Quantum statistical mechanics molecular partition function

Thermodynamic properties of an assembly of many mutually independent molecules of the same kind are determined by one single quantity, the so called molecular partition function. The partition function is a statistical mechanics concept representing a link between microscopic and macroscopic thermodynamic properties. It enables the expression of the equilibrium constant in terms of energies of individual degrees of freedom for the molecules. The molecular partition function is defined as the sum over stationary quantum states of the molecules (numerated by i = 1,2,3,...) ... 

The computation of internal state densities and partition functions for polyatomic molecules is an essential task in the theoretical treatment of molecular gases. A first principles approach to the statistical thermodynamics of polyatomic gases requires the computation of the internal molecular energy levels based on an ab initio quantum mechanical (QM) determination of portions of the potential energy surface. Likewise, statistical theories of chemical reactions, such as Rice-Ramsberger-KasseUMarcus (RRKM) theory or transition state... 

The partition function is defined in terms of the different possible energies of the individual particles in a system. The developers of statistical thermodynamics derived their equations without an understanding of the quantum theory of nature. But now, we recognize that atomic and molecular behavior is described by quantum mechanics, and our development of statistical thermodynamics must recognize that. It is why we have put off a discussion of statistical thermodynamics until after our treatment of quantum mechanics. 

The introduction of coupled cluster theory into quantum chemistry is attributed to Cfzek who, in 1966, published a seminal paper [61] in the Journal of Chemical Physics entitled On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods. The theory uses an exponential ansatz which was originally employed in statistical mechanics to compute the partition function of a non... 

The connection between the quantum mechanical treatment of individual atoms and molecules and macroscopic properties and phenomena is the goal of statistical mechanical analysis. Statistical mechanics is the means for averaging contributions to properties and to energies over a large collection of atoms and molecules. The first part of the analysis is directed to the distribution of particles among available quantum states. An outcome of this analysis is the partition function, which proves to be an essential element in thermodynamics, in reaction kinetics, and in the intensity information of molecular spectra. 

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