A Concise Method for Kinetic Energy Quantisation

TL;DR

This paper introduces a simple, transparent method for deriving exact classical and quantum molecular Hamiltonians in arbitrary coordinates, applicable even to constrained systems, with demonstrated examples.

Contribution

The authors propose a concise, physically transparent approach for kinetic energy quantisation that simplifies calculations and extends applicability to constrained molecular systems.

Findings

Method yields compact Hamiltonians with clear physical interpretation.

Applicable to constrained systems unlike many traditional approaches.

Validated with examples: monohydrated hydroxide anion and protonated ammonia dimer.

Abstract

We present a straightforward method for obtaining exact classical and quantum molecular Hamiltonians in terms of arbitrary coordinates. As compared to other approaches the resulting expression are rather compact, the physical meaning of each quantity is quite transparent, and in some cases the calculation effort will be greatly reduced. We also investigate systems with constrains to find the suggested method to be applicable in contrast to most conventional approaches to kinetic energy operators which cannot directly be applied to constrained systems. Two examples are discussed in detail, the monohydrated hydroxide anion and the protonated ammonia dimer.