scholarly journals Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

2021 ◽  
Author(s):  
Sangeeth Das Kallullathil ◽  
Tucker Carrington, Jr.
Keyword(s):  
Vibrational Energy ◽  
Energy Levels ◽  
Linear Equations ◽  
Tensor Method ◽  
Vibrational Energy Levels

scholarly journals Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

2021 ◽  
Author(s):  
Tucker Carrington ◽  
Sangeeth Kallullathil
Keyword(s):  
Vibrational Energy ◽  
Least Squares Method ◽  
Energy Levels ◽  
Linear Equations ◽  
Coupled Model ◽  
High Dimensional ◽  
Rank Reduction ◽  
Model Hamiltonian ◽  
Fixed Rank ◽  
Vibrational Energy Levels

Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about 5 atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use CP format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block inverse iteration method with multiple shifts. The CP rank of the tensors is fixed and the linear equations are solved with an Alternating Least Squares method. There is no need for rank reduction, no need for orthogonalization, and tensors with rank larger than the fixed rank used to solve the linear equations are never generated. The ideas are tested by computing vibrational energy levels of a 64-D bilinearly coupled model Hamiltonian and of acetonitrile(12-D).

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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