An internal coordinate model for molecular vibrations: the energy levels of H2O and H2S and related isotopic molecules

1978 ◽  
Vol 56 (16) ◽  
pp. 2167-2172 ◽  
Author(s):  
Jan Bron ◽  
R. Wallace
Keyword(s):  
Potential Function ◽  
Energy Levels ◽  
Vibrational Analysis ◽  
Polyatomic Molecules ◽  
Bending Vibration ◽  
Relative Simplicity ◽  
Anharmonic Vibrations ◽  
Vibrational Excitations ◽  
Coordinate Model ◽  
Good Agreement

Refinement of a previously described model for describing the anharmonic vibrations of polyatomic molecules is presented. The nonlinear molecules XY2 (H2O, D2O, H2S, D2S) are used as examples and it is shown that quite good agreement with the observed spectrum can be obtained for the first twenty vibrational excitations with a six parameter potential function. Apart from its relative simplicity, the main improvement over previously reported work is the inclusion of the bending vibration within the formalism and refinement of the form of potential. It is pointed out that the model is readily extendable to the vibrational analysis of larger molecules.

Vibrational theory of polyatomic molecules: energy levels of CH4/CD4 and CH3Cl/CD3Cl

1979 ◽  
Vol 57 (17) ◽  
pp. 2321-2324 ◽  
Author(s):  
Jan Bron ◽  
R. Wallace
Keyword(s):  
Simple Model ◽  
Energy Levels ◽  
Polyatomic Molecules ◽  
Triatomic Molecules ◽  
Combination Bands ◽  
Good Agreement

A relatively simple model, previously used to describe polyatomic vibrations of nonlinear triatomic molecules, has been employed to evaluate the fundamentals, first overtones and combination bands of CX4 and CX3Cl (X = H, D). Relatively good agreement is obtained between calculated and observed frequencies. Interesting splittings of certain overtone and combination bands result from these calculations.

Algebraic study of vibrational spectra of the tetra-atomic molecules N15C12C12N15 and N14C13C13N14

2016 ◽  
Vol 15 (04) ◽  
pp. 1650036 ◽  
Author(s):  
Kamal Ziadi ◽  
Abdelhamid Bouldjedri
Keyword(s):  
Experimental Data ◽  
Potential Energy ◽  
Energy Levels ◽  
Algebraic Approach ◽  
Potential Energy Function ◽  
Vibration Modes ◽  
Bending Vibration ◽  
Dissociation Energies ◽  
Algebraic Technique ◽  
Good Agreement

In this paper, an accurate and efficient algebraic technique is used to compute linear tetra-atomic molecules stretching and bending vibration modes. Namely, several collective energy levels of linear XYYX molecules N[Formula: see text]C[Formula: see text]C[Formula: see text]N[Formula: see text] and N[Formula: see text]C[Formula: see text]C[Formula: see text]N[Formula: see text] have been described in the framework of the algebraic approach based on U[Formula: see text] Lie algebra. The results are compared to experimental data, good agreement has been obtained. The potential energy function of the two molecules is analyzed and the dissociation energies are derived.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

The derivation of the rotational potential function from atom–atom potentials. III. Borohydride compounds

1988 ◽  
Vol 66 (4) ◽  
pp. 791-793 ◽  
Author(s):  
David Smith
Keyword(s):  
Transition Temperature ◽  
Experimental Method ◽  
Potential Function ◽  
Ground Level ◽  
Potential Functions ◽  
The Difference ◽  
Level Degeneracy ◽  
Entropy Of Transition ◽  
Good Agreement

The rotational potential functions for the borohydride ion embedded in potassium and rubidium halides are derived from atom–atom potentials of the Buckingham (exp-6) type. The librational frequencies computed from the potential functions are in good agreement with the observed frequencies. The potential functions for rubidium and potassium borohydrides derived from the atom–atom potentials yield librational frequencies that are about 10% higher than the observed values. Since the entropy of transition for potassium and rubidium borohydrides is less than expected, there is a possibility that there is some ordering of the borohydride ions above the transition temperature. An experimental method is presented for studying the ordering of the borohydride ions based on the difference in the ground level degeneracy of a tetrahedral ion in ordered and disordered states.

scholarly journals Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

2021 ◽  
Author(s):  
Toru Shiozaki ◽  
Bess Vlaisavljevich
Keyword(s):  
Spectroscopic Data ◽  
Technological Development ◽  
Vibrational Analysis ◽  
Bond Distance ◽  
Coordination Complexes ◽  
Vibrational Structure ◽  
Complete Active Space ◽  
Computational Spectroscopy ◽  
First Time ◽  
Good Agreement

We report the accurate computational vibrational analysis of the Cr–Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr–Cr vibrational stretching modes, ν(Cr2), have suggested weaker bonding, even for so-called ultrashort Cr–Cr bonds, while others are in line with the bond distance. Here we optimize the geometries and compute ν(Cr2) with CASPT2 for three well-characterized complexes, Cr2(O2CCH3)4(H2O)2, Cr2(mhp)4, and Cr2(dmp)4. We obtain CASPT2 harmonic ν(Cr2) modes in good agreement with experiment at 282 cm−1 for Cr2(mhp)4 and 353 cm−1 for Cr2(dmp)4, compute 50Cr and 54Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr–Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν(Cr2) leading to an anharmonic mode of 272 cm−1 for Cr2(mhp)4 and 333 cm−1 for Cr2(dmp)4.

scholarly journals Electronic Structure of Two New Bis-Schiff Base Ligands using DFT Method

2021 ◽  
pp. 10-15
Author(s):  
Elham Abdalrahem Bin Selim ◽  
Mohammed Hadi Al–Douh ◽  
Hassan Hadi Abdullah ◽  
Dahab Salim Al–Nohey
Keyword(s):  
Experimental Data ◽  
Biological Activity ◽  
Metal Ion ◽  
Energy Levels ◽  
Dft Method ◽  
Ftir Spectra ◽  
Schiff Base Ligands ◽  
Lumo Energy ◽  
Homo Lumo ◽  
Good Agreement

Two bis-Schiff Bases 1 and 2 are ligands that can coordinate with manganese metal to form stable complexes and have biological activity. Thermodynamic parameters, HOMO-LUMO energy levels and FTIR spectra of two ligands have been computed using B3LYP/6-311++G(d,p) functional of the DFT calculations. Both ligands are favored thermodynamically, and the ligand 1 has been shown to be more stable than ligand 2. The Polarizability values of two ligands have been investigated. The results refer that ligand 2 interacts earlier than ligand 1 to the metal ion. The FTIR spectra of two ligands have been evaluated. All results show the good agreement between the theoretical and experimental data.

Shape coexistence in $^{76}$Se within the neutron-proton interacting boson model

2021 ◽  
Author(s):  
Chengfu Mu ◽  
Dali Zhang
Keyword(s):  
Experimental Data ◽  
Energy Spectrum ◽  
Excitation Energy ◽  
Energy Levels ◽  
Spherical Shape ◽  
Interacting Boson Model ◽  
Shape Coexistence ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Good Agreement

Abstract We have investigated the low-lying energy spectrum and electromagnetic transition strengths in even-even $^{76}$Se using the proton-neutron interacting boson model (IBM-2). The theoretical calculation for the energy levels and $E2$ and $M1$ transition strengths is in good agreement with the experimental data. Especially, the excitation energy and $E2$ transition of $0^+_2$ state, which is intimately associated with shape coexistence, can be well reproduced. The analysis on low-lying states and some key structure indicators indicates that there is a coexistence between spherical shape and $\gamma$-soft shape in $^{76}$Se.

scholarly journals Energy levels of one-dimensional anharmonic oscillator via neural networks

2019 ◽  
Vol 34 (12) ◽  
pp. 1950088 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Field Theory ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
High Accuracy ◽  
Network System ◽  
Quantum Field ◽  
One Dimensional ◽  
Neural Network System ◽  
Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

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