Preponderant configuration

The MO (molecular orbitals) of a polyatomic system are one-electron wave-function k which can be used as a (more or less successful) result for constructing the many-electron k as an anti-symmetrized Slater determinant. However, at the same time the k (usually) forms a preponderant configuration, and it is an important fact67 that the relevant symmetry for the MO may not always be the point-group determined by the equilibrium nuclear positions but may be a higher symmetry. For many years, it was felt that the mathematical result (that a closed-shell Slater determinant contains k which can be arranged in fairly arbitrary new linear combinations by a unitary transformation without modifying k) removed the individual subsistence... 

It is by no means easy to say whether d polarization orbitals are needed in the quantum-chemical description of phosphorus and sulphur compounds. Because of the variational principle, one has to be exceptionally unlucky not to ameliorate an approximate P when introducing a new free parameter. But the question is whether the d polarization orbitals are an essential aspect of the unknown (and somewhat Platonic) true St. This is a very profound question related to the problem whether the natural spin-orbitals (introduced by Lowdin) having occupation numbers closely below 1 are those which define the preponderant configuration. It is now known... 

We have several reasons to want define preponderant configurations. In an atom or molecule containing several electrons, the wavefunction T of a given state can be expanded on a series of mutually orthogonal configurations ... 

In transition group complexes where the ligands are Hnnocent —i.e., do not have partly occupied subshells in their preponderant configuration, the oxidation state of the central atom can be determined from the number of electrons in the partly filled shell of the preponderant configuration. 

We run into the important problem for transition group chemistry that the exact form of the Aufbau principle depends on the ionic charge. Actually, gaseous M+ and M+ do not seem to present exceptions to the preponderant configuration of the ground state, being obtained by consecutive filling of the shells... 

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