The internal coordinate Morse oscillator as a means to simplify the anharmonicity problem in the thermodynamics of systems of polyatomic molecules

1977 ◽  
Vol 55 (12) ◽  
pp. 2292-2296 ◽  
Author(s):  
Jan Bron ◽  
R. Wallace
Keyword(s):  
Vibrational Energy ◽  
Algebraic Complexity ◽  
Morse Oscillator ◽  
Bond Stretching ◽  
Anharmonic Correction ◽  
Computer Calculations ◽  
Anharmonic Corrections ◽  
Vibrational Energies ◽  
Good Agreement ◽  
Anharmonicity Of Vibration

Two postulates simplify the evaluation and algebraic complexity of the expression for the anharmonic correction to the ground rotational–vibrational energy of a polyatomic molecule. The two postulates are: (1) anharmonicity of vibration is associated with bond stretching coordinates only; all other internal coordinates can be represented by harmonic potentials; (2) bonds vibrate according to a Morse potential. The result is the replacement of tedious computer calculations by a 'back of an envelope' type of computation. Relationships between anharmonic corrections to the ground state vibrational energies of isotopically different molecules are derived. Good agreement with exact results is obtained. Quantitative and qualitative applications are given.

scholarly journals Bound-state solutions and thermal properties of the modified Tietz–Hua potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
M. C. Onyeaju ◽  
E. Omugbe ◽  
I. B. Okon ◽  
O. E. Osafile
Keyword(s):  
Thermal Properties ◽  
Vibrational Energy ◽  
Approximate Solutions ◽  
Bound State ◽  
Effect Of Temperature ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Vibrational Energies ◽  
Good Agreement ◽  
Supersymmetric Approach

AbstractAn approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

VIBRATIONAL ENERGIES OF MEMBERS IN STRUCTURAL NETWORKS FITTED WITH TUNED VIBRATION ABSORBERS

2006 ◽  
Vol 06 (02) ◽  
pp. 269-284 ◽  
Author(s):  
SUNNY K. GEORGE ◽  
K. SHANKAR
Keyword(s):  
Energy Level ◽  
Vibrational Energy ◽  
General Structure ◽  
Energy Levels ◽  
Complex Structure ◽  
Input Power ◽  
Vibration Absorbers ◽  
Tuned Vibration Absorbers ◽  
Vibrational Energies ◽  
Structural Networks

The distribution of vibrational energy in members of a complex structure with tuned absorbers attached at the joints and subjected to dynamic loading is studied. The concept of power flows through the structure is used to determine the time-averaged energy levels of each member in the structure. The power flows are calculated using the time-averaged product of force and velocity at the input and coupling points (joints) of a general structure made of axially vibrating rods. The receptance approach is used to calculate the coupling forces and velocities in the structure. By balancing the input power against the dissipated powers, the time-averaged energy levels in members are determined. The main criteria studied here is the reduction in the frequency-averaged vibrational energy level of a member when an absorber is attached, expressed as a percentage compared to the case where there are no absorbers. The concept is first illustrated with a simple model of 2 axially vibrating rods with an absorber attached to the joint. Next, a more complex structure comprising 8 rods with arbitrary orientations and several absorbers attached to junctions is studied. The effect of activating absorbers at various locations on reducing the energy levels of certain members is examined. It is possible to estimate the usefulness of the absorber with respect to any member by determining the percentage reduction of energy level for that member.

Contributions to Silicon-Hydrogen Bond-Stretching Frequency in Amorphous Si Alloys

1992 ◽  
Vol 258 ◽  
Author(s):  
Z. Jing ◽  
J. L. Whitten ◽  
G. Lucovsky
Keyword(s):  
Experimental Data ◽  
Hydrogen Bond ◽  
Dielectric Constant ◽  
Ab Initio ◽  
Effective Dielectric Constant ◽  
Bond Energies ◽  
Calculated Frequency ◽  
Bond Stretching ◽  
Amorphous Si ◽  
Good Agreement

ABSTRACTWe have performed ab initio calculations and determined the bond-energies and vibrational frequencies of Si-H groups that are: i) attached to Si-atoms as their immediate, and also more distant neighbors; and ii) attached to three O-atoms as their immediate neighbors, but are connected to an all Si-atom matrix. These arrangements simulate bonding geometries on Si surfaces, and the calculated frequency for i) is in good agreement with that of an Si-H group on an Si surface. To compare these results with a-Si:H alloys it is necessary to take into account an additional factor: the effective dielectric constant of the host. We show how to do this, demonstrating the way results of the ab initio calculations should then be compared with experimental data.

scholarly journals Structural elastic and thermal properties of SrxCd1−x O mixed compounds — a theoretical approach

2014 ◽  
Vol 32 (3) ◽  
pp. 350-357
Author(s):  
Purvee Bhardwaj
Keyword(s):  
Phase Transition ◽  
Vibrational Energy ◽  
Zero Point ◽  
Study Phase ◽  
Energy Effect ◽  
Phase Transition Pressure ◽  
Vegard’S Law ◽  
Extended Interaction ◽  
Experimental Values ◽  
Good Agreement

AbstractIn the present paper, the structural and mechanical properties of alkaline earth oxides mixed compound SrxCd1−x O (0 ≤ x ≤ 1) under high pressure have been reported. An extended interaction potential (EIP) model, including the zero point vibrational energy effect, has been developed for this study. Phase transition pressures are associated with a sudden collapse in volume. Phase transition pressure and associated volume collapses [ΔV (Pt)/V(0)] calculated from this approach are in good agreement with the experimental values for the parent compounds (x = 0 and x = 1). The results for the mixed crystal counterparts are also in fair agreement with experimental data generated from the application of Vegard’s law to the data for the parent compounds.

scholarly journals Resolving the mesospheric nighttime 4.3 µm emission puzzle: comparison of the CO<sub>2</sub>(<i>ν</i><sub>3</sub>) and OH(<i>ν</i>) emission models

2017 ◽  
Vol 17 (16) ◽  
pp. 9751-9760 ◽  
Author(s):  
Peter A. Panka ◽  
Alexander A. Kutepov ◽  
Konstantinos S. Kalogerakis ◽  
Diego Janches ◽  
James M. Russell ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Vibrational Energy ◽  
Lower Thermosphere ◽  
Vibrational Energy Relaxation ◽  
Density Distributions ◽  
Direct Mechanism ◽  
Vibrational Levels ◽  
Emission Models ◽  
The Impact ◽  
Good Agreement

Abstract. In the 1970s, the mechanism of vibrational energy transfer from chemically produced OH(ν) in the nighttime mesosphere to the CO2(ν3) vibration, OH(ν) ⇒ N2(ν) ⇒ CO2(ν3), was proposed. In later studies it was shown that this "direct" mechanism for simulated nighttime 4.3 µm emissions of the mesosphere is not sufficient to explain space observations. In order to better simulate these observations, an additional enhancement is needed that would be equivalent to the production of 2.8–3 N2(1) molecules instead of one N2(1) molecule in each quenching reaction of OH(ν) + N2(0). Recently a new "indirect" channel of the OH(ν) energy transfer to N2(ν) vibrations, OH(ν) ⇒ O(1D) ⇒ N2(ν), was suggested and then confirmed in a laboratory experiment, where its rate for OH(ν = 9) + O(3P) was measured. We studied in detail the impact of the "direct" and "indirect" mechanisms on CO2(ν3) and OH(ν) vibrational level populations and emissions. We also compared our calculations with (a) the SABER/TIMED nighttime 4.3 µm CO2 and OH 1.6 and 2.0 µm limb radiances of the mesosphere–lower thermosphere (MLT) and (b) with ground- and space-based observations of OH(ν) densities in the nighttime mesosphere. We found that the new "indirect" channel provides a strong enhancement of the 4.3 µm CO2 emission, which is comparable to that obtained with the "direct" mechanism alone but assuming an efficiency that is 3 times higher. The model based on the "indirect" channel also produces OH(ν) density distributions which are in good agreement with both SABER limb OH emission observations and ground and space measurements. This is, however, not true for the model which relies on the "direct" mechanism alone. This discrepancy is caused by the lack of an efficient redistribution of the OH(ν) energy from higher vibrational levels emitting at 2.0 µm to lower levels emitting at 1.6 µm. In contrast, the new  indirect  mechanism efficiently removes at least five quanta in each OH(ν ≥ 5) + O(3P) collision and provides the OH(ν) distributions which agree with both SABER limb OH emission observations and ground- and space-based OH(ν) density measurements. This analysis suggests that the important mechanism of the OH(ν) vibrational energy relaxation in the nighttime MLT, which was missing in the emission models of this atmospheric layer, has been finally identified.

A nuclear phenomenological study of the even–even Thorium Isotopes 228–232Th

2018 ◽  
Vol 27 (05) ◽  
pp. 1850040 ◽  
Author(s):  
S. B. Doma ◽  
H. S. El-Gendy
Keyword(s):  
Potential Energy Surfaces ◽  
Phenomenological Study ◽  
Transition Probability ◽  
Phenomenological Approach ◽  
Vibrational Energies ◽  
Boson Model ◽  
Electric Transition ◽  
Energy Surfaces ◽  
Good Agreement ◽  
Thorium Isotopes

The rotational and vibrational energies and the electric transition probability B [Formula: see text] of the even–even [Formula: see text]Th isotopes are studied empirically in framework of a nuclear phenomenological approach by using the SU(3) dynamical symmetries of the Interacting Boson Model-1 (IBM-1). Furthermore, the potential energy surfaces for these isotopes are plotted as functions of the deformation parameters [Formula: see text] and [Formula: see text]. Moreover, we introduce empirical fit formulas for rotational and vibrational energies, which used to calculate these energies for the thorium isotopes. The obtained results by applying the IBM-1 and the authors’ formulas are in good agreement with the corresponding experimental data for most of the nuclear states.

OH A2Σ+ –X2Π band ratios observed in the mesosphere by OSIRIS

2008 ◽  
Vol 86 (7) ◽  
pp. 857-862 ◽  
Author(s):  
R L Gattinger ◽  
D A Degenstein ◽  
E J Llewellyn ◽  
M H Stevens
Keyword(s):  
Infrared Imaging ◽  
Vibrational Energy ◽  
Imaging System ◽  
Band System ◽  
Resonance Fluorescence ◽  
Model Predictions ◽  
Spectral Components ◽  
Band Ratios ◽  
Good Agreement

In this study, we present spectra of the mesospheric OH A2Σ+ –X2Π band system, including the 0–0, 1–1, and 1–0 bands, as observed by OSIRIS (Optical Spectrograph and Infrared Imaging System). Spectral components due to Rayleigh-scattered sunlight, lower thermospheric dayglow emission features, and baffle scatter have been removed to isolate the OH emission signature. The observed spectra are compared with model spectra assembled using rotational emission rate factors for solar resonance fluorescence (g-factors) plus prompt emission of the OH A2Σ+ –X2Π band system from solar Lyman-α photodissociation of water. The observed band ratios are in good agreement with the model values. The altitude variation of the 0–0 band, relative to the 1–1 band, is in agreement with model predictions based on vibrational energy transfer from OH A2Σ+ ν′ = 1 to OH A2Σ+ ν′ = 0. This detailed understanding of the OH A2Σ+ –X2Π system is critical for the successful application of OH observations to the determination of mesospheric OH densities and water vapor concentrations.PACS Nos.: 33.20.Lg, 33.20.Tp, 33.70.Fd, 92.60.hc, 92.60.hw

Diatomic molecules energy spectra for the generalized Mobius square potential model

2020 ◽  
Vol 34 (21) ◽  
pp. 2050209
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
M. U. Ibezim-Ezeani ◽  
Hewa Y. Abdullah
Keyword(s):  
Dissociation Energy ◽  
Approximation Scheme ◽  
Potential Model ◽  
Vibrational Energy ◽  
Diatomic Molecules ◽  
Energy Spectra ◽  
Equilibrium Bond Length ◽  
Quantum Numbers ◽  
Vibrational Energies ◽  
Potential Parameters

The modified version of the generalized Mobius square (GMS) potential has been obtained by employing the dissociation energy and equilibrium bond length as explicit parameters. The potential parameters have been defined in terms of the molecular parameters. The modified GMS potential has also been used to model internuclear interaction potential curves for different states of diatomic molecules. Also, we have obtained the rotational–vibrational energy spectra of the new GMS potential model, both analytically and numerically for the different diatomic molecules. This was done by employing a Pekeris-type approximation scheme and an appropriate coordinate transformation to solve the Schrodinger equation. Our results have been compared with the experimental Rydberg–Klein–Rees (RKR) data and its corresponding average absolute deviations in terms of the dissociation energy computed. The effects of the vibrational and rotational quantum numbers on the rotational–vibrational energies for the different states of the various diatomic molecules have also been discussed. This paper has shown to be highly relevant to the studies of thermodynamic and thermochemical functions of diatomic molecules.

VIBRATING NEUTRON STARS

1967 ◽  
Vol 45 (9) ◽  
pp. 2823-2831 ◽  
Author(s):  
Carl J. Hansen ◽  
Sachiko Tsuruta
Keyword(s):  
Neutron Stars ◽  
Storage Capacity ◽  
Vibrational Energy ◽  
Crab Nebula ◽  
X Rays ◽  
Vibrational Heating ◽  
Large Spread ◽  
Vibrational Energies ◽  
The Crab Nebula ◽  
Urca Process

The time variation of some interesting properties of vibrating neutron stars is considered. The models used are based on two nuclear potentials that cover a large spread of possibilities. The modified URCA neutrino process has been assumed to be the major damping mechanism. The calculations are performed both for the case when the vibration energy is partially converted into heat through the URCA process and for the case when this conversion does not take place. It is found that the vibrational energy-storage capacity is extremely model-dependent. The vibrational energies at 1 000 years range from about 1047 to 1050 ergs, which are sufficiently large as a possible energy source for the X rays from the Crab Nebula, ft is shown also that the cooling times of neutron stars will not be significantly increased by the inclusion of the vibrational heating.

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