An efficient and numerically stable procedure for generating sextic force fields in normal mode coordinates

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Molecular Physics

Background:

• Calculating accurate molecular force fields is crucial for understanding molecular vibrations.
• Strongly coupled force fields often require computationally intensive methods.
• Existing methods may struggle with scalability and efficiency for high-order calculations.

Purpose of the Study:

• To develop a general, scalable, and black-box approach for calculating high-order strongly coupled force fields.
• To enable efficient and accurate determination of molecular vibrational properties.
• To facilitate analytical evaluation of integrals for solving the nuclear vibrational problem.

Main Methods:

• Constructing low-order expansions in curvilinear coordinates with limited mode-mode coupling.
• Analytically transforming between curvilinear and rectilinear normal mode coordinates.
• Employing a reduced mode-representation strategy: 3-mode quartic to 4-mode sextic force fields.

Main Results:

• The coordinate transformation method achieves an optimal balance between accuracy and efficiency.
• An average error of only 1 cm⁻¹ in fundamental frequencies was observed across various molecules.
• The procedure is computationally fast with modest memory demands when an initial semi-quartic force field is available.

Conclusions:

• The developed approach provides a general and scalable solution for calculating strongly coupled force fields.
• This method significantly aids in solving the nuclear vibrational problem through analytical integral evaluation.
• The coordinate transformation code is integrated into the PyPES library, enhancing its utility.