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

! **************************************************************************************************
!> \brief Calculation of Coulomb integrals over Cartesian Gaussian-type functions
!>      (electron repulsion integrals, ERIs).
!> \par Literature
!>      S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986)
!> \par History
!>      none
!> \par Parameters
!>       - ax,ay,az    : Angular momentum index numbers of orbital a.
!>       - bx,by,bz    : Angular momentum index numbers of orbital b.
!>       - coset       : Cartesian orbital set pointer.
!>       - dab         : Distance between the atomic centers a and b.
!>       - dac         : Distance between the atomic centers a and c.
!>       - dbc         : Distance between the atomic centers b and c.
!>       - l{a,b,c}    : Angular momentum quantum number of shell a, b or c.
!>       - l{a,b,c}_max: Maximum angular momentum quantum number of shell a, b or c.
!>       - l{a,b,c}_min: Minimum angular momentum quantum number of shell a, b or c.
!>       - ncoset      : Number of orbitals in a Cartesian orbital set.
!>       - npgf{a,b}   : Degree of contraction of shell a or b.
!>       - rab         : Distance vector between the atomic centers a and b.
!>       - rab2        : Square of the distance between the atomic centers a and b.
!>       - rac         : Distance vector between the atomic centers a and c.
!>       - rac2        : Square of the distance between the atomic centers a and c.
!>       - rbc         : Distance vector between the atomic centers b and c.
!>       - rbc2        : Square of the distance between the atomic centers b and c.
!>       - rpgf{a,b,c} : Radius of the primitive Gaussian-type function a, b or c.
!>       - zet{a,b,c}  : Exponents of the Gaussian-type functions a, b or c.
!>       - zetp        : Reciprocal of the sum of the exponents of orbital a and b.
!> \author VW
! **************************************************************************************************
MODULE ai_elec_field
   USE ai_os_rr,                        ONLY: os_rr_coul
   USE kinds,                           ONLY: dp
   USE mathconstants,                   ONLY: pi
   USE orbital_pointers,                ONLY: coset,&
                                              ncoset
#include "../base/base_uses.f90"

   IMPLICIT NONE
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'ai_elec_field'
   PRIVATE

   ! *** Public subroutines ***

   PUBLIC :: efg

CONTAINS

! **************************************************************************************************
!> \brief   Calculation of the primitive electric field integrals over
!>          Cartesian Gaussian-type functions.
!> \param la_max ...
!> \param la_min ...
!> \param npgfa ...
!> \param rpgfa ...
!> \param zeta ...
!> \param lb_max ...
!> \param lb_min ...
!> \param npgfb ...
!> \param rpgfb ...
!> \param zetb ...
!> \param rac ...
!> \param rbc ...
!> \param rab ...
!> \param vab ...
!> \param ldrr1 ...
!> \param ldrr2 ...
!> \param rr ...
!> \date    02.03.2009
!> \author  VW
!> \version 1.0
! **************************************************************************************************
   SUBROUTINE efg(la_max, la_min, npgfa, rpgfa, zeta, &
                  lb_max, lb_min, npgfb, rpgfb, zetb, &
                  rac, rbc, rab, vab, ldrr1, ldrr2, rr)
      INTEGER, INTENT(IN)                                :: la_max, la_min, npgfa
      REAL(KIND=dp), DIMENSION(:), INTENT(IN)            :: rpgfa, zeta
      INTEGER, INTENT(IN)                                :: lb_max, lb_min, npgfb
      REAL(KIND=dp), DIMENSION(:), INTENT(IN)            :: rpgfb, zetb
      REAL(KIND=dp), DIMENSION(3), INTENT(IN)            :: rac, rbc, rab
      REAL(KIND=dp), DIMENSION(:, :, :), INTENT(INOUT)   :: vab
      INTEGER, INTENT(IN)                                :: ldrr1, ldrr2
      REAL(KIND=dp), DIMENSION(0:ldrr1-1, ldrr2, *), &
         INTENT(INOUT)                                   :: rr

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

      INTEGER :: ax, ay, az, bx, by, bz, coa, coam1x, coam1y, coam1z, coam2x, coam2y, coam2z, &
         coamxpy, coamxpz, coamxy, coamxz, coamypx, coamypz, coamyz, coamzpx, coamzpy, coap1x, &
         coap1y, coap1z, coap2x, coap2y, coap2z, coapxy, coapxz, coapyz, cob, cobm1x, cobm1y, &
         cobm1z, cobm2x, cobm2y, cobm2z, cobmxpy, cobmxpz, cobmxy, cobmxz, cobmypx, cobmypz, &
         cobmyz, cobmzpx, cobmzpy, cobp1x, cobp1y, cobp1z, cobp2x, cobp2y, cobp2z, cobpxy, cobpxz, &
         cobpyz, i, ipgf, j, jpgf, la, lb, ma, mb, na, nb
      REAL(KIND=dp)                                      :: dab, dum, dumxx, dumxy, dumxz, dumyy, &
                                                            dumyz, dumzz, f0, rab2, xhi, za, zb, &
                                                            zet
      REAL(KIND=dp), DIMENSION(3)                        :: rap, rbp, rcp

! *** Calculate the distance of the centers a and c ***

      rab2 = rab(1)**2+rab(2)**2+rab(3)**2
      dab = SQRT(rab2)

      ! *** Loop over all pairs of primitive Gaussian-type functions ***

      na = 0

      DO ipgf = 1, npgfa

         nb = 0

         DO jpgf = 1, npgfb

            ! *** Screening ***

            IF (rpgfa(ipgf)+rpgfb(jpgf) < dab) THEN
               DO j = nb+1, nb+ncoset(lb_max)
                  DO i = na+1, na+ncoset(la_max)
                     vab(i, j, 1) = 0.0_dp
                     vab(i, j, 2) = 0.0_dp
                     vab(i, j, 3) = 0.0_dp
                     vab(i, j, 4) = 0.0_dp
                     vab(i, j, 5) = 0.0_dp
                     vab(i, j, 6) = 0.0_dp
                  ENDDO
               ENDDO
               nb = nb+ncoset(lb_max)
               CYCLE
            ENDIF

            ! *** Calculate some prefactors ***

            za = zeta(ipgf)
            zb = zetb(jpgf)
            zet = za+zb
            xhi = za*zb/zet
            rap = zb*rab/zet
            rbp = -za*rab/zet
            rcp = -(za*rac+zb*rbc)/zet
            f0 = 2.0_dp*SQRT(zet/pi)*(pi/zet)**(1.5_dp)*EXP(-xhi*rab2)

            ! *** Calculate the reccurence relation

            CALL os_rr_coul(rap, la_max+2, rbp, lb_max+2, rcp, zet, ldrr1, ldrr2, rr)

            ! *** Calculate the primitive electric field gradient integrals ***

            DO lb = lb_min, lb_max
            DO bx = 0, lb
            DO by = 0, lb-bx
               bz = lb-bx-by
               cob = coset(bx, by, bz)
               cobm1x = coset(MAX(bx-1, 0), by, bz)
               cobm1y = coset(bx, MAX(by-1, 0), bz)
               cobm1z = coset(bx, by, MAX(bz-1, 0))
               cobm2x = coset(MAX(bx-2, 0), by, bz)
               cobm2y = coset(bx, MAX(by-2, 0), bz)
               cobm2z = coset(bx, by, MAX(bz-2, 0))
               cobmxy = coset(MAX(bx-1, 0), MAX(by-1, 0), bz)
               cobmxz = coset(MAX(bx-1, 0), by, MAX(bz-1, 0))
               cobmyz = coset(bx, MAX(by-1, 0), MAX(bz-1, 0))
               cobp1x = coset(bx+1, by, bz)
               cobp1y = coset(bx, by+1, bz)
               cobp1z = coset(bx, by, bz+1)
               cobp2x = coset(bx+2, by, bz)
               cobp2y = coset(bx, by+2, bz)
               cobp2z = coset(bx, by, bz+2)
               cobpxy = coset(bx+1, by+1, bz)
               cobpxz = coset(bx+1, by, bz+1)
               cobpyz = coset(bx, by+1, bz+1)
               cobmxpy = coset(MAX(bx-1, 0), by+1, bz)
               cobmxpz = coset(MAX(bx-1, 0), by, bz+1)
               cobmypx = coset(bx+1, MAX(by-1, 0), bz)
               cobmypz = coset(bx, MAX(by-1, 0), bz+1)
               cobmzpx = coset(bx+1, by, MAX(bz-1, 0))
               cobmzpy = coset(bx, by+1, MAX(bz-1, 0))
               mb = nb+cob
               DO la = la_min, la_max
               DO ax = 0, la
               DO ay = 0, la-ax
                  az = la-ax-ay
                  coa = coset(ax, ay, az)
                  coap1x = coset(ax+1, ay, az)
                  coap1y = coset(ax, ay+1, az)
                  coap1z = coset(ax, ay, az+1)
                  coap2x = coset(ax+2, ay, az)
                  coap2y = coset(ax, ay+2, az)
                  coap2z = coset(ax, ay, az+2)
                  coapxy = coset(ax+1, ay+1, az)
                  coapxz = coset(ax+1, ay, az+1)
                  coapyz = coset(ax, ay+1, az+1)
                  coam1x = coset(MAX(ax-1, 0), ay, az)
                  coam1y = coset(ax, MAX(ay-1, 0), az)
                  coam1z = coset(ax, ay, MAX(az-1, 0))
                  coam2x = coset(MAX(ax-2, 0), ay, az)
                  coam2y = coset(ax, MAX(ay-2, 0), az)
                  coam2z = coset(ax, ay, MAX(az-2, 0))
                  coamxy = coset(MAX(ax-1, 0), MAX(ay-1, 0), az)
                  coamxz = coset(MAX(ax-1, 0), ay, MAX(az-1, 0))
                  coamyz = coset(ax, MAX(ay-1, 0), MAX(az-1, 0))
                  coamxpy = coset(MAX(ax-1, 0), ay+1, az)
                  coamxpz = coset(MAX(ax-1, 0), ay, az+1)
                  coamypx = coset(ax+1, MAX(ay-1, 0), az)
                  coamypz = coset(ax, MAX(ay-1, 0), az+1)
                  coamzpx = coset(ax+1, ay, MAX(az-1, 0))
                  coamzpy = coset(ax, ay+1, MAX(az-1, 0))
                  ma = na+coa
                  !
                  ! (a|xx|b)
                  dum = 4.0_dp*(za**2*rr(0, coap2x, cob)+zb**2*rr(0, coa, cobp2x) &
                       &         +2.0_dp*za*zb*rr(0, coap1x, cobp1x)) &
                       -2.0_dp*rr(0, coa, cob)*(za*REAL(2*ax+1, dp)+zb*REAL(2*bx+1, dp))
                  IF (ax .GT. 1) dum = dum+REAL(ax*(ax-1), dp)*rr(0, coam2x, cob)
                  IF (bx .GT. 1) dum = dum+REAL(bx*(bx-1), dp)*rr(0, coa, cobm2x)
                  IF (ax .GT. 0) dum = dum-4.0_dp*zb*REAL(ax, dp)*rr(0, coam1x, cobp1x)
                  IF (bx .GT. 0) dum = dum-4.0_dp*za*REAL(bx, dp)*rr(0, coap1x, cobm1x)
                  IF (ax .GT. 0 .AND. bx .GT. 0) dum = dum+2.0_dp*REAL(ax*bx, dp)*rr(0, coam1x, cobm1x)
                  dumxx = f0*dum
                  !
                  ! (a|yy|b)
                  dum = 4.0_dp*(za**2*rr(0, coap2y, cob)+zb**2*rr(0, coa, cobp2y) &
                       &         +2.0_dp*za*zb*rr(0, coap1y, cobp1y)) &
                       -2.0_dp*rr(0, coa, cob)*(za*REAL(2*ay+1, dp)+zb*REAL(2*by+1, dp))
                  IF (ay .GT. 1) dum = dum+REAL(ay*(ay-1), dp)*rr(0, coam2y, cob)
                  IF (by .GT. 1) dum = dum+REAL(by*(by-1), dp)*rr(0, coa, cobm2y)
                  IF (ay .GT. 0) dum = dum-4.0_dp*zb*REAL(ay, dp)*rr(0, coam1y, cobp1y)
                  IF (by .GT. 0) dum = dum-4.0_dp*za*REAL(by, dp)*rr(0, coap1y, cobm1y)
                  IF (ay .GT. 0 .AND. by .GT. 0) dum = dum+2.0_dp*REAL(ay*by, dp)*rr(0, coam1y, cobm1y)
                  dumyy = f0*dum
                  !
                  ! (a|zz|b)
                  dum = 4.0_dp*(za**2*rr(0, coap2z, cob)+zb**2*rr(0, coa, cobp2z) &
                       &         +2.0_dp*za*zb*rr(0, coap1z, cobp1z)) &
                       -2.0_dp*rr(0, coa, cob)*(za*REAL(2*az+1, dp)+zb*REAL(2*bz+1, dp))
                  IF (az .GT. 1) dum = dum+REAL(az*(az-1), dp)*rr(0, coam2z, cob)
                  IF (bz .GT. 1) dum = dum+REAL(bz*(bz-1), dp)*rr(0, coa, cobm2z)
                  IF (az .GT. 0) dum = dum-4.0_dp*zb*REAL(az, dp)*rr(0, coam1z, cobp1z)
                  IF (bz .GT. 0) dum = dum-4.0_dp*za*REAL(bz, dp)*rr(0, coap1z, cobm1z)
                  IF (az .GT. 0 .AND. bz .GT. 0) dum = dum+2.0_dp*REAL(az*bz, dp)*rr(0, coam1z, cobm1z)
                  dumzz = f0*dum
                  !
                  ! (a|xy|b)
                  dum = 4.0_dp*(za**2*rr(0, coapxy, cob)+zb**2*rr(0, coa, cobpxy) &
                       &         +za*zb*(rr(0, coap1x, cobp1y)+rr(0, coap1y, cobp1x)))
                  IF (ax .GT. 0) dum = dum-2.0_dp*REAL(ax, dp)* &
                       &  (za*rr(0, coamxpy, cob)+zb*rr(0, coam1x, cobp1y))
                  IF (ay .GT. 0) dum = dum-2.0_dp*REAL(ay, dp)* &
                       &  (za*rr(0, coamypx, cob)+zb*rr(0, coam1y, cobp1x))
                  IF (ax .GT. 0 .AND. ay .GT. 0) dum = dum+REAL(ax*ay, dp)*rr(0, coamxy, cob)
                  IF (bx .GT. 0) dum = dum-2.0_dp*REAL(bx, dp)* &
                       &  (zb*rr(0, coa, cobmxpy)+za*rr(0, coap1y, cobm1x))
                  IF (by .GT. 0) dum = dum-2.0_dp*REAL(by, dp)* &
                       &  (zb*rr(0, coa, cobmypx)+za*rr(0, coap1x, cobm1y))
                  IF (bx .GT. 0 .AND. by .GT. 0) dum = dum+REAL(bx*by, dp)*rr(0, coa, cobmxy)
                  IF (ax .GT. 0 .AND. by .GT. 0) dum = dum+REAL(ax*by, dp)*rr(0, coam1x, cobm1y)
                  IF (ay .GT. 0 .AND. bx .GT. 0) dum = dum+REAL(ay*bx, dp)*rr(0, coam1y, cobm1x)
                  dumxy = f0*dum
                  !
                  ! (a|xz|b)
                  dum = 4.0_dp*(za**2*rr(0, coapxz, cob)+zb**2*rr(0, coa, cobpxz) &
                       &         +za*zb*(rr(0, coap1x, cobp1z)+rr(0, coap1z, cobp1x)))
                  IF (ax .GT. 0) dum = dum-2.0_dp*REAL(ax, dp)* &
                       &  (za*rr(0, coamxpz, cob)+zb*rr(0, coam1x, cobp1z))
                  IF (az .GT. 0) dum = dum-2.0_dp*REAL(az, dp)* &
                       &  (za*rr(0, coamzpx, cob)+zb*rr(0, coam1z, cobp1x))
                  IF (ax .GT. 0 .AND. az .GT. 0) dum = dum+REAL(ax*az, dp)*rr(0, coamxz, cob)
                  IF (bx .GT. 0) dum = dum-2.0_dp*REAL(bx, dp)* &
                       &  (zb*rr(0, coa, cobmxpz)+za*rr(0, coap1z, cobm1x))
                  IF (bz .GT. 0) dum = dum-2.0_dp*REAL(bz, dp)* &
                       &  (zb*rr(0, coa, cobmzpx)+za*rr(0, coap1x, cobm1z))
                  IF (bx .GT. 0 .AND. bz .GT. 0) dum = dum+REAL(bx*bz, dp)*rr(0, coa, cobmxz)
                  IF (ax .GT. 0 .AND. bz .GT. 0) dum = dum+REAL(ax*bz, dp)*rr(0, coam1x, cobm1z)
                  IF (az .GT. 0 .AND. bx .GT. 0) dum = dum+REAL(az*bx, dp)*rr(0, coam1z, cobm1x)
                  dumxz = f0*dum
                  !
                  ! (a|yz|b)
                  dum = 4.0_dp*(za**2*rr(0, coapyz, cob)+zb**2*rr(0, coa, cobpyz) &
                       &         +za*zb*(rr(0, coap1y, cobp1z)+rr(0, coap1z, cobp1y)))
                  IF (ay .GT. 0) dum = dum-2.0_dp*REAL(ay, dp)* &
                       &  (za*rr(0, coamypz, cob)+zb*rr(0, coam1y, cobp1z))
                  IF (az .GT. 0) dum = dum-2.0_dp*REAL(az, dp)* &
                       &  (za*rr(0, coamzpy, cob)+zb*rr(0, coam1z, cobp1y))
                  IF (ay .GT. 0 .AND. az .GT. 0) dum = dum+REAL(ay*az, dp)*rr(0, coamyz, cob)
                  IF (by .GT. 0) dum = dum-2.0_dp*REAL(by, dp)* &
                       &  (zb*rr(0, coa, cobmypz)+za*rr(0, coap1z, cobm1y))
                  IF (bz .GT. 0) dum = dum-2.0_dp*REAL(bz, dp)* &
                       &  (zb*rr(0, coa, cobmzpy)+za*rr(0, coap1y, cobm1z))
                  IF (by .GT. 0 .AND. bz .GT. 0) dum = dum+REAL(by*bz, dp)*rr(0, coa, cobmyz)
                  IF (ay .GT. 0 .AND. bz .GT. 0) dum = dum+REAL(ay*bz, dp)*rr(0, coam1y, cobm1z)
                  IF (az .GT. 0 .AND. by .GT. 0) dum = dum+REAL(az*by, dp)*rr(0, coam1z, cobm1y)
                  dumyz = f0*dum
                  !
                  !
                  vab(ma, mb, 1) = (2.0_dp*dumxx-dumyy-dumzz)/3.0_dp !xx
                  vab(ma, mb, 2) = dumxy !xy
                  vab(ma, mb, 3) = dumxz !xz
                  vab(ma, mb, 4) = (2.0_dp*dumyy-dumzz-dumxx)/3.0_dp !yy
                  vab(ma, mb, 5) = dumyz !yz
                  vab(ma, mb, 6) = (2.0_dp*dumzz-dumxx-dumyy)/3.0_dp !zz
               ENDDO
               ENDDO
               ENDDO !la

            ENDDO
            ENDDO
            ENDDO !lb

            nb = nb+ncoset(lb_max)

         ENDDO

         na = na+ncoset(la_max)

      ENDDO

   END SUBROUTINE efg

END MODULE ai_elec_field
