Hydrogen bonds statistical mechanical approach

Besides this statistical mechanical approach to the question of helix stability, the problem has also been addressed by conformational energy calculations. First, the helix-breaking tendencies of such residues as serine and aspartic acid can be accounted for by the tendency toward formation of side chain-backbone hydrogen bonds in nonhelical conformations163 (Figures 20 and 21). Second, the free energies of the helical and statistical coil forms in water have... 

A new approach to the problem of clustering of particles (atoms or molecules) in condensed media has been applied to systems with hydrogen bonds. The aforementioned statistical mechanical approach has allowed us to investigate the spatial nonhomogeneous distribution of interacting particles starting from the initially homogeneous particle system. The major peculiarity of the concept is that it separates the paired potential to two independent... 

The fact that surfaces disrupt the natural order of a bulk phase serves as basis for Stillinger s attention to supercooling of water in small droplets or clusters [1]. His statistical mechanical approach to the structure of ice Ih and water as hydrogen-bonded in ordered and disordered polygonal structures, respectively, results in a qualitative estimate of the depression of temperature of maximum density. His approach also explains the behavior of supercooled water in terms of structural fluctuations in the bonded bicyclic octameric water network that represents ice Ih. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

In the next section we describe the most general approaches that are successfully employed at the theoretical study of the hydrogen behavior in compounds with hydrogen bonds. Then in the following sections we will show how some concrete problems are solved using methods developed in quantum mechanics, quantum field theory of solids, and statistical mechanics. 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

The molecular models adopt a statistical mechanical treatment of the adsorbed layer. In most cases a lattice structure is assumed and the differences of the various models lie in the effects on which the emphasis is put. There are two main molecular approaches one has been developed by Guidelli and his colleagues and the other is based on the LBS theory. Guidelli s approach emphasizes local order and hydrogen bonding among adsorbed water (solvent) molecules, whereas the models based on the LBS theory disregard local order and focus their attention on the polarizability of the adsorbed molecules. 

The problem that must be faced is how to evaluate 5gtr. On first consideration one might expect the deviation from Trouton s rule to be proportional to but unfortunately this describes the structure of the various liquids only at their respective boiling points, which may be markedly different from their structures at 25°C. Another approach would entail the use of the entropy of self-association of the various solvents in some inert solvent . This raises the question as to what is meant by an inert solvent , and in any event data are not presently available to make such calculations. A third method would be to calculate the difference in the experimentally measured entropy of vaporisation at 25°C and a statistical mechanical calculation in which hydrogen bonding and dipole-dipole interactions have been purposely neglected. To the knowledge of the authors no such calculations have been performed for these systems. 

Molecular sciences look for explanations of macroscopic properties, e.g., solubility, from the microscopic properties of matter. Statistical mechanics is one of such disciplines, which hnks those two pictures through the probabilistic treatment of particle ensembles. The application of Kirkwood s continuum solvent approach to nondissociating fluids resulted in a variety of simulation techniques. Applications of such techniques to study phase equilibria have been reported widely in literature [1-10]. Although some simple hydrocarbons can nowadays be reasonably well described by molecular modeling (molecular dynamics and Monte Carlo simulations), water and especially water mixtures, still represent challenges for such simulations techniques despite 30 years of active parameterization of appropriate force-fields. This is due to the extremely strong and complicated electrostatic and hydrogen-bond interactions. 

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