Simple models for predicting electron correlation

Išvanková, Zuzana (2014) Simple models for predicting electron correlation. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (2MB)

Abstract

After almost a century since the postulation of quantum mechanics, the only chemical systems that can be treated exactly are those with one electron. For all many-electron problems we rely on approximate solutions to the electronic Schrödinger equation. The single largest error in the calculations is due to the lack of an accurate representation of what happens when two electrons come close together. How the motion of one electron is affected by that of the other electron is referred to as electron correlation. Not only is electron correlation a fundamental problem in quantum chemistry, it is also crucial in determining the important chemical effects. The correlated motion of electrons with opposite spins, completely neglected in single-determinantal Hartree-Fock theory, remains as one of the central unsolved challenges in quantum chemistry. Simple models that can account for the missing correlation energy have been investigated for the isoelectronic atomic series of two to eighteen electrons in order to gain further insight into the form of a correlation operator. The strength of the electron correlation likely depends on both their separation in position space and their separation in momentum space; hence, it is expected that the correlation energy is related to the average inter-electron distance and to their kinetic energy. It has been previously shown that the average electron-electron distance is inversely proportional to the Coulomb energy; thus, the correlation energy was modelled as a function of Coulomb repulsion and kinetic energies. Additionally, application of the atomic correlation models to the modeling of the correlation energy for simple molecular systems have been explored.

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