eplf/src/eplf_function.irp.f

BEGIN_PROVIDER  [ real, eplf_gamma ]
 implicit none
 BEGIN_DOC  
! Value of the gaussian for the EPLF
 END_DOC
 include 'constants.F'
 real            :: eps
 eps = -real(dlog(tiny(1.d0)))
!real :: N
!N = 0.1
!eplf_gamma = (4./(3.*N)*pi*density_value_p)**(2./3.) * eps
 eplf_gamma = density_value_p * eps
!eplf_gamma = 1.e10
!eplf_gamma = 1.e5
END_PROVIDER

BEGIN_PROVIDER [ double precision, ao_eplf_integral_matrix, (ao_num,ao_num) ]
 implicit none
 BEGIN_DOC  
! Array of all the <chi_i chi_j | exp(-gamma r^2)> for EPLF
 END_DOC
 integer :: i, j
 double precision :: ao_eplf_integral
 do i=1,ao_num
  do j=i,ao_num
    ao_eplf_integral_matrix(j,i) = ao_eplf_integral(j,i,eplf_gamma,point)
    ao_eplf_integral_matrix(i,j) = ao_eplf_integral_matrix(j,i)
  enddo
 enddo
END_PROVIDER

BEGIN_PROVIDER [ double precision, mo_eplf_integral_matrix, (mo_num,mo_num) ]
 implicit none
 BEGIN_DOC  
! Array of all the <chi_i chi_j | exp(-gamma r^2)> for EPLF
 END_DOC
 integer :: i, j, k, l
 double precision :: t
 PROVIDE ao_eplf_integral_matrix
 PROVIDE mo_coef
 do i=1,mo_num
  do j=i,mo_num
    mo_eplf_integral_matrix(j,i) = 0.d0
  enddo


  do k=1,ao_num
   if (mo_coef(k,i) /= 0.) then
    do l=1,ao_num
     t = mo_coef(k,i)*ao_eplf_integral_matrix(l,k)
     do j=i,mo_num
      mo_eplf_integral_matrix(j,i) += t*mo_coef_transp(j,l)
     enddo
    enddo
   endif
  enddo

 enddo

 do i=1,mo_num
  do j=i+1,mo_num
    mo_eplf_integral_matrix(i,j) = mo_eplf_integral_matrix(j,i)
  enddo
 enddo
END_PROVIDER

 BEGIN_PROVIDER [ double precision, eplf_up_up ]
&BEGIN_PROVIDER [ double precision, eplf_up_dn ]
 implicit none
 BEGIN_DOC  
! Value of the d_upup and d_updn quantities needed for EPLF
 END_DOC

 integer :: i, j

 eplf_up_up = 0.d0
 eplf_up_dn = 0.d0

 PROVIDE mo_coef_transp

 do j=1,mo_closed_num
  do i=1,mo_closed_num
    eplf_up_up += 2.d0* mo_value_p(i)* (  &
      mo_value_p(i)*mo_eplf_integral_matrix(j,j) - &
      mo_value_p(j)*mo_eplf_integral_matrix(i,j) )
    eplf_up_dn += 2.d0* mo_value_p(i)*mo_value_p(i)* &
        mo_eplf_integral_matrix(j,j)
  enddo
 enddo

 integer :: k,l,m,n,p
 integer :: ik,il,jk,jl
 double precision :: ckl
 double precision :: phase
 integer :: exc

 PROVIDE det
 PROVIDE elec_num_2

 do k=1,det_num
  do l=1,det_num

   ckl = det_coef(k)*det_coef(l)

   exc = det_exc(k,l,3)

   if ( exc < 0 ) then
    phase = -1.0d0
    exc = -exc
   else
    phase = 1.0d0
   endif

   if ( exc == 0 ) then
     ! Sum over all alpha-alpha and beta-beta interactions
     do p=1,2
      do m=1,elec_num_2(p)-mo_closed_num
       jk = det(m,k,p)
       jl = det(m,l,p)
       do n=1,elec_num_2(p)-mo_closed_num
         ik = det(n,k,p)
         il = det(n,l,p)
         eplf_up_up += phase*ckl*mo_value_p(ik)* (  &
           mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
           mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )
       enddo
      enddo
     enddo

     ! Sum over all alpha-beta interactions
     do m=1,elec_beta_num-mo_closed_num
      jk = det(m,k,2)
      jl = det(m,l,2)
      do n=1,elec_alpha_num-mo_closed_num
        ik = det(n,k,1)
        il = det(n,l,1)
        eplf_up_dn += phase*ckl * ( mo_value_p(ik)*mo_value_p(il) * mo_eplf_integral_matrix(jk,jl) &
                            + mo_value_p(jk)*mo_value_p(jl) * mo_eplf_integral_matrix(ik,il) )
      enddo
     enddo

   else if ( exc == 1 ) then
    
     do p=1,2
      if ( det_exc(k,l,p) == 1 ) then
      ! Sum over only the sigma-sigma interactions involving the excitation
       call get_single_excitation(k,l,ik,il,p)
       do m=1,elec_num_2(p)-mo_closed_num
        jk = det(m,k,p)
        jl = det(m,l,p)
        eplf_up_up += phase*ckl*mo_value_p(ik)* (  &
            mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
            mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )
       enddo

       ! Sum over only the sigma-(sigma_bar) interactions involving the excitation
       integer :: p2
       p2 = 1+mod(p,2)
       do m=1,elec_num_2(p2)-mo_closed_num
        jk = det(m,k,p2)
        jl = det(m,l,p2)
        eplf_up_dn += phase*ckl * ( mo_value_p(ik)*mo_value_p(il) * mo_eplf_integral_matrix(jk,jl) &
                            + mo_value_p(jk)*mo_value_p(jl) * mo_eplf_integral_matrix(ik,il) )
       enddo
      endif
     enddo

   else if (exc == 2) then

     if ( ( det_exc(k,l,1) == 2 ).or.( det_exc(k,l,2) == 2 ) ) then
     
      ! Consider only the double excitations of same-spin electrons
      if ( det_exc(k,l,1) == 2 ) then
       call get_double_excitation(k,l,ik,jk,il,jl,1)
      else if ( det_exc(k,l,2) == 2 ) then
       call get_double_excitation(k,l,ik,jk,il,jl,2)
      endif

      eplf_up_up += phase*ckl*mo_value_p(ik)* (  &
           mo_value_p(il)*mo_eplf_integral_matrix(jk,jl) - &
           mo_value_p(jl)*mo_eplf_integral_matrix(jk,il) )

     else if ( det_exc(k,l,1) == 1 ) then
      ! Consider only the double excitations of opposite-spin electrons
      call get_single_excitation(k,l,ik,jk,1)
      call get_single_excitation(k,l,il,jl,2)

      eplf_up_dn += phase*ckl * ( mo_value_p(ik)*mo_value_p(il) * mo_eplf_integral_matrix(jk,jl) &
                  + mo_value_p(jk)*mo_value_p(jl) * mo_eplf_integral_matrix(ik,il) )
     endif

   endif

  enddo
 enddo
 

END_PROVIDER


BEGIN_PROVIDER [ real, eplf_value_p ]
 implicit none
 BEGIN_DOC  
! Value of the EPLF at the current point.
 END_DOC
 double precision :: aa, ab
 double precision, parameter :: eps = tiny(1.d0)

 aa = eplf_up_up
 ab = eplf_up_dn
 if ( (aa > 0.d0).and.(ab > 0.d0) ) then
   aa = min(1.d0,aa)
   ab = min(1.d0,ab)
   aa = -(dlog(aa)/eplf_gamma)
   ab = -(dlog(ab)/eplf_gamma)
   aa = dsqrt(aa)
   ab = dsqrt(ab)
   eplf_value_p = (aa-ab)/(aa+ab+eps)
 else
   eplf_value_p = 0.d0
 endif

END_PROVIDER


double precision function ao_eplf_integral_primitive_oneD_numeric(a,xa,i,b,xb,j,gmma,xr)
 implicit none
 include 'constants.F'

 real, intent(in)    :: a,b,gmma ! Exponents
 real, intent(in)    :: xa,xb,xr ! Centers
 integer, intent(in) :: i,j   ! Powers of xa and xb
 integer,parameter :: Npoints=10000
 real :: x, xmin, xmax, dx

 ASSERT (a>0.)
 ASSERT (b>0.)
 ASSERT (i>=0)
 ASSERT (j>=0)

 xmin = min(xa,xb)
 xmax = max(xa,xb)
 xmin = min(xmin,xr) - 10.
 xmax = max(xmax,xr) + 10.
 dx = (xmax-xmin)/real(Npoints)

 real :: dtemp
 dtemp = 0.
 x = xmin
 integer :: k
 do k=1,Npoints
  dtemp += &
   (x-xa)**i * (x-xb)**j * exp(-(a*(x-xa)**2+b*(x-xb)**2+gmma*(x-xr)**2))
  x = x+dx
 enddo
 ao_eplf_integral_primitive_oneD_numeric = dtemp*dx

end function

double precision function ao_eplf_integral_numeric(i,j,gmma,center)
 implicit none
 integer, intent(in) :: i, j
 integer :: p,q,k
 double precision :: integral
 double precision :: ao_eplf_integral_primitive_oneD_numeric
 real :: gmma, center(3), c

 
  ao_eplf_integral_numeric = 0.d0
  do q=1,ao_prim_num(j)
   do p=1,ao_prim_num(i)
    c = ao_coef(i,p)*ao_coef(j,q)
    integral =                              &
    ao_eplf_integral_primitive_oneD_numeric(   &
     ao_expo(i,p),                          &
     nucl_coord(ao_nucl(i),1),              &
     ao_power(i,1),                         &
     ao_expo(j,q),                          &
     nucl_coord(ao_nucl(j),1),              &
     ao_power(j,1),                         &
     gmma,                                  &
     center(1))   *                         &
    ao_eplf_integral_primitive_oneD_numeric(   &
     ao_expo(i,p),                          &
     nucl_coord(ao_nucl(i),2),              &
     ao_power(i,2),                         &
     ao_expo(j,q),                          &
     nucl_coord(ao_nucl(j),2),              &
     ao_power(j,2),                         &
     gmma,                                  &
     center(2))   *                         &
    ao_eplf_integral_primitive_oneD_numeric(   &
     ao_expo(i,p),                          &
     nucl_coord(ao_nucl(i),3),              &
     ao_power(i,3),                         &
     ao_expo(j,q),                          &
     nucl_coord(ao_nucl(j),3),              &
     ao_power(j,3),                         &
     gmma,                                  &
     center(3))
    ao_eplf_integral_numeric = ao_eplf_integral_numeric + c*integral
   enddo
  enddo
  
end function
 
 double precision function ao_eplf_integral_primitive_oneD(a,xa,i,b,xb,j,gmma,xr)
  implicit none
  include 'constants.F'
 
  real, intent(in)    :: a,b,gmma ! Exponents
  real, intent(in)    :: xa,xb,xr ! Centers
  integer, intent(in) :: i,j   ! Powers of xa and xb
  integer :: ii, jj, kk, ll
  real :: xp1,xp
  real :: p1,p
  double precision :: S(0:i+1,0:j+1)
  double precision :: inv_p(2), di(max(i,j)), dj(j), c
 
  ASSERT (a>0.)
  ASSERT (b>0.)
  ASSERT (i>=0)
  ASSERT (j>=0)
 
  ! Gaussian product
 ! Inlined Gaussian products (same as call gaussian_product)
 real :: t(2), xab(2), ab(2)
 inv_p(1) = 1.d0/(a+b)
 p1 = a+b
 ab(1) = a*b
 inv_p(2) = 1.d0/(p1+gmma)
 t(1) = (a*xa+b*xb)
 xab(1) = xa-xb
 xp1 = t(1)*inv_p(1)
 p = p1+gmma
 ab(2) = p1*gmma
 t(2) = (p1*xp1+gmma*xr)
 xab(2) = xp1-xr
 xp = t(2)*inv_p(2)
 c = exp(- real(ab(1)*inv_p(1)*xab(1)**2 + &
             ab(2)*inv_p(2)*xab(2)**2) )

  S(0,0) = dsqrt(pi*inv_p(2))*c
  
  ! Obara-Saika recursion
 
  do ii=1,max(i,j)
   di(ii) = 0.5d0*inv_p(2)*dble(ii)
  enddo
 
  S(1,0) = (xp-xa) * S(0,0)
  if (i>1) then
   do ii=1,i-1
    S(ii+1,0) = (xp-xa) * S(ii,0) + di(ii)*S(ii-1,0)
   enddo
  endif
 
  S(0,1) = (xp-xb) * S(0,0)
  if (j>1) then
   do jj=1,j-1
    S(0,jj+1) = (xp-xb) * S(0,jj) + di(jj)*S(0,jj-1)
   enddo
  endif
 
  do jj=1,j
   S(1,jj) = (xp-xa) * S(0,jj) + di(jj) * S(0,jj-1)
   do ii=2,i
    S(ii,jj) = (xp-xa) * S(ii-1,jj) + di(ii-1) * S(ii-2,jj) + di(jj) * S(ii-1,jj-1)
   enddo
  enddo
 
  ao_eplf_integral_primitive_oneD = S(i,j)
 
 end function

!double precision function ao_eplf_integral_primitive_oneD(a,xa,i,b,xb,j,gmma,xr)
! implicit none
! include 'constants.F'
!!
! real, intent(in)    :: a,b,gmma ! Exponents
! real, intent(in)    :: xa,xb,xr ! Centers
! integer, intent(in) :: i,j   ! Powers of xa and xb
! integer :: ii, jj, kk, ll
! real :: xp1,xp
! real :: p1,p
! double precision :: xpa, xpb
! double precision :: inv_p(2),S00, c
! double precision :: ObaraS
!!
! ASSERT (a>0.)
! ASSERT (b>0.)
! ASSERT (i>=0)
! ASSERT (j>=0)
!!
! ! Inlined Gaussian products (same as call gaussian_product)
! real :: t(2), xab(2), ab(2)
! inv_p(1) = 1.d0/(a+b)
! p1 = a+b
! ab(1) = a*b
! inv_p(2) = 1.d0/(p1+gmma)
! t(1) = (a*xa+b*xb)
! xab(1) = xa-xb
! xp1 = t(1)*inv_p(1)
! p = p1+gmma
! ab(2) = p1*gmma
! t(2) = (p1*xp1+gmma*xr)
! xab(2) = xp1-xr
! xp = t(2)*inv_p(2)
! c = exp(- real(ab(1)*inv_p(1)*xab(1)**2 + &
!             ab(2)*inv_p(2)*xab(2)**2) )
!!
! xpa = xp-xa
! xpb = xp-xb
! S00 = sqrt(real(pi*inv_p(2)))*c
! ao_eplf_integral_primitive_oneD = ObaraS(i,j,xpa,xpb,inv_p(2),S00)
!!
!end function
!!
!recursive double precision function ObaraS(i,j,xpa,xpb,inv_p,S00) result(res)
! implicit none
! integer, intent(in) :: i, j
! double precision, intent(in) :: xpa, xpb, inv_p
! double precision,intent(in) :: S00
!!
! if (i == 0) then
!  if (j == 0) then
!   res = S00
!  else ! (j>0)
!   res = xpb*ObaraS(0,j-1,xpa,xpb,inv_p,S00)
!   if (j>1) then
!    res += 0.5d0*dble(j-1)*inv_p*ObaraS(0,j-2,xpa,xpb,inv_p,S00)
!   endif
!  endif ! (i==0).and.(j>0)
! else   ! (i>0)
!  if (j==0) then
!   res = xpa*ObaraS(i-1,0,xpa,xpb,inv_p,S00) 
!   if (i>1) then
!     res += 0.5d0*dble(i-1)*inv_p*ObaraS(i-2,0,xpa,xpb,inv_p,S00) 
!   endif
!  else  ! (i>0).and.(j>0)
!   res = xpa * ObaraS(i-1,j,xpa,xpb,inv_p,S00) 
!   if (i>1) then
!    res += 0.5d0*dble(i-1)*inv_p*ObaraS(i-2,j,xpa,xpb,inv_p,S00) 
!   endif
!   res += 0.5d0*dble(j)*inv_p*ObaraS(i-1,j-1,xpa,xpb,inv_p,S00) 
!  endif  ! (i>0).and.(j>0)
! endif  ! (i>0)
!!
!end function

double precision function ao_eplf_integral(i,j,gmma,center)
 implicit none
 integer, intent(in) :: i, j
 integer :: p,q,k
 double precision :: integral
!DEC$ ATTRIBUTES FORCEINLINE
 double precision :: ao_eplf_integral_primitive_oneD
 real :: gmma, center(3)
 double precision :: buffer(100)


 ASSERT(i>0)
 ASSERT(j>0)
 ASSERT(i<=ao_num)
 ASSERT(j<=ao_num)

 ao_eplf_integral = 0.d0
 do p=1,ao_prim_num_max
   buffer(p) = 0.d0
 enddo

 do q=1,ao_prim_num(j)
  do p=1,ao_prim_num(i)
   integral =                              &
   ao_eplf_integral_primitive_oneD(        &
    ao_expo(i,p),                          &
    nucl_coord(ao_nucl(i),1),              &
    ao_power(i,1),                         &
    ao_expo(j,q),                          &
    nucl_coord(ao_nucl(j),1),              &
    ao_power(j,1),                         &
    gmma,                                  &
    center(1))   *                         &
   ao_eplf_integral_primitive_oneD(        &
    ao_expo(i,p),                          &
    nucl_coord(ao_nucl(i),2),              &
    ao_power(i,2),                         &
    ao_expo(j,q),                          &
    nucl_coord(ao_nucl(j),2),              &
    ao_power(j,2),                         &
    gmma,                                  &
    center(2))   *                         &
   ao_eplf_integral_primitive_oneD(        &
    ao_expo(i,p),                          &
    nucl_coord(ao_nucl(i),3),              &
    ao_power(i,3),                         &
    ao_expo(j,q),                          &
    nucl_coord(ao_nucl(j),3),              &
    ao_power(j,3),                         &
    gmma,                                  &
    center(3))
!  ao_eplf_integral += integral*ao_coef(i,p)*ao_coef(j,q)
   buffer(p) += integral*ao_coef(i,p)*ao_coef(j,q)
  enddo
 enddo
 do p=1,ao_prim_num_max
   ao_eplf_integral += buffer(p)
 enddo
 
end function

double precision function mo_eplf_integral(i,j)
  implicit none
  integer :: i, j, k, l
  PROVIDE ao_eplf_integral_matrix
  PROVIDE mo_coef
  mo_eplf_integral = 0.d0
 
   do k=1,ao_num
     if (mo_coef(k,i) /= 0.) then
       do l=1,ao_num
        mo_eplf_integral +=  &
          mo_coef(k,i)*mo_coef(l,j)*ao_eplf_integral_matrix(k,l)
       enddo
     endif
   enddo
 
end function