A new approach to the exact and approximate anharmonic vibrational partition function of diatomic and polyatomic molecules utilizing Morse and Rosen-Morse oscillators

2011 ◽  
Vol 111 (9) ◽  
pp. 1885-1892 ◽  
Author(s):  
Mohamad Toutounji
Keyword(s):  
Partition Function ◽  
Polyatomic Molecules ◽  
New Approach ◽  
Morse Oscillators ◽  
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.

scholarly journals UNITARY MATRIX INTEGRALS IN THE FRAMEWORK OF THE GENERALIZED KONTSEVICH MODEL

1996 ◽  
Vol 11 (28) ◽  
pp. 5031-5080 ◽  
Author(s):  
A. MIRONOV ◽  
A. MOROZOV ◽  
G. W. SEMENOFF
Keyword(s):  
Partition Function ◽  
External Field ◽  
Matrix Models ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Unitary Matrix ◽  
Simple Method ◽  
Generating Functional ◽  
New Approach ◽  
Matrix Integrals

We advocate a new approach to the study of unitary matrix models in external fields which emphasizes their relationship to generalized Kontsevich models (GKM's) with nonpolynomial potentials. For example, we show that the partition function of the Brezin–Gross–Witten model (BGWM), which is defined as an integral over unitary N × N matrices, [Formula: see text], can also be considered as a GKM with potential [Formula: see text]. Moreover, it can be interpreted as the generating functional for correlators in the Penner model. The strong and weak coupling phases of the BGWM are identified with the "character" (weak coupling) and "Kontsevich" (strong coupling) phases of the GKM, respectively. This type of GKM deserves classification as a p = −2 model (i.e. c = 28 or c = −2) when in the Kontsevich phase. This approach allows us to further identify the Harish-Chandra–Itzykson–Zuber integral with a peculiar GKM, which arises in the study of c = 1, theory, and, further, with a conventional two-matrix model which is rewritten in Miwa coordinates. Some further extensions of the GKM treatment which are inspired by the unitary matrix models which we have considered are also developed. In particular, as a by-product, a new, simple method of fixing the Ward identities for matrix models in an external field is presented.

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