An initial value representation semiclassical approach for the study of molecular systems with geometric constraints

Abstract

We present an approach for the inclusion of geometric constraints in quantum dynamics calculations based on the semiclassical initial value representation. An important feature of the method is that a Cartesian coordinate system is used throughout, resulting in a general approach that does not require the definition of new coordinates. The Herman–Kluk [M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984)] coherent state formulation is used. The required (constrained) classical trajectories are calculated using the standard techniques of molecular dynamics and initial conditions are sampled from a distribution that obeys the constraints. An approximate form of the Herman–Kluk prefactor is used and its evaluation requires the construction of a projected Hessian matrix. In its present form, the approach allows the calculation of energy levels from the Fourier transform of the autocorrelation function. The approach is tested on a model problem consisting of two particles in a harmonic trap and constrained to remain at a fixed distance from one another. The approach yields exact results for this simplified case when compared to the exact quantum mechanical formulation. The method is then applied to a real molecular system consisting of a water molecule with fixed OH bonds and yields accurate results when compared to exact quantum mechanical results. The accuracy of the method is comparable to that of the usual semiclassical implementation where the problem is written in a new set of coordinates. The approach can be extended to more complex cases in a straightforward manner.