Partitioning of the molecular density matrix over atoms and bonds

TL;DR

This paper introduces a double-index atomic partitioning method for the molecular density matrix that effectively localizes atomic and bonding information, aligning well with established electron density partitions and correlating with bond indices.

Contribution

It presents a novel double-index partitioning scheme for the molecular density matrix that captures atomic and bonding contributions with improved localization.

Findings

The method produces localized atomic and bond matrices.

Electron density from the partition aligns with AIM basin partitions.

Bond matrices correlate with the SEDI bond index.

Abstract

A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made con- sistent with well-known partitions of the electron density over AIM basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the SEDI (shared electron density index) bond index.