Electronic structure calculations: an introduction

In Electronic Structure Calculations: An introduction Judith de Paula Araújo presents a text dedicated mainly to undergraduate students and researchers in the fields of Physics and Theoretical Chemistry. One of the author's concerns was to produce a didactically organized text, with several examples and exercises solved step by step. The main purpose of this book is to explore methods for obtaining solutions to the electronic Schrödinger equation for N-body systems. To this end, the author first presents a formal demonstration for the Born-Oppenheimer Approximation proving that the nuclei move according to classical mechanics. Then, the Hartree-Fock Approximation is discussed, showing that it is possible to replace the complicated problem of many electrons with a problem of one electron. In the chapter Configuration Interaction, the energy differences produced by the Hartree-Fock Approximation are calculated, that is, the correlation energies. In a session dedicated to Second Quantization, the author shows that the Principle of Antisymmetry can be satisfied from this, as an alternative to the use of Slater Determinants. A rigorous solution of the Schrödinger equation determining the stationary states for the Harmonic Oscillator, which is one of the simplest systems, is presented. In addition, it also demonstrates how to obtain energy levels via annihilation and creation operators. The penultimate chapter discusses the Coupled-Cluster Theory. This method is capable of recovering much of the correlation energy and can be applied to larger systems. The coupled cluster wave function provides an accurate correction to the Hartree-Fock description. Finally, a short introduction to Many-Body Perturbation Theory is presented and exemplified by the perturbations containing two-particles interactions.