Introduction Mulliken population analysis

It is instructive to study the vacant atomic orbital population in dimers and trimers. As mentioned in the Introduction, in the 80 s Bauschlicher et al. [10,11] came to the conclusion that the promotion of ns-electrons to np-orbitals leading to sp-hybridization is the main mechanism responsible for binding in alkaline-earth clusters. This conclusion was based on a study of the SCF Mulliken population analysis for tetramers, which are stable at the SCF level. At present, we can perform more precise analysis using the Natural Bond Orbital Analysis and calculate it at the electron correlation level. 

Up until now we have discussed the general methods for computing the cluster wavefunctions we now consider how the wavefunctions can be analyzed to obtain insights into the nature of chemical interactions at surfaces. In the introduction, we pointed out that the most commonly used method of analysis is the Mulliken population analysis and that this method of analysis may give misleading results. One alternative to a population analysis to get information about the charge associated with a given atom is the orbital projection approach. Here, one takes an atomic or molecular orbital, projection operator, P(( ) = spin orbital. The expectation value of P(v>) taken with respect to the cluster wavefunction provides a measure of the extent to which

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We shall explore how the orbital symmetries and energies of these small molecular fragments contribute to the observed properties of these compounds by using semiempirical electronic structure calculations. Our tools for analysis include an arsenal of computational indices, e.g. overlap populations and Mulliken populations.4 The remainder of this introduction... 

The author would like to thank Dr. Jun Yasui of Toyobo co., ltd. for his helpful discussion especially on Mulliken s population analysis. He is grateful to Mr. Fumihito Mohri of Institute for Fundamental Chemistry (now of Kaneka corporation) for his kind introduction of Okada s works(4,5) and Lowdin s work(7). He is also grateful to Dr. Shigeto Nishitani of Kyoto Univ. for his kind introduction of works of Pettifor and his coauthors(12-14). 

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