Preface

Abstract

This chapter discusses the anharmonic properties of solids. It illustrates the ab initio calculations of phonons in metals and insulators. A major development in theoretical studies of anharmonic properties of crystals has been the emergence of numerical simulation approaches that can be used in the regime of low temperatures, where quantum effects are large, and where traditional molecular dynamics simulations or classical Monte Carlo methods are inapplicable. One of these approaches—the path-integral quantum Monte Carlo method—originally developed for the study of quantum spin systems—has been applied successfully to the determination of low temperature thermodynamic (static) properties of anharmonic crystals and to certain dynamical (time-dependent) properties. In this method, the calculation of low temperature vibrational properties of an n -dimensional crystal is transformed into a classical calculation of these properties in an effective ( n + 1)-dimensional crystal. It is a computationally intensive method—a fact that has stimulated efforts to find alternative simulation approaches possessing comparable accuracy but which are easier to implement. A significant step in this direction is provided by the effective potential method, in which the atoms in an anharmonic crystal interact through a variationally determined effective potential that incorporates quantum effects in an approximate, yet accurate, fashion.