Solvation force constant

UCW = capped water, TW = tethered water (see text), k = force constant for restraining potential (kcal/mol/A2). b Radius (A) of solvation sphere. 1 Numbers of dynamical water molecules within solvation sphere. d Mean and standard error for the forward (i.e. 8-methyl-N5-deazapterin —> 8-methylpterin) and reverse mutation of the electrostatic force field Cutoff for protein-ligand and solvent-ligand interaction all other interactions are subject to a 9 A cutoff. 

Gas-phase solvation has so far given only very indirect evidence concerning the structure and details of molecular interactions in solvation complexes. Complex geometries and force constants, which are frequently subjects of theoretical calculations, must therefore be compared with solution properties, however, the relevant results are obscured by influences arising from changes in the bulk liquid or by the dynamic nature of the solvation shells. With few exceptions, structural information from solutions cannot be adequately resolved to yield more than a semiquantitative picture of individual molecular interactions. The concepts used to convert the complex experimental results to information for structural models are often those of solvation numbers 33>, and of structure-making or structure-... 

The same subdivision is used in the qualitative discussion of ionic solvation energies, and it is found that the outer-sphere part is satisfactorily predicted by electrostatic continuum theories (as reviewed in Section III), whereas the inner-sphere part is best obtained by considering the distortion of individual bonds, using force constants from vibrational spectroscopy. 

A linear relationship between log P s will exist if one of two requirements is met the primary solvation forces in the two solvent systems can be so similar that a variety of lipophilic and hydrophilic solute groups are accommodated proportionately, or the structural differences in the solute set being considered are such that one of the right hand terms in Equation 2 is essentially constant. The latter condition often applies to a homologous series where the hydrophilic group (an OH or C02H) contributes a constant component to the total transfer free energy. 

Sf/scwMb t)e calculated from Eq. (2.109) if v scw known. Waters that are not coordinated solvationally with the ion (NSCW) have as attractive force only an ion-induced dipole component (AW ,). Thus, the force constant k/ cw can be worked out by using Eqs. (2.111)-(2.114) ... 

Recendy, validity of the two assumptions regarding the free energy proflie, parabolic and solute independence of the force constants, has been examined by several authors. These assumptions have been predicted from the continuum dielecuic models and commonly adopted in many of the early works. Kakitani et alJ discussed the nonlinearity of solvation related to ET in polar solvents, and Carter and Hynes performed molecular dynamics simulations of the charge separation (CS) and the charge recombination (CR) reactions to observe such non-linear effects. More recently, Ando et alf discussed these problems and they observed no such non-linear effects. Due to the non-linear nature of the hypemetted chain (HNC) closure to solve the RISM equation, our method can shed light on the non-linearity of the free energy profiles. In section III, we apply our method, which is outlined briefly in section II, to the CS reaction which was previously studied by Carter and Hynes, and discuss the problems mentioned above based on the obtained free energy profiles. 

The quantity (FC) is the Franck-Condon factor it is a sum of products of overlap integrals of the vibrational and solvation wavefunctions of the reactants with those of the products, suitably weighted by Boltzmann factors. The value of the Franck-Condon factor may be expressed analytically by considering the effective potential energy curves, of both the initial and the final states, as a function of their nuclear configurations. Relatively simple relationships can be derived if the appropriate curves are harmonic with identical force constants. Under these conditions ... 

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