Diatomic molecule energies of the modified Rosen−Morse potential energy model

2014 ◽  
Vol 92 (4) ◽  
pp. 341-345 ◽  
Author(s):  
Hong-Ming Tang ◽  
Guang-Chuan Liang ◽  
Lie-Hui Zhang ◽  
Feng Zhao ◽  
Chun-Sheng Jia
Keyword(s):  
Morse Potential ◽  
Potential Model ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Wave Functions ◽  
Energy Spectra ◽  
Radial Wave ◽  
Empirical Potential ◽  
Vibrational Energy Levels ◽  
Π State

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

Molecular energies of the improved Rosen−Morse potential energy model

2014 ◽  
Vol 92 (1) ◽  
pp. 40-44 ◽  
Author(s):  
Jian-Yi Liu ◽  
Xue-Tao Hu ◽  
Chun-Sheng Jia
Keyword(s):  
Potential Energy ◽  
Morse Potential ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Energy Model ◽  
Wave Functions ◽  
Radial Wave ◽  
Empirical Potential ◽  
Interaction Potential Energy ◽  
Vibrational Energy Levels

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Molecular energies of the improved Tietz potential energy model

2014 ◽  
Vol 92 (3) ◽  
pp. 201-205 ◽  
Author(s):  
Hong-Ming Tang ◽  
Guang-Chuan Liang ◽  
Lie-Hui Zhang ◽  
Feng Zhao ◽  
Chun-Sheng Jia
Keyword(s):  
Potential Energy ◽  
Potential Model ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Energy Model ◽  
Radial Wave ◽  
Empirical Potential ◽  
Tietz Potential ◽  
Vibrational Energy Levels ◽  
Good Agreement

We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 51Δg state and C1Πu state of the Na2 molecule are in good agreement with the experimental Rydberg−Klein−Rees data.

Ab Initio Calculations of Vibrational Energy Levels and Transition Dipole Moments of CO2 Molecules

2008 ◽  
Author(s):  
Zhi Liang ◽  
Hai-Lung Tsai
Keyword(s):  
Ab Initio ◽  
Vibrational Energy ◽  
Molecular Spectroscopy ◽  
Dipole Moments ◽  
Energy Levels ◽  
Wave Functions ◽  
Molecular Vibration ◽  
Transition Dipole ◽  
Transition Dipole Moments ◽  
Vibrational Energy Levels

Ab initio MD simulation of laser-matter interactions is a hot area in the study of the mechanisms of photo-dissociation, photo-ionization and laser induced chemical reactions. The major problems in the study of laser-molecule interactions are to determine the energies and wave functions of molecular vibration states and the molecular transition dipole moments. An efficient method is presented to calculate the intramolecular potential energies and electrical dipole moments of CO2 molecules at the electronic ground state by solving the Kohn-Sham (KS) equation for a total of 101,992 nuclear configurations. The Projector-Augmented Wave (PAW) exchange-correlation potential functionals and Plane Wave (PW) basis functions were used in solving the KS equation. The calculated intra-molecular potential function was then included in the pure vibrational Schro¨dinger equation to determine the vibrational energy eigen values and eigen functions. The vibrational wave functions combined with the calculated dipole moment function were used to determine the transition dipole moments. The calculated results have a good agreement with experimental values. These results can be further used to determinations of molecular spectroscopy and laser absorption coefficients.

scholarly journals A study of the stretching vibrational spectroscopy of C120O and C120O2 by u(2) lie algebra

2013 ◽  
Vol 78 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Rupam Sen ◽  
Ashim Kalyan ◽  
Ramendu Bhattacharjee
Keyword(s):  
Lie Algebra ◽  
Vibrational Spectroscopy ◽  
Morse Potential ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Tight Binding ◽  
Endohedral Fullerene ◽  
Modes Of Vibration ◽  
Fullerene Dimers ◽  
Vibrational Energy Levels

The vibrational energy levels of endohedral fullerene dimers C120O and C120O2 are calculated considering the local Hamiltonian of Morse potential using the algebra. Here each bond of the molecules is replaced by a corresponding Lie algebra and finally the Hamiltonian is constructed considering the interacting Casimir and Majorana operators. The fundamental stretching modes of vibration of both the dimmers C120O and C120O2 are then calculated using this Hamiltonian to compare the results of functional-based tight-binding (DF-TB) calculations.

scholarly journals Penentuan Tingkat-Tingkat Energi Vibrasi Molekul Hidrogen Pada Keadaan Elektronik Dasar Menggunakan Potensial Morse

Wahana Fisika ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 1-9
Author(s):  
Redi Kristian Pingak ◽  
Albert Zicko Johannes
Keyword(s):  
Morse Potential ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Classical Method ◽  
Energy Levels ◽  
Vibrational Levels ◽  
Oppenheimer Approximation ◽  
False Position ◽  
Vibrational Energies ◽  
Vibrational Energy Levels

Pendekatan Born-Oppenheimer diterapkan untuk menghitung tingkat energi vibrasi keadaan dasar molekul hidrogen. Persamaan Schrodinger untuk inti atom diselesaikan dengan menggunakan metode semi-klasik, di mana inti atom diasumsikan bergerak secara klasik dalam sumur potensial dan energi vibrasi ditentukan dengan menerapkan aturan kuantisasi kuantum. Potensial yang digunakan pada penelitian adalah potensial Morse. Dalam penelitian ini, tingkat energi vibrasi dihitung dengan metode numerik, yaitu metode integrasi Simpson dan metode regula falsi. 15 Tingkat energi vibrasi dari molekul H2 diperoleh dan dibandingkan dengan data hasil eksperimen. Perbandingan ini mengindikasikan pendekatan yang digunakan pada penelitian ini memberikan hasil yang sangat akurat pada tingkat energi vibrasi yang relatif rendah (0≤n≤4), dengan kesalahan kurang dari 0,7%, dan untuk 5≤n≤8 dengan kesalahan maksimum 7,3%. Keakuratan menurun ketika tingkat energi vibrasi meningkat. Secara khusus, untuk n = 13 dan n = 14, kesalahan meningkat secara signifikan, menunjukkan gagalnya pendekatan ini untuk tingkat energi vibrasi yang relatif tinggi, khususnya untuk dua tingkat energi ini. Born-Oppenheimer approximation was applied to calculate vibrational energy levels of ground state of Hydrogen molecule. The Schrodinger equation for the nuclei was solved using a semi-classical method, in which the nuclei are assumed to move classically in a potential well and the vibrational energies are determined by applying the quantum mechanical quantization rules. Potential used in this research was the Morse potential. Here, vibrational energy levels of the molecule were calculated using numerical methods, i.e. Simpson integration method and false position method. 15 Vibrational energy levels of the H2 molecule were obtained and compared to the corresponding results from experiments. The comparison indicated that the approximation used in this research yielded very accurate results for relatively low vibrational levels (0≤n≤4), with errors being less than 0.7% and for 5≤n≤8 with maximum of 7.3% errors. The accuracy decreased as the vibrational levels increased, as expected. In particular, for n=13 and n=14, errors significantly increased, indicating the breakdown of the approximation for relatively high vibrational levels, in particular for these two energy levels.           Keywords: Hydrogen Molecule; Morse Potential; Born-Oppenheimer Approximation; Simpson Method; False Position Method

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.

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