Configurational density functions determination

Equation (4.65) or (4.68), originally due to Green (see Refs. 9 and 10), is the desired result for the entropy in pairwise additive systems. The essential problem then is to determine the two-particle configurational density function from the solution to Eq. (4.52). However, to simply illustrate numerical calculations, we first consider the dilute gas system. 

The electronic wave function of an n-electron molecule is defined in 3n-dimensional configuration space, consistent with any conceivable molecular geometry. If the only aim is to characterize a molecule of fixed Born-Oppenheimer geometry the amount of information contained in the molecular wave function is therefore quite excessive. It turns out that the three-dimensional electron density function contains adequate information to uniquely determine the ground-state electronic properties of the molecule, as first demonstrated by Hohenberg and Kohn [104]. The approach is equivalent to the Thomas-Fermi model of an atom applied to molecules. 

The majority of the molecular-scale information concerning the effects of structure and local chemistry on proton dissociation and separation in PEM fragments alluded to previously " were initially determined using HE theory and split valence local basis sets. Refinements to the equilibrium configurations were made using both Mailer-Plesset (MP) perturbation schemes and hybrid density functional theory (described below). 

Wang and Rikvold [60] have applied ab initio total-energy density-functional methods in combination with supercell models to calculate the c(2 x 2) structure of bromide adsorbed on Au(lOO) and Ag(lOO) surfaces. The preferred bonding sites have been determined. The calculations have shown that bromide favorably binds the bridge site on the Au(lOO) surfaces. These results explain experimental observations that adsorption of bromide on the Au(lOO) and Ag( 100) surfaces proceeds via different bonding configurations. 

Stephens PJ, Pan JJ, Krohn K. Determination of the Absolute Configurations of Pharmacological Natural Products via Density Functional Theory Calculations of Vibrational Circular Dichroism The New Cytotoxic Iridoid Piismatomerin. Journal of Organic Chemistry 2007 72(20) 7641-7649. 

The statistical behavior of interest is encapsulated in the equilibrium probability density function P )( q c). This PDF is determined by an appropriate ensemble-dependent, dimensionless [6] configurational energy 6( q, c). The relationship takes the generic form... 

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