H2O Molecular Orbital Calculation in C2v 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 Hamiltonian 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 coefficients 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 simple 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 H2+ unless the basis function decay constants f 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 flxed, values of f. 

In this appendix we will look in detail at the results for the H2O example from Chapter 7, which employed a set of basis functions developed by Pople and co-workers with the code name 6-3IG. This code tells us about the types and numbers of functions used in the 

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0 70-85347-4 

---