Explicit calculation of Coulomb correlation in bond orbitals

An efficient generalized polyelectron population analysis in orbital spaces: the hole-expansion methodology

We present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzed electrons and electron holes. It is based on the hole-expansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valence-bond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the pre-NAO's (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.

Control of delocalization and structural changes by means of an electric field

The strength and, mainly, the direction of a static electric field can be used to control delocalization effects occurring in a non-polar pi-system. The delocalization energy, the weights, and the probabilities of some local electronic structures, the behavior of electron pairs, and the electronic fluctuations are considered and examined in cis-butadiene, used as model system. The effects of the electric field are detected and evaluated in the basis of natural orbital spaces appropriate to investigate the behavior of one- and poly-electron distributions. The consequences of modifying the delocalization effects on structural changes are also investigated. Full geometry optimizations in both Hartree-Fock and MP2 levels show that the changes in bond lengths, guided by the changes of the behavior of the electronic assembly, can be controlled by means of the electric field.

Correlated holes and their relationships with reduced density matrices and cumulants

This paper describes a matrix formulation for the correlated hole theory within the framework of the domain-averaged model in many electron systems (atoms, molecules, condensed matter, etc.). General relationships between this quantity and one-particle reduced density matrices for any independent particle or correlated state functions are presented. This formulation turns out to be suitable for computational purposes due to the straightforward introduction of cumulants of two-particle reduced density matrices within the quantum field structure. Numerical calculations in selected simple molecular systems have been performed in order to determine preliminary correlated values for such a quantity.