Wave functions symmetry

In SCF problems, there are some cases where the wave function must have a lower symmetry than the molecule. This is due to the way that the wave function is constructed from orbitals and basis functions. For example, the carbon monoxide molecule might be computed with a wave function of 41 symmetry even though the molecule has a C-xt symmetry. This is because the orbitals obey C41 constraints. 

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The way in which the calculation is performed is also important. Unrestricted calculations will allow the system to shift from one spin state to another. It is also often necessary to run the calculation without using wave function symmetry. The calculation of geometries far from equilibrium tends to result in more SCF convergence problems, which are discussed in Chapter 22. 

Owing to the wave function symmetry and operators structure, the expectation values of and can be written in terms of y = y[ E] and or... 

The (n - 71 )1 3 excited states of the pyrazine molecule are a well-known case of wave function symmetry breaking [27,55]. An accidental degeneracy arises when one considers the valence electronic excitations within the equivalent nitrogen lone pairs. The pairs are in opposite and equivalent positions and, when there are two singly occupied orbitals in different symmetries, we will have a pair of accidentally degenerate states as shown below ... 

Section 22.3 Nuclear Spins and Wave Function Symmetry... 

The selection rules for the space part of the electronic wave function can be derived using group theory to investigate the effects of wave function symmetry. We state only the most important rule ... 

Rg. 1.1 Helium-atom energy levels, showing dependence of energy on wave-function symmetry. 

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