The von Neumann basis in non-Cartesian coordinates: application to floppy triatomic molecules.

Area of Science:

• Quantum chemistry
• Molecular spectroscopy
• Computational physics

Background:

• Accurate calculation of molecular bound states is crucial for understanding chemical reactions and properties.
• Traditional methods often face challenges with complex molecular geometries and large systems.
• Isomerizing triatomic molecules like LiCN/LiNC and HCN/HNC present unique computational challenges due to their complex potential energy surfaces.

Purpose of the Study:

• To extend the periodic von Neumann basis set to non-Cartesian coordinates for enhanced flexibility.
• To accurately calculate the vibrational bound states of isomerizing triatomic molecules.
• To demonstrate the efficiency and accuracy of the phase space localized basis functions.

Main Methods:

• Utilized a periodic von Neumann basis adapted for non-Cartesian coordinates.
• Employed Jacobi coordinates for the vibrational Hamiltonian of triatomic molecules.
• Implemented phase space localization for basis functions to improve Hamiltonian representation.

Main Results:

• Successfully calculated bound states for LiCN/LiNC and HCN/HNC isomerizing systems.
• Achieved a flexible and accurate representation of the molecular Hamiltonian.
• Demonstrated significant computational savings compared to coordinate-space localized bases.
• Observed favorable scaling of the method with increasing system dimensionality.

Conclusions:

• The extended periodic von Neumann basis in non-Cartesian coordinates provides an accurate and efficient method for molecular bound state calculations.
• Phase space localization offers advantages in representing the Hamiltonian, leading to computational efficiency.
• This method shows great promise for tackling larger and more complex molecular systems in computational chemistry.