626 lines
17 KiB
Fortran
626 lines
17 KiB
Fortran
!*****************************************************************************
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subroutine GauSlaOverlap(expGau,cGau,aGau,expSla,cSla,result)
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implicit none
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BEGIN_DOC
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! Compute the overlap integral between a Gaussian function
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! with arbitrary angular momemtum and a s-type Slater function
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END_DOC
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! Input variables
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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double precision,intent(out) :: result
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! Final value of the integrals
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double precision :: ss,ps,ds
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double precision :: pxs,pys,pzs
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double precision :: dxxs,dyys,dzzs,dxys,dxzs,dyzs
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double precision :: pi,E,AB,AxBx,AyBy,AzBz,t,u,k
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pi = 4d0*atan(1d0)
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! calculate the length AB between the two centers and other usful quantities
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AB = (cGau(1)-cSla(1))**2 + (cGau(2)-cSla(2))**2 + (cGau(3)-cSla(3))**2
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AB = dsqrt(AB)
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AxBx = (cGau(1)-cSla(1))/2d0
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AyBy = (cGau(2)-cSla(2))/2d0
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AzBz = (cGau(3)-cSla(3))/2d0
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ds = 0.d0
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! intermediate variables
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t = expSla*dsqrt(0.25d0/expGau)
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u = dsqrt(expGau)*AB
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double precision :: d, et2
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if(AB > 0d0) then
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! (s|s)
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ss = 0.d0
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d = derfc(t+u)
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if (dabs(d) > 1.d-30) then
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ss = (t+u)*d*dexp(2d0*t*(t+u))
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endif
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d = derfc(t-u)
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if (dabs(d) > 1.d-30) then
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ss -= (t-u)*d*dexp(2d0*t*(t-u))
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endif
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! (p|s)
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ps = 0.d0
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if (t*t-u*u > 300.d0) then
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et2 = huge(1.0)
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else
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et2 = dexp(t*t-u*u)
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endif
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if (et2 /= 0.d0) then
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d = derfc(t-u)
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if (d /= 0.d0) then
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ps += dexp((t-u)**2)*(1d0+2d0*t*(t-u))*d
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endif
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d = derfc(t+u)
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if (d /= 0.d0) then
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ps += dexp((t+u)**2)*(1d0+2d0*t*(t+u))*d
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endif
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ps *= dsqrt(pi)
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ps -= 4d0*t
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ps *= et2/dsqrt(pi)
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endif
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! (d|s)
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! ds = 4d0*dexp(2d0*t*(t-u))*t*(-((1d0+t**2-t*u)*derfc(t-u))+dexp(4d0*t*u)*(1d0+t*(t+u))*derfc(t+u))
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ds = 0.d0
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d = derfc(t+u)
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if (d /= 0.d0) then
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ds = dexp(4d0*t*u)*(1d0+t*(t+u))*d
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endif
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d = derfc(t-u)
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if (d /= 0.d0) then
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ds -= (1d0+t*t-t*u)*d
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endif
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if ( dabs(ds) > 1.d-100) then
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ds *= 4d0*dexp(2d0*t*(t-u))*t
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endif
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! backward scaling
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ds = 3d0*ss/u**5d0 - 3d0*ps/u**4d0 + ds/u**3d0
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ps = ps/u**2-ss/u**3d0
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ss = ss/u
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else
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! concentric case
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d = derfc(t)
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if (d /= 0.d0) then
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et2 = dexp(t*t)
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ss = 2d0*et2*((-2d0*t)/dsqrt(pi)+et2*(1d0+2d0*t*t)*d)
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ps = (8d0*et2*t*(-2d0*(1d0+t*t)+et2*dsqrt(pi)*t*(3d0+2d0*t*t)*d))/(3d0*dsqrt(pi))
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else
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ss = 0.d0
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ps = 0.d0
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endif
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endif
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k = t**3d0*dexp(-t*t)*4d0*pi/expSla**(3d0/2d0)
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! (s|s)
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ss = k*ss
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! (p|s)
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ps = k*ps
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pxs = AxBx*ps
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pys = AyBy*ps
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pzs = AzBz*ps
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! (d|s)
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ds = k*ds
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dxxs = (2d0*ss+ps)/(4d0*expGau) + AxBx**2*ds
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dyys = (2d0*ss+ps)/(4d0*expGau) + AyBy**2*ds
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dzzs = (2d0*ss+ps)/(4d0*expGau) + AzBz**2*ds
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dxys = AxBx*AyBy*ds
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dxzs = AxBx*AzBz*ds
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dyzs = AyBy*AzBz*ds
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select case (sum(aGau))
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case (0)
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result = ss
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case (1)
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if (aGau(1) == 1) then
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result = pxs
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else if (aGau(2) == 1) then
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result = pys
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else if (aGau(3) == 1) then
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result = pzs
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endif
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case (2)
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if (aGau(1) == 2) then
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result = dxxs
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else if (aGau(2) == 2) then
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result = dyys
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else if (aGau(3) == 2) then
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result = dzzs
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else if (aGau(1)+aGau(2) == 2) then
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result = dxys
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else if (aGau(1)+aGau(3) == 2) then
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result = dxzs
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else if (aGau(2)+aGau(3) == 2) then
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result = dyzs
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endif
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case default
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stop 'GauSlaOverlap not implemented'
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end select
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end
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!*****************************************************************************
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!*****************************************************************************
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subroutine GauSlaKinetic(expGau,cGau,aGau,expSla,cSla,result)
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implicit none
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BEGIN_DOC
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! Compute the kinetic energy integral between a Gaussian function
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! with arbitrary angular momemtum and a s-type Slater function
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END_DOC
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! Input variables
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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double precision,intent(out) :: result
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! Final value of the integrals
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double precision :: ss,ps,ds
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double precision :: pxs,pys,pzs
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double precision :: dxxs,dyys,dzzs,dxys,dxzs,dyzs
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double precision :: pi,E,AB,AxBx,AyBy,AzBz,t,u,k
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pi = 4d0*atan(1d0)
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! calculate the length AB between the two centers
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AB = (cGau(1)-cSla(1))**2 + (cGau(2)-cSla(2))**2 + (cGau(3)-cSla(3))**2
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AB = dsqrt(AB)
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AxBx = (cGau(1)-cSla(1))/2d0
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AyBy = (cGau(2)-cSla(2))/2d0
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AzBz = (cGau(3)-cSla(3))/2d0
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! intermediate variables
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t = expSla*dsqrt(0.25d0/expGau)
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u = dsqrt(expGau)*AB
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if(AB > 0d0) then
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! (s|s)
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ss = (1d0+t*(t-u))*derfc(t-u)*dexp(2d0*t*(t-u)) - (1d0+t*(t+u))*derfc(t+u)*dexp(2d0*t*(t+u))
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! (p|s)
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ps = (dexp(t**2-2d0*t*u-u**2)*(4d0*dexp(2d0*t*u)*(1d0+t**2) &
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+ dsqrt(pi)*t*(-(dexp(t**2+u**2)*(3d0+2d0*t*(t-u))*derfc(t-u)) &
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- dexp(2d0*t*u+(t+u)**2)*(3d0+2d0*t*(t+u))*derfc(t+u))))/dsqrt(pi)
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! (d|s)
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ds = (-8d0*dexp(t**2-u**2)*u+4d0*dexp(2d0*t*(t-u))*dsqrt(pi)*t**2*((2d0+t**2-t*u)*derfc(t-u) &
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- dexp(4d0*t*u)*(2d0+t*(t+u))*derfc(t+u)))/dsqrt(pi)
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! backward scaling
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ds = 3d0*ss/u**5d0 - 3d0*ps/u**4d0 + ds/u**3d0
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ps = ps/u**2-ss/u**3d0
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ss = ss/u
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else
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! concentric case
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ss = (4d0*dexp(t**2)*(1d0+t**2))/dsqrt(pi)-2d0*dexp(2d0*t**2)*t*(3d0+2d0*t**2)*derfc(t)
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ps = (8d0*dexp(t**2)*(-1d0+4d0*t**2+2d0*t**4d0-dexp(t**2)*dsqrt(pi)*t**3d0*(5d0+2d0*t**2)*derfc(t)))/(3d0*dsqrt(pi))
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endif
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k = expSla*dsqrt(expGau)*t**3d0*dexp(-t*t)*4d0*pi/expSla**(3d0/2d0)
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! (s|s)
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ss = k*ss
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! (p|s)
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ps = k*ps
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pxs = AxBx*ps
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pys = AyBy*ps
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pzs = AzBz*ps
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! (d|s)
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ds = k*ds
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dxxs = (2d0*ss+ps)/(4d0*expGau) + AxBx**2*ds
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dyys = (2d0*ss+ps)/(4d0*expGau) + AyBy**2*ds
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dzzs = (2d0*ss+ps)/(4d0*expGau) + AzBz**2*ds
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dxys = AxBx*AyBy*ds
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dxzs = AxBx*AzBz*ds
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dyzs = AyBy*AzBz*ds
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select case (sum(aGau))
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case (0)
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result = ss
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case (1)
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if (aGau(1) == 1) then
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result = pxs
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else if (aGau(2) == 1) then
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result = pys
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else if (aGau(3) == 1) then
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result = pzs
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endif
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case (2)
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if (aGau(1) == 2) then
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result = dxxs
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else if (aGau(2) == 2) then
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result = dyys
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else if (aGau(3) == 2) then
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result = dzzs
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else if (aGau(1)+aGau(2) == 2) then
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result = dxys
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else if (aGau(1)+aGau(3) == 2) then
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result = dxzs
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else if (aGau(2)+aGau(3) == 2) then
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result = dyzs
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endif
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case default
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stop 'GauSlaOverlap not implemented'
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end select
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end
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!*****************************************************************************
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!*****************************************************************************
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subroutine GauSlaNuclear(expGau,cGau,aGau,expSla,cSla,ZNuc,cNuc,result)
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implicit none
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BEGIN_DOC
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! Compute the nuclear attraction integral between a Gaussian function
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! with arbitrary angular momemtum and a s-type Slater function
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END_DOC
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! Input variables
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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double precision,intent(in) :: cNuc(3)
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double precision,intent(in) :: ZNuc
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double precision,intent(out) :: result
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! Final value of the overlap integral
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double precision :: ss,ps,ds,fs
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double precision :: pxs,pys,pzs
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double precision :: pi,E,AB,x,y,k
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pi = 4d0*atan(1d0)
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E = exp(1d0)
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! calculate the length AB between the two centers
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AB = (cGau(1)-cSla(1))**2 + (cGau(2)-cSla(2))**2 + (cGau(3)-cSla(3))**2
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AB = dsqrt(AB)
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! intermediate variables
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x = dsqrt(expSla**2/(4d0*expGau))
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y = dsqrt(expGau)*AB
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if(AB > 0d0) then
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ss = (1d0+x*(x+y))*derfc(x+y)*dexp(2d0*x*(x+y)) - (1d0+x*(x-y))*derfc(x-y)*dexp(2d0*x*(x-y))
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ss = ss/y
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else
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ss = (4d0*E**x**2*(1d0+x**2))/dsqrt(Pi)-2d0*E**(2d0*x**2)*x*(3d0+2d0*x**2)*dErfc(x)
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endif
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k = expSla*dsqrt(expGau)*x**3d0*dexp(-x*x)*4d0*pi/expSla**(3d0/2d0)
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ss = k*ss
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! Print result
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! write(*,*) ss
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result = 0.d0
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end
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!*****************************************************************************
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double precision function BoysF0(t)
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implicit none
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double precision, intent(in) :: t
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double precision :: pi
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pi = 4d0*atan(1d0)
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if(t > 0d0) then
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BoysF0 = 0.5d0*dsqrt(pi/t)*derf(dsqrt(t))
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else
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BoysF0 = 1d0
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endif
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end
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!*****************************************************************************
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!TODO
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subroutine GauSlaOverlap_write(expGau,cGau,aGau,expSla,cSla,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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write(iunit, *) &
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'SDrSla[ {',expGau,',{',cGau(1),',',cGau(2),',',cGau(3),'},{',aGau(1),',',aGau(2),',',aGau(3),'} },{', expSla,', {',cSla(1),',',cSla(2),',',cSla(3),'} } ],'
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result = 0.d0
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end
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subroutine GauSlaOverlap_read(expGau,cGau,aGau,expSla,cSla,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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read(iunit, *) result
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end
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subroutine GauSlaKinetic_write(expGau,cGau,aGau,expSla,cSla,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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write(iunit, *) &
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'TDrSla[ {',expGau,',{',cGau(1),',',cGau(2),',',cGau(3),'},{',aGau(1),',',aGau(2),',',aGau(3),'} },{', expSla,',{',cSla(1),',',cSla(2),',',cSla(3),'} } ],'
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result = 0.d0
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end
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subroutine GauSlaKinetic_read(expGau,cGau,aGau,expSla,cSla,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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read(iunit, *) result
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end
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subroutine GauSlaNuclear_write(expGau,cGau,aGau,expSla,cSla,ZNuc,cNuc,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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double precision,intent(in) :: cNuc(3)
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double precision,intent(in) :: ZNuc
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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write(iunit, *) &
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'VDrSla[ {',expGau,',{',cGau(1),',',cGau(2),',',cGau(3),'},{',aGau(1),',',aGau(2),',',aGau(3),'} },{ ', expSla,',{',cSla(1),',',cSla(2),',',cSla(3),'} }, {', ZNuc, ',{', cNuc(1),',', cNuc(2),',', cNuc(3), '} } ],'
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result = 0.d0
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end
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subroutine GauSlaNuclear_read(expGau,cGau,aGau,expSla,cSla,ZNuc,cNuc,result,iunit)
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implicit none
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double precision,intent(in) :: expGau,expSla
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double precision,intent(in) :: cGau(3),cSla(3)
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integer,intent(in) :: aGau(3)
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double precision,intent(in) :: cNuc(3)
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double precision,intent(in) :: ZNuc
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integer,intent(in) :: iunit
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double precision,intent(out) :: result
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read(iunit, *) result
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end
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!TODO
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BEGIN_TEMPLATE
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BEGIN_PROVIDER [ double precision, GauSla$X_matrix, (ao_num, nucl_num) ]
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implicit none
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BEGIN_DOC
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! <Gaussian | Slater> overlap matrix
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END_DOC
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integer :: i,j,k
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double precision :: cGau(3)
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double precision :: cSla(3)
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double precision :: expSla, res, expGau
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integer :: aGau(3)
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!TODO
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! logical :: read
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! integer :: iunit
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! integer :: getunitandopen
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!
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! inquire(FILE=trim(ezfio_filename)//'/work/GauSla$X.dat',EXIST=read)
|
|
! if (read) then
|
|
! print *, 'READ $X'
|
|
! iunit = getunitandopen(trim(ezfio_filename)//'/work/GauSla$X.dat','r')
|
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! else
|
|
! print *, 'WRITE $X'
|
|
! iunit = getunitandopen(trim(ezfio_filename)//'/work/GauSla$X.inp','w')
|
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! write(iunit,*) '{'
|
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! endif
|
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!TODO
|
|
|
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do k=1,nucl_num
|
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cSla(1:3) = nucl_coord_transp(1:3,k)
|
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expSla = slater_expo(k)
|
|
|
|
do i=1,ao_num
|
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cGau(1:3) = nucl_coord_transp(1:3, ao_nucl(i))
|
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aGau(1:3) = ao_power(i,1:3)
|
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GauSla$X_matrix(i,k) = 0.d0
|
|
|
|
do j=1,ao_prim_num(i)
|
|
expGau = ao_expo_ordered_transp(j,i)
|
|
call GauSla$X(expGau,cGau,aGau,expSla,cSla,res)
|
|
! if (read) then
|
|
! call GauSla$X_read(expGau,cGau,aGau,expSla,cSla,res,iunit)
|
|
! else
|
|
! call GauSla$X_write(expGau,cGau,aGau,expSla,cSla,res,iunit)
|
|
! endif
|
|
GauSla$X_matrix(i,k) += ao_coef_normalized_ordered_transp(j,i) * res
|
|
enddo
|
|
|
|
enddo
|
|
|
|
enddo
|
|
! if (.not.read) then
|
|
! write(iunit,*) '0.}'
|
|
! endif
|
|
! close(iunit)
|
|
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, MOSla$X_matrix, (mo_tot_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! <MO | Slater>
|
|
END_DOC
|
|
call dgemm('T','N',mo_tot_num,nucl_num,ao_num,1.d0, &
|
|
mo_coef, size(mo_coef,1), &
|
|
GauSla$X_matrix, size(GauSla$X_matrix,1), &
|
|
0.d0, MOSla$X_matrix, size(MOSla$X_matrix,1))
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, AO_orthoSla$X_matrix, (ao_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! <AO_ortho | Slater>
|
|
END_DOC
|
|
call dgemm('T','N',ao_num,nucl_num,ao_num,1.d0, &
|
|
ao_ortho_canonical_coef, size(ao_ortho_canonical_coef,1), &
|
|
GauSla$X_matrix, size(GauSla$X_matrix,1), &
|
|
0.d0, AO_orthoSla$X_matrix, size(AO_orthoSla$X_matrix,1))
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
SUBST [ X ]
|
|
|
|
Overlap ;;
|
|
Kinetic ;;
|
|
|
|
END_TEMPLATE
|
|
|
|
BEGIN_PROVIDER [ double precision, GauSlaNuclear_matrix, (ao_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! <Gaussian | Slater> overlap matrix
|
|
END_DOC
|
|
integer :: i,j,k,A
|
|
double precision :: cGau(3)
|
|
double precision :: cSla(3)
|
|
double precision :: expSla, res, expGau, Znuc, cNuc(3)
|
|
integer :: aGau(3)
|
|
|
|
!TODO
|
|
logical :: read
|
|
integer :: iunit
|
|
integer :: getunitandopen
|
|
|
|
inquire(FILE=trim(ezfio_filename)//'/work/GauSlaNuclear.dat',EXIST=read)
|
|
if (read) then
|
|
print *, 'READ Nuclear'
|
|
iunit = getunitandopen(trim(ezfio_filename)//'/work/GauSlaNuclear.dat','r')
|
|
else
|
|
print *, 'WRITE Nuclear'
|
|
iunit = getunitandopen(trim(ezfio_filename)//'/work/GauSlaNuclear.inp','w')
|
|
write(iunit,*)'{'
|
|
endif
|
|
!TODO
|
|
|
|
do k=1,nucl_num
|
|
cSla(1:3) = nucl_coord_transp(1:3,k)
|
|
expSla = slater_expo(k)
|
|
|
|
do i=1,ao_num
|
|
cGau(1:3) = nucl_coord_transp(1:3, ao_nucl(i))
|
|
aGau(1:3) = ao_power(i,1:3)
|
|
GauSlaNuclear_matrix(i,k) = 0.d0
|
|
|
|
do j=1,ao_prim_num(i)
|
|
expGau = ao_expo_ordered_transp(j,i)
|
|
do A=1,nucl_num
|
|
cNuc(1:3) = nucl_coord_transp(1:3,A)
|
|
Znuc = nucl_charge(A)
|
|
! call GauSlaNuclear(expGau,cGau,aGau,expSla,cSla,Znuc,cNuc,res)
|
|
if (read) then
|
|
call GauSlaNuclear_read(expGau,cGau,aGau,expSla,cSla,Znuc,cNuc,res,iunit)
|
|
else
|
|
call GauSlaNuclear_write(expGau,cGau,aGau,expSla,cSla,Znuc,cNuc,res,iunit)
|
|
endif
|
|
GauSlaNuclear_matrix(i,k) += ao_coef_normalized_ordered_transp(j,i) * res
|
|
enddo
|
|
enddo
|
|
|
|
enddo
|
|
|
|
enddo
|
|
if (.not.read) then
|
|
write(iunit,*) '0.}'
|
|
endif
|
|
close(iunit)
|
|
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, GauSlaH_matrix, (ao_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! Core hamiltonian in AO basis
|
|
END_DOC
|
|
GauSlaH_matrix(1:ao_num,1:nucl_num) = &
|
|
GauSlaKinetic_matrix(1:ao_num,1:nucl_num) + &
|
|
GauSlaNuclear_matrix(1:ao_num,1:nucl_num)
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
BEGIN_PROVIDER [ double precision, MOSlaNuclear_matrix, (mo_tot_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! <MO | Slater>
|
|
END_DOC
|
|
call dgemm('N','N',mo_tot_num,nucl_num,ao_num,1.d0, &
|
|
mo_coef_transp, size(mo_coef_transp,1), &
|
|
GauSlaNuclear_matrix, size(GauSlaNuclear_matrix,1), &
|
|
0.d0, MOSlaNuclear_matrix, size(MOSlaNuclear_matrix,1))
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, AO_orthoSlaH_matrix, (ao_num, nucl_num) ]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! <AO ortho | Slater>
|
|
END_DOC
|
|
call dgemm('T','N',ao_num,nucl_num,ao_num,1.d0, &
|
|
ao_ortho_canonical_coef, size(ao_ortho_canonical_coef,1), &
|
|
GauSlaH_matrix, size(GauSlaH_matrix,1), &
|
|
0.d0, AO_orthoSlaH_matrix, size(AO_orthoSlaH_matrix,1))
|
|
END_PROVIDER
|
|
|