Chemistry Reference
In-Depth Information
to the paper quoted above (Magnasco, 2008), the origin of the quantum
mechanical exchange-overlap densities was studied in detail, showing
their different behaviour in the case of the chemical bond in ground-state
H
2
and of the Pauli repulsion between two ground-state He atoms. This
made clear the relation between such VB 'exchange-overlap' densities and
the MO density 'interference' terms introduced time ago by Ruedenberg
(1962).
The values at the minima of the potential energy calculations, not
shown in the tables, are
86
506
10
3
E
h
at R
e
¼
2a
0
with c
0
¼
1
:
:
238
for H
2
2
g
079
10
3
E
h
at R
e
¼
1
ð
S
Þ
,
139
:
:
41a
0
with c
0
¼
1
:
165 for
1
g
498
10
3
E
h
at R
e
¼
2
H
2
ð
S
Þ
,
90
:
:
06a
0
with c
0
¼
1
:
832 for
He
2
2
u
ð
S
Þ
, while the He(1s)-He(1s)
interaction is
repulsive by
964
10
3
E
h
at R
¼
3a
0
with c
0
¼
1
12
691. In this way, it is seen that
practically correct R
e
bond lengths and about 85% of the experimentally
observed or accurately calculated
:
:
D
E
e
bond energies (Peek, 1965; Huber
and Herzberg, 1979 for H
2
þ
; Wolniewicz, 1993 for H
2
; Cencek and
Rychlewski, 1995 for He
2
þ
) are obtained from these optimized calcula-
tions, while the calculated Pauli repulsion for He(1s)-He(1s) in the
medium range at, say, R
¼
3a
0
, gives over 95% of the correct repulsion
(Liu andMcLean, 1973). It should be remarked that the optimized orbital
exponents c
0
contract over the hydrogenic valueZ
¼
1 forH
2
andH
2
and
expand over Z
¼
2 for He
2
and He
2
. This change in shapes of the
optimized AOs suggests that the guiding principle in the elementary VB
theory of the chemical bond is the maximum of the exchange-overlap
energy and not the maximum overlap, as discussed elsewhere (Magnasco
and Costa, 2005).
9.4 VALENCE BOND THEORY AND THE
CHEMICAL BOND
This is amulti-determinant theorywhich originates from theHL theory of
the H
2
molecule just discussed above.
9.4.1 Schematization of Valence Bond Theory
Basis of (spatial) AOs
)
atomic spin-orbitals (ASOs)
)
antisymmetrized
products (APs), that is, Slater determinants of order equal to the numberN
of the electrons in the molecule, eigenfunctions of the S
z
operator with
eigenvalue M
S
¼ð
N
a
N
b
Þ=
2
2
)
VB structures, eigenstates of S
with
