Quantum statistical thermodynamics

The examples cited above are only two of the many possible cases of H-bond isomerization. Because of the low kinetic barriers separating these species, equilibration of H-bonded isomer populations to limiting thermodynamic values is generally expected to be much faster than for covalent isomers. Methods of quantum statistical thermodynamics can be used to calculate partition functions and equilibrium population distributions for H-bonded isomers,41 just as in the parallel case for covalent isomers and conformers. 

Figure 4.2. Variation of heat capacity with temperature as calculated from the equations of Frenkel et al. [4]. The differences observed between isotopic species and the way heat capacity depends on molecular size and structure can be described thermodynamically, but they must be explained by the methods of quantum-statistical thermodynamics. The right-hand scale is for H2 and D2 the left-hand scale is for the other compounds.

The rich metric structure of macroscopic thermodynamics also presents unusually stringent tests of theoretical models. Attempts to understand thermodynamic phenomena at a molecular level seem to demand improved dynamical and quantum statistical thermodynamic models that adequately incorporate the subtleties of quantum-mechanical valency and bonding interactions. Development of such models is an active area of modem physical chemistry research, but a more complete survey of the current molecular theory of gases and liquids is beyond the scope of the present work. 

QUANTUM STATISTICAL THERMODYNAMIC ORIGINS OF CHEMICAL AND PHASE THERMODYNAMICS... 

In the following, we first describe (Section 13.3.1) a statistical mechanical formulation of Mayer and co-workers that anticipated certain features of thermodynamic geometry. We then outline (Section 13.3.2) the standard quantum statistical thermodynamic treatment of chemical equilibrium in the Gibbs canonical ensemble in order to trace the statistical origins of metric geometry in Boltzmann s probabilistic assumptions. In the concluding two sections, we illustrate how modem ab initio molecular calculations can be enlisted to predict thermodynamic properties of chemical reaction (Sections 13.3.3) and cluster equilibrium mixtures (Section 13.3.4), thereby relating chemical and phase thermodynamics to a modem ab initio electronic stmcture picture of molecular and supramolecular interactions. 

Quantum Statistical Thermodynamics and the Statistical Origins of Metric Geometry... 

By considering the radiation as such a gas, the principles of quantum-statistical thermodynamics can be applied to derive an expression for the energy density of radiation per unit volume and per unit wavelength ast... 

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