Generalization of the New Resonance Theory: Second Quantization Operator, Localization Scheme, and Basis Set

We have recently proposed a method to evaluate the weights of resonance structures embedded in a molecular orbital by utilizing singlet-coupling scheme of an electron pair [J. Phys. Chem. A 2006, 110, 9028]. The method was formulated on the basis of the second quantization, in which a biorthogonal operator related to Mulliken population (MP) was used together with the Boys-Foster (BF) localization scheme. Our method is very easy to use; only a standard localization procedure is required to obtain the resonance weights. In addition, obtained results agreed well with our chemical intuition. In the present Article, the restrictions, namely MP and BF, were removed, and an operator related to Lowdin population (LP) and other various types of localization schemes were employed to examine the generality of the method. We found that computed resonance weights were virtually independent not only on the choice of these combinations but also on basis set. This new finding, the invariant nature in terms of resonance, may suggest that the present approach could be promising for analyzing molecular orbitals.