arr_a=spread(diff_arr0(:,:),1,num)
do i_l=0,lb
help_mat(:,:,1)=spread(fact6*(2.0_r8_kind*fact2)**i_l,&
2,laposq)
magnetic_number_b: do mb=1,2*i_l+1
! overlap
overlap(:,1:laposq,counter)=help_mat(:,:,1)*&
prod_rule(spread(diff_arr0(:,counter),1,num),clmamb(:,:),1,laposq)
! now calculate derivatives of overlap
do k_gr=1,3
do l=1,laposq
overlap_xyz(:,l,counter,k_gr)=overlap(:,l,counter)*&
(-2.0_r8_kind*fact2)*xd(k_gr)
end do
overlap_xyz(:,1:laposq,counter,k_gr)=overlap_xyz(:,1:laposq,counter,k_gr)+&
help_mat(:,:,1)*&
(prod_rule(diff_arr_xyz_a(:,:,counter,k_gr),clmamb(:,:),1,laposq)+&
& prod_rule(diff_arr_a(:,:,counter), clmamb_xyz(:,:,k_gr),1,laposq))
end do
counter=counter+1
end do magnetic_number_b
enddo
! Call integral_interrupt_2cob3c ()
fact8 = 2.0_r8_kind * Sqrt (fact0/pi)
aqapb (:, 0) = 1.0_r8_kind
aqapb (:, 1) = aexp_arr / fact0
Do i_l = 2, ly_max + 2
aqapb (:, i_l) = aqapb (:, i_l-1) * aqapb (:, 1)
End Do
!
Allocate (gamma_help(num, max_order), Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (3.1) failed")
Allocate ( gamma_second_der(num,1+la+lb, 6) , Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (3.2) failed")
Allocate ( gamma_first_der(num, 1+la+lb, 3) , Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (3.3) failed")
Allocate ( gamma_arg2(num) , Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (3.4) failed")
Allocate ( help_arr0(num, laposq), Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (3.5) failed")
Allocate (nuc_second_der(num, nm_la, nm_lb, 9),nuc_2grad_ac(num, nm_la, nm_lb, 6), Stat=alloc_stat)
If (alloc_stat .Ne. 0) Call error_handler ("LL_CALCULATE_HFC: allocat&
&ion (4) failed")
! Allocate (finite_nuc_iso(num, nm_la, nm_lb), Stat=alloc_stat)
Allocate (finite_nuc_iso(num, (la+1)**2, (lb+1)**2), Stat=alloc_stat)
If (alloc_stat .Ne. 0) Call error_handler ("LL_CALCULATE_HFC: allocat&
&ion (4) failed")
!7,8,9 - include isotropic part
! nuc_second_der = 0.0_r8_kind
! nuc_2grad_ac = 0.0_r8_kind
!
Allocate (yl_arr(num, (ly_max+1)**2), yl_arr2(num, (ly_max+1)**2),&
& yl_arr_fin_a(num, (ly_max+1)**2),yl_arr_fin_b(num, (ly_max+1)**2),&
& prod_arr(num,(la+1)**2, (lb+1)**2, 0:la+lb, 6),&
& prod_arr1(num,(la+1)**2, (lb+1)**2, 0:la+lb, 6),&
& yl_arr_xyz(num, (ly_max+1)**2, 3),&
& yl_arr_axyz(num, (ly_max+1)**2, 3),&
& yl_arr_2axyz(num,(ly_max+1)**2, 6),&
& yl_arr_2xyz(num, (ly_max+1)**2, 6), &
& diff_arr(num, (la+1)**2, (lb+1)**2),&
& diff_arr_fin(num, (la+1)**2, (lb+1)**2),&
& diff_arr_xyz(num, laposq, lbposq, 3),&
& diff_arr_axyz(num, laposq, lbposq, 3),&
& diff_arr_2xyz(num, laposq, lbposq, 6),&
& diff_arr_2axyz(num, laposq, lbposq, 6),&
&Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : alloc&
&ation (5) failed")
! Initialisation
! do a precalculation of a factor needed for the
! product rule
counter = 1
fact4 = 1.0_r8_kind
Do i_l = 0, ly_max
Do ma = 1, 2 * i_l + 1
fact10 (:, counter) = fact4
counter = counter + 1
End Do
fact4 = fact4 * aexp_arr / (fact0)
End Do
!
! main_ua_loop: Do i = 1, n_unique_atoms
ualoop: Do i_ua = 1, n_unique_atoms ! loop over third center
gamma_help = 0.0_r8_kind
gamma_second_der = 0.0_r8_kind
gamma_first_der = 0.0_r8_kind
gamma_arg2 = 0.0_r8_kind
help_arr0 = 0.0_r8_kind
yl_arr = 0.0_r8_kind
yl_arr_fin_a = 0.0_r8_kind
yl_arr_fin_b = 0.0_r8_kind
yl_arr2 = 0.0_r8_kind
prod_arr = 0.0_r8_kind
prod_arr1 = 0.0_r8_kind
yl_arr_xyz = 0.0_r8_kind
yl_arr_axyz = 0.0_r8_kind
yl_arr_2axyz = 0.0_r8_kind
diff_arr = 0.0_r8_kind
diff_arr_fin = 0.0_r8_kind
diff_arr_xyz = 0.0_r8_kind
diff_arr_axyz = 0.0_r8_kind
diff_arr_2xyz = 0.0_r8_kind
diff_arr_2axyz = 0.0_r8_kind
nuc_second_der = 0.0_r8_kind
finite_nuc_iso = 0.0_r8_kind
nuc_2grad_ac = 0.0_r8_kind
fact8 = 0.0_r8_kind
fact81 = 0.0_r8_kind
ua_pointer => unique_atoms (i_ua)
n_equals = ua_pointer%n_equal_atoms
! precalculate prod_arr and calculate nuclear attraction
! precalculate prod_arr and calculate nuclear attraction
equal_atoms: Do j_ua = 1, n_equals
! Call integral_interrupt_2cob3c ()
!
xc = unique_atoms(i_ua)%position(:, j_ua)
! xc = unique_atoms(i_ua)%position(:, 1)
! xc = 0.0_r8_kind
!yl_arr([alfabeta],[lm]) = Clm(d)
yl_arr (:, :) = solid_harmonics_calc &
(ly_max, gamma_arg(:,:)-spread(xc, 1, num))
!gamma_arg2([alfabeta]) = (alfa+beta)*d*d
gamma_arg2 (:) = ((gamma_arg(:, 1)-xc(1))**2+&
(gamma_arg(:, 2)-xc(2))**2+(gamma_arg(:,3)-xc(3))**2) * fact0
!gamma_help([]) = I_l((alfa+beta)*d*d)
!old version gamma_help (:, 1:1+la+lb) = gamma (1+la+lb, gamma_arg2(:, j))
! a new version for the term 1
! we need I_l+2((alfa+beta)*d*d)*(2(alfa+beta))^2 * d_i * d_j
gamma_help (:, 1:1+la+lb+2) = gamma (1+la+lb+2, gamma_arg2(:))
! for the double derivatives the following mapping is valued
!
! Actual mapping is : C11 = z; C12 = x; C13 = y
opt_finite: if (options_finite_nucleus) then
cexp = (3.0_r8_kind/2.0_r8_kind/ua_pointer%nuclear_radius/ua_pointer%nuclear_radius)
! cexp = cexp + 0.000001_r8_kind
! xc(1) = xc(1) + 1.0_r8_kind
!((b+c)*vec_a-c*vec_c)/b
gamma_arg_fin_a (:, 1) = ((bexp_arr+cexp)*xa(1) - cexp * xc(1)) / bexp_arr
!
gamma_arg_fin_a (:, 2) = ((bexp_arr+cexp)*xa(2) - cexp * xc(2)) / bexp_arr
!
gamma_arg_fin_a (:, 3) = ((bexp_arr+cexp)*xa(3) - cexp * xc(3)) / bexp_arr
!((a+c)*vec_b-c*vec_c)/a
gamma_arg_fin_b (:, 1) = ((aexp_arr+cexp)*xb(1) - cexp * xc(1)) / aexp_arr
!
gamma_arg_fin_b (:, 2) = ((aexp_arr+cexp)*xb(2) - cexp * xc(2)) / aexp_arr
!
gamma_arg_fin_b (:, 3) = ((aexp_arr+cexp)*xb(3) - cexp * xc(3)) / aexp_arr
! Clm(vec_a-(b*vec_b+c*vec_c)/(b+c)) ! [ab],[lm]
yl_arr_fin_b (:, :) = solid_harmonics_calc(ly_max, -gamma_arg_fin_b(:,:) + spread(xa, 1, num))
! Clm(vec_b-(a*vec_a+c*vec_c)/(a+c))
yl_arr_fin_a (:, :) = solid_harmonics_calc(ly_max, -gamma_arg_fin_a(:,:) + spread(xb, 1, num))
fact4 = 1.0_r8_kind
counter = 1
Do l = 0, la
Do m = 1, 2 * l + 1
yl_arr_fin_a (:, counter) = yl_arr_fin_a (:, counter) * fact4
counter = counter + 1
end Do
! fact4 = -fact4 * 2.0_r8_kind * fact1/(fact0 + cexp)
fact4 = fact4 * 2.0_r8_kind * fact1/(fact0 + cexp)
end Do
!calculate diff array
counter = 1
Do i_l = 0, lb
Do mb = 1, 2 * i_l + 1
! calculate Clm(grad a)Clm(vec_a -((a + c)*vec_b-c*vec_c)/a )
diff_arr_fin (:, :, counter) = diff_rule &
& (yl_arr_fin_b(:, :), 1, laposq, counter)
counter = counter + 1
end Do
end Do
! precalculation of two factors
fact81 = (4.0_r8_kind*fact1/PI/PI) ** 0.75_r8_kind &
/ Sqrt (aexp_arr**la*dfac(la))/Sqrt(bexp_arr**lb*dfac(lb))*&
Sqrt (cexp/(fact0+cexp)) * &
& (cexp/(fact0+cexp)) * Exp (-fact1/(fact0+cexp)*sum ((xa-xb)**2)-&
& bexp_arr*cexp/(fact0+cexp)*sum ((xb-xc)**2)-aexp_arr*cexp/(fact0+cexp)*sum ((xa-xc)**2) )
! now the acutal calculation starts
counter = 1
help_mat(:,:,1)= 0.0_r8_kind
Do i_l = 0, lb
help_mat(:,:,1)=spread(fact81 *(2.0_r8_kind * fact1/(fact0 + cexp))**i_l,2,laposq)
Do mb = 1, 2 * i_l + 1
finite_nuc_iso(:,:, counter) = finite_nuc_iso(:,:,counter)&
+ help_mat(:,:,1) * prod_rule(diff_arr_fin(:,:,counter), yl_arr_fin_a(:,:),1,laposq)
counter = counter + 1
End Do! loop over l
End Do
end if opt_finite
Do i_l = 1, 1 + la + lb
Do k_gr = 1, 3
gamma_first_der (:, i_l, k_gr) =&
& gamma_help (:, i_l+1) * 2 * fact0 * (gamma_arg(:, k_gr)-xc(k_gr))
gamma_second_der (:, i_l, k_gr) =&
& gamma_help (:, i_l+2) * 4 * fact0 * fact0 *&
& (gamma_arg(:,k_gr)-xc(k_gr)) * (gamma_arg(:, k_gr)-xc(k_gr))
End Do
Do k_gr = 4, 6
gamma_second_der (:, i_l, k_gr) =&
gamma_help (:,i_l+2) * 4 * fact0 * fact0 *&
& (gamma_arg(:, meta2xyz(k_gr, 1))-xc(meta2xyz(k_gr, 1))) * &
& (gamma_arg(:, meta2xyz(k_gr, 2))-xc(meta2xyz(k_gr, 2)))
End Do
End Do
!
fact8 = 2.0_r8_kind * Sqrt (fact0/pi)
!yl_arr2([alfabeta],[lm]) =Clm(d)/(alfa/alfa+beta)^2
yl_arr2 (:, :) = yl_arr (:, :) / fact10 (:, 1:((ly_max+1)**2))
!
!
! now calculation of derivatives of yl_arr with respect to -c
yl_arr_xyz = 0.0_r8_kind
yl_arr_axyz = 0.0_r8_kind
! fact6 = spread(-aexp_arr(:)/fact0(:),1,num)
Do l = 0, ly_max
Do m = 1, 2 * l + 1
l2pm = l * l + m
Do k_gr = 1, 3
Do k = 1, solhrules_differential(xyz_map(k_gr), l2pm)%n_summands
yl_arr_xyz (:, l2pm, k_gr) = yl_arr_xyz (:, l2pm, k_gr) - & ! + & Now with respect to c
& solhrules_differential(xyz_map(k_gr), l2pm)%coef(k) * &
& yl_arr (:, solhrules_differential(xyz_map(k_gr), l2pm)%lm_sh(k))
yl_arr_axyz(:,l2pm, k_gr) =-aexp_arr/fact0 * yl_arr_xyz (:, l2pm, k_gr)
End Do
End Do
End Do
End Do!loop over l
!now calculate the second derivative of yl_arr with reepect to -c
yl_arr_2xyz = 0.0_r8_kind
yl_arr_2axyz = 0.0_r8_kind
Do l = 0, ly_max
Do m = 1, 2 * l + 1
l2pm = l * l + m
Do k_gr = 1, 6
Do k = 1, solhrules_differential(xyz_map(meta2xyz(k_gr, 2)), l2pm)%n_summands
yl_arr_2xyz (:, l2pm, k_gr) =yl_arr_2xyz (:,l2pm, k_gr) - &! Now with respect to c
& solhrules_differential(xyz_map(meta2xyz(k_gr,2)), l2pm)%coef(k) *&
& yl_arr_xyz (:,solhrules_differential(xyz_map(meta2xyz(k_gr,2)), l2pm)%lm_sh(k), meta2xyz(k_gr, 1))
! Debug Wrong!!!!!
! yl_arr_2axyz (:, l2pm, k_gr) = -aexp_arr/fact0 * yl_arr_2xyz (:, l2pm, k_gr)
! yl_arr_2axyz (:, l2pm, k_gr) = yl_arr_2xyz (:, l2pm, k_gr)
End Do
End Do
End Do
End Do !loop over l
! FIXME: this cannot be correct. See how l2pm = l^2 + m
! is used here as a fixed constant, not as a running
! index. Also cf. the warning issued by the compiler
! that l2pm may be used uninitialed here. The comment
! cannot be right:
ABORT('needs some work')
! tipa pravilno ("appears correct", rus.)
Do k_gr = 4, 6
yl_arr_2axyz (:, l2pm, k_gr) = -aexp_arr/fact0 * yl_arr_2xyz (:, l2pm, k_gr)
yl_arr_2axyz (:, l2pm, k_gr-3) = -aexp_arr/fact0 * yl_arr_2xyz (:, l2pm, k_gr)
End Do
!
!calculation of diff_arr and diff_arr_xyz
counter = 1
Do i_l = 0, lb
help_arr0 = spread (aqapb(:, i_l), 2, laposq)
Do mb = 1, 2 * i_l + 1
diff_arr (:, :, counter) = help_arr0 * diff_rule &
& (yl_arr2(:, :), 1, laposq, counter)
! now let us differentiate diff_arr and second der of diff_arr
Do k_gr = 1, 3
diff_arr_xyz (:, :, counter,k_gr ) = help_arr0 * &
& diff_rule (yl_arr_xyz(:, :, k_gr)/fact10, 1, &
& laposq, counter)
diff_arr_axyz (:, :, counter,k_gr ) = help_arr0 * &
& diff_rule (yl_arr_axyz(:, :, k_gr)/fact10, 1, &
& laposq, counter)
diff_arr_2xyz (:, :, counter, k_gr) = help_arr0 * & !Coefficient
& diff_rule(yl_arr_2xyz(:, :, k_gr)/fact10, &
& 1, laposq, counter)
diff_arr_2axyz (:, :, counter, k_gr) = help_arr0 * & !Coefficient
& diff_rule(yl_arr_2axyz(:, :, k_gr)/fact10, &
& 1, laposq, counter)
End Do!
Do k_gr = 4, 6
diff_arr_2xyz (:, :, counter, k_gr) = help_arr0 * & !Coefficient
& diff_rule(yl_arr_2xyz(:, :, k_gr)/fact10, 1, laposq, counter)
diff_arr_2axyz (:, :, counter, k_gr) = help_arr0 * & !Coefficient
& diff_rule(yl_arr_2axyz(:, :, k_gr)/fact10, 1, laposq, counter)
End Do
counter = counter + 1
!
End Do
End Do
!calculation of second derivative of diff_arr_xyz
!
!
!------------------ The first term----------------------------
!d2I((a+b)d^2)/dcidcj * X
prod_arr = 0.0_r8_kind
Do i_l = 0, lb
Do mb = 1, 2 * i_l + 1
prod_arr (:, :, i_l**2+mb, 0:la+i_l, 1) = &
& prod_rule_nested2 (yl_arr(:, :), diff_arr(:, :, :), &
& overlap(:, :, :), la, i_l, mb, &
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))
End Do
End Do
Do mb = 1, 2 * lb + 1
Do i_l = 0, lb + la
Do k_gr = 1,3
nuc_second_der (:, :, mb, k_gr) = nuc_second_der &
& (:, :, mb, k_gr) +&
& prod_arr (:, la**2+1:(la+1)**2, lb**2+mb, i_l, 1) *&
& spread (fact8*gamma_second_der(:, i_l+1, k_gr), 2, 2*la+1)
!isotropic part
nuc_second_der (:, :, mb, k_gr+6) =&
& nuc_second_der (:, :, mb, k_gr+6) +&
& prod_arr (:, la**2+1:(la+1)**2, lb**2+mb, i_l, 1) *&
& spread ((-2*fact0*fact8*gamma_help(:, i_l+2)), 2, 2*la+1)
!------------------------------!
End Do
Do k_gr = 4,6
nuc_second_der (:, :, mb, k_gr) =&
nuc_second_der (:, :, mb, k_gr) +&
& prod_arr (:, la**2+1:(la+1)**2, lb**2+mb, i_l, 1) *&
& spread (fact8*gamma_second_der(:, i_l+1, k_gr), 2, 2*la+1)
!
End Do
End Do
End Do
! spread (fact8*gamma_help(:, i_l+1), 2, 2*la+1)
!Extra term
!---------------- The second and the third term --------------------
!dI((a+b)d^2)/dci * dX/dcj + dI((a+b)d^2)/dcj * dX/dci
!dI((a+b)d^2)/dci * dX/daj + dI((a+b)d^2)/daj * dX/dci
prod_arr = 0.0_r8_kind
prod_arr1 = 0.0_r8_kind
Do k_gr = 1, 3
Do i_l = 0, lb
Do mb = 1, 2 * i_l + 1
!dX/dci
prod_arr (:, :, i_l**2+mb, 0:la+i_l, k_gr) = &
& prod_rule_nested2&
& (yl_arr_xyz(:, :, k_gr),diff_arr(:, :, :), overlap(:, :, :), la, i_l, mb, &
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr(:, :), diff_arr_xyz(:, :, :, k_gr), overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))
!dX/daj
prod_arr1 (:, :, i_l**2+mb, 0:la+i_l, k_gr) = &
& prod_rule_nested2&
& (yl_arr(:, :),diff_arr(:, :, :), overlap_xyz(:, :, :,k_gr), la, i_l, mb, &
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr_axyz(:, :,k_gr), diff_arr(:, :, :), overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr(:, :), diff_arr_axyz(:, :, :,k_gr), overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))
End Do
End Do
End Do
!
!
Do mb = 1, 2 * lb + 1
Do i_l = 0, lb + la
Do k_gr = 1, 6
nuc_second_der (:, :, mb, k_gr) = nuc_second_der (:, :, mb, k_gr) +&
& prod_arr (:, la**2+1:(la+1)**2, lb**2+mb, i_l, meta2xyz(k_gr, 1)) *&
& spread (fact8*gamma_first_der(:, i_l+1,meta2xyz(k_gr, 2)), 2, 2*la+1) +&
& prod_arr (:,la**2+1:(la+1)**2, lb**2+mb, i_l, meta2xyz(k_gr, 2)) *&
& spread (fact8*gamma_first_der(:, i_l+1, meta2xyz(k_gr, 1)), 2, 2*la+1)
nuc_2grad_ac (:, :, mb, k_gr) = nuc_2grad_ac (:, :, mb, k_gr) +&
& prod_arr1 (:, la**2+1:(la+1)**2, lb**2+mb, i_l, meta2xyzL(k_gr, 1)) *&
& spread (fact8*gamma_first_der(:, i_l+1,meta2xyzL(k_gr, 2)), 2, 2*la+1) +&
& prod_arr (:,la**2+1:(la+1)**2, lb**2+mb, i_l, meta2xyzL(k_gr, 2)) *&
& spread (fact8*(-aexp_arr/fact0)*gamma_first_der(:, i_l+1, meta2xyzL(k_gr, 1)), 2, 2*la+1)
End Do
End Do
End Do
!
!------------------the last term-----------------
!I((a+b)d^2) * d2X/dcidcj
prod_arr = 0.0_r8_kind
prod_arr1 = 0.0_r8_kind
Do k_gr = 1, 6
Do i_l = 0, lb
Do mb = 1, 2 * i_l + 1
prod_arr (:, :, i_l**2+mb, 0:la+i_l, k_gr) = &
& prod_rule_nested2&
& (yl_arr_2xyz(:, :, k_gr),diff_arr(:, :, :), overlap(:, :, :), la, i_l, mb, &
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr_xyz(:, :, meta2xyz(k_gr, 1)), diff_arr_xyz(:, :, :, meta2xyz(k_gr, 2)),overlap(:, :, :), la, i_l,mb,&
& (-2.0_r8_kind*aexp_arr),(-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2 &
& ( yl_arr_xyz(:, :, meta2xyz(k_gr, 2)) , diff_arr_xyz(:,:,:,meta2xyz(k_gr, 1)),overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr(:, :),diff_arr_2xyz(:, :, :, k_gr),overlap(:, :, :),la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))
!
!d2X/daidcj
prod_arr1 (:, :, i_l**2+mb, 0:la+i_l, k_gr) = &
& prod_rule_nested2&
& (yl_arr_xyz(:, :,meta2xyzL(k_gr,2)),diff_arr(:, :, :),&
& overlap_xyz(:, :, :,meta2xyzL(k_gr,1)), la, i_l, mb, &
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr(:, :), diff_arr_xyz(:, :, :, meta2xyzL(k_gr,2)),&
& overlap_xyz(:, :, :,meta2xyzL(k_gr,1)), la, i_l,mb,&
& (-2.0_r8_kind*aexp_arr),(-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2 &
& ( yl_arr_2axyz(:, :, k_gr) , diff_arr(:,:,:),overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr_axyz(:, :,meta2xyzL(k_gr,1)),diff_arr_xyz(:, :, :, meta2xyzL(k_gr,2)),&
& overlap(:, :, :),la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))&
& + prod_rule_nested2 &
& ( yl_arr_xyz(:, :, meta2xyzL(k_gr,2)) , diff_arr_axyz(:,:,:,meta2xyzL(k_gr,1)),&
& overlap(:, :, :), la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr)) &
& + prod_rule_nested2&
& (yl_arr(:, :),diff_arr_2axyz(:, :, :, k_gr),overlap(:, :, :),la, i_l, mb,&
& (-2.0_r8_kind*aexp_arr), (-2.0_r8_kind*bexp_arr))
End Do
End Do
End Do
Do k_gr = 1, 6
Do mb = 1, 2 * lb + 1
Do i_l = 0, lb + la
nuc_second_der (:, :, mb, k_gr) =&
nuc_second_der (:, :, mb, k_gr) +&
prod_arr (:, la**2+1:(la+1)**2, lb**2+mb, i_l, k_gr) *&
spread (fact8*gamma_help(:, i_l+1), 2, 2*la+1)
nuc_2grad_ac (:, :, mb, k_gr) =&
nuc_2grad_ac (:, :, mb, k_gr) +&
prod_arr1 (:, la**2+1:(la+1)**2, lb**2+mb, i_l, k_gr) *&
spread (fact8*gamma_help(:, i_l+1), 2, 2*la+1)
End Do
End Do
End Do
!
end Do equal_atoms
! End Do ualoop
!--------------------- Initialisation-----------------------
! using mapping x=1 , y=2, z=3 for two indecses use metaindex
! Integrals type1 type2
! x y z x y z
!x 1 4 5 x 4 5
!y 2 6 y 1 6
!z 3 z 2 3
! meta2xyz(k_gr,{1,2})
! Mapping to contracted primitive integrals
! d2/dx2 means d2(1/R)/dx2 = (3xx -rr)/r^5
! 1 = d2/dx2 4 = d2/dxdy
! 2 = d2/dy2 5 = d2/dxdz
! 3 = d2/dz2 6 = d2/dydz
! 7 = Lx/r^3
! 8 = Ly/r^3
! 9 = Lz/r^3
do k_gr = 1,6
do mb=1,2*lb+1
do ma=1,2*la+1
prim_int_2cob_hfc(:,:,mb,ma,k_gr,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,k_gr,i_ua)+&
unpack(nuc_second_der(:,ma,mb,k_gr)/n_equals,cutoff,zero)!
enddo
end do
end do
if (options_finite_nucleus) then
! coef_finite_nucleus = (3/2/ua_pointer%nuclear_radius/ua_pointer%nuclear_radius/PI)**(1.5_r8_kind)
do mb=1,2*lb+1
do ma=1,2*la+1
prim_int_2cob_hfc(:,:,mb,ma,7,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,7,i_ua)+& !Lx/r^3
unpack((nuc_2grad_ac (:, ma, mb, 6)-nuc_2grad_ac (:, ma, mb, 3))/n_equals , cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,8,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,8,i_ua)+& !Ly/r^3
unpack((nuc_2grad_ac (:, ma, mb, 2)-nuc_2grad_ac (:, ma, mb, 5))/n_equals , cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,9,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,9,i_ua)+& !Lz/r^3
unpack((nuc_2grad_ac (:, ma, mb, 4)-nuc_2grad_ac (:, ma, mb, 1))/n_equals ,cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,10,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,10,i_ua)+&
unpack(finite_nuc_iso(:,(la)**2+ma,(lb)**2+mb)/n_equals,cutoff,zero)
enddo
end do
else
do mb=1,2*lb+1
do ma=1,2*la+1
prim_int_2cob_hfc(:,:,mb,ma,7,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,7,i_ua)+& !Lx/r^3
unpack((nuc_2grad_ac (:, ma, mb, 6)-nuc_2grad_ac (:, ma, mb, 3))/n_equals , cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,8,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,8,i_ua)+& !Ly/r^3
unpack((nuc_2grad_ac (:, ma, mb, 2)-nuc_2grad_ac (:, ma, mb, 5))/n_equals , cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,9,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,9,i_ua)+& !Lz/r^3
unpack((nuc_2grad_ac (:, ma, mb, 4)-nuc_2grad_ac (:, ma, mb, 1))/n_equals ,cutoff,zero)! / n_equals
prim_int_2cob_hfc(:,:,mb,ma,10,i_ua)=prim_int_2cob_hfc(:,:,mb,ma,10,i_ua)+& ! d2/dx2 + d2/dy2+d2/dz2 (1/r)
unpack((nuc_second_der(:,ma,mb,1)+nuc_second_der(:,ma,mb,2)+& ! avoiding delta function operator
nuc_second_der(:,ma,mb,3)+nuc_second_der(:,ma,mb,7)+nuc_second_der(:,ma,mb,8)+&
nuc_second_der(:,ma,mb,9))/n_equals,cutoff,zero)!
enddo
end do
end if
end Do ualoop
!
Deallocate (yl_arr,yl_arr_fin_a,yl_arr_fin_b, yl_arr2,&
& yl_arr_xyz,yl_arr_axyz,&
& yl_arr_2xyz,yl_arr_2axyz, &
& gamma_help,&
& gamma_second_der,&
& gamma_first_der,&
& gamma_arg2, &
& prod_arr,&
& prod_arr1,&
& help_arr0, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CACLULATE_HFC : deall&
&ocation (4) failed")
Deallocate (nuc_second_der,&
& finite_nuc_iso,&
& nuc_2grad_ac,&
& diff_arr, &
& diff_arr_fin,&
& diff_arr_xyz,&
& diff_arr_axyz,&
& diff_arr_2xyz,&
& diff_arr_2axyz, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (5) failed")
Deallocate (clmamb, clmamb2, tau, clmamb_scalar, clmamb_scalar_xyz,clmamb_xyz, fact10, fact6, &
& fact7, fact2, fact1, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (6) failed")
Deallocate (fact8,fact81, fact5, fact0,rcsabc, fact4, overlap,overlap_xyz,help_mat,&
gamma_arg,gamma_arg_fin_a, gamma_arg_fin_b, &
& Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (7) failed")
Deallocate (aexp_arr, bexp_arr, diff_arr0, diff_arr0_xyz, &
& diff_arr_a, diff_arr_xyz_a, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (8) failed")
Deallocate (cutoff, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (9) failed")
Deallocate (aqapb, Stat=alloc_stat)
If (alloc_stat /= 0) Call error_handler ("LL_CALCULATE_HFC: deallocat&
&ion (10) failed")
End Subroutine ll_calculate_hfc