Electrostatic solute-solvent interaction

The structure of yint depends, in general, on the nature of the solute-solvent interaction considered by the solvation model. As already noted in the contribution by Tomasi, a good solvation model must describe in a balanced way all the four fundamental components of the solute-solvent interaction electrostatic, dispersion, repulsion, charge transfer. However, we limit our exposition to the electrostatic components, this being components of central relevance, also for historical reason, for the development of QM continuum models. This is not a severe limitation. As a matter of fact, the QM problem associated with the solute-solvent electrostatic component defines a general framework in which all the other solute-solvent interaction components may be easily collocated, without altering the nature of the QM problem [5],... 

The most inclnsive definition of hydration shell describes it as consisting of all thermodynamically altered water molecnles in the vicinity of a solnte. From a thermodynamic standpoint, hydration can be viewed as binding of water molecnles to the hydration sites of a solnte. The energetics of this association is modulated by the type of solute-solvent interactions (electrostatic, hydrogen bonding, van der Waals) and by solnte-indnced solvent reorganization. The latter occnrs even in the absence of appreciable solute-solvent interactions becanse the eqnUib-rium distribution of hydrogen-bonded water networks of the bulk becomes disrupted at the solute surface. 

Considering, for simplicity, only electrostatic interactions, one may write the solute-solvent interaction temi of the Hamiltonian for a solute molecule surrounded by S solvent molecules as... 

The electrostatic free energy contribution in Eq. (14) may be expressed as a thennody-namic integration corresponding to a reversible process between two states of the system no solute-solvent electrostatic interactions (X = 0) and full electrostatic solute-solvent interactions (X = 1). The electrostatic free energy has a particularly simple form if the thermodynamic parameter X corresponds to a scaling of the solute charges, i.e., (X,... 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

In a recent paper. Mo and Gao [5] used a sophisticated computational method [block-localized wave function energy decomposition (BLW-ED)] to decompose the total interaction energy between two prototypical ionic systems, acetate and meth-ylammonium ions, and water into permanent electrostatic (including Pauli exclusion), electronic polarization and charge-transfer contributions. Furthermore, the use of quantum mechanics also enabled them to account for the charge flow between the species involved in the interaction. Their calculations (Table 12.2) demonstrated that the permanent electrostatic interaction energy dominates solute-solvent interactions, as expected in the presence of ion species (76.1 and 84.6% for acetate and methylammonium ions, respectively) and showed the active involvement of solvent molecules in the interaction, even with a small but evident flow of electrons (Eig. 12.3). Evidently, by changing the solvent, different results could be obtained. 

The tilde indicates solute-solvent interactions without electrostatic interactions. The contribution of electrostatic interactions is then isolated as < /x x = /x x — /2f, which we obtain from... 

Here SU = AU — AC/is the electrostatic contribution to the solute-solvent interactions. The final expression is another partition function formula,... 

To make an accurate FEP calculation, a good description of the system is required. This means that the parameters for the chosen force field must reproduce the dynamic behaviour of both species correctly. A realistic description of the environment, e.g. size of water box, and the treatment of the solute-solvent interaction energy is also required. The majority of the parameters can usually be taken from the standard atom types of a force field. The electrostatic description of the species at both ends of the perturbation is, however, the key to a good simulation of many systems. This is also the part that usually requires tailoring to the system of interest. Most force fields require atom centered charges obtained by fitting to the molecular electrostatic potential (MEP), usually over the van der Waals surface. Most authors in the studies discussed above used RHF/6-31G or higher methods to obtain the MEP. 

The assumption of linear response played a prominent role in the derivation (given above) of the SCRF equations, and one aspect of the physics implied by this assumption is worthy of special emphasis. This aspect is the partitioning of Gp into a solute-solvent interaction part Gss and a intrasolvent part Gss The partitioning is quite general since it follows entirely from the assumption of linear response. Since classical electrostatics with a constant permittivity is a special case of linear response, it can be derived by any number of classical electrostatic arguments. The result is [114, 116-119]... 

The physical properties of atoms and molecules embedded in polar liquids have usually been described in the frame of the effective medium approximation. Within this model, the solute-solvent interactions are accounted for by means of the RF theory [1-3], The basic quantity of this formalism is the RF potential. It is usually variationally derived from a model energy functional describing the effective energy of the solute in the field of an external electrostatic perturbation. For instance, if a singly negative or positive charged atomic system is considered, the RF potential is simply given by... 

The solvent polarization contribution (third term of Eq (81)), may be obtained from the fundamental theorem of the RF theory, relating the electrostatic solute-solvent interaction energy and the solvent polarization contribution [2,3,7,14] ... 

Self-consistent reaction field (SCRF) models are the most efficient way to include condensed-phase effects into quantum mechanical calculations [8-11]. This is accomplished by using SCRF approach for the electrostatic component. By design, it considers only one physical effect accompanying the insertion of a solute in a solvent, namely, the bulk polarization of the solvent by the mean field of the solute. This approach efficiently takes into account the long range solute-solvent electrostatic interaction and effect of solvent polarization. However, by design, this model cannot describe local solute-solvent interactions. 

It follows from the Hellmann-Feynman theorem1,2 that these interactions are essentially Coulombic, and hence can be described accurately in terms of classical electrostatics, given the correct charge distributions. This has been discussed by Hirschfelder et al.3 4 The problem, with regard to solute-solvent interactions, is one of scale, i.e., the large number of molecules of the solvent that must be taken into account in order to realistically represent its effects. Thus, whereas interaction energies of relatively small noncovalently-bound complexes are... 

Nonspecific interactions Solute-solute or solute-solvent interactions that occur within solutions without causing the formation or breakage of a chemical bond. In seawater, most nonspecific effects are electrostatic in nature. 

The calculation of the energy for the interaction between the solvent and solute is more complicated. Formally, the free energy for the process, AC/ini, is composed of two chemical parts and an essentially entropic term. The chemical terms are associated with van der Waals interactions AGvdw> electrostatic effects, AG, between solute and solvent. The entropic term measures the free volume i.e., the volume a molecule explores before encountering another, which is assumed to be proportional to the molar volume of the solvent. Thus, the free energy change associated with solute-solvent interactions at temperature T is given by... 

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