On a Unified Theory of Harmonic Oscillator Two-Centre Integrals

1972 ◽  
Vol 27 (2) ◽  
pp. 180-187
Author(s):  
W Wltschel
Keyword(s):  
Quantum Chemistry ◽  
Harmonic Oscillator ◽  
Molecular Spectroscopy ◽  
Occupation Number ◽  
Operator Technique ◽  
Unified Theory ◽  
Number Representation ◽  
Molecular Physics ◽  
Operator Identity

Abstract Occupation number representation and operator-technique are used in the calculation of harmonic oscillator matrixelements for one and two centres and for equal and different frequencies. The potentials treated are generalized Gauss-potentials of the form p̑k x̑l exp{a x̑2 }, x̑k p̑l exp{a p̑2 }, and p̑k x̑l exp{a x̑ p̑} which by application of an operator identity could be reduced to the same form. Applications in nuclear and molecular physics, in molecular spectroscopy and in quantum chemistry are discussed briefly.

On a Unified Theory of Twocentre Harmonic Oscillator Integrals

1971 ◽  
Vol 26 (6) ◽  
pp. 943-946 ◽  
Author(s):  
W . Wltschel
Keyword(s):  
Kinetic Energy ◽  
Harmonic Oscillator ◽  
Operator Technique ◽  
Unified Theory ◽  
Overlap Integrals ◽  
Second Quantization ◽  
Energy Integrals ◽  
Franck Condon

Abstract Twocentre harmonic oscillator overlap integrals (Franck-Condon-integrals) are calculated in a simple way for twodimensional oscillators of different frequencies. Second quantization and operator technique are applied. It is further shown that transition and kinetic energy integrals can be derived in the same representation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

Molecular Physics and Elements of Quantum Chemistry: Introduction to Experiments and Theory

Physics Today ◽  
1997 ◽  
Vol 50 (2) ◽  
pp. 66-67 ◽  
Author(s):  
Hermann Haken ◽  
Hans Christoph Wolf ◽  
Zoltán Géza Soos
Keyword(s):  
Quantum Chemistry ◽  
Molecular Physics

scholarly journals Shermo: A General Code for Calculating Molecular Thermochemistry Properties

2020 ◽  
Author(s):  
Tian Lu ◽  
qinxue chen
Keyword(s):  
Quantum Chemistry ◽  
Harmonic Oscillator ◽  
Thermodynamic Data ◽  
Thermodynamic Quantities ◽  
Rigid Rotor ◽  
Low Frequencies ◽  
Frequency Scale ◽  
Scale Factors ◽  
Temperature And Pressure ◽  
Output Information

Calculation of molecular thermodynamic quantities is one of the most frequently involved task in daily quantum chemistry studies. In this article, we present a general, stand-alone, powerful and flexible code named Shermo for calculating various common thermochemistry data. This code is compatible with Gaussian, ORCA, GAMESS-US and NWChem and has many unique advantages: the output information is very easy to comprehend; thermodynamic quantities can be fully decomposed to contributions of various sources; temperature and pressure can be conveniently scanned; two quasi-rigid-rotor harmonic oscillator (quasi-RRHO) models are supported to properly deal with low frequencies; different frequency scale factors can be simultaneously specified for calculating different thermodynamic quantities; conformation weighted thermodynamic data can be directly evaluated; the code can be easily run and embedded into shell script. We hope the Shermo program will bring great convenience to quantum chemists. This code can be freely obtained at http://sobereva.com/soft/shermo.

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