The classical partition function of a bound three-particle cluster

2001 ◽  
Vol 99 (18) ◽  
pp. 1563-1567 ◽  
Author(s):  
JOHN S. DAHLER
Keyword(s):  
Partition Function ◽  
Particle Cluster ◽  
Classical Partition Function

A REMARK ON PRIME DIVISORS OF PARTITION FUNCTIONS

2014 ◽  
Vol 10 (01) ◽  
pp. 125-131
Author(s):  
PAUL POLLACK
Keyword(s):  
Partition Function ◽  
Wide Class ◽  
Analogous Result ◽  
Partition Functions ◽  
Prime Divisors ◽  
Classical Partition Function

Schinzel showed that the set of primes that divide some value of the classical partition function is infinite. For a wide class of sets 𝒜, we prove an analogous result for the function p𝒜(n) that counts partitions of n into terms belonging to 𝒜.

Thermodynamic Functions of Pendular Molecules

1993 ◽  
Vol 58 (10) ◽  
pp. 2458-2473 ◽  
Author(s):  
Břetislav Friedrich ◽  
Dudley R. Herschbach
Keyword(s):  
Partition Function ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Quantum Statistical Mechanics ◽  
Rotational Constant ◽  
Chemical Equilibria ◽  
Rotational States ◽  
Dipolar Molecules ◽  
Linear Molecules ◽  
Classical Partition Function

External electric or magnetic fields can hybridize rotational states of individual dipolar molecules and thus create pendular states whose field-dependent eigenproperties differ qualitatively from those of a rotor or an oscilator. The pendular eigenfunctions are directional, so the molecular axis id oriented. Here we use quantum statistical mechanics to evaluate ensamble properties of the pendular states. For linear molecules, the partition function and the averages that determine the thermodynamic functions can be specified by two reduced variables involving the dipole moment, field strength, rotational constant, and temperature. We examine a simple approximation due to Pitzer that employs the classical partition function with quantum corrections. This provides explicit analytic formulas which permit thermodynamic properties to be evaluated to good accuracy without computing energy levels. As applications we evaluate the high-field average orientation of the molecular dipoles and field-induced shifts of chemical equilibria.

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.

Classical partition function ofN interacting particles in the new statistical mechanics

1981 ◽  
Vol 30 (14) ◽  
pp. 432-434 ◽  
Author(s):  
A. Jannussis ◽  
A. Leodaris ◽  
G. Brodimas ◽  
V. Papatheou ◽  
K. Vlachos
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Interacting Particles ◽  
Classical Partition Function
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