CONSERVATION OF ZERO-POINT ENERGY IN CLASSICAL TRAJECTORY COMPUTATIONS BY A SIMPLE SEMICLASSICAL CORRESPONDENCE

A simple practical procedure which ensures that the energy in a molecu lar vibrational mode does not decrease below its zero-point value is d iscussed and applied. The method is based on taking the classical limi t of the Hamiltonian and thereby deriving classical equations of motio n which are solved via a standard classical trajectory computation. We refer to this as the ''reference'' trajectory. It is argued that the reference solution differs from what one would obtain if one were to b egin with a classical description of the problem; the difference being that the reference computation puts the zero of energy at the correct , quantum-theoretic, zero, i.e., at the zero point. To obtain a fully classical-like solution one needs to shift the energy and period of th e reference trajectory and the different ways of doing this are discus sed. The resulting, energy, and phase shifted, equivalent classical tr ajectory cannot, by construction, lose the zero-point energy from the modes in which it is placed. The method is discussed first for the obv ious case of a single oscillator, including the role of the anharmonic ity, and is then applied to a variety of dimers [I2He, ArHBr, (HF)(2)] where a higher frequency mode is coupled to a low-frequency one and t he problem is to prevent the (high) zero-point energy from being made available for transfer to the far weaker mode. Other advantages of the proposed scheme, such as the correct frequency dependence of the powe r spectrum, and its application to an unbound motion in the continuum are also discussed.