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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions.

James Brown¹, Tucker Carrington¹

¹Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.

The Journal of Chemical Physics

|August 3, 2015

Summary

Localized Gaussians can effectively contract discrete variable representation bases for computing vibrational energy levels. This method works even when discarded basis functions have significant matrix elements, using iterative eigensolvers.

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Area of Science:

Quantum chemistry
Computational physics
Molecular dynamics

Background:

Discrete Variable Representation (DVR) is a powerful method for calculating molecular properties.
Standard DVR basis sets can be computationally expensive.
Phase-space localized Gaussians are typically not ideal basis functions.

Purpose of the Study:

To investigate the effectiveness of phase-space localized Gaussians in contracting DVR bases.
To develop an efficient computational method for determining vibrational energy levels.
To address the challenge of non-negligible matrix elements from discarded basis functions.

Main Methods:

Formulating the problem as a standard matrix eigenvalue problem, avoiding generalized eigenvalue problems.
Utilizing iterative eigensolvers for computation.
Employing phase-space localized Gaussians within the DVR framework.

Main Results:

Demonstrated that localized Gaussians can effectively contract DVR bases.
Successfully computed vibrational energy levels using this approach.
Showed the method's viability despite discarded basis functions not being small.

Conclusions:

Localized Gaussians offer an efficient alternative for basis set contraction in DVR.
Iterative eigensolvers combined with this Gaussian basis approach provide a robust method for vibrational energy calculations.
This technique enhances computational efficiency in quantum chemistry and molecular dynamics.