Adaptive sparse grid expansions of the vibrational Hamiltonian

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Spectroscopy

Background:

• Accurate calculation of molecular vibrational spectra requires precise representation of the kinetic energy operator (KEO) and potential energy surface (PES).
• Approximating high-dimensional KEO and PES is challenging for systems with more than a few atoms, limiting accuracy in traditional methods like truncated Taylor or many-body expansions (MBE).
• Existing approximation schemes lack robust error estimation and predefined precision.

Purpose of the Study:

• To develop a unified, fully adaptive representation for the KEO and PES.
• To introduce a novel hybrid approach combining adaptive MBEs with modified sparse grids (SG).
• To enable accurate computation of vibrational spectra with predefined precision and error estimates.

Main Methods:

• Development of modified sparse grids (SG) integrated with adaptive many-body expansions (MBE).
• Implementation of refinement criteria based on vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods.
• Application of the hybrid MBE/SG approach with VSCF and VCI for calculating vibrational spectra.

Main Results:

• The hybrid MBE/SG approach provides a unified and fully adaptive representation of KEO and PES.
• The combined adaptive MBE/SG and VSCF/VCI methods offer a 'black box' procedure for accurate vibrational spectra.
• Calculations on water, formaldehyde, methanimine, and ethylene demonstrate convergence for semi-empirical PM3-PESs and accurate spectra from CCSD(T)-PESs, matching experimental values.

Conclusions:

• The adaptive MBE/SG hybrid method is a significant advancement for approximating high-dimensional KEO and PES.
• This approach allows for operators of predefined precision and provides error estimates, outperforming truncated Taylor or MBE methods.
• The developed methodology successfully computes accurate vibrational spectra, validating its utility across various molecular systems.