Vibrational Energy Levels for an SCF Wavefunction of the Hydrogen Molecule

1963 ◽  
Vol 39 (4) ◽  
pp. 1137-1138 ◽  
Author(s):  
Gerard M. Leies
Keyword(s):  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Energy Levels

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

ON THE VIBRATIONAL FREQUENCIES OF THE HYDROGEN MOLECULE

1966 ◽  
Vol 44 (7) ◽  
pp. 1467-1477 ◽  
Author(s):  
J. D. Poll ◽  
G. Karl
Keyword(s):  
Ground State ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Nuclear Motion ◽  
Vibrational Transition ◽  
Frequency Shifts ◽  
Vibrational Levels ◽  
Vibrational Energy Levels ◽  
Better Than

The results of numerical calculations of the vibrational energy levels of the H2 molecule in the ground electronic state are presented. These were obtained by solving the Schrödinger equation for the nuclear motion using the adiabatic potential calculated by Kolos and Wolniewicz (1965). In agreement with experiment, it was found that H2 has 15 vibrational levels in the ground state. The vibrational transition frequencies agree with the experimental ones (Herzberg and Howe 1959) to better than one part in a thousand. For the lower levels, the remaining discrepancies can be accounted for using Van Vleck's (1936) estimate of the nonadiabatic frequency shifts. Results of similar calculations for D2 and T2 are also given.

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.

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