Electron locahzation function molecules

With the advent of the density functional theory, i.e., with the growing recognition of the role that electronic density plays in describing quantum states of atoms and molecules, there also spears the possibility of visualizing bonds and electronic locahzation through procedures applied on electronic densities. 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

The two fundamental building blocks of Hartree-Fock theory are the molecular orbital and its occupation number. In closed-shell systems each occupied molecular orbital carries two electrons, with opposite spin. The occupied orbitals themselves are only defined as an occupied one-electron subspace of the full space spanned by the eigenfunctions of the Fock operator. Transformations between them leave the total HF wave function invariant. Normally the orbitals are obtained in a delocalized form as the solutions to the HF equations. This formulation is the most relevant one in studies of spectroscopic properties of the molecule, that is, excitation and ionization. The invariance property, however, makes a transformation to locahzed orbitals possible. Such localized orbitals can be valuable for an analysis of the chemical bonds in the system. 

From a computational point of view, it should be stressed that the computational tool of Francisco et al. [35] results in obtaining the electron number probability distribution functions of an -electron molecule through an exhaustive partitioning of the real space into arbitrary regions. From the computed probabilities, several magnitudes relevant to chemical bonding theory are obtained, such as average electronic populations and locahzation/delocalization indices. 

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