ABSTRACT:A functional of the same-spin electron pair density is proposed as a measure of electron localizability. This functional yields the average number of samespin electron pairs in a region ⍀ enclosing a fixed charge. The functional equals zero if the fixed charge in ⍀ originates from one electron only, with all other same-spin electrons outside the region ⍀. Then, the correlation of the electronic motion in ⍀ and thus the localizability of an electron is high. If the motion of the same-spin electrons becomes less correlated, more electrons participate in the fixed charge contained in ⍀, the average number of same-spin electron pairs (the functional) increases. In the Hartree-Fock approximation the Taylor expansion of the proposed localizability functional can be related to the electron localization function of Becke and Edgecombe without using an arbitrary reference to the uniform electron gas.

The novel functional electron localizability indicator is a useful tool for investigating chemical bonding in molecules and solids. In contrast to the traditional electron localization function (ELF), the electron localizability indicator is shown to be exactly decomposable into partial orbital contributions even though it displays at the single-determinantal level of theory the same topology as the ELF. This approach is generally valid for molecules and crystals at either the single-determinantal or the explicitly correlated level of theory. The advantages of the new approach are illustrated for the argon atom, homonuclear dimers N2 and F2, unsaturated hydrocarbons C2H4 and C6H6, and the transition-metal-containing molecules Sc(2)2+ and TiF4.

The bonding analysis of a chemical system is usually based on some descriptors. Distinct approaches are used to generate the bonding descriptors, whereby the usefulness of a particular approach is emphasized by the desire to yield a description consistent with the examined effects. Thus, whereas the bond path from the electron density gradient field yields the connectivity of the atomic fragments, the orbital picture can easily rationalize the rotational rigidity of a double bond. On the other hand none of the former is able to describe the volume demand of the bonds, which can be accessed by descriptors originating from approaches using space partitioning. As a conceivable way to describe the bonding situation a class of functionals based on the electron pair density integrals in both, direct and momentum space, is proposed. The localizability indicators defined by those functionals are examined on several molecules.

rnThe electron localization function (ELF) was calculated for the atoms Li to Sr. The ELF maxima reveal the atomic shell structure for all these atoms. The shells are separated from each other by ELF minima. The integration of the electron density in a shell gives electron numbers. For the valence shell those are in good agreement with the ones

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