scholarly journals The Utility of Constraining Basis Function Indices When Using the Lanczos Algorithm to Calculate Vibrational Energy Levels†

2001 ◽  
Vol 105 (12) ◽  
pp. 2575-2581 ◽  
Author(s):  
Xiao-Gang Wang ◽  
Tucker Carrington
Keyword(s):  
Basis Function ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Lanczos Algorithm ◽  
Vibrational Energy Levels

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.

scholarly journals Research progress in the effects of terahertz waves on biomacromolecules

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Liu Sun ◽  
Li Zhao ◽  
Rui-Yun Peng
Keyword(s):  
Vibrational Energy ◽  
Rapid Development ◽  
Energy Levels ◽  
Basic Research ◽  
Research Progress ◽  
Biological Macromolecules ◽  
Terahertz Waves ◽  
Terahertz Spectrum ◽  
Biomedical Field ◽  
Vibrational Energy Levels

AbstractWith the rapid development of terahertz technologies, basic research and applications of terahertz waves in biomedicine have attracted increasing attention. The rotation and vibrational energy levels of biomacromolecules fall in the energy range of terahertz waves; thus, terahertz waves might interact with biomacromolecules. Therefore, terahertz waves have been widely applied to explore features of the terahertz spectrum of biomacromolecules. However, the effects of terahertz waves on biomacromolecules are largely unexplored. Although some progress has been reported, there are still numerous technical barriers to clarifying the relation between terahertz waves and biomacromolecules and to realizing the accurate regulation of biological macromolecules by terahertz waves. Therefore, further investigations should be conducted in the future. In this paper, we reviewed terahertz waves and their biomedical research advantages, applications of terahertz waves on biomacromolecules and the effects of terahertz waves on biomacromolecules. These findings will provide novel ideas and methods for the research and application of terahertz waves in the biomedical field.

scholarly journals MARVEL: measured active rotational–vibrational energy levels

2007 ◽  
Vol 245 (2) ◽  
pp. 115-125 ◽  
Author(s):  
Tibor Furtenbacher ◽  
Attila G. Császár ◽  
Jonathan Tennyson
Keyword(s):  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Energy Levels

scholarly journals Vibrational band-structures caused by internal rotations of the boron Wankel rotor B11−

RSC Advances ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 3613-3621
Author(s):  
Yonghong Xu ◽  
Huihui Wang ◽  
Yonggang Yang ◽  
Changyong Li ◽  
Liantuan Xiao ◽  
...  
Keyword(s):  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Band ◽  
Spectral Broadening ◽  
Band Structures ◽  
Internal Rotations ◽  
Vibrational Energy Levels

The band structures of the vibrational energy levels of B11− lead to corresponding spectral broadening. The vibrational band-structures of planar boron rotors are caused by internal rotations.

Potential energy curves, spectroscopic constants, and vibrational energy levels of CS+(X2Σ+/A2Π)

2019 ◽  
Vol 118 (2) ◽  
pp. e1597199
Author(s):  
Lulu Zhang ◽  
Daguang Yue ◽  
Juan Zhao ◽  
Yuzhi Song ◽  
Qingtian Meng
Keyword(s):  
Potential Energy ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Potential Energy Curves ◽  
Spectroscopic Constants ◽  
Vibrational Energy Levels
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