Quantum Monte Carlo method for some model and realistic coupled anharmonic oscillators

Abstract

A new quantum Monte Carlo (QMC) method of evaluating low lying vibrational levels for coupled modes is presented. We use a modified fixed-node (FN) approach in which an extremum principle for energy levels is invoked. In this way, the nodal hypersurfaces of the nuclear wave function are parametrized and then optimized for each excited state. The method is tested on the fundamental excitations of some two-dimensional model potentials and is applied to the case of realistic coupled modes of the CO molecule adsorbed on a palladium cluster. The effect of an external electric field is also examined. The quantum Monte Carlo results are compared with those obtained in the conventional variational treatment of the nuclear Schrödinger equation for coupled vibrations. The QMC results give the exact values with an error which is in general less than 1 cm−1 . In all cases (even in the case of strong coupling) the use of our procedure leads to ‘‘optimal’’ nodal lines (in the sense of the extremum principle used in this work) which are practically undistorted. A salient feature of the Monte Carlo method presented here is that it readily permits the evaluation of the fundamental excitations of an arbitrary number of coupled vibrations. Furthermore, the potential energy surface may be represented by any analytical form without practical difficulties.