Solvation in a continuum dielectric environment

Solvation in a continuum dielectric environment 15.2.1 General observations... 

The continuum dielectric theory used above is a linear response theory, as expressed by the linear relation between the perturbation T> and the response , Eq. (15.1b). Thus, our treatment of solvation dynamics was done within a linear response framework. Linear response theory of solvation dynamics may be cast in a general form that does not depend on the model used for the dielectric environment and can therefore be applied also in molecular (as opposed to continuum) level theories. Here we derive this general formalism. For simplicity we disregard the fast electronic response of the solvent and focus on the observed nuclear dielectric relaxation. 

For many chemical problems, it is crucial to consider solvent effects. This was demonstrated in our recent studies on the hydration free energy of U02 and the model reduction of uranyl by water [232,233]. The ParaGauss code [21,22] allows to carry out DKH DF calculations combined with a treatment of solvent effects via the self-consistent polarizable continuum method (PCM) COSMO [227]. If one aims at a realistic description of solvated species, it is not sufficient to represent an aqueous environment simply as a dielectric continuum because of the covalent nature of the bonding between an actinide and aqua ligands [232]. Ideally, one uses a combination model, in which one or more solvation shells (typically the first shell) are treated quantum-mechanically, while long-range electrostatic and other solvent effects are accounted for with a continuum model. Both contributions to the solvation free energy of U02 were... 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

Solvent interactions in the present study have been calculated by following the approach of Sinanoglu [2] who separates mathematically the solvation energies into two parts or steps. In the first step a hole is prepared in the liquid. In the second step a solute molecule is placed in the hole and interacts with its new environment. In calculating the interaction energy of the solute molecule with its environment the concept of continuum reaction field of Onsager [24] has been applied. The solvent is considered as a continuum which possesses the macroscopic dielectric properties of the solution, which coincide with those of a pure liquid in the case of a dilute solution. A fuller description of the theory and computational details will be presented in Section 2.2 and in Section 3. Our procedure differs from that presented by Sinanoglu [2] in the calculation of dispersion interaction, which follows the method developed by Linder [25], which takes into account many body effects and thermodynamic fluctuations. The calculational scheme has been already applied by Nir [26] for the... 

An accurate description of the aqueous environment is essential for atom-level biomolec-ular simulations, but may become very expensive computationally. An imphcit model replaces the discrete water molecules by an infinite continuum medium with some of the dielectric and hydrophobic properties of water. The continuum implicit solvent models have several advantages over the explicit water representation, especially in molecular dynamics simulations (e.g., they are often less expensive, and generally scale better on parallel machines they correspond to instantaneous solvent dielectric response the continuum model corresponds to solvation in an infinite volume of solvent, there are no artifacts of periodic boundary conditions estimating free energies of solvated structares is much more straightforward than with explicit water models). Despite the fact that the methodology represents an approximation at a fundamental level, it has in many cases been successful in calculating various macromolecular properties (Case et al. 2005). 

Many of the available computations on radicals are strictly applicable only to the gas phase they do not account for any medium effects on the molecules being studied. However, in many cases, medium effects cannot be ignored. The solvated electron, for instance, is all medium effect. The principal frameworks for incorporating the molecular environment into quantum chemistry either place the molecule of interest within a small cluster of substrate molecules and compute the entire cluster quantum mechanically, or describe the central molecule quantum mechanically but add to the Hamiltonian a potential that provides a semiclassical description of the effects of the environment. The 1975 study by Newton (28) of the hydrated and ammoniated electron is the classic example of merging these two frameworks Hartree-Fock wavefunctions were used to describe the solvated electron together with all the electrons of the first solvent shell, while more distant solvent molecules were represented by a dielectric continuum. The intervening quarter century has seen considerable refinement in both quantum chemical techniques and dielectric continuum methods relative to Newton s seminal work, but many of his basic conclusions... 

The dielectric continuum models may allow us to predict speciation in aqueous solutions as a function of temperature simply by changing dielectric constant of the polarizing medium. At first glance, this may simply appear to be a return to the Bom-model formalism. However, the inner sphere solvation would be included explicitly. To include temperature effects on the inner solvation shells, we would have to calculate the partition functions of the cluster defining the metal atom and its first and, possibly, second coordination environment. 

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