Computation of Husimi intracules

Computation and interpretation of molecular Omega intracules

The Omega intracule is a three-dimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions.

Intracule functional models: I. Angle-corrected correlation kernels

We explore the merits of applying a simple angle-dependent correction to the correlation kernel within the framework of Hartree-Fock-Wigner theory. Based on numerical results for the first eighteen atoms, we conclude that such a correction offers a significant improvement over the action kernel that we and others have explored previously.

Application of Wigner and Husimi intracule based electron correlation models to excited states

A new approach to the electron correlation problem based on phase space intracules derived from the Wigner distribution is applied to excited states. The computed electron correlation energy reduces the mean absolute error in the prediction of the excitation energies of 55 atomic excited states from 0.65 eV for unrestricted Hartree-Fock to 0.32 eV. This compares favorably to a mean absolute deviation of 0.52 eV for second order Moller-Plesset perturbation theory and 0.35 eV for the Lee-Yang-Parr functional. An analogous correlation model based on the Husimi distribution is developed. Predicted correlation energies and excitation energies from this model are significantly worse than for the Wigner intracule based model. Alternative correlation kernels may be more suitable for the Husimi intracule based approach.

A family of intracules, a conjecture and the electron correlation problem

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.