Quantum Monte Carlo method importance sampling

Most of the details of the trajectory calculations are the same as described previously. All of the calculations are quasiclassical, i.e,y the vibrational and rotational action variables are restricted to have the correct quantized values at the start of the collision but, except for this and the final-state analysis after the collision, the internuclear motion is purely classical under the influence of the quantum mechanical potential energy surface.The only initial states considered were para-hydrogen states, i.e., states with even rotational quantum numbers. As will be indicated, some runs are for a given initial vibration-rotation state while other runs are for vibration-rotation states selected by Monte Carlo methods from the distribution of quantized states that has the desired temperature. Similarly, the relative translational energy is sometimes fixed for a run while for other runs a random selection is made from a predetermined distribution characteristic of a temperature. In the latter case importance sampling is sometimes used to improve the convergence of the calculated quantities such as the... 

Equilibrium properties for a quantum particle in a classical solvent can be calculated by immersing the polymer in the classical solvent and treating the combined many-particle system by standard Monte Carlo or molecular dynamics techniques the latter often provide a viable alternative to importance sampling methods. 

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