Efficiency of Monte Carlo methods for densities and sums of rovibrational states

Absolute quantum densities of rovibrational states of fully coupled Hamiltonians are computed using Wang–Landau, virtual-move parallel tempering (VMPT), and the Bortz–Kalos–Lebowitz (or kMC) Monte Carlo methods. The validity of the methods is checked by comparing to exact counting in the case of the H2SiO molecule, but applications are also presented for vinyl fluoride and neutral naphthalene. The numerical efficiencies obtained by measuring the statistical deviation to the converged value under finite sampling times suggest that the Wang–Landau and kMC methods are generally superior to VMPT for this class of problem. A simple application to isomerization in protonated pyrene is presented.