Single-electron molecular configurations

There are several possible single-electron molecular configurations, as shown schematically in Figure 5-1. In the neutral molecule in the ground slate, represented as A/,i, all of the electrons in the molecule are occupying only the lowest allowed energy levels (V)), while the V) levels am empty. The other panels illus-... 

Figure 5-1. Schematic illustration of some single-electron molecular configurations. The different configurations are discussed in the text.

In order to further describe the molecular wavefunctions or the molecular orbitals. Linear Combinations of Atomic Orbitals (LCAO) are normally used (LCAO method). Such a method of solution is possible since the directional dependence of the spherical-harmonic functions for the atomic orbitals can be used. The Pauli principle can be applied to the single-electron molecular orbitals and by filling the states with the available electrons the molecular electron configurations are attained. Coupling of the angular momenta of the open shell then gives rise to molecular terms. 

The simplest and most widely-employed method is the so-called configuration interaction singles or CIS method. This involves singleelectron promotions only (from occupied molecular orbitals in the reference wavefunction to unoccupied molecular orbitals). Because there are relatively few of these, CIS is in fact practical for molecules of moderate complexity. As noted previously, single-electron promotions do not lead to improvement in either the ground-state wavefunction or energy over the corresponding Hartree-Fock... 

The only model available for direct quantum-mechanical study of interatomic interaction is the hydrogen molecular ion Hj. If the two protons are considered clamped in position at a fixed distance apart, the single electron is represented by a Schrodinger equation, which can be separated in confo-cal elliptic coordinates. On varying the interproton distance for a series of calculations a complete mapping of the interaction for all possible configurations is presumably achieved. This is not the case. Despite its reasonable appearance the model is by no means unbiased. 

Many of the principles and techniques for calculations on atoms, described in section 6.2 of this chapter, can be applied to molecules. In atoms the electronic wave function was written as a determinant of one-electron atomic orbitals which contain the electrons these atomic orbitals could be represented by a range of different analytical expressions. We showed how the Hartree-Fock self-consistent-field methods could be applied to calculate the single determinantal best energy, and how configuration interaction calculations of the mixing of different determinantal wave functions could be performed to calculate the correlation energy. We will now see that these technques can be applied to the calculation of molecular wave functions, the atomic orbitals of section 6.2 being replaced by one-electron molecular orbitals, constructed as linear combinations of atomic orbitals (l.c.a.o. method). 

---