New ideas for using contracted basis functions with a Lanczos eigensolver for computing vibrational spectra of molecules with four or more atoms

2002 ◽  
Vol 117 (15) ◽  
pp. 6923-6934 ◽  
Author(s):  
Xiao-Gang Wang ◽  
Tucker Carrington
Keyword(s):  
Vibrational Spectra ◽  
Basis Functions ◽  
New Ideas

Methods for calculating vibrational energy levels

2004 ◽  
Vol 82 (6) ◽  
pp. 900-914 ◽  
Author(s):  
Tucker Carrington
Keyword(s):  
Iterative Methods ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Basis Functions ◽  
Basis Set ◽  
Hamiltonian Matrix ◽  
Lanczos Algorithm ◽  
New Ideas ◽  
Recent Method ◽  
Vibrational Energy Levels

This article reviews new methods for computing vibrational energy levels of small polyatomic molecules. The principal impediment to the calculation of energy levels is the size of the required basis set. If one uses a product basis the Hamiltonian matrix for a four-atom molecule is too large to store in core memory. We discuss iterative methods that enable one to use a product basis to compute energy levels (and spectra) without storing a Hamiltonian matrix. Despite the advantages of iterative methods it is not possible, using product basis functions, to calculate vibrational spectra of molecules with more than four atoms. A very recent method combining contracted basis functions and the Lanczos algorithm with which vibrational energy levels of methane have been computed is described. New ideas, based on exploiting preconditioning, for reducing the number of matrix-vector products required to converge energy levels of interest are also summarized.Key words: vibrational energy levels, kinetic energy operators, Lanczos algorithm, contracted basis functions, preconditioning.

Other Applications of Neural Networks to Quantum Mechanical Problems

2012 ◽  
Author(s):  
Lionel Raff ◽  
Ranga Komanduri ◽  
Martin Hagan ◽  
Satish Bukkapatnam
Keyword(s):  
Neural Networks ◽  
Wave Function ◽  
Linear Combination ◽  
Vibrational Spectra ◽  
Schrodinger Equation ◽  
Usual Method ◽  
Basis Functions ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Vibrational Wave Function

The usual method for solving the vibrational Schrödinger equation to obtain molecular vibrational spectra and the associated wave functions generally involves the expansion of the vibrational wave function, ψk(y), in terms of a linear combination of a set of basis functions.

scholarly journals Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions

2016 ◽  
Vol 115 (15-16) ◽  
pp. 1740-1749 ◽  
Author(s):  
Arnaud Leclerc ◽  
Phillip S. Thomas ◽  
Tucker Carrington
Keyword(s):  
Vibrational Spectra ◽  
Basis Functions ◽  
Low Rank
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