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hfkei.f
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Subroutine hfkei(alpha,E,Tab,Ti,Nints,NPP,La,Lb,Li,canAB)
c $Id$
Implicit none
integer La,Lb,Li,Nints,NPP
logical canAB
c--> Hermite Linear Expansion Coefficients
double precision E(3,NPP,0:((La+Li)+(Lb+Li)),0:(La+Li),0:(Lb+Li))
c--> Exponents
double precision alpha(2,NPP)
c--> Kinetic Energy Integrals
double precision Tab(Nints)
c--> Scratch Space
integer Nxyz(3)
double precision Ti(NPP)
c--> Local variables
integer nn,ma,mb,mb_limit,m,La2,Lb2
integer Ia,Ja,Ka, Ib,Jb,Kb
double precision dia,dja,dka,dib,djb,dkb
c
c Compute the kinetic energy integrals.
c
c Formula:
c
c 1 / Ia,Ib Ja,Jb Ka,Kb \
c Tab = - | T Ey Ez + "Y-term" + "Z-term" |
c 2 \ X 0 0 /
c
c i,j i-1,j-1 i-1,j+1 i+1,j-1 i+1,j+1
c T = ijEx - 2ibEx - 2ajEx + 4abEx
c X 0 0 0 0
c
c******************************************************************************
c Initialize the block of KEIs.
c Define the number of shell components on each center.
La2 = ((La+1)*(La+2))/2
Lb2 = ((Lb+1)*(Lb+2))/2
c Loop over shell components.
nn = 0
do ma = 1,La2
c Define the angular momentum indices for shell "A".
call getNxyz(La,ma,Nxyz)
Ia = Nxyz(1)
Ja = Nxyz(2)
Ka = Nxyz(3)
dia = dble(ia)
dja = dble(ja)
dka = dble(ka)
if( canAB )then
mb_limit = ma
else
mb_limit = Lb2
end if
do mb = 1,mb_limit
c Define the angular momentum indices for shell "B".
call getNxyz(Lb,mb,Nxyz)
Ib = Nxyz(1)
Jb = Nxyz(2)
Kb = Nxyz(3)
dib = dble(ib)
djb = dble(jb)
dkb = dble(kb)
nn = nn + 1
tab(nn)=0d0
c Build Tx.
if( Ia.gt.0 .and. Ib.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dia*dib )*E(1,m,0,Ia-1,Ib-1)
& - ( dia*alpha(2,m))*E(1,m,0,Ia-1,Ib+1)
& - (alpha(1,m)*dib )*E(1,m,0,Ia+1,Ib-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else if( Ia.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dIa*alpha(2,m))*E(1,m,0,Ia-1,Ib+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else if( Ib.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dIb )*E(1,m,0,Ia+1,Ib-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
end if
c Add Tx*Ey*Ez to Tab
do m = 1,NPP
Tab(nn) = Tab(nn) + Ti(m)*E(2,m,0,Ja,Jb)*E(3,m,0,Ka,Kb)
end do
c Build Ty.
if( Ja.gt.0 .and. Jb.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dJa*dJb )*E(2,m,0,Ja-1,Jb-1)
& - ( dJa*alpha(2,m))*E(2,m,0,Ja-1,Jb+1)
& - (alpha(1,m)*dJb )*E(2,m,0,Ja+1,Jb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else if( Ja.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dJa*alpha(2,m))*E(2,m,0,Ja-1,Jb+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else if( Jb.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dJb )*E(2,m,0,Ja+1,Jb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
end if
c Add Ex*Ty*Ez to Tab.
do m = 1,NPP
Tab(nn) = Tab(nn) + E(1,m,0,Ia,Ib)*Ti(m)*E(3,m,0,Ka,Kb)
end do
c Build Tz.
if( Ka.gt.0 .and. Kb.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dKa*dKb )*E(3,m,0,Ka-1,Kb-1)
& - ( dKa*alpha(2,m))*E(3,m,0,Ka-1,Kb+1)
& - (alpha(1,m)*dKb )*E(3,m,0,Ka+1,Kb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else if( Ka.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dKa*alpha(2,m))*E(3,m,0,Ka-1,Kb+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else if( Kb.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dKb )*E(3,m,0,Ka+1,Kb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
end if
c Add Ex*Ey*Tz to Tab.
do m = 1,NPP
Tab(nn) = Tab(nn) + E(1,m,0,Ia,Ib)*E(2,m,0,Ja,Jb)*Ti(m)
end do
end do
end do
end
************************************************************************
Subroutine hfkei_gc(alpha,E,Tab,TabP,TabH,Ti,Acoefs,Bcoefs,ipairp,
& NPA,NPB,NCA,NCB,NPP,La,Lb,La2,Lb2,Li,canAB)
c
implicit none
integer NPA,NPB,NCA,NCB,NPP,La,Lb,La2,Lb2,Li
logical canAB
c--> Hermite Linear Expansion Coefficients
double precision E(3,NPP,0:((La+Li)+(Lb+Li)),0:(La+Li),0:(Lb+Li))
c--> Index of primitives
integer ipairp(2,NPP)
c--> Exponents
double precision alpha(2,NPP)
c--> Kinetic Energy Integrals
double precision Tab(Lb2,ncb,La2,nca)
double precision TabP(NPP)
double precision TabH(NPA,NCB)
c--> general contraction matrices
double precision Acoefs(NPA,NCA)
double precision Bcoefs(NPB,NCB)
c--> Scratch Space
double precision Ti(NPP)
integer Nxyz(3)
c--> Local variables
integer ma,mb,m, ica,icb,icb_limit,ipa,ipb
integer Ia,Ja,Ka, Ib,Jb,Kb
double precision dia,dja,dka,dib,djb,dkb
c
c Compute the kinetic energy integrals.
c
c Formula:
c
c 1 / Ia,Ib Ja,Jb Ka,Kb \
c Tab = - | T Ey Ez + "Y-term" + "Z-term" |
c 2 \ X 0 0 /
c
c i,j i-1,j-1 i-1,j+1 i+1,j-1 i+1,j+1
c T = ijEx - 2ibEx - 2ajEx + 4abEx
c X 0 0 0 0
c
c******************************************************************************
c Initialize the block of KEIs.
call dfill(La2*Lb2*nca*ncb,0.0d00,Tab,1)
c Loop over shell components.
do ma = 1,La2
c Define the angular momentum indices for shell "A".
call getNxyz(La,ma,Nxyz)
Ia = Nxyz(1)
Ja = Nxyz(2)
Ka = Nxyz(3)
dia = dble(ia)
dja = dble(ja)
dka = dble(ka)
do mb = 1,Lb2
c Define the angular momentum indices for shell "B".
call getNxyz(Lb,mb,Nxyz)
Ib = Nxyz(1)
Jb = Nxyz(2)
Kb = Nxyz(3)
dib = dble(ib)
djb = dble(jb)
dkb = dble(kb)
call dfill(NPP,0.0d00,TabP,1)
c Build Tx.
if( Ia.gt.0 .and. Ib.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dia*dib )*E(1,m,0,Ia-1,Ib-1)
& - ( dia*alpha(2,m))*E(1,m,0,Ia-1,Ib+1)
& - (alpha(1,m)*dib )*E(1,m,0,Ia+1,Ib-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else if( Ia.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dIa*alpha(2,m))*E(1,m,0,Ia-1,Ib+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else if( Ib.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dIb )*E(1,m,0,Ia+1,Ib-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(1,m,0,Ia+1,Ib+1)
end do
end if
c Add Tx*Ey*Ez to Tab
do m = 1,NPP
TabP(m) = TabP(m) + Ti(m)*E(2,m,0,Ja,Jb)*E(3,m,0,Ka,Kb)
end do
c Build Ty.
if( Ja.gt.0 .and. Jb.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dJa*dJb )*E(2,m,0,Ja-1,Jb-1)
& - ( dJa*alpha(2,m))*E(2,m,0,Ja-1,Jb+1)
& - (alpha(1,m)*dJb )*E(2,m,0,Ja+1,Jb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else if( Ja.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dJa*alpha(2,m))*E(2,m,0,Ja-1,Jb+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else if( Jb.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dJb )*E(2,m,0,Ja+1,Jb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(2,m,0,Ja+1,Jb+1)
end do
end if
c Add Ex*Ty*Ez to Tab.
do m = 1,NPP
TabP(m) = TabP(m) + E(1,m,0,Ia,Ib)*Ti(m)*E(3,m,0,Ka,Kb)
end do
c Build Tz.
if( Ka.gt.0 .and. Kb.gt.0 )then
do m = 1,NPP
Ti(m) = 0.5D0*( dKa*dKb )*E(3,m,0,Ka-1,Kb-1)
& - ( dKa*alpha(2,m))*E(3,m,0,Ka-1,Kb+1)
& - (alpha(1,m)*dKb )*E(3,m,0,Ka+1,Kb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else if( Ka.gt.0 )then
do m = 1,NPP
Ti(m) = - ( dKa*alpha(2,m))*E(3,m,0,Ka-1,Kb+1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else if( Kb.gt.0 )then
do m = 1,NPP
Ti(m) = - (alpha(1,m)*dKb )*E(3,m,0,Ka+1,Kb-1)
& + 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
else
do m = 1,NPP
Ti(m) = 2.0D0*(alpha(1,m)*alpha(2,m))*E(3,m,0,Ka+1,Kb+1)
end do
end if
c Add Ex*Ey*Tz to Tab.
do m = 1,NPP
TabP(m) = TabP(m) + E(1,m,0,Ia,Ib)*E(2,m,0,Ja,Jb)*Ti(m)
end do
c Contract over B shell
call dfill(NCB*NPA,0.0d00,TabH,1)
do icb = 1,NCB
do m = 1,NPP
ipa = ipairp(1,m)
ipb = ipairp(2,m)
TabH(ipa,icb) = TabH(ipa,icb)+TabP(m)*Bcoefs(ipb,icb)
end do
end do
c Contract over A shell
do ica = 1,NCA
if( canAB )then
icb_limit = ica
else
icb_limit = NCB
end if
do icb = 1,icb_limit
do ipa = 1,NPA
Tab(mb,icb,ma,ica) = Tab(mb,icb,ma,ica) +
& TabH(ipa,icb)*Acoefs(ipa,ica)
end do
end do
end do
end do
end do
if (canAB) call canon_ab(Tab,Tab,Lb2*NCB,La2*NCA)
end