A perturbation theory (PT) is developed in the classical limit which is based on an infinite series of diagrams composed of the loops and bubbles arising from the first-and second-order matrix elements of the PT, 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 summation versions of the theory up to O(lambda(8)), with results of standard PT of O(lambda(2)) and O(lambda(4)), and with results of molecular dynamics (MD) simulations carried out for the same potential energy surface (i.e., the potential energy expansion truncated at the quartic term). The results show that the theory which includes all powers of temperature gives better agreement with the MD results throughout a wide temperature range than does the standard PT of O(lambda(2)) and O(lambda(4)). (C) 1997 American Institute of Physics.