Taylor-mode automatic differentiation for constructing molecular rovibrational Hamiltonian operators.

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Molecular Physics

Background:

• Accurate representation of molecular vibrations and rotations is crucial for understanding molecular properties.
• Constructing rovibrational operators can be complex and computationally intensive.
• Existing methods may lack flexibility for arbitrary molecular systems or coordinate choices.

Purpose of the Study:

• To develop an automated and efficient framework for generating Taylor series expansions of rovibrational operators.
• To enable the representation of kinetic and potential energy operators for arbitrary molecules.
• To facilitate computationally efficient evaluations of matrix elements in rovibrational calculations.

Main Methods:

• Utilizing automatic differentiation with the JAX library for high-order Taylor expansions.
• Implementing a framework for arbitrary molecules, internal coordinate systems, and molecular frame embeddings.
• Expressing operators in a sum-of-products form for efficient matrix element evaluation.

Main Results:

• An automated framework for constructing high-order Taylor series expansions of rovibrational operators has been successfully developed.
• The framework handles arbitrary molecules, internal coordinates, and embedding conditions.
• The sum-of-products form ensures computationally efficient evaluations of matrix elements.

Conclusions:

• The developed framework provides an efficient and accurate method for generating rovibrational operators.
• This tool can significantly streamline calculations in rovibrational spectroscopy and dynamics.
• The open-source implementation facilitates broader adoption and further development.