Entropy density functional theory

This so-called Hirshfeld scheme is particularly popular within the so-called conceptual density functional theory (DFT) [26,27], The weighting function, which identifies the AIM as one that is most similar to the isolated atom [28], has been shown to be directly derivable from information entropy [6,29-33]. Here again, the atoms do not... 

The effects of the solvent and finite temperature (entropy) on the Wittig reaction are studied by using density functional theory in combination with molecular dynamics and a continuum solvation model.21 The introduction of the solvent dimethyl sulfoxide causes a change in the structure of the intermediate from the oxaphosphetane structure to the dipolar betaine structure. 

The reactions for which thermochemical properties of transition states are calculated by ab initio or Density Functional Theory methods, oo s are fit by three parameters n, and over the temperature range of 298-2000 K, kao = A T)T exp( a/ 7). Entropy differences between the reactants and transition state structures are used to determine the pre-exponential factor. A, via canonical Transition State Theory [197]. 

Entropies and heat capacities are estimated from Density Functional Theory calculations data, and compared with Groups Additivity (GA) estimations. The group needed to estimate the enthalpies of formation, the entropies and the heat capacities of these species were developed in a previous chapter. These groups were estimated from a series of calculated oxygenated hydrocarbons and reported in chapter 4. 

Abstract. Onsager s paper on the effect of shape on the interaction of colloidal particles is seminal in many ways. I shall focus on two aspects it is (to my knowledge) the earliest classical density functional theory, and it demonstrates the possibility of ordering transitions driven by entropy... 

Coupled cluster and DFT (density functional theory) computations for the permanganate oxidation of sulfides and sulfoxides indicated a [l,3]-dipolar cycloaddition of permanganate (Scheme 1), as opposed to earlier mechanisms involving attack of the sulfur atom by one of the oxygens or by manganese. The ab initio activation enthalpies are in reasonable agreement with the experimental data, but the ab initio activation entropies are not. " ... 

Quantum chemistry approaches, such as density functional theory (DFT), can be used within the framework of microkinetic modeling to estimate thermochemical parameters, like enthalpies and entropies, as well as kinetic parameters like activation energies and frequency factors of chemical reactions. Some examples of the values of pre-exponential factors for different types of surface reactions are presented in Table 3.4. The appealing feature of DFT is in the description of the system of interacting fermions by their density rather than through its many-body wave function, lowering substantially the computational cost. 

In this review, we begin with a treatment of the functional theory employing as basis the maximum entropy principle for the determination of the density matrix of equilibrium ensembles of any system. This naturally leads to the time-dependent functional theory which will be based on the TD-density matrix which obeys the von Neumann equation of motion. In this way, we present a unified formulation of the functional theory of a condensed matter system for both equilibrium and non-equilibrium situations, which we hope will give the reader a complete picture of the functional approach to many-body interacting systems of interest to condensed matter physics and chemistry. 

Collins, D. M. Extrapolative filtering. I. Maximization of resolution for onedimensional positive density functions. Acta Cryst. A34, 533-541 (1978). Bricogne, G. A Bayesian statistical theory of the phase problem. I. A multichannel maximum-entropy formalism for constructing generalized joint probability distributions of structure factors. Acta Cryst. A44, 517-545 (1988). 

In modem physics, there exist alternative theories for the equilibrium statistical mechanics [1, 2] based on the generalized statistical entropy [3-12]. They are compatible with the second part of the second law of thermodynamics, i.e., the maximum entropy principle [13-14], which leads to uncertainty in the definition of the statistical entropy and consequently the equilibrium probability density functions. This means that the equilibrium statistical mechanics is in a crisis. Thus, the requirements of the equilibrium thermodynamics shall have an exclusive role in selection of the right theory for the equilibrium statistical mechanics. The main difficulty in foundation of the statistical mechanics based on the generalized statistical entropy, i.e., the deformed Boltzmann-Gibbs entropy, is the problem of its connection with the equilibrium thermodynamics. The proof of the zero law of thermodynamics and the principle of additivity... 

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