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Title: An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.1488575· OSTI ID:1303029
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
+ Show Author Affiliations

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC00112704; AC02-98CH10886
OSTI ID:
1303029
Report Number(s):
BNL-112549-2016-JA; JCPSA6; R&D Project: CO-006; KC0301020
Journal Information:
Journal of Chemical Physics, Vol. 117, Issue 5; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 73 works
Citation information provided by
Web of Science

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Cited By (13)

A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions journal July 2003
Using experimental data and a contracted basis Lanczos method to determine an accurate methane potential energy surface from a least squares optimization journal October 2014
An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: Tetrahedral molecules journal March 2015
First fully ab initio potential energy surface of methane with a spectroscopic accuracy journal September 2016
Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms journal March 2017
On the use of nonrigid-molecular symmetry in nuclear motion computations employing a discrete variable representation: A case study of the bending energy levels of C H 5 + journal October 2017
Computing energy levels of CH 4 , CHD 3 , CH 3 D, and CH 3 F with a direct product basis and coordinates based on the methyl subsystem journal February 2018
Highly excited vibrational levels of methane up to 10 300 cm −1 : Comparative study of variational methods journal September 2018
Variational quantum approaches for computing vibrational energies of polyatomic molecules journal August 2008
K -independent vibrational bases for systems with large amplitude motion journal May 2012
Using Wavelets to Extend Quantum Dynamics Calculations to ten or more Degrees of Freedom journal March 2003
Exact and Constrained Kinetic Energy Operators in Polyspherical Coordinates journal December 2003
Iterative Methods for Computing Vibrational Spectra journal January 2018

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Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
Vibrational spectrum
iterative diagonalization
spectral transform Lanczos method