ISOMERISM AND THE VIBRATIONAL PARTITION FUNCTION OF VERY SMALL ATOMIC MICROCRYSTALLITES

1977 ◽  
Vol 38 (C2) ◽  
pp. C2-55-C2-55
Author(s):  
J. A. McINNES
Keyword(s):  
Partition Function ◽  
Vibrational Partition Function

RO-VIBRATIONAL PARTITION FUNCTION AND MEAN THERMAL ENERGY OF THE IMPROVED WEI OSCILLATOR

2021 ◽  
Vol 5 (1) ◽  
pp. 261-270
Author(s):  
Bako M. Bitrus ◽  
C. M. Nwabueze ◽  
J. U. Ojar ◽  
E. S. Eyube
Keyword(s):  
Partition Function ◽  
Potential Energy ◽  
Thermal Energy ◽  
Vibrational Energy ◽  
Sharp Decrease ◽  
Bound State ◽  
Solid State Physics ◽  
Absolute Deviation ◽  
Potential Energy Functions ◽  
Vibrational Partition Function

In this paper, the improved Wei oscillator has been used to model the experimental Rydberg-Klein-Rees data of the X2 Σg+ state of N2+ diatomic ions. Average absolute deviation from the dissociation energy of 0.3211% and mean absolute percentage deviation of 0.6107% were obtained. These results are quite satisfactory since they are within error requirement rate of less than 1% of the Lippincott’s criterion. Using an existing equation in the literature for bound state ro-vibrational energy, expressions for ro-vibrational partition function and mean thermal energy were derived for the improved Wei oscillator within the context of classical physics. The formulas obtained for ro-vibrational partition function and mean thermal energy were subsequently applied to the spectroscopic data of N2+ (X2 Σg+) diatomic ions. Studies have revealed that the partition function of the system decreases monotonically with decrease in temperature and increases with increase in upper bound vibrational quantum number. On the other hand, the mean thermal energies of the diatomic ions show an initial sharp decrease when the temperature is decreased and afterwards remains fairly stable as the temperature is further lowered. The results obtained in this work may find suitable applications in astrophysics were potential energy functions are required to model experimentally determined potential energy data with high precision. The work may also be useful in many other areas of physics which include: chemical physics, molecular physics, atomic physics and solid-state physics

Quantum vibrational partition function in the non-extensive Tsallis framework

2010 ◽  
Vol 389 (14) ◽  
pp. 2733-2738 ◽  
Author(s):  
Ezat Keshavarzi ◽  
Mozhgan Sabzehzari ◽  
Mehdi Eliasi
Keyword(s):  
Partition Function ◽  
Vibrational Partition Function

Approximate energy spectra and statistical mechanical functions of some diatomic molecular hydrides

2021 ◽  
pp. 1-6
Author(s):  
A.N. Ikot ◽  
U.S. Okorie ◽  
G.J. Rampho ◽  
Hewa Y. Abdullah
Keyword(s):  
Mechanical Properties ◽  
Partition Function ◽  
Thermodynamic Functions ◽  
Potential Model ◽  
Energy Spectra ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Statistical Mechanical ◽  
Vibrational Partition Function ◽  
Maclaurin Formula

In this study, we have investigated the statistical mechanical properties of the Varshni potential model for some diatomic molecular hydrides via the Euler–Maclaurin formula. This was done using the approximate analytical energy eigenvalues, which were obtained by solving the radial Schrödinger equation with the Greene–Aldrich approximation and suitable coordinate transformation schemes. The effect of high temperatures and upper bound vibration quantum number on the vibrational partition function and other thermodynamic functions of the selected diatomic molecular hydrides were studied. We also show that these effects on the thermodynamic functions considered were similar for all the diatomic molecular hydrides selected.

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