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 DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

2016 ◽  
Vol 4 (2) ◽  
pp. 179
Author(s):  
R. Yosi Aprian Sari ◽  
W. S. B. Dwandaru
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Canonical Partition Function ◽  
Thermodynamics Properties ◽  
Grand Canonical Partition Function ◽  
Bose Einstein ◽  
Grand Canonical ◽  
Number Of Particles

This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties

Introduction

1984 ◽  
Author(s):  
C. G. Gray ◽  
K. E. Gubbins
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Great Accuracy ◽  
Perfect Gas ◽  
Mathematical Basis ◽  
Virial Series ◽  
Simple Molecules

The application of statistical mechanics to the study of fluids over the past fifty years † or so has progressed through a series of problems of gradually increasing difficulty. The first and most elementary calculations were for the thermodynamic functions (heat capacities, entropies, free energies, etc.) of perfect gases. These properties are related to the molecular energy levels, which for perfect gases can be determined theoretically (by quantum calculations) or experimentally (by spectroscopic methods, for example). For simple molecules (CO2 , CH4 , etc.) the energy levels, and hence the thermodynamic properties, can be determined with great accuracy, and even for quite complex organic molecules it is now possible to obtain thermodynamic properties with satisfactory accuracy. With the advent of digital computers it became possible to calculate thermodynamic properties for a wide variety of substances and temperatures, and several useful tabulations of perfect gas properties now exist. Having successfully treated the perfect gas, it was natural to consider gases of moderate density, where intermolecular forces begin to have an effect, by expanding the thermodynamic functions in a power series (or virial series) in density. Although the mathematical basis for a theoretical treatment of this series was laid by Ursell in 1927, it was not exploited until ten years later, when Mayer re-examined the problem. Since that time a great deal of effort has been put into evaluating the virial coefficients that appear in the series for a variety of intermolecular force models. As the expressions for the virial coefficients are exact, they provide a very useful means of checking such force models by comparison of calculated and experimental coefficients. While the theory of dilute gases at equilibrium is essentially complete, this is far from being the case for all dense gases and liquids. The virial series cannot be applied directly to liquids. As an alternative to the ‘dense gas’ approach to liquids, there were early attempts to treat liquids as disordered solids by using cell or lattice theories; these were popular from the mid-1930s until the early 1960s.

Spectroscopy

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Condensed Phase ◽  
Molecular Spectroscopy ◽  
Fundamental Problem ◽  
Optical Transition ◽  
Energy Levels ◽  
Quantum Statistical Mechanics ◽  
Potential Surfaces ◽  
Molecular Systems ◽  
Matter Interaction ◽  
Particle Level

The interaction of light with matter provides some of the most important tools for studying structure and dynamics on the microscopic scale. Atomic and molecular spectroscopy in the low pressure gas phase probes this interaction essentially on the single particle level and yields information about energy levels, state symmetries, and intramolecular potential surfaces. Understanding environmental effects in spectroscopy is important both as a fundamental problem in quantum statistical mechanics and as a prerequisite to the intelligent use of spectroscopic tools to probe and analyze molecular interactions and processes in condensed phases. Spectroscopic observables can be categorized in several ways. We can follow a temporal profile or a frequency resolved spectrum; we may distinguish between observables that reflect linear or nonlinear response to the probe beam; we can study different energy domains and different timescales and we can look at resonant and nonresonant response. This chapter discusses some concepts, issues, and methodologies that pertain to the effect of a condensed phase environment on these observables. For an in-depth look at these issues the reader may consult many texts that focus on particular spectroscopies. With focus on the optical response of molecular systems, effects of condensed phase environments can be broadly discussed within four categories: 1. Several important effects are equilibrium in nature, for example spectral shifts associated with solvent induced changes in solute energy levels are equilibrium properties of the solvent–solute system. Obviously, such observables may themselves be associated with dynamical phenomena, in the example of solvent shifts it is the dynamics of solvation that affects their dynamical evolution. Another class of equilibrium effects on radiation– matter interaction includes properties derived from symmetry rules. A solvent can affect a change in the equilibrium configuration of a chromophore solute and consequently the associated selection rules for a given optical transition. Some optical phenomena are sensitive to the symmetry of the environment, for example, surface versus bulk geometry. 2. The environment affects the properties of the radiation field; the simplest example is the appearance of the dielectric coefficient ε in the theory of radiation–matter interaction.

DERIVATIVES OF MONOGERMANE: PART I. THE VIBRATION–ROTATION SPECTRA OF GERMYL FLUORIDE AND BROMIDE

1962 ◽  
Vol 40 (4) ◽  
pp. 579-589 ◽  
Author(s):  
J. E. Griffiths ◽  
T. N. Srivastava ◽  
M. Onyszchuk
Keyword(s):  
Harmonic Oscillator ◽  
Infrared Absorption ◽  
Thermodynamic Functions ◽  
Low Frequency ◽  
Rotational Constant ◽  
Rigid Rotator ◽  
Harmonic Oscillator Model ◽  
Infrared Absorption Spectra ◽  
Vibration Rotation ◽  
Derivatives Of

The vibration–rotation infrared absorption spectra of germyl fluoride and bromide have been observed. All of the fundamentals in GeH3F were located, and the rotational structure of the E-type bands were resolved and analyzed. The low-frequency band, ν3(a1), in GeH3Br was not observed but an estimate of its position was made from the frequencies of the combination band ν3 + ν6 and of ν6. The rotational constant A″ and the Coriolis constants ζ4, ζ5, and ζ6 were calculated for both molecules, and agreement with microwave A″ values was satisfactory. Thermodynamic functions based upon a rigid-rotator, harmonic-oscillator model have been evaluated for germyl fluoride and bromide.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Semiclassical energy levels for linear molecules

1978 ◽  
Vol 35 (3) ◽  
pp. 649-663 ◽  
Author(s):  
I.C. Percival ◽  
N. Pomphrey
Keyword(s):  
Energy Levels ◽  
Linear Molecules
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