Chemistry Reference
In-Depth Information
Appendix 11
H
2
O Molecular Orbital
Calculation in
C
2
v
Symmetry
The MOs plotted for molecules containing main-group elements in Chapter 7 were
produced using restricted Hartree-Fock (RHF)-level calculations. In this approach the
electron-nuclear and electron-electron interactions are taken into account in the Hamil-
tonian through Coulomb and exchange integrals, as described in the Further Reading
section at the end of this appendix. The term 'restricted' means that spin-up and spin-down
electrons must occupy identical spatial orbitals.
The inclusion of the electron-electron interaction in these calculations involves terms
in the Hamiltionian for each MO which depend on the current shape of all the other
occupied states. The shapes of the orbitals, in turn, are controlled by the sets of coeffi-
cients in the SALCs that describe the MOs in terms of basis functions. The optimization
of the SALCs involves finding the set of coefficients which minimize the total energy
of the molecule. Each electron experiences the potential of all the others, and so the
MOs affect one another's energies. The problem must be solved in such a way that the
electron-generated potentials and MOs are consistent with one another.
The results of such self-consistent field (SCF) calculations appear as coefficients for the
linear combination of basis functions used in the calculations. In Chapter 7 we used a sim-
ple basis consisting of only one function per AO. However, we have seen in Appendix 10
that these minimal basis sets do not give reliable energies even for the simple problem
of H
2
+
unless the basis function decay constants
are adjusted. In calculations for larger
molecules of the type discussed here, this is accommodated by the use of more complex
basis sets. These allow the orbital radial flexibility to be described by combining several
basis functions with differing, but fixed, values of
ζ
.
In this appendix we will look in detail at the results for the H
2
O example from Chapter 7,
which employed a set of basis functions developed by Pople and co-workers with the code
name 6-31G. This code tells us about the types and numbers of functions used in the
ζ
