Chemistry Reference
In-Depth Information
where
0
is the simple product two-electron hydrogen-like wavefunction
for ground-state He, gives a cusp-corrected CI expansion rapidly con-
vergent with the biexcitations with
Y
(s
2
,p
2
,d
2
,f
2
,g
2
,
' ¼
0
;
1
;
2
;
3
;
4
; ...
...
type):
just 156 interconfigurational
functions up to
' ¼
4 give
E
¼
2
903 722E
h
, roughly the same energy value obtained by including
about 8000 interconfigurational functions with
:
'
6 in the ordinary
CI expansion starting from
Y
0
. The accurate comparison value, due to
Frankowski and Pekeris
903 724 377 033E
h
,a
'benchmark' for the He atom correct to the last decimal figure (picohar-
tree). Of course, use of the wavefunction (8.7) as a starting point in the
CI expansion (8.1) involves the more difficult evaluation of unconven-
tional one- and two-electron integrals.
(1966),
is E
¼
2
:
8.2 MULTICONFIGURATION SELF-
CONSISTENT-FIELD
In this method, mostly due toWahl and coworkers (Wahl andDas, 1977),
both the formof the orbitals in each single determinantal function and the
coefficients of the linear combination of the configurations are optimized
in a wavefunction like (8.1). The orbitals of a few valence-selected
configurations are adjusted iteratively until self-consistency with the
simultaneous optimization of the linear coefficients is obtained. The
method predicts a reasonable well depth in He
2
and reasonable atomiza-
tion energies (within 2 kcal mol
1
) for a fewdiatomics, such as H
2
,Li
2
,F
2
,
CH, NH, OH and FH.
2
8.3 MØLLER-PLESSET THEORY
Since the Møller-Plesset approach is based on Rayleigh-Schroedinger
(RS) perturbation theory, which will be introduced to some extent only in
Chapter 10, it seems appropriate to give a short r
e of it here.
Stationary RS perturbation theory is based on the partition of the
Hamiltonian
esum
H into an unperturbed Hamiltonian
H
0
and a
small
perturbation V, and on the expansion of the actual eigenfunction
and
eigenvalue E into powers of the perturbation, each correction being
specified by a definite order given by the power of an expansion parameter
l
c
. For the method to be applied safely, it is necessary (i) that the expansion
2
He
2
,F
2
and NH are not bonded at the SCF level.
