recursive function VRR3e(m,AngMomBra,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & result(a1a2a3) ! Vertical recurrence relations for three-electron integrals implicit none include 'parameters.h' ! Input variables integer,intent(in) :: m integer,intent(in) :: AngMomBra(3,3) integer,intent(in) :: maxm double precision,intent(in) :: Om(0:maxm),ExpZ(3),CenterZA(3,3) double precision,intent(in) :: DY0(3),DY1(3),D2Y0(3,3),D2Y1(3,3) ! Local variables logical :: NegAngMomBra(3) integer :: TotAngMomBra(3) integer :: a1m(3,3),a2m(3,3),a3m(3,3) integer :: a1mm(3,3),a2mm(3,3),a3mm(3,3) integer :: a1m2m(3,3),a1m3m(3,3),a2m3m(3,3) integer :: i,j,xyz ! Output variables double precision :: a1a2a3 do i=1,3 NegAngMomBra(i) = AngMomBra(i,1) < 0 .or. AngMomBra(i,2) < 0 .or. AngMomBra(i,3) < 0 TotAngMomBra(i) = AngMomBra(i,1) + AngMomBra(i,2) + AngMomBra(i,3) end do !------------------------------------------------------------------------ ! Termination condition !------------------------------------------------------------------------ if(NegAngMomBra(1) .or. NegAngMomBra(2) .or. NegAngMomBra(3)) then a1a2a3 = 0d0 !------------------------------------------------------------------------ ! Fundamental integral: (000|000)^m !------------------------------------------------------------------------ elseif(TotAngMomBra(1) == 0 .and. TotAngMomBra(2) == 0 .and. TotAngMomBra(3) == 0) then a1a2a3 = Om(m) !------------------------------------------------------------------------ ! 1st vertical recurrence relation (4 terms): (a1+00|000)^m !------------------------------------------------------------------------ elseif(TotAngMomBra(2) == 0 .and. TotAngMomBra(3) == 0) then do i=1,3 do j=1,3 a1m(i,j) = AngMomBra(i,j) a1mm(i,j) = AngMomBra(i,j) end do end do ! Loop over cartesian directions xyz = 0 if (AngMomBra(1,1) > 0) then xyz = 1 elseif(AngMomBra(1,2) > 0) then xyz = 2 elseif(AngMomBra(1,3) > 0) then xyz = 3 else write(*,*) 'xyz = 0 in VRR3e!' end if ! End loop over cartesian directions a1m(1,xyz) = a1m(1,xyz) - 1 a1mm(1,xyz) = a1mm(1,xyz) - 2 if(AngMomBra(1,xyz) == 0) then a1a2a3 = 0d0 elseif(AngMomBra(1,xyz) == 1) then a1a2a3 = (CenterZA(1,xyz) - DY0(1))*VRR3e(m, a1m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(1) - DY0(1))*VRR3e(m+1,a1m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) else a1a2a3 = (CenterZA(1,xyz) - DY0(1))*VRR3e(m, a1m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(1) - DY0(1))*VRR3e(m+1,a1m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & + dble(AngMomBra(1,xyz)-1)*(0.5d0/ExpZ(1) - D2Y0(1,1))*VRR3e(m, a1mm,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(1,xyz)-1)*(D2Y1(1,1) - D2Y0(1,1))*VRR3e(m+1,a1mm,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) end if !------------------------------------------------------------------------ ! 2nd vertical recurrence relation (6 terms): (a1a2+0|000)^m !------------------------------------------------------------------------ elseif(TotAngMomBra(3) == 0) then do i=1,3 do j=1,3 a2m(i,j) = AngMomBra(i,j) a2mm(i,j) = AngMomBra(i,j) a1m2m(i,j) = AngMomBra(i,j) end do end do ! Loop over cartesian directions xyz = 0 if (AngMomBra(2,1) > 0) then xyz = 1 elseif(AngMomBra(2,2) > 0) then xyz = 2 elseif(AngMomBra(2,3) > 0) then xyz = 3 else write(*,*) 'xyz = 0 in VRR3e!' end if ! End loop over cartesian directions a2m(2,xyz) = a2m(2,xyz) - 1 a2mm(2,xyz) = a2mm(2,xyz) - 2 a1m2m(1,xyz) = a1m2m(1,xyz) - 1 a1m2m(2,xyz) = a1m2m(2,xyz) - 1 if(AngMomBra(2,xyz) == 0) then a1a2a3 = 0d0 elseif(AngMomBra(2,xyz) == 1) then a1a2a3 = (CenterZA(2,xyz) - DY0(2))*VRR3e(m, a2m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(2) - DY0(2))*VRR3e(m+1,a2m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) else a1a2a3 = (CenterZA(2,xyz) - DY0(2))*VRR3e(m, a2m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(2) - DY0(2))*VRR3e(m+1,a2m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & + dble(AngMomBra(2,xyz)-1)*(0.5d0/ExpZ(2) - D2Y0(2,2))*VRR3e(m, a2mm, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(2,xyz)-1)*(D2Y1(2,2) - D2Y0(2,2))*VRR3e(m+1,a2mm, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) end if if(AngMomBra(1,xyz) > 0) & a1a2a3 = a1a2a3 & + dble(AngMomBra(1,xyz))*(-D2Y0(2,1))*VRR3e(m, a1m2m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(1,xyz))*(D2Y1(2,1) - D2Y0(2,1))*VRR3e(m+1,a1m2m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) !------------------------------------------------------------------------ ! 3rd vertical recurrence relation (8 terms): (a1a2a3+|000)^m !------------------------------------------------------------------------ else do i=1,3 do j=1,3 a3m(i,j) = AngMomBra(i,j) a3mm(i,j) = AngMomBra(i,j) a1m3m(i,j) = AngMomBra(i,j) a2m3m(i,j) = AngMomBra(i,j) end do end do ! Loop over cartesian directions xyz = 0 if (AngMomBra(3,1) > 0) then xyz = 1 elseif(AngMomBra(3,2) > 0) then xyz = 2 elseif(AngMomBra(3,3) > 0) then xyz = 3 else write(*,*) 'xyz = 0 in VRR3e!' end if ! End loop over cartesian directions a3m(3,xyz) = a3m(3,xyz) - 1 a3mm(3,xyz) = a3mm(3,xyz) - 2 a1m3m(1,xyz) = a1m3m(1,xyz) - 1 a1m3m(3,xyz) = a1m3m(3,xyz) - 1 a2m3m(2,xyz) = a2m3m(2,xyz) - 1 a2m3m(3,xyz) = a2m3m(3,xyz) - 1 if(AngMomBra(3,xyz) == 0) then a1a2a3 = 0d0 elseif(AngMomBra(3,xyz) == 1) then a1a2a3 = (CenterZA(3,xyz) - DY0(3))*VRR3e(m, a3m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(3) - DY0(3))*VRR3e(m+1,a3m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) else a1a2a3 = (CenterZA(3,xyz) - DY0(3))*VRR3e(m, a3m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - (DY1(3) - DY0(3))*VRR3e(m+1,a3m, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & + dble(AngMomBra(3,xyz)-1)*(0.5d0/ExpZ(3) - D2Y0(3,3))*VRR3e(m, a3mm, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(3,xyz)-1)*(D2Y1(3,3) - D2Y0(3,3))*VRR3e(m+1,a3mm, maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) end if if(dble(AngMomBra(1,xyz)) > 0) & a1a2a3 = a1a2a3 & + dble(AngMomBra(1,xyz))*(-D2Y0(3,1))*VRR3e(m, a1m3m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(1,xyz))*(D2Y1(3,1) - D2Y0(3,1))*VRR3e(m+1,a1m3m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) if(dble(AngMomBra(2,xyz)) > 0) & a1a2a3 = a1a2a3 & + dble(AngMomBra(2,xyz))*(-D2Y0(3,2))*VRR3e(m, a2m3m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) & - dble(AngMomBra(2,xyz))*(D2Y1(3,2) - D2Y0(3,2))*VRR3e(m+1,a2m3m,maxm,Om,ExpZ,CenterZA,DY0,DY1,D2Y0,D2Y1) end if end function VRR3e