Electronic correlation analysis using intracule functions

Abstract

This study explores electronic correlation, a fundamental concept for analyzing the approximations used in quantum mechanics to simulate chemical processes. Electronic correlation affects all physical observables, and understanding this concept is key to enabling increasingly realistic simulations. To study electronic correlation, we present the pair density, which contains explicit information about the interaction between two particles. However, the pair density is defined in an eight-dimensional space, and its direct analysis is computationally demanding and difficult to interpret. For this reason, we introduce the concept of the McWeeny hole, which fixes the position of one electron, and the concept of the intracule function, which leads to the definition of the Coulson hole. Both methods reduce the dimensionality of the problem and offer an intuitive picture of electronic correlation, which we analyze in model systems. However, we ultimately focus the study on the decomposition of the Coulomb hole, which has the advantage of reducing the analysis to a single dimension and offers a direct connection to a component of the system’s energy. Lastly, we present a model system based on the hydrogen molecule that the reader can analyze exactly. This conceptual framework allows for a deeper understanding of electronic correlation and contributes to the development of electronic structure methods that enable more accurate simulations.