scholarly journals Vibrational Spectra of Ozone (O3) Using Lie Algebraic Method

2018 ◽  
Vol 34 (4) ◽  
pp. 2208-2210
Author(s):  
J. Vijayasekhar
Keyword(s):  
Experimental Data ◽  
Lie Algebra ◽  
Vibrational Spectra ◽  
Algebraic Method ◽  
Hamiltonian Operator ◽  
Vibrational Frequencies

We have calculated the vibrational frequencies of Ozone (O3) upto second overtone using Hamiltonian operator which is based on the Lie algebra. The determined symmetric and antisymmetric fundamental vibrational frequencies by Lie algebraic method are compared with experimental data. It has been observed that results from the method reveal near to the exact, consistent with the experimental data.

scholarly journals Anharmonic Vibrational Frequencies of Water Borane and Associated Molecules

Molecules ◽  
2021 ◽  
Vol 26 (23) ◽  
pp. 7348
Author(s):  
Brent R. Westbrook ◽  
Ryan C. Fortenberry
Keyword(s):  
Experimental Data ◽  
Gas Phase ◽  
Vibrational Spectra ◽  
Quantum Chemical ◽  
Hydrogen Generation ◽  
Vibrational Frequencies ◽  
Rotational Spectroscopy ◽  
Vibrational Modes ◽  
Theoretical Predictions ◽  
Borinic Acid

Water borane (BH3OH2) and borinic acid (BH2OH) have been proposed as intermediates along the pathway of hydrogen generation from simple reactants: water and borane. However, the vibrational spectra for neither water borane nor borinic acid has been investigaged experimentally due to the difficulty of isolating them in the gas phase, making accurate quantum chemical predictions for such properties the most viable means of their determination. This work presents theoretical predictions of the full rotational and fundamental vibrational spectra of these two potentially application-rich molecules using quartic force fields at the CCSD(T)-F12b/cc-pCVTZ-F12 level with additional corrections included for the effects of scalar relativity. This computational scheme is further benchmarked against the available gas-phase experimental data for the related borane and HBO molecules. The differences are found to be within 3 cm−1 for the fundamental vibrational frequencies and as close as 15 MHz in the B0 and C0 principal rotational constants. Both BH2OH and BH3OH2 have multiple vibrational modes with intensities greater than 100 km mol−1, namely ν2 and ν4 in BH2OH, and ν1, ν3, ν4, ν9, and ν13 in BH3OH2. Finally, BH3OH2 has a large dipole moment of 4.24 D, which should enable it to be observable by rotational spectroscopy, as well.

Comparison of the Conformational Stability for Several Vinylhalomethanes and Silanes with Experiment Using MP2 Perturbation Theory and DFT

2007 ◽  
Vol 72 (1) ◽  
pp. 15-50 ◽  
Author(s):  
Wolfgang Förner ◽  
Hassan M. Badawi
Keyword(s):  
Experimental Data ◽  
Vibrational Spectra ◽  
Recent Literature ◽  
Conformational Stability ◽  
Basis Set ◽  
Major Conclusion ◽  
Stable Conformer ◽  
Polarization Functions ◽  
Complete Series ◽  
Triple Zeta

In recent literature it was reported that the valence triple zeta basis set augmented by polarization functions is not too reliable for vinyl monohalo- and dihalomethanes and -silanes, the halogen being fluorine and chlorine. The major conclusion was that a valence triple zeta basis is too small to be augmented by polarization functions in a balanced way, at least on vinylmonofluoromethane. Thus we decided to apply the 6-311++G** basis set to the complete series of methanes, silanes and germanes (the latter ones are just added for completeness because no experimental data are available for them and, moreover, we published them already previously) and to compare the results to experimental data available in the literature to see whether the failures of this basis set show up in the complete series of molecules. In the literature we found five such molecules and the information which of the conformers is the most stable. Indeed we found that predictions on the relative stability of conformers in those systems with this basis set and MP2 as well as DFT are with a 60:40 chance, three being correct predictions and two being incorrect ones out of the five. However, since the energy differences are rather small in these systems and due to the fact that - as a consequence of twofold degeneracy of the gauche conformer on the potential curve of the torsional vibration - the abundances of the conformers in equilibrium do not change too much, we decided to calculate also vibrational spectra for three examples and to compare them also to experiment. It is reported that besides the failures in total energy (we have chosen two examples where predictions of the nature of the stable conformer are correct, and one where it is not), the vibrational spectra are rather well reproduced, especially when experimental energies are used to calculate abundances in equilibrium in the case where the prediction of the stable conformer failed.

Calculating Fundamental Vibrational Frequencies of Rutile by Combining Ab Initio Method with GF Matrix Method

1994 ◽  
Vol 05 (02) ◽  
pp. 299-301
Author(s):  
Lin Libin ◽  
Zheng Xiangyin
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Matrix Method ◽  
Cluster Model ◽  
Normal Modes ◽  
Vibrational Frequencies ◽  
Ab Initio Method ◽  
Environment Factor ◽  
Factor Α ◽  
Good Agreement

Based on cluster model, we have calculated the fundamental vibrational frequencies of rutile by combining ab initio method and Wilson’s GF-matrix method. In the calculation, we have introduced the concept of environment factor α to correct the force field of the cluster model. The results of calculation are in good agreement to the experimental data and the normal modes give us clear physical picture of the crystal vibration.

scholarly journals Lie Algebra Solution of Population Models Based on Time-Inhomogeneous Markov Chains

2012 ◽  
Vol 49 (02) ◽  
pp. 472-481 ◽  
Author(s):  
Thomas House
Keyword(s):  
Markov Chains ◽  
Stochastic Processes ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Natural Populations ◽  
Algebraic Method ◽  
Population Models ◽  
Physical Sciences ◽  
Solution Form ◽  
Social Applications

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical, and social applications. In this paper we present the Lie algebraic method, and apply it to three biologically well-motivated examples. The result of this is a solution form that is often highly computationally advantageous.

scholarly journals The bicomplex quantum Coulomb potential problem

2013 ◽  
Vol 91 (12) ◽  
pp. 1093-1100 ◽  
Author(s):  
J. Mathieu ◽  
L. Marchildon ◽  
D. Rochon
Keyword(s):  
Differential Equation ◽  
Coulomb Potential ◽  
Potential Problem ◽  
Orthonormal System ◽  
Mathematical Formulation ◽  
Algebraic Method ◽  
Hamiltonian Operator ◽  
Number System ◽  
Bicomplex Numbers ◽  
Bicomplex Number

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [Formula: see text], where ξ is a bicomplex number. Following Pauli’s algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrödinger’s time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.

CALCULATION OF THE NATURAL VIBRATIONAL FREQUENCY OF THE PULSE-LOADED EMBEDDED FOUNDATION

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Aleksey Kolesnikov ◽  
Vladimir Popov ◽  
Tatiana Kostiuk
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Wave Model ◽  
Vibrational Frequencies ◽  
Shallow Foundations ◽  
Shallow Foundation ◽  
Test Results ◽  
Dynamic Loadings ◽  
Embedded Foundations ◽  
Vertical Vibrations

Applicability of formulas obtained within the framework of wave model and Russian design code SP 26.13330.2012 were considered to determine the dynamic stiffness in respect to vertical and horizontal vibrations of shallow and pile embedded foundations. The target is to calculate the system’s varying natural vibrational frequencies regarding the deepening. Obtained results are compared with experimental data of a series of pulse dynamic loadings under half-full-scale conditions on foundation models. Values of transversal wave velocities are found directly on test section from test results. It is found that deepening results in natural vibrational frequencies growth, both in case of pile and shallow foundations. Full deepening of more than 1.6 times increases frequencies at horizontal vibrations, and up to 1.4 times at vertical vibrations; the effect is stronger for shallow foundations. Benefit of the results obtained by wave model against the SP 26.13330.2012 method is demonstrated, as well as the good agreement between calculation and experimental results, which permits finding reliable amplitude-frequency characteristics of the foundations. Results obtained in accordance with SP 26.13330.2012 show lower values of natural vibrational frequencies and do not completely regard the deepening effect. Maximal discrepancy with experimental data is 33% for vertical vibrations on shallow and pile foundations. In case of horizontal vibrations, the maximal discrepancy is from 20% for shallow foundation to 27% for shallow and pile foundation.

A Theoretical Study Of The Energetics And Vibrational Spectra Of Oxygenated (100) Diamond Surfaces

1995 ◽  
Vol 416 ◽  
Author(s):  
S. Skokov ◽  
B. Weiner ◽  
M. Frenklach
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Hydrogen Bonds ◽  
Vibrational Spectra ◽  
Theoretical Study ◽  
Local Environment ◽  
Hydroxyl Groups ◽  
Vibrational Modes ◽  
Diamond Surfaces ◽  
Molecular Dynamics Calculations

ABSTRACTStatic quantum ab initio and quantum semiempirical molecular dynamics calculations were employed to study reconstructions of (100) diamond surfaces in presence of hydrogen and oxygen. The results indicate that the energetically most favorable structures of oxygenated surfaces are those with chemisorbed hydroxyl groups. It was found that hydrogen bonds are formed among chemisorbed oxygenated species. The formation of these hydrogen bonds is shown to be an important factor in stabilization of adlayers. A number of important vibrational modes characteristic of oxygenated diamond surfaces were identified. The analysis of surface vibrational spectra demonstrates the influence of the local environment on the position of vibrational modes and can be useful for interpretation of experimental data.

An ab initio and DFT study of structure and vibrational spectra of γ form of Oleic acid: Comparison to experimental data

2010 ◽  
Vol 163 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Soni Mishra ◽  
Deepika Chaturvedi ◽  
Naresh Kumar ◽  
Poonam Tandon ◽  
H.W. Siesler
Keyword(s):  
Experimental Data ◽  
Oleic Acid ◽  
Ab Initio ◽  
Vibrational Spectra ◽  
Dft Study ◽  
Acid Comparison ◽  
Ab Initio And Dft
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