HIGHER-ORDER PERTURBATION-THEORY FOR THE THERMODYNAMIC PROPERTIES OF A SOLID WITH A TRUNCATED POTENTIAL-ENERGY EXPANSION

A perturbation theory (PT) is developed in the classical limit which i s based on an infinite series of diagrams composed of the loops and bu bbles arising from the first-and second-order matrix elements of the P T, respectively. This theory leads to a closed form expression for the free energy, which on expansion gives an infinite power series in the temperature. Results from this theory are obtained for a Hamiltonian in which the Taylor expansion of the potential energy is truncated at the quartic term. These results are compared with results of finite su mmation versions of the theory up to O(lambda(8)), with results of sta ndard PT of O(lambda(2)) and O(lambda(4)), and with results of molecul ar dynamics (MD) simulations carried out for the same potential energy surface (i.e., the potential energy expansion truncated at the quarti c term). The results show that the theory which includes all powers of temperature gives better agreement with the MD results throughout a w ide temperature range than does the standard PT of O(lambda(2)) and O( lambda(4)). (C) 1997 American Institute of Physics.