Multilayer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules
Abstract
We report a rigorous full dimensional quantum dynamics algorithm, the multilayer Lanczos method, for computing vibrational energies and dipole transition intensities of polyatomic molecules without any dynamics approximation. The multilayer Lanczos method is developed by using a few advanced techniques including the guided spectral transform Lanczos method, multilayer Lanczos iteration approach, recursive residue generation method, and dipolewavefunction contraction. The quantum molecular Hamiltonian at the total angular momentum J = 0 is represented in a set of orthogonal polyspherical coordinates so that the large amplitude motions of vibrations are naturally described. In particular, the algorithm is general and problemindependent. An application is illustrated by calculating the infrared vibrational dipole transition spectrum of CH₄ based on the ab initio T8 potential energy surface of Schwenke and Partridge and the loworder truncated ab initio dipole moment surfaces of Yurchenko and coworkers. A comparison with experiments is made. The algorithm is also applicable for Raman polarizability active spectra.
 Authors:
 Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Chemistry
 Publication Date:
 Research Org.:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1182509
 Alternate Identifier(s):
 OSTI ID: 1228133
 Report Number(s):
 BNL1074752015JA
Journal ID: ISSN 00219606; JCPSA6; R&D Project: CO006; KC0301020; TRN: US1500507
 Grant/Contract Number:
 SC00112704; AC0298CH10886
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 142; Journal Issue: 4; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Eigenvalues; Wave functions; Lanczos method; Molecular spectra; dipole transition intensities; polyatomic molecules
Citation Formats
Yu, HuaGen. Multilayer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules. United States: N. p., 2015.
Web. doi:10.1063/1.4906492.
Yu, HuaGen. Multilayer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules. United States. doi:10.1063/1.4906492.
Yu, HuaGen. 2015.
"Multilayer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules". United States.
doi:10.1063/1.4906492. https://www.osti.gov/servlets/purl/1182509.
@article{osti_1182509,
title = {Multilayer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules},
author = {Yu, HuaGen},
abstractNote = {We report a rigorous full dimensional quantum dynamics algorithm, the multilayer Lanczos method, for computing vibrational energies and dipole transition intensities of polyatomic molecules without any dynamics approximation. The multilayer Lanczos method is developed by using a few advanced techniques including the guided spectral transform Lanczos method, multilayer Lanczos iteration approach, recursive residue generation method, and dipolewavefunction contraction. The quantum molecular Hamiltonian at the total angular momentum J = 0 is represented in a set of orthogonal polyspherical coordinates so that the large amplitude motions of vibrations are naturally described. In particular, the algorithm is general and problemindependent. An application is illustrated by calculating the infrared vibrational dipole transition spectrum of CH₄ based on the ab initio T8 potential energy surface of Schwenke and Partridge and the loworder truncated ab initio dipole moment surfaces of Yurchenko and coworkers. A comparison with experiments is made. The algorithm is also applicable for Raman polarizability active spectra.},
doi = {10.1063/1.4906492},
journal = {Journal of Chemical Physics},
number = 4,
volume = 142,
place = {United States},
year = 2015,
month = 1
}
Web of Science

We report a rigorous full dimensional quantum dynamics algorithm, the multilayer Lanczos method, for computing vibrational energies and dipole transition intensities of polyatomic molecules without any dynamics approximation. The multilayer Lanczos method is developed by using a few advanced techniques including the guided spectral transform Lanczos method, multilayer Lanczos iteration approach, recursive residue generation method, and dipolewavefunction contraction. The quantum molecular Hamiltonian at the total angular momentum J = 0 is represented in a set of orthogonal polyspherical coordinates so that the large amplitude motions of vibrations are naturally described. In particular, the algorithm is general and problemindependent. An applicationmore »

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Calculation and fitting of potential energy and dipole moment surfaces for the water molecule: Fully {ital ab initio} determination of vibrational transition energies and band intensities
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Full dimensional FranckCondon factors for the acetylene A{sup ~} {sup 1}A{sub u}—X{sup ~1}Σ{sup +}{sub g} transition. I. Method for calculating polyatomic linear—bent vibrational intensity factors and evaluation of calculated intensities for the gerade vibrational modes in acetylene
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