Order-N methodologies and their applications

An exhaustive inventory of existing order-N methodologies for the calculation of the total energy as well as the atomic forces up to 1999 has been conducted. These methodologies are discussed in terms of the key approximations involved in each method. Emphasis is placed on the roles played by these approximations and how they affect the accuracy and efficiency of the method. Issues affecting the implementation of various order-N procedures, such as the choice of the tight-binding model in the order-N tight-binding approaches and the construction of the Hamiltonian in the order-N ab initio approaches, are also discussed. Some typical examples of applications of the order-N methods to study problems of realistic sizes are presented to provide a glimpse of the capability of utilizing the order-N methods to predict the stable structures and properties of complex systems with reduced symmetry. This review is expected to serve as a clearinghouse where a single resource is provided to help guide the reader to decide, among the existing methodologies, which method can best fulfill the task at hand. (C) 2002 Elsevier Science B.V. All rights reserved.