Total projection probabilities on non-orthogonal states: Calculation of electronic populations in molecules

✍ Scribed by N. De Leon; S.P. Neshyba

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 394 KB
• Volume: 151
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(88)85291-6

✦ Synopsis

It is often desirable to expand a quantum state in terms of a non-orthogonal basis set. Hem WC USC projection operators to obtain rigorous formulas for the tota/pro/ected prohabdity ofthe quantum state on each basis state. The derivation of the general expression for N basis states is outlmed and a closed form expression for the case of N=2 is given. The formalism is applied to the problem of atomic electronic populations in molecules. Mulliken used an approximation to the above to study the populations in H20 and CO. We reexamine Mulliken's data with the projectlon operator formalism and fnd that our results differ significantly from his and that negative populations (often encountered in Mulliken's formalism) are eliminated. We discuss the extension of our formalism to the characterlzatlon of vibrational states in polyatomic molecules.