Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate...

Area of Science:

• Quantum chemistry
• Computational physics
• Chemical dynamics

Background:

• Semiclassical methods are crucial for simulating molecular dynamics.
• Incorporating geometric constraints in these calculations is computationally challenging.
• Existing methods often lack generality or require complex coordinate transformations.

Purpose of the Study:

• To develop a general and accurate method for including geometric constraints in semiclassical initial value representation (SC-IVR) calculations.
• To utilize Cartesian coordinates exclusively for computational efficiency and broader applicability.
• To accurately assess the impact of constraints on system properties like zero-point energy.

Main Methods:

• Development of an algorithm for constrained sampling of initial conditions using a projected Hessian and multivariate Gaussian distribution.
• Proposal of a method for evaluating the Herman-Kluk prefactor in its exact log-derivative form under constraints.
• Application of the method to rare-gas trimers in both free and constrained configurations.

Main Results:

• The proposed approach accurately quantifies the reduction in zero-point energy due to geometric constraints.
• Validation of semiclassical results against exact basis set calculations demonstrates high accuracy.
• The use of Cartesian coordinates ensures the method's generality across various molecular and atomic systems.

Conclusions:

• The developed method provides an accurate and computationally feasible way to include geometric constraints in SC-IVR calculations.
• The exclusive use of Cartesian coordinates simplifies the implementation and broadens the applicability of the technique.
• This approach offers a significant advancement for studying constrained molecular systems in quantum chemistry and physics.