Accurate computation of quantum densities of states and RRKM rate constants for large polyatomic molecules: The STAIR method

A new method is given for the computation of quantum mechanical microcanoni cal densities of states of large molecules. The method is based on the obse rvation that for large molecules with many vibrational degrees of freedom, the complex time partition function dephases rapidly allowing for a good sh ort-time approximation. The short-time approximation up to third order give s an Airy function expression for the thermal density of states at a given temperature T. The microcanonical density of states is then deduced from th e thermal density. The input needed for the method is the first three momen ts of the Hamiltonian at a series of temperatures, which adequately cover t he energy range of interest. These may be computed using quantum Monte Carl o methods. The method is tested for a harmonic model of trans-stilbene, a s eparable anharmonic model of cyclopropane, and a separable anharmonic model of a system with 50 degrees of freedom. The short-time Airy method is foun d to give accurate estimates for the density of states, the integrated dens ity of states, and RRKM microcanonical rate constants. (C) 1999 American In stitute of Physics. [S0021-9606(99)30616-4].