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168
APPENDIX A. INTEGRAL APPLICATION PROGRAMMER’S INTERFACE
integer maxg
! [output] max buf size for blocked 2e4c ints
integer mscratch_2e ! [output] max scr size for blocked 2e4c ints
A.3 INT-API: Integral Routines
These routines compute and return integrals based on shell quartets or groups of shell quartets.
int 1estv
A.3.1
This is an internal routine that most of the external 1 electron routines call. This is the actual workhorse routine. This
routine computes the 1 electron integrals S, T, and V:
S
= (µ|ν)
Z ∞
=
−∞
T
V
gµ (Xµ , r1 )gν (Xν , r1 )dr1
1
= (µ| − ∇2 |ν)
2
Z
1 ∞
= −
gµ (Xµ , r1 )∇2 (r1 )gν (Xν , r1 )dr1
2 −∞
−Zα
= (µ| ∑
|ν)
|r
− Rα |
1
α
Z ∞
−Zα
=
gν (Xν , r1 )dr1
gµ (Xµ , r1 ) ∑
|r
− Rα |
−∞
1
α
If an ECP is defined then the ECP integral contributions are summed directly into the V integrals.
If a relativistic basis is defined then the one-electron integrals for the case where both shells are relativistic are
modified to
S
T
V
α2 2 S
∇ |ν )
4
1
1
1
= − (µL |∇2 |νS ) − (µS |∇2 |νL ) + (µS |∇2 |νS )
2
2
2
2
−Zα
α
−Zα
= (µL | ∑
|νL ) − (µS |∇ ∑
· ∇|νS )
|r
−
R
|
4
|r
−
R
|
1
α
1
α
α
α
= (µL |νL ) − (µS |
Syntax:
subroutine int_1estv(i_basis,ish,j_basis,jsh,lscr,scr,lstv,S,T,V,
&
doS,doT,doV)
integer
integer
integer
integer
i_basis
ish
j_basis
jsh
!
!
!
!
[input]
[input]
[input]
[input]
basis set handle for ish
i shell/contraction
basis set handle for jsh
j shell/contraction