Chemistry Reference
In-Depth Information
eigenvalue S(S
þ
1) (defined S)
)
symmetry combinations of VB struc-
tures
)
multi-determinant wavefunctions describing at the full-VB level
the electronic states of the molecule.
9.4.2 Schematization of Molecular Orbital Theory
Basis of (spatial) AOs
)
MOs by the LCAOmethod, classified according
to symmetry-adapted types (Chapter 12)
)
single Slater determinant of
doubly occupied MOs (for closed shells)
)
MO-CI among all determi-
nants belonging to the same symmetry
)
multi-determinant wavefunc-
tions describing at the MO-full-CI level the electronic states of the
molecule.
Starting from the same AO basis, full-VB and MO-full-CI methods are
entirely equivalent at the end of each process, but may be deeply different
in their early stages (as we have seen for the H
2
molecule).
9.4.3 Advantages of the Valence Bond Method
1. VB structures (such as H
H, H
H
þ
,H
þ
H
,Li
H, Li
þ
H
,
N
O
þ
) are related to the existence of chemical bonds
in molecules, the most important ones corresponding to the rule of
the so-called 'perfect-pairing of bonds' (see Figure 9.6 for H
2
O).
2. Principle of maximum overlap (better, minimum of exchange-over-
lap bond energy)
)
bond stereochemistry in polyatomic molecules
(Magnasco and Costa, 2005).
3. It allows for a correct description of the dissociation of the chemical
bonds (of crucial importance for studying chemical reactions).
4. It gives a sufficiently accurate description of the spin densities in
radicals (see the example of the allyl radical in Section 9.6).
5. For small molecules, the ab initio formulation of the theory allows
one to account up to about 80% of the electronic correlation and to
get bond distances within 0.02a
0
.
N, C
:
:
9.4.4 Disadvantages of the Valence Bond Method
1. Nonorthogonal basic AOs
)
nonorthogonal VB structures
)
difficulties in the evaluation of
the matrix elements of
the
Hamiltonian.
