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

! **************************************************************************************************
!> \brief Contains some functions used in the context of adiabatic hybrid functionals
!> \par History
!>      01.2008 created [Manuel Guidon]
!> \author Manuel Guidon
! **************************************************************************************************
MODULE xc_adiabatic_methods

   USE input_constants,                 ONLY: do_hfx_potential_coulomb
   USE kinds,                           ONLY: dp
   USE mathconstants,                   ONLY: oorootpi
   USE qs_energy_types,                 ONLY: qs_energy_type
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_mo_types,                     ONLY: get_mo_set,&
                                              mo_set_p_type
#include "./base/base_uses.f90"

   IMPLICIT NONE
   PRIVATE

   PUBLIC :: rescale_MCY3_pade

CONTAINS

! **************************************************************************************************
!> \brief - Calculates rescaling factors for XC potentials and energy expression
!> \param qs_env ...
!> \param hf_energy Array of size 2 containing the two HF energies (Ex^{HF} and Ex^{HF,LR}
!> \param energy QS energy type
!> \param adiabatic_lambda , adiabatic_omega: Parameters for adiabatic connection
!> \param adiabatic_omega ...
!> \param scale_dEx1 scaling coefficient for xc-potentials to be calculated
!> \param scale_ddW0 scaling coefficient for xc-potentials to be calculated
!> \param scale_dDFA scaling coefficient for xc-potentials to be calculated
!> \param scale_dEx2 scaling coefficient for xc-potentials to be calculated
!> \param total_energy_xc will contain the full xc energy
!> \par History
!>      09.2007 created [Manuel Guidon]
!> \author Manuel Guidon
!> \note
!>      - Model for adiabatic connection:
!>
!>         W_lambda = a + b*lambda/(1+c*lambda)
!>         Exc = a + b*(c-log(1+c)/c^2)
!>         a = Ex^{HF}
!>         b = -c1*2*omega/sqrt(PI)*nelectron
!>         c = -1/lambda - b/(Ex^{HF}-W_lambda^{BLYP} + c2*W_lambda^{B88,LR}-c3*W_lambda^{HF,LR}
! **************************************************************************************************
   SUBROUTINE rescale_MCY3_pade(qs_env, hf_energy, energy, adiabatic_lambda, &
                                adiabatic_omega, scale_dEx1, scale_ddW0, scale_dDFA, &
                                scale_dEx2, total_energy_xc)

      TYPE(qs_environment_type), POINTER                 :: qs_env
      REAL(dp), INTENT(INOUT)                            :: hf_energy(*)
      TYPE(qs_energy_type), POINTER                      :: energy
      REAL(dp), INTENT(IN)                               :: adiabatic_lambda, adiabatic_omega
      REAL(dp), INTENT(INOUT)                            :: scale_dEx1, scale_ddW0, scale_dDFA, &
                                                            scale_dEx2, total_energy_xc

      INTEGER                                            :: nelec_a, nelec_b, nelectron, nspins
      LOGICAL                                            :: do_swap_hf
      REAL(dp) :: a, b, c, c1, da_dDFA, da_ddW0, da_dEx1, da_dEx2, db_dDFA, db_ddW0, db_dEx1, &
         db_dEx2, dc_dDFA, dc_ddW0, dc_dEx1, dc_dEx2, dExc_da, dExc_db, dExc_dc, dfa_energy, &
         swap_value
      TYPE(mo_set_p_type), DIMENSION(:), POINTER         :: mos

      do_swap_hf = .FALSE.
      !! Assume the first HF section is the Coulomb one
      IF (qs_env%x_data(1, 1)%potential_parameter%potential_type /= do_hfx_potential_coulomb) do_swap_hf = .TRUE.

      IF (do_swap_hf) THEN
         swap_value = hf_energy(1)
         hf_energy(1) = hf_energy(2)
         hf_energy(2) = swap_value
      END IF

      c1 = 0.23163_dp

      CALL get_qs_env(qs_env=qs_env, mos=mos)
      CALL get_mo_set(mo_set=mos(1)%mo_set, nelectron=nelec_a)
      nspins = SIZE(mos)
      IF (nspins == 2) THEN
         CALL get_mo_set(mo_set=mos(2)%mo_set, nelectron=nelec_b)
      ELSE
         nelec_b = 0
      END IF
      nelectron = nelec_a+nelec_b
      dfa_energy = energy%exc+energy%exc1
      a = hf_energy(1)
      b = -c1*2.0_dp*adiabatic_omega*oorootpi*nelectron !-0.23163_dp*2.0_dp*0.2_dp*oorootpi*nelectron
      c = -1.0_dp/adiabatic_lambda-b/(hf_energy(1)-dfa_energy-hf_energy(2))

      dExc_da = 1.0_dp
      dExc_db = 1.0_dp/c-(LOG(ABS(1.0_dp+c))/(c*c))
      dExc_dc = -b/(c*c*c*(1.0_dp+c))*(2.0_dp*c+c*c-2.0_dp*LOG(ABS(1.0_dp+c))-2.0_dp*LOG(ABS(1.0_dp+c))*c)

      da_dEx1 = 1.0_dp
      da_ddW0 = 0.0_dp
      da_dDFA = 0.0_dp
      da_dEx2 = 0.0_dp

      db_dEx1 = 0.0_dp
      db_ddW0 = 1.0_dp
      db_dDFA = 0.0_dp
      db_dEx2 = 0.0_dp

      dc_dEx1 = b/(hf_energy(1)-dfa_energy-hf_energy(2))**2
      dc_ddW0 = -1.0_dp/(hf_energy(1)-dfa_energy-hf_energy(2))
      dc_dDFA = -dc_dEx1
      dc_dEx2 = -dc_dEx1

      scale_dEx1 = dExc_da*da_dEx1+dExc_db*db_dEx1+dExc_dc*dc_dEx1
      scale_ddW0 = dExc_da*da_ddW0+dExc_db*db_ddW0+dExc_dc*dc_ddW0
      scale_dDFA = dExc_da*da_dDFA+dExc_db*db_dDFA+dExc_dc*dc_dDFA
      scale_dEx2 = dExc_da*da_dEx2+dExc_db*db_dEx2+dExc_dc*dc_dEx2

      total_energy_xc = a+b/(c*c)*(c-LOG(ABS(1.0_dp+c)))
      IF (do_swap_hf) THEN
         swap_value = scale_dEx1
         scale_dEx1 = scale_dEx2
         scale_dEx2 = swap_value
      END IF
   END SUBROUTINE rescale_MCY3_pade

END MODULE xc_adiabatic_methods
