Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Physics

Background:

• Deriving exact analytical kinetic energy operators is crucial for accurate molecular simulations.
• Traditional methods can be complex and time-consuming, especially for large molecular systems.
• Polyspherical coordinates offer a flexible framework for describing molecular geometries.

Purpose of the Study:

• To develop a general computational code for automatically deriving exact analytical kinetic energy operators.
• To implement computer procedures based on symbolic calculations for operator derivation.
• To handle molecular systems parametrized by orthogonal or non-orthogonal vectors in polyspherical coordinates.

Main Methods:

• Development of a general code utilizing symbolic computation.
• Implementation of procedures to derive kinetic energy operators in polyspherical coordinates.
• Parametrization of molecular systems using sets of orthogonal or non-orthogonal vectors.

Main Results:

• The code successfully derives exact analytical kinetic energy operators for molecular systems.
• The derived operators accurately include terms for overall rotation and Coriolis coupling.
• The program's correctness was validated across different vector sets and system sizes.

Conclusions:

• The developed code provides an efficient and general method for obtaining exact kinetic energy operators.
• This tool facilitates advanced quantum mechanical calculations in molecular systems.
• The implementation demonstrates the feasibility of automated derivation for complex operators.