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 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 Anab initiobased full-dimensional potential energy surface for OH + O2⇄ HO3and low-lying vibrational levels of HO3

2019 ◽  
Vol 21 (25) ◽  
pp. 13766-13775 ◽  
Author(s):  
Xixi Hu ◽  
Junxiang Zuo ◽  
Changjian Xie ◽  
Richard Dawes ◽  
Hua Guo ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Quantum Dynamics ◽  
Energy Surface ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Levels ◽  
Vibrational Energy Levels

A full-dimensional potential energy surface for HO3, including the HO + O2dissociation asymptote, is developed and rigorous quantum dynamics calculations based on this PES have been carried out to compute the vibrational energy levels of HO3.

A Quantum Model for Bending Vibrations and Thermodynamic Properties of C3

1973 ◽  
Vol 51 (7) ◽  
pp. 751-760 ◽  
Author(s):  
C. Frederick Hansen ◽  
Walter E. Pearson
Keyword(s):  
Thermodynamic Properties ◽  
Vibrational Energy ◽  
Classical Model ◽  
Energy Levels ◽  
Quantum Model ◽  
Bending Vibrations ◽  
Bending Mode ◽  
Vibrational Levels ◽  
Vibrational Energy Levels ◽  
Vapor Pressure Measurements

A quadratically perturbed square well potential is used to derive quantized bending mode vibrational energy levels for the C3 molecule. Coupling with rotational modes and l doubling is neglected for simplicity. The model is constrained to a best fit with observed lower vibrational levels in the lowest rotational state, and subject to this constraint the upper vibrational levels have maximum possible divergence. Thus a lower limit for the partition function and the entropy of C3 is established; the neglected rotational coupling has little influence on these quantities because the splitting of levels is almost symmetrical. The limits obtained support the classical model of Strauss and Thiele for the thermodynamic properties of C3 rather than the estimates listed in current JANAF Thermochemical Tables, and imply that recent graphite vapor pressure measurements made by Zavitsanos and by Wachi and Gilmartin are more correct than earlier measurements.

Quantum and classical dynamics of H + CaCl(X 2Σ+) → HCl + Ca(1S) reaction and vibrational energy levels of the HCaCl complex

2016 ◽  
Vol 18 (23) ◽  
pp. 15673-15685 ◽  
Author(s):  
Rui Shan Tan ◽  
Huan Chen Zhai ◽  
Feng Gao ◽  
Dianmin Tong ◽  
Shi Ying Lin
Keyword(s):  
Wave Packet ◽  
Cross Sections ◽  
Ground State ◽  
Energy Surface ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Classical Trajectory ◽  
Classical Dynamics ◽  
Quantum Wave ◽  
Vibrational Energy Levels

We carried out accurate quantum wave packet as well as quasi-classical trajectory (QCT) calculations for H + CaCl (νi = 0, ji = 0) reaction occurring on an adiabatic ground state. Recent ab initio potential energy surface is employed to calculate the quantum and QCT reaction probabilities for several partial waves (J = 0, 10, and 20) as well as state resolved QCT integral and differential cross sections.

Large Amplitude Hamiltonian of a Triatomic Molecule

1977 ◽  
Vol 32 (12) ◽  
pp. 1450-1456 ◽  
Author(s):  
R. Wallace ◽  
Ch. V. S. Ramachandra Rao
Keyword(s):  
Ground State ◽  
Large Amplitude ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Curvilinear Coordinates ◽  
Large Displacements ◽  
Triatomic Molecule ◽  
Quadratic Potential ◽  
Method Of Calculation ◽  
Vibrational Energy Levels

Abstract An expression for the Hamiltonian H(ρ1, ρ2, ρ3) of a vibrating-rotating triatomic molecule is derived using three curvilinear coordinates gi, Q 3 in such a way that the Hamiltonian obtained is applicable to any bent triatomic molecule and allows for large displacements in all the three modes of motion. A variational technique is then used to calculate the low lying vibrational energy levels (υ1, υ2, υ3) of the H2O molecule in its X̃1A1 ground state. The kinetic energy of the Hamiltonian T(ρ1, ρ2, ρ3) takes into account the large amplitude character of the three modes together with their interaction. But in order to minimize the formidable amount of computation, a simple quadratic potential F(ρ1, ρ2, ρ3) is assumed for all the three modes which only serves to illustrate the method of calculation.

scholarly journals N3+: Full-dimensional ground state potential energy surface, vibrational energy levels, and dynamics

2020 ◽  
Vol 153 (4) ◽  
pp. 044302
Author(s):  
Debasish Koner ◽  
Max Schwilk ◽  
Sarbani Patra ◽  
Evan J. Bieske ◽  
Markus Meuwly
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ground State ◽  
Energy Surface ◽  
Vibrational Energy ◽  
Energy Levels ◽  
State Potential ◽  
Vibrational Energy Levels

Vibrational energy levels for the electronic ground state of the diazocarbene (CNN) molecule

2008 ◽  
Vol 106 (2-4) ◽  
pp. 357-365 ◽  
Author(s):  
Stuart Carter ◽  
Nicholas C. Handy ◽  
Yukio Yamaguchi ◽  
Justin M. Turney ◽  
Henry F. Schaefer III
Keyword(s):  
Ground State ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Electronic Ground State ◽  
Vibrational Energy Levels ◽  
Electronic Ground
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