mirror of https://gitlab.com/scemama/eplf
478 lines
13 KiB
Fortran
478 lines
13 KiB
Fortran
BEGIN_PROVIDER [ real, eplf_gamma ]
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implicit none
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BEGIN_DOC
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! Value of the gaussian for the EPLF
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END_DOC
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include 'constants.F'
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real :: eps, N
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! N = 0.1
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! eps = -real(dlog(tiny(1.d0)))
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! eplf_gamma = (4./3.*pi*density_value_p/N)**(2./3.) * eps
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N=0.001
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eps = 50.
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eplf_gamma = eps**2 *0.5d0*(4./9.*pi*density_value_p * N**(-1./3.))**(2./3.)
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!eplf_gamma = 1.e10
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!eplf_gamma = 1.e5
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, ao_eplf_integral_matrix, (ao_num,ao_num) ]
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implicit none
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BEGIN_DOC
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! Array of all the <chi_i chi_j | exp(-gamma r^2)> for EPLF
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END_DOC
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integer :: i, j
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double precision :: ao_eplf_integral
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do i=1,ao_num
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do j=i,ao_num
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ao_eplf_integral_matrix(j,i) = ao_eplf_integral(j,i,dble(eplf_gamma),point)
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ao_eplf_integral_matrix(i,j) = ao_eplf_integral_matrix(j,i)
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, mo_eplf_integral_matrix, (mo_num,mo_num) ]
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implicit none
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BEGIN_DOC
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! Array of all the <phi_i phi_j | exp(-gamma r^2)> for EPLF
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END_DOC
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integer :: i, j, k, l
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double precision :: t
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PROVIDE ao_eplf_integral_matrix
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PROVIDE mo_coef
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do i=1,mo_num
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do j=i,mo_num
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mo_eplf_integral_matrix(j,i) = 0.d0
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enddo
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do k=1,ao_num
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if (mo_coef(k,i) /= 0.) then
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do l=1,ao_num
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if (abs(ao_eplf_integral_matrix(l,k))>1.d-16) then
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t = mo_coef(k,i)*ao_eplf_integral_matrix(l,k)
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do j=i,mo_num
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mo_eplf_integral_matrix(j,i) += t*mo_coef_transp(j,l)
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enddo
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endif
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enddo
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endif
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enddo
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enddo
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do i=1,mo_num
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do j=i+1,mo_num
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mo_eplf_integral_matrix(i,j) = mo_eplf_integral_matrix(j,i)
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, eplf_up_up ]
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&BEGIN_PROVIDER [ double precision, eplf_up_dn ]
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implicit none
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BEGIN_DOC
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! Value of the d_upup and d_updn quantities needed for EPLF
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END_DOC
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integer :: i, j
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eplf_up_up = 0.d0
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eplf_up_dn = 0.d0
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PROVIDE mo_coef_transp
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do i=1,mo_closed_num
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do j=1,mo_closed_num
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eplf_up_up += mo_value_p(i)* ( &
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mo_value_p(i)*mo_eplf_integral_matrix(j,j) - &
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mo_value_p(j)*mo_eplf_integral_matrix(j,i) )
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eplf_up_dn += mo_value_p(i)*mo_value_p(i)* &
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mo_eplf_integral_matrix(j,j)
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enddo
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enddo
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eplf_up_up *= 2.d0
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eplf_up_dn *= 2.d0
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integer :: k,l,m,n,p,p2
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integer :: ik,il,jk,jl
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double precision :: phase,dtemp(2)
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integer :: exc(4)
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PROVIDE det
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PROVIDE elec_num_2
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do k=1,det_num
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do l=1,det_num
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exc(1) = abs(det_exc(k,l,1))
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exc(2) = abs(det_exc(k,l,2))
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exc(3) = exc(1)+exc(2)
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exc(4) = det_exc(k,l,1)*det_exc(k,l,2)
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if (exc(4) /= 0) then
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exc(4) = exc(4)/abs(exc(4))
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else
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exc(4) = 1
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endif
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dtemp(1) = 0.d0
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dtemp(2) = 0.d0
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do p=1,2
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p2 = 1+mod(p,2)
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if ( exc(3) == 0 ) then
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! Closed-open shell interactions
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do j=1,mo_closed_num
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do n=1,elec_num_2(p)-mo_closed_num
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ik = det(n,k,p)
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il = det(n,l,p)
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dtemp(1) += mo_value_p(ik)* ( &
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mo_value_p(il)*mo_eplf_integral_matrix(j,j) - &
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mo_value_p(j)*mo_eplf_integral_matrix(j,il) )
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dtemp(2) += mo_value_p(ik)*mo_value_p(il)*mo_eplf_integral_matrix(j,j)
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enddo
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enddo
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!- Open-closed shell interactions
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do m=1,elec_num_2(p)-mo_closed_num
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jk = det(m,k,p)
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jl = det(m,l,p)
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do i=1,mo_closed_num
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dtemp(1) += mo_value_p(i)* ( &
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mo_value_p(i)*mo_eplf_integral_matrix(jk,jl) - &
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mo_value_p(jl)*mo_eplf_integral_matrix(jk,i) )
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dtemp(2) += mo_value_p(i)*mo_value_p(i)*mo_eplf_integral_matrix(jk,jl)
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enddo
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enddo
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!- Open-open shell interactions
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do m=1,elec_num_2(p)-mo_closed_num
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jk = det(m,k,p)
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jl = det(m,l,p)
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do n=1,elec_num_2(p)-mo_closed_num
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ik = det(n,k,p)
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il = det(n,l,p)
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dtemp(1) += mo_value_p(ik)* ( &
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mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
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mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )
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enddo
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do n=1,elec_num_2(p2)-mo_closed_num
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ik = det(n,k,p2)
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il = det(n,l,p2)
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dtemp(2) += mo_value_p(ik)*mo_value_p(il)*mo_eplf_integral_matrix(jk,jl)
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enddo
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enddo
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else if ( (exc(3) == 1).and.(exc(p) == 1) ) then
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! Sum over only the sigma-sigma interactions involving the excitation
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call get_single_excitation(k,l,ik,il,p)
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!- Open-closed shell interactions
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do j=1,mo_closed_num
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dtemp(1) += mo_value_p(ik)* ( &
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mo_value_p(il)*mo_eplf_integral_matrix(j,j) - &
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mo_value_p(j)*mo_eplf_integral_matrix(j,il) )
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dtemp(2) += mo_value_p(ik)*mo_value_p(il)*mo_eplf_integral_matrix(j,j)
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enddo
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!- Closed-open shell interactions
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do i=1,mo_closed_num
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dtemp(1) += mo_value_p(i)* ( &
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mo_value_p(i)*mo_eplf_integral_matrix(jk,jl) - &
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mo_value_p(jl)*mo_eplf_integral_matrix(jk,i) )
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dtemp(2) += mo_value_p(i)*mo_value_p(i)*mo_eplf_integral_matrix(jk,jl)
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enddo
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!- Open-open shell interactions
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do m=1,elec_num_2(p)-mo_closed_num
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jk = det(m,k,p)
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jl = det(m,l,p)
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dtemp(1) += mo_value_p(ik)* ( &
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mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
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mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )
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enddo
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do m=1,elec_num_2(p2)-mo_closed_num
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jk = det(m,k,p2)
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jl = det(m,l,p2)
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dtemp(2) += mo_value_p(ik)*mo_value_p(il)*mo_eplf_integral_matrix(jk,jl)
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enddo
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else if ( (exc(3) == 2).and.(exc(p) == 2) ) then
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! Consider only the double excitations of same-spin electrons
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call get_double_excitation(k,l,ik,il,jk,jl,p)
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dtemp(1) += mo_value_p(ik)* ( &
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mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
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mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )
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else if ( (exc(3) == 2).and.(exc(p) == 1) ) then
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! Consider only the double excitations of opposite-spin electrons
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call get_single_excitation(k,l,ik,il,p)
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call get_single_excitation(k,l,jk,jl,p2)
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dtemp(2) += mo_value_p(ik)*mo_value_p(il)*mo_eplf_integral_matrix(jk,jl)
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endif
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enddo
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phase = dble(exc(4))
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eplf_up_up += phase * det_coef(k)*det_coef(l) * dtemp(1)
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eplf_up_dn += phase * det_coef(k)*det_coef(l) * dtemp(2)
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ real, eplf_value_p ]
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implicit none
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BEGIN_DOC
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! Value of the EPLF at the current point.
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END_DOC
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double precision :: aa, ab
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double precision, parameter :: eps = tiny(1.d0)
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aa = eplf_up_up
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ab = eplf_up_dn
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if ( (aa > 0.d0).and.(ab > 0.d0) ) then
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aa = min(1.d0,aa)
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ab = min(1.d0,ab)
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aa = -dlog(aa)
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aa = dsqrt(aa)
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ab = -dlog(ab)
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ab = dsqrt(ab)
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eplf_value_p = (aa-ab)/(aa+ab+eps)
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else
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eplf_value_p = 0.d0
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endif
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END_PROVIDER
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!double precision function ao_eplf_integral_primitive_oneD_numeric(a,xa,i,b,xb,j,gmma,xr)
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! implicit none
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! include 'constants.F'
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!
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! real, intent(in) :: a,b,gmma ! Exponents
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! real, intent(in) :: xa,xb,xr ! Centers
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! integer, intent(in) :: i,j ! Powers of xa and xb
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! integer,parameter :: Npoints=10000
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! real :: x, xmin, xmax, dx
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!
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! ASSERT (a>0.)
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! ASSERT (b>0.)
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! ASSERT (i>=0)
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! ASSERT (j>=0)
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!
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! xmin = min(xa,xb)
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! xmax = max(xa,xb)
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! xmin = min(xmin,xr) - 10.
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! xmax = max(xmax,xr) + 10.
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! dx = (xmax-xmin)/real(Npoints)
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!
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! real :: dtemp
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! dtemp = 0.
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! x = xmin
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! integer :: k
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! do k=1,Npoints
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! dtemp += &
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! (x-xa)**i * (x-xb)**j * exp(-(a*(x-xa)**2+b*(x-xb)**2+gmma*(x-xr)**2))
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! x = x+dx
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! enddo
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! ao_eplf_integral_primitive_oneD_numeric = dtemp*dx
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!
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!end function
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!
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!double precision function ao_eplf_integral_numeric(i,j,gmma,center)
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! implicit none
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! integer, intent(in) :: i, j
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! integer :: p,q,k
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! double precision :: integral
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! double precision :: ao_eplf_integral_primitive_oneD_numeric
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! real :: gmma, center(3), c
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!
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!
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! ao_eplf_integral_numeric = 0.d0
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! do q=1,ao_prim_num(j)
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! do p=1,ao_prim_num(i)
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! c = ao_coef(i,p)*ao_coef(j,q)
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! integral = &
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! ao_eplf_integral_primitive_oneD_numeric( &
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! ao_expo(i,p), &
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! nucl_coord(ao_nucl(i),1), &
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! ao_power(i,1), &
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! ao_expo(j,q), &
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! nucl_coord(ao_nucl(j),1), &
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! ao_power(j,1), &
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! gmma, &
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! center(1)) * &
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! ao_eplf_integral_primitive_oneD_numeric( &
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! ao_expo(i,p), &
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! nucl_coord(ao_nucl(i),2), &
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! ao_power(i,2), &
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! ao_expo(j,q), &
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! nucl_coord(ao_nucl(j),2), &
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! ao_power(j,2), &
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! gmma, &
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! center(2)) * &
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! ao_eplf_integral_primitive_oneD_numeric( &
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! ao_expo(i,p), &
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! nucl_coord(ao_nucl(i),3), &
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! ao_power(i,3), &
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! ao_expo(j,q), &
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! nucl_coord(ao_nucl(j),3), &
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! ao_power(j,3), &
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! gmma, &
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! center(3))
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! ao_eplf_integral_numeric = ao_eplf_integral_numeric + c*integral
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! enddo
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! enddo
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!
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!end function
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double precision function ao_eplf_integral_primitive_oneD(a,xa,i,b,xb,j,gmma,xr)
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implicit none
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include 'constants.F'
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real, intent(in) :: a,b ! Exponents
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double precision , intent(in) :: gmma ! eplf_gamma
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real, intent(in) :: xa,xb,xr ! Centers
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integer, intent(in) :: i,j ! Powers of xa and xb
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integer :: ii, jj, kk
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ASSERT (a>0.)
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ASSERT (b>0.)
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ASSERT (i>=0)
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ASSERT (j>=0)
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double precision :: alpha, beta, delta, c
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alpha = a*xa*xa + b*xb*xb + gmma*xr*xr
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delta = a*xa + b*xb + gmma*xr
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beta = a + b + gmma
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c = alpha-delta**2/beta
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if ( c > 32.d0 ) then ! Cut-off on exp(-32)
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ao_eplf_integral_primitive_oneD = 0.d0
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return
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endif
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double precision :: u,v,w
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c = exp(-c)
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w = 1.d0/sqrt(beta)
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u=delta/beta-xa
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v=delta/beta-xb
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double precision :: fact2, binom, f, ac
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ac = 0.d0
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integer :: istart(0:1)
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istart = (/ 0, 1 /)
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do ii=0,i
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do jj=istart(mod(ii,2)),j,2
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kk=(ii+jj)/2
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f=binom(ii,i)*binom(jj,j)*fact2(ii+jj-1)
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ac += u**(i-ii)*v**(j-jj)*w**(ii+jj)*f/dble(2**kk)
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enddo
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enddo
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ao_eplf_integral_primitive_oneD = dsqrt_pi*w*c*ac
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end function
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double precision function ao_eplf_integral(i,j,gmma,center)
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implicit none
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integer, intent(in) :: i, j
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real, intent(in) :: center(3)
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double precision, intent(in) :: gmma
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!DEC$ ATTRIBUTES FORCEINLINE
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integer :: p,q,k
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double precision :: integral
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double precision :: ao_eplf_integral_primitive_oneD
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double precision :: buffer(100)
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ASSERT(i>0)
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ASSERT(j>0)
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ASSERT(ao_prim_num_max < 100)
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ASSERT(i<=ao_num)
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ASSERT(j<=ao_num)
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ao_eplf_integral = 0.d0
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do p=1,ao_prim_num_max
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buffer(p) = 0.d0
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enddo
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do q=1,ao_prim_num(j)
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do p=1,ao_prim_num(i)
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integral = &
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ao_eplf_integral_primitive_oneD( &
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ao_expo(i,p), &
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nucl_coord(ao_nucl(i),1), &
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ao_power(i,1), &
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ao_expo(j,q), &
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nucl_coord(ao_nucl(j),1), &
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ao_power(j,1), &
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gmma, &
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center(1))
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if (integral /= 0.d0) then
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integral *= &
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ao_eplf_integral_primitive_oneD( &
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ao_expo(i,p), &
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nucl_coord(ao_nucl(i),2), &
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ao_power(i,2), &
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ao_expo(j,q), &
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nucl_coord(ao_nucl(j),2), &
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ao_power(j,2), &
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gmma, &
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center(2))
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if (integral /= 0.d0) then
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integral *= &
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ao_eplf_integral_primitive_oneD( &
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ao_expo(i,p), &
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nucl_coord(ao_nucl(i),3), &
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ao_power(i,3), &
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ao_expo(j,q), &
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nucl_coord(ao_nucl(j),3), &
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ao_power(j,3), &
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gmma, &
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center(3))
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buffer(p) += integral*ao_coef(i,p)*ao_coef(j,q)
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endif
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endif
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enddo
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enddo
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do p=1,ao_prim_num_max
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ao_eplf_integral += buffer(p)
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enddo
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end function
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double precision function mo_eplf_integral(i,j)
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implicit none
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integer :: i, j, k, l
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PROVIDE ao_eplf_integral_matrix
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PROVIDE mo_coef
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mo_eplf_integral = 0.d0
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do k=1,ao_num
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if (mo_coef(k,i) /= 0.) then
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do l=1,ao_num
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mo_eplf_integral += &
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mo_coef(k,i)*mo_coef(l,j)*ao_eplf_integral_matrix(k,l)
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enddo
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endif
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enddo
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end function
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