!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2018  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief Calculate the Perdew Correlation from 1986
!> \par History
!>      JGH (26.02.2003) : OpenMP enabled
!>      fawzi (04.2004)  : adapted to the new xc interface
!> \author JGH (03.03.2002)
! **************************************************************************************************
MODULE xc_perdew86

   USE input_section_types,             ONLY: section_vals_type
   USE kinds,                           ONLY: dp
   USE xc_derivative_set_types,         ONLY: xc_derivative_set_type,&
                                              xc_dset_get_derivative
   USE xc_derivative_types,             ONLY: xc_derivative_get,&
                                              xc_derivative_type
   USE xc_functionals_utilities,        ONLY: calc_rs_pw,&
                                              set_util
   USE xc_input_constants,              ONLY: pz_orig
   USE xc_perdew_zunger,                ONLY: pz_lda_eval
   USE xc_rho_cflags_types,             ONLY: xc_rho_cflags_type
   USE xc_rho_set_types,                ONLY: xc_rho_set_get,&
                                              xc_rho_set_type
#include "../base/base_uses.f90"

   IMPLICIT NONE

   PRIVATE

! *** Global parameters ***

   REAL(KIND=dp), PARAMETER :: pi = 3.14159265358979323846264338_dp
   REAL(KIND=dp), PARAMETER :: f13 = 1.0_dp/3.0_dp, &
                               f23 = 2.0_dp*f13, &
                               f43 = 4.0_dp*f13, &
                               f53 = 5.0_dp*f13, &
                               f76 = 7.0_dp/6.0_dp, &
                               frs = 1.6119919540164696407_dp, &
                               fpe = 0.19199566167376364_dp

   PUBLIC :: p86_lda_info, p86_lda_eval

   REAL(KIND=dp) :: eps_rho
   LOGICAL :: debug_flag

   REAL(KIND=dp), PARAMETER :: a = 0.023266_dp, &
                               b = 7.389e-6_dp, &
                               c = 8.723_dp, &
                               d = 0.472_dp, &
                               pc1 = 0.001667_dp, &
                               pc2 = 0.002568_dp, &
                               pci = pc1+pc2
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_perdew86'

CONTAINS

! **************************************************************************************************
!> \brief ...
!> \param cutoff ...
!> \param debug ...
! **************************************************************************************************
   SUBROUTINE p86_init(cutoff, debug)

      REAL(KIND=dp), INTENT(IN)                          :: cutoff
      LOGICAL, INTENT(IN), OPTIONAL                      :: debug

      eps_rho = cutoff
      CALL set_util(cutoff)

      IF (PRESENT(debug)) THEN
         debug_flag = debug
      ELSE
         debug_flag = .FALSE.
      ENDIF

   END SUBROUTINE p86_init

! **************************************************************************************************
!> \brief ...
!> \param reference ...
!> \param shortform ...
!> \param needs ...
!> \param max_deriv ...
! **************************************************************************************************
   SUBROUTINE p86_lda_info(reference, shortform, needs, max_deriv)
      CHARACTER(LEN=*), INTENT(OUT), OPTIONAL            :: reference, shortform
      TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL  :: needs
      INTEGER, INTENT(out), OPTIONAL                     :: max_deriv

      IF (PRESENT(reference)) THEN
         reference = "J. P. Perdew, Phys. Rev. B, 33, 8822 (1986) {LDA version}"
      END IF
      IF (PRESENT(shortform)) THEN
         shortform = "Perdew 1986 correlation energy functional {LDA}"
      END IF
      IF (PRESENT(needs)) THEN
         needs%rho = .TRUE.
         needs%norm_drho = .TRUE.
      END IF
      IF (PRESENT(max_deriv)) max_deriv = 3

   END SUBROUTINE p86_lda_info

! **************************************************************************************************
!> \brief ...
!> \param rho_set ...
!> \param deriv_set ...
!> \param order ...
!> \param p86_params ...
! **************************************************************************************************
   SUBROUTINE p86_lda_eval(rho_set, deriv_set, order, p86_params)

      TYPE(xc_rho_set_type), POINTER                     :: rho_set
      TYPE(xc_derivative_set_type), POINTER              :: deriv_set
      INTEGER, INTENT(IN)                                :: order
      TYPE(section_vals_type), POINTER                   :: p86_params

      CHARACTER(len=*), PARAMETER :: routineN = 'p86_lda_eval', routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, m, npoints
      INTEGER, DIMENSION(:, :), POINTER                  :: bo
      REAL(KIND=dp)                                      :: drho_cutoff, rho_cutoff
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: rs
      REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: e_0, e_ndrho, e_ndrho_ndrho, &
         e_ndrho_ndrho_ndrho, e_rho, e_rho_ndrho, e_rho_ndrho_ndrho, e_rho_rho, e_rho_rho_ndrho, &
         e_rho_rho_rho, grho, rho
      TYPE(xc_derivative_type), POINTER                  :: deriv

      CALL timeset(routineN, handle)
      NULLIFY (bo, rho, e_0, e_rho, e_ndrho, &
               e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
               e_rho_rho_rho, e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho)
      CPASSERT(ASSOCIATED(rho_set))
      CPASSERT(rho_set%ref_count > 0)
      CPASSERT(ASSOCIATED(deriv_set))
      CPASSERT(deriv_set%ref_count > 0)

      ! calculate the perdew_zunger correlation
      CALL pz_lda_eval(pz_orig, rho_set, deriv_set, order, p86_params)

      CALL xc_rho_set_get(rho_set, rho=rho, &
                          norm_drho=grho, local_bounds=bo, rho_cutoff=rho_cutoff, &
                          drho_cutoff=drho_cutoff)
      npoints = (bo(2, 1)-bo(1, 1)+1)*(bo(2, 2)-bo(1, 2)+1)*(bo(2, 3)-bo(1, 3)+1)
      CALL p86_init(rho_cutoff)
      m = ABS(order)

      ALLOCATE (rs(npoints))

      CALL calc_rs_pw(rho, rs, npoints)
      IF (order >= 0) THEN
         deriv => xc_dset_get_derivative(deriv_set, "", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_0)

         CALL p86_u_0(rho, rs, grho, e_0, npoints)
      END IF
      IF (order >= 1 .OR. order == -1) THEN
         deriv => xc_dset_get_derivative(deriv_set, "(rho)", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho)
         deriv => xc_dset_get_derivative(deriv_set, "(norm_drho)", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_ndrho)

         CALL p86_u_1(rho, grho, rs, e_rho, &
                      e_ndrho, npoints)
      END IF
      IF (order >= 2 .OR. order == -2) THEN
         deriv => xc_dset_get_derivative(deriv_set, "(rho)(rho)", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
         deriv => xc_dset_get_derivative(deriv_set, "(rho)(norm_drho)", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho)
         deriv => xc_dset_get_derivative(deriv_set, &
                                         "(norm_drho)(norm_drho)", allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)

         CALL p86_u_2(rho, grho, rs, e_rho_rho, &
                      e_rho_ndrho, e_ndrho_ndrho, npoints)
      END IF
      IF (order >= 3 .OR. order == -3) THEN
         deriv => xc_dset_get_derivative(deriv_set, "(rho)(rho)(rho)", &
                                         allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
         deriv => xc_dset_get_derivative(deriv_set, &
                                         "(rho)(rho)(norm_drho)", allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_ndrho)
         deriv => xc_dset_get_derivative(deriv_set, &
                                         "(rho)(norm_drho)(norm_drho)", allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho_ndrho)
         deriv => xc_dset_get_derivative(deriv_set, &
                                         "(norm_drho)(norm_drho)(norm_drho)", allocate_deriv=.TRUE.)
         CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)

         CALL p86_u_3(rho, grho, rs, e_rho_rho_rho, &
                      e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, &
                      npoints)
      END IF
      IF (order > 3 .OR. order < -3) THEN
         CPABORT("derivatives bigger than 3 not implemented")
      END IF
      DEALLOCATE (rs)
      CALL timestop(handle)

   END SUBROUTINE p86_lda_eval

! **************************************************************************************************
!> \brief ...
!> \param rho ...
!> \param rs ...
!> \param grho ...
!> \param e_0 ...
!> \param npoints ...
! **************************************************************************************************
   SUBROUTINE p86_u_0(rho, rs, grho, e_0, npoints)

      REAL(KIND=dp), DIMENSION(*), INTENT(IN)            :: rho, rs, grho
      REAL(KIND=dp), DIMENSION(*), INTENT(INOUT)         :: e_0
      INTEGER, INTENT(in)                                :: npoints

      INTEGER                                            :: ip
      REAL(KIND=dp)                                      :: cr, ep, g, or, phi, r, x

!$OMP PARALLEL DO PRIVATE(ip,g,r,x,or,cr,phi,ep) DEFAULT(NONE)&
!$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_0)
      DO ip = 1, npoints

         IF (rho(ip) > eps_rho) THEN
            g = grho(ip)
            r = rs(ip)
            x = r*frs
            or = 1.0_dp/rho(ip)
            cr = pc1+(pc2+a*r+b*r*r)/(1.0_dp+c*r+d*r*r+1.e4_dp*b*r*r*r)
            phi = fpe*pci/cr*g*SQRT(x)*or
            ep = EXP(-phi)
            e_0(ip) = e_0(ip)+x*or*g*g*cr*ep
         END IF

      END DO

   END SUBROUTINE p86_u_0

! **************************************************************************************************
!> \brief ...
!> \param rho ...
!> \param grho ...
!> \param rs ...
!> \param e_rho ...
!> \param e_ndrho ...
!> \param npoints ...
! **************************************************************************************************
   SUBROUTINE p86_u_1(rho, grho, rs, e_rho, e_ndrho, npoints)

      REAL(KIND=dp), DIMENSION(*), INTENT(IN)            :: rho, grho, rs
      REAL(KIND=dp), DIMENSION(*), INTENT(INOUT)         :: e_rho, e_ndrho
      INTEGER, INTENT(in)                                :: npoints

      INTEGER                                            :: ip
      REAL(KIND=dp)                                      :: cr, dcr, dphig, dphir, dpv, dq, ep, ff, &
                                                            g, or, p, phi, q, r, x

!$OMP PARALLEL DO PRIVATE(ip,g,r,x,or,p,dpv,q,dq,cr,dcr,dphig,phi,dphir,ep,ff) DEFAULT(NONE)&
!$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_rho,e_ndrho)
      DO ip = 1, npoints

         IF (rho(ip) > eps_rho) THEN
            g = grho(ip)
            r = rs(ip)
            x = r*frs
            or = 1.0_dp/rho(ip)
            p = pc2+a*r+b*r*r
            dpv = a+2.0_dp*b*r
            q = 1.0_dp+c*r+d*r*r+1.e4_dp*b*r*r*r
            dq = c+2.0_dp*d*r+3.e4_dp*b*r*r
            cr = pc1+p/q
            dcr = (dpv*q-p*dq)/(q*q)*(-f13*r*or)
            dphig = fpe*pci/cr*SQRT(x)*or
            phi = dphig*g
            dphir = -phi*(dcr/cr+f76*or)
            ep = EXP(-phi)
            ff = x*or*g*ep
            e_rho(ip) = e_rho(ip)+ff*g*dcr-ff*g*cr*dphir-ff*g*cr*f43*or
            e_ndrho(ip) = e_ndrho(ip)+ff*cr*(2.0_dp-g*dphig)
         END IF

      END DO

   END SUBROUTINE p86_u_1

! **************************************************************************************************
!> \brief ...
!> \param rho ...
!> \param grho ...
!> \param rs ...
!> \param e_rho_rho ...
!> \param e_rho_ndrho ...
!> \param e_ndrho_ndrho ...
!> \param npoints ...
! **************************************************************************************************
   SUBROUTINE p86_u_2(rho, grho, rs, e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
                      npoints)

      REAL(KIND=dp), DIMENSION(*), INTENT(IN)            :: rho, grho, rs
      REAL(KIND=dp), DIMENSION(*), INTENT(INOUT)         :: e_rho_rho, e_rho_ndrho, e_ndrho_ndrho
      INTEGER, INTENT(in)                                :: npoints

      INTEGER                                            :: ip
      REAL(KIND=dp)                                      :: cr, d2cr, d2p, d2phir, d2q, dcr, dphig, &
                                                            dphigr, dphir, dpv, dq, ep, g, or, p, &
                                                            phi, q, r, x

!$OMP PARALLEL DO PRIVATE(ip,x,r,cr,phi,ep,g,or,p,q,dpv,dq,dphir,dcr) &
!$OMP             PRIVATE(dphig,dphigr,d2phir,d2cr,d2p,d2q) DEFAULT(NONE) &
!$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_rho_rho,e_rho_ndrho,e_ndrho_ndrho)
      DO ip = 1, npoints

         IF (rho(ip) > eps_rho) THEN
            g = grho(ip)
            r = rs(ip)
            x = r*frs
            or = 1.0_dp/rho(ip)
            p = pc2+a*r+b*r*r
            dpv = a+2.0_dp*b*r
            d2p = 2.0_dp*b
            q = 1.0_dp+c*r+d*r*r+1.e4_dp*b*r*r*r
            dq = c+2.0_dp*d*r+3.e4_dp*b*r*r
            d2q = 2.0_dp*d+6.e4_dp*b*r
            cr = pc1+p/q
            dcr = (dpv*q-p*dq)/(q*q)*(-f13*r*or)
            d2cr = (d2p*q*q-p*q*d2q-2*dpv*dq*q+2*p*dq*dq)/(q*q*q)*(f13*r*or)**2+ &
                   (dpv*q-p*dq)/(q*q)*f13*f43*r*or*or
            dphig = fpe*pci/cr*SQRT(x)*or
            phi = dphig*g
            dphir = -phi*(dcr/cr+f76*or)
            d2phir = -dphir*(dcr/cr+f76*or)- &
                     phi*((d2cr*cr-dcr*dcr)/(cr*cr)-f76*or*or)
            dphigr = -dphig*(dcr/cr+f76*or)
            ep = EXP(-phi)
            e_rho_rho(ip) = e_rho_rho(ip)+x*or*ep*g*g* &
                            (-f43*or*dcr+d2cr-dcr*dphir+ &
                             f43*or*cr*dphir-dcr*dphir-cr*d2phir+cr*dphir*dphir+ &
                             f43*or*(7.*f13*or*cr-dcr+cr*dphir))
            e_rho_ndrho(ip) = e_rho_ndrho(ip)+x*or*ep*g* &
                              (-2*f43*cr*or+2*dcr-2*cr*dphir+f43*or*g*cr*dphig- &
                               g*dcr*dphig+g*cr*dphir*dphig-g*cr*dphigr)
            e_ndrho_ndrho(ip) = e_ndrho_ndrho(ip)+x*or*ep*cr* &
                                (2.0_dp-4.0_dp*g*dphig+g*g*dphig*dphig)
         END IF

      END DO

   END SUBROUTINE p86_u_2

! **************************************************************************************************
!> \brief ...
!> \param rho ...
!> \param grho ...
!> \param rs ...
!> \param e_rho_rho_rho ...
!> \param e_rho_rho_ndrho ...
!> \param e_rho_ndrho_ndrho ...
!> \param e_ndrho_ndrho_ndrho ...
!> \param npoints ...
! **************************************************************************************************
   SUBROUTINE p86_u_3(rho, grho, rs, e_rho_rho_rho, &
                      e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, &
                      npoints)

      REAL(KIND=dp), DIMENSION(*), INTENT(IN)            :: rho, grho, rs
      REAL(KIND=dp), DIMENSION(*), INTENT(INOUT)         :: e_rho_rho_rho, e_rho_rho_ndrho, &
                                                            e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho
      INTEGER, INTENT(in)                                :: npoints

      INTEGER                                            :: ip
      REAL(KIND=dp) :: cr, d2cr, d2p, d2phir, d2phirg, d2pq, d2q, d2z, d3cr, d3phir, d3pq, d3q, &
         d3z, dcr, dphig, dphigr, dphir, dpq, dpv, dq, dz, ep, g, or, oz, p, phi, pq, q, r, x

!$OMP PARALLEL DO PRIVATE(ip,x, r, cr, phi, ep, g, or, p, q, dpv, dq, dphir, dcr, dphig) &
!$OMP             PRIVATE(dphigr, d2phir, d3phir, d2cr, d3cr, d2p, d2q, d2phirg, d3q) &
!$OMP             PRIVATE(pq, dpq, d2pq, d3pq, oz, dz, d2z, d3z) DEFAULT(NONE) &
!$OMP             SHARED(npoints,rho,eps_rho,grho,e_rho_rho_rho,e_rho_rho_ndrho,e_rho_ndrho_ndrho,e_ndrho_ndrho_ndrho)
      DO ip = 1, npoints

         IF (rho(ip) > eps_rho) THEN
            g = grho(ip)
            r = rs(ip)
            x = r*frs
            or = 1.0_dp/rho(ip)
            p = pc2+a*r+b*r*r
            dpv = a+2.0_dp*b*r
            d2p = 2.0_dp*b
            q = 1.0_dp+c*r+d*r*r+1.e4_dp*b*r*r*r
            dq = c+2.0_dp*d*r+3.e4_dp*b*r*r
            d2q = 2.0_dp*d+6.e4*b*r
            d3q = 6.e4*b
            pq = p/q
            dpq = (dpv*q-p*dq)/(q*q)
            d2pq = (d2p*q*q-2*dpv*dq*q+2*p*dq*dq-p*d2q*q)/(q*q*q)
            d3pq = -(3*d2p*dq*q*q-6*dpv*dq*dq*q+3*dpv*d2q*q*q+6*p*dq*dq*dq-6*p*dq*d2q*q &
                     +p*d3q*q*q)/(q*q*q*q)
            cr = pc1+pq
            dcr = dpq*(-f13*r*or)
            d2cr = d2pq*f13*f13*r*r*or*or+dpq*f13*f43*r*or*or
            d3cr = d3pq*(-f13*r*or)**3+3*d2pq*(-f13*f13*f43*r*r*or*or*or)+ &
                   dpq*(-f13*f43*f13*7*r*or*or*or)
            oz = SQRT(x)*or/cr
            dz = dcr/cr+f76*or
            d2z = d2cr/cr+2*f76*dcr/cr*or+f76/6.*or*or
            d3z = d3cr/cr+3*f76*d2cr/cr*or+3*f76/6.*dcr/cr*or*or-5*f76/36.*or*or*or
            dphig = fpe*pci*oz
            phi = dphig*g
            dphir = -phi*dz
            dphigr = -dphig*dz
            d2phir = -phi*(d2z-2*dz*dz)
            d3phir = -phi*(d3z-6*d2z*dz+6*dz*dz*dz)
            d2phirg = -dphigr*dz- &
                      dphig*((d2cr*cr-dcr*dcr)/(cr*cr)-f76*or*or)
            ep = EXP(-phi)
            e_rho_rho_rho(ip) = e_rho_rho_rho(ip) &
                                +g*g*x*or*ep*(-280./27.*or*or*or*cr+3*28./9.*or*or*dcr+ &
                                              3*28./9.*or*or*cr*(-dphir)-4*or*d2cr-8*or*dcr*(-dphir)- &
                                              4*or*cr*(-d2phir+dphir*dphir)+d3cr+3*d2cr*(-dphir)+ &
                                              3*dcr*(-d2phir+dphir*dphir)+cr*(-d3phir+3*dphir*d2phir- &
                                                                              dphir**3))
            e_rho_rho_ndrho(ip) = e_rho_rho_ndrho(ip) &
                                  +2.*x*or*ep*g*(-f43*or*dcr+d2cr-dcr*dphir+ &
                                                 f43*or*cr*dphir-dcr*dphir-cr*d2phir+cr*dphir*dphir+ &
                                                 f43*or*(7.*f13*or*cr-dcr+cr*dphir))- &
                                  dphig*x*or*ep*g*g*(-f43*or*dcr+d2cr-dcr*dphir+ &
                                                     f43*or*cr*dphir-dcr*dphir-cr*d2phir+cr*dphir*dphir+ &
                                                     f43*or*(7.*f13*or*cr-dcr+cr*dphir))+ &
                                  x*or*ep*g*g*(-dcr*dphigr+f43*or*cr*dphigr-dcr*dphigr-cr*d2phirg+ &
                                               2.*cr*dphigr*dphir+f43*or*cr*dphigr)
            e_rho_ndrho_ndrho(ip) = e_rho_ndrho_ndrho(ip) &
                                    +x*or*ep*(-2*f43*cr*or+2*dcr-2*cr*dphir+f43*or*g*cr*dphig- &
                                              g*dcr*dphig+g*cr*dphir*dphig-g*cr*dphigr)+ &
                                    x*or*ep*g*(-2*cr*dphigr+f43*or*cr*dphig- &
                                               dcr*dphig+cr*dphir*dphig+g*cr*dphigr*dphig-cr*dphigr)- &
                                    x*or*ep*g*dphig*(-2*f43*cr*or+2*dcr-2*cr*dphir+f43*or*g*cr*dphig- &
                                                     g*dcr*dphig+g*cr*dphir*dphig-g*cr*dphigr)
            e_ndrho_ndrho_ndrho(ip) = e_ndrho_ndrho_ndrho(ip) &
                                      +x*or*ep*cr*dphig*(-6.0_dp+6.0_dp*g*dphig-g*g*dphig*dphig)
         END IF

      END DO

   END SUBROUTINE p86_u_3

END MODULE xc_perdew86

