1 - The many-electron problem: introduction

Summary

The calculation of a wavefunction took about two afternoons, and five wavefunctions were calculated in the whole ….

Wigner and Seitz, 1933

Summary

In order to explain many important properties of materials and phenomena, it is necessary to go beyond independent-particle approximations and directly account for many-body effects that result from electronic interaction. The many-body problem is a major scientific challenge, but there has been great progress resulting from theoretical developments and advances in computation. This chapter is a short introduction to the interacting-electron problem, with some of the history that has led up to the concepts and methods described in this book.

The many-body interacting-electron problem ranks among the most fascinating and fruitful areas of research in physics and chemistry. It has a rich history, starting from the early days of quantum mechanics and continuing with new intellectual challenges and opportunities. The vitality of electronic structure theory arises in large part from the close connection with experiment and applications. It is spurred on by new discoveries and advances in techniques that probe the behavior of electrons in depth. In turn, theoretical concepts and calculations can now make predictions that suggest new experiments, as well as provide quantitative information that is difficult or not yet possible to measure experimentally.

This book is concerned with the effects of interactions between electrons beyond independent-particle approximations. Some phenomena cannot be explained by any independent-electron method, such as broadening and lifetime of excited states and two-particle bound states (excitons) that are crucial for optical properties of materials. There are many other examples, such as the van derWaals interaction between neutral molecules that arises from the dipole–induced dipole interaction. This force, which is entirely due to correlation between electrons, is an essential mechanism determining the functions of biological systems. Other properties, such as thermodynamically stable magnetic phases, would not exist if there were no interactions between electrons; even though mean-field approximations can describe average effects, they do not account for fluctuations around the average. Ground-state properties, such as the equilibrium structures of molecules and solids, can be described by density functional theory (DFT) and the Kohn–Sham independent-particle equations. However, present approximations are often not sufficient, and for many properties the equations, when used in a straightforward way, do not give a proper description, even in principle.