scholarly journals Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons

2014 ◽  
Author(s):  
Ralph Menikoff
Keyword(s):  
Harmonic Oscillator ◽  
Harmonic Oscillator Approximation ◽  
Molecular Solid

The Influence of Molecular Vibration on Brayton-Cycle Performance

1962 ◽  
Vol 29 (2) ◽  
pp. 396-398
Author(s):  
T. A. Jacobs ◽  
J. R. Lloyd
Keyword(s):  
Harmonic Oscillator ◽  
Cycle Performance ◽  
Molecular Vibration ◽  
Brayton Cycle ◽  
Harmonic Oscillator Approximation

By means of the harmonic-oscillator approximation, the influence of molecular vibration on Brayton-cycle performance is demonstrated.

A Modified Harmonic Oscillator Approximation Scheme for the Dielectric Constants of GaAs, InP and GaP

1996 ◽  
Vol 35 (Part 1, No. 3) ◽  
pp. 1617-1623 ◽  
Author(s):  
Guolin Yu ◽  
Tetsuo Soga ◽  
Takashi Jimbo ◽  
Masayoshi Umeno
Keyword(s):  
Harmonic Oscillator ◽  
Approximation Scheme ◽  
Dielectric Constants ◽  
Harmonic Oscillator Approximation

Normal Coordinate Treatments and Calculated Thermodynamic Properties of Phosphoryl Fluorodichloride, Phosphoryl Chlorodifluoride, Thiophosphoryl Bromide, Thiophosphoryl Fluorodibromide, and Thiophosphoryl Bromodifluoride

1971 ◽  
Vol 25 (2) ◽  
pp. 212-217 ◽  
Author(s):  
Joseph S. Ziomek ◽  
Frank J. Fillwalk ◽  
Edward A. Piotrowski
Keyword(s):  
Thermodynamic Properties ◽  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Normal Coordinate ◽  
Rigid Rotator ◽  
Gaseous State ◽  
Harmonic Oscillator Approximation ◽  
The One ◽  
Raman And Ir Spectra ◽  
The Ideal

The Raman and ir spectra of phosphoryl dichlorofluoride, phosphoryl difluorochloride, thiophosphoryl tribromide, thiophosphoryl dibromofluoride, and thiophosphoiyl difluorobromide were collected and examined for the most probable values for the wavenumbers, intensities, and depolarization factors. The data are as follows: The Raman displacements Δσ in cm−1, the relative intensities I, and the depolarization factors ρ are for POFCl2: Δσ ( I) ρ = 207(3.6)0.55, 254(1.8)6/7, 330(1)0.6, 372(3.4)6/7, 386(5.5)0.3, 547(10)0.05, 620( w)6/7, 894( w)0.45, and 1331 ( m) p; for POF2Cl: 274(10)0.65, 274 (calculated), 410(17)0.23, 424(7)6/7, 424 (calculated), 618(10)0.05, 895( m)0.1, 948( w>)6/7, and 1358( m)0.2; for PSBr3: 115(5.5)6/7, 165(4.1)0.3, 179(5)6/7, 299(10)0.05, 438( w)6/7, and 718 ( m) p; for PSFBr2:129(7)0.6, 159.5(11)6/7, 219(10)0.5, 254(4)6/7, 274(5)0.3, 377(10)0.2, 470( w)6/7, 718( m) p, and 887 ( vw) p; and for PSF2Br: 175(28)0.5, 231(3)6/7, 288(29)0.3, 298( w)6/7, 384(7)0.25, 462( w)0.1, 474(10)0.1, 711(9)0.1, 899( w)0.75, and 930( w)0.75. No published ir spectral data were found for POFCl2, POF2Cl, PSBr3, PSFBr2, and PSF2Br. Also normal coordinate treatments were conducted for POFCl2, POF2Cl, PSFBr2, and PSF2Br on the basis of the Cs model and the one for PSBr3 on the basis of the C3 v model. The results of these treatments established the above listed wavenumbers as fundamentals and lend support for 424 and 274 cm−1 bands for POF2Cl as the missing Raman bands. The F matrix elements obtained for these molecules were determined in such a way that F matrix elements common to POF3, POF2Cl, POFCl2, and POCl3 had nearly the same values and those common to PSF3, PSF2Br, PSFBr2, and PSBr3 also had nearly the same values. Finally, the values of the thermodynamic properties for these substances were computed for the ideal gaseous state using the rigid rotator harmonic oscillator approximation at 1 atm from 200 to 1000 K.

scholarly journals On the Complementarity of the Harmonic Oscillator Model and the Classical Wigner–Kirkwood Corrected Partition Functions of Diatomic Molecules

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 853
Author(s):  
Marcin Buchowiecki
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Harmonic Oscillator ◽  
High Temperatures ◽  
Low Temperatures ◽  
Diatomic Molecules ◽  
Partition Functions ◽  
Harmonic Oscillator Model ◽  
Harmonic Oscillator Approximation ◽  
Classical Partition Function

The vibrational and rovibrational partition functions of diatomic molecules are considered in the regime of intermediate temperatures. The low temperatures are those at which the harmonic oscillator approximation is appropriate, and the high temperatures are those at which classical partition function (with Wigner–Kirkwood correction) is applicable. The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.

scholarly journals The harmonic oscillator approximation to the density matrix

1979 ◽  
Vol 57 (11) ◽  
pp. 1990-1998 ◽  
Author(s):  
R. K. Bhaduri ◽  
L. F. Zaifman
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Numerical Comparisons ◽  
Isotropic Harmonic Oscillator ◽  
Matrix Expansion ◽  
Harmonic Oscillator Approximation ◽  
Spherical Nuclei ◽  
Special Case

The density matrix expansion for a system of nucleons moving in an isotropic harmonic oscillator potential is derived. This series is assumed to be a good approximation for the angle averaged density matrix of spherical nuclei, and is summed under a certain approximation. The form proposed by Campi and Bouyssy is obtained in our model as a special case. Other alternative forms are proposed and numerical comparisons are made using the Skyrme-III force.

Rotational Cut-Off and Anharmonicity Effects on Thermodynamic Properties of Gases at High Temperatures

1974 ◽  
Vol 25 (4) ◽  
pp. 287-292
Author(s):  
N M Reddy
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Harmonic Oscillator ◽  
Specific Heat ◽  
High Temperatures ◽  
Anharmonic Oscillator ◽  
Rigid Rotator ◽  
Temperature Range ◽  
Vibrational Levels ◽  
Harmonic Oscillator Approximation

SummaryThe exact expressions for the partition function Q and the coefficient of specific heat at constant volume Cv for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100°K to 100 000°K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigidrotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000°K for O2 and N2. Beyond these temperatures the error in Cv will be significant, owing to anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000°K.

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