Nonadiabatic corrections to the lowest EF 1Σg and I 1Πg− vibrational levels of the hydrogen molecule

1996 ◽  
Vol 105 (24) ◽  
pp. 10691-10695 ◽  
Author(s):  
L. Wolniewicz
Keyword(s):  
Hydrogen Molecule ◽  
Vibrational Levels

New ab initio Potential Energy Curve and Vibrational Levels for the B1Σu+ State of the Hydrogen Molecule

1975 ◽  
Vol 53 (19) ◽  
pp. 2189-2197 ◽  
Author(s):  
W. Kotos ◽  
L. Wolniewicz
Keyword(s):  
Wave Function ◽  
Potential Energy ◽  
Hydrogen Molecule ◽  
Potential Energy Curve ◽  
Energy Curve ◽  
Elliptic Coordinates ◽  
Dissociation Energies ◽  
Vibrational Levels ◽  
Nonadiabatic Effects ◽  
Experimental Values

The Born–Oppenheimer potential energy curve for the B1Σu+ state of the hydrogen molecule has been computed using a wave-function in the form of an 88 term expansion in elliptic coordinates and including the interelectronic distance. At R = Re the computed energy is 5.2 cm−1 lower than the previous most accurate value, in agreement with the prediction by Dabrowski and Herzberg. The new potential energy curve, with the previously computed adiabatic corrections, has been used to calculate the vibrational levels for H2, HD, and D2. The resulting dissociation energies differ from the experimental values by less than 1 cm−1. The discrepancies between the theoretical and experimental energies for various vibrational levels amount up to 12 cm−1 for H2 and 8 cm−1 for D2. Their analysis suggests that most of the discrepancy is due to the nonadiabatic effects, but partly also to incomplete convergence of the Born–Oppenheimer potential energy curve, especially at large internuclear separations.

On the theory of the Stark shifts of the rotational–vibrational levels of the hydrogen molecule and its isotopes produced by a point charge. I: H2, D2, and T2

1985 ◽  
Vol 63 (1) ◽  
pp. 84-93 ◽  
Author(s):  
J. D. Poll ◽  
J. L. Hunt
Keyword(s):  
Diatomic Molecule ◽  
Point Charge ◽  
Hydrogen Molecule ◽  
Stark Shift ◽  
Numerical Results ◽  
Centre Of Mass ◽  
Fixed Distance ◽  
Homonuclear Diatomic Molecule ◽  
Vibrational Levels

The Hamiltonian describing the rotation and vibration of a homonuclear diatomic molecule in the field of a point charge at a fixed distance from its centre-of-mass is given. Numerical results for the Stark shift of the molecular levels due to a point charge of either sign are listed for H2, D2, and T2 as a function of the separation of the point charge from the molecule. The intensity associated with transitions between perturbed levels is discussed briefly.

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.

On the theory of the Stark shifts of the rotational–vibrational levels of the hydrogen molecule and its isotopes produced by a point charge. II: HD, HT, and DT

1991 ◽  
Vol 69 (5) ◽  
pp. 606-611 ◽  
Author(s):  
J. J. Miller ◽  
J. D. Poll ◽  
J. L. Hunt
Keyword(s):  
Point Charge ◽  
Hydrogen Molecule ◽  
Stark Shift ◽  
Vibrational Levels

In continuation of paper I of this series on the homonuclear molecules H2, D2, and T2, the Hamiltonian describing the rotation and vibration of a heteronuclear molecule in the field of a point charge is given. Numercial results for the Stark shift of the molecular levels due to a point charge of either sign are listed for HD, HT, and DT as a function of the separation of this charge from the molecule. An application of the calculations to the charge-induced spectrum of HD is presented.

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