Explicit solute-solvent interactions

Clearly, the present approach precludes the detailed study of the dynamics of explicit solute-solvent interactions because the solvent (bath) degrees of freedom have been eliminated. Also, as in the stochastic boundary model,... 

More realistic kinetic behavior in implicit solvent simulations can be obtained with the Langevin thermostat [18] where stochastic collisions and friction forces provide kinetic energy transfer to and from the solute in an analogous fashion to explicit solute-solvent interactions. As a result, kinetic transition rates similar to rates from explicit solvent simulations can be recovered with an appropriate choice of the friction constant [2]. 

In the previous chapter we considered a rather simple solvent model, treating each solvent molecule as a Langevin-type dipole. Although this model represents the key solvent effects, it is important to examine more realistic models that include explicitly all the solvent atoms. In principle, we should adopt a model where both the solvent and the solute atoms are treated quantum mechanically. Such a model, however, is entirely impractical for studying large molecules in solution. Furthermore, we are interested here in the effect of the solvent on the solute potential surface and not in quantum mechanical effects of the pure solvent. Fortunately, the contributions to the Born-Oppenheimer potential surface that describe the solvent-solvent and solute-solvent interactions can be approximated by some type of analytical potential functions (rather than by the actual solution of the Schrodinger equation for the entire solute-solvent system). For example, the simplest way to describe the potential surface of a collection of water molecules is to represent it as a sum of two-body interactions (the interac-... 

This Chapter has outlined several different approaches to the computational determination of solution properties. Two of these address solute-solvent interactions directly, either treating the effects of individual solvent molecules upon the solute explicitly or by means of a reaction field due to a continuum model of the solvent. The other procedures establish correlations between properties of interest and certain features of the solute and/or solvent molecules. There are empirical elements in all of these methods, even the seemingly more rigorous ones, such as the parameters in the molecular dynamics/Monte Carlo intermolecular potentials, Eqs. (16) and (17), or in the continuum model s Gcavitation and Gvdw, Eqs. (40) and (41), etc. 

Summing up, the structure of the effective Hamiltonian of Equation (1.107) makes explicit the nonlinear nature of the QM problem, due to the solute-solvent interaction operator depending on the wavefunction, via the expectation value of the electronic density operator. The consequences of the nonlinearity of the QM problem may be essentially reduced to two aspects (i) the necessity of an iterative solution of the Schrodinger Equation (1.107) and (ii) the necessity to introduce a new fundamental energetic quantity, not described by the effective molecular Hamiltonian. The contrast with the corresponding QM problem for an isolated molecule is evident. 

Continuum solvation models are generally focused on purely electrostatic effects the solvent is a homogeneous continuous medium and its response is determined by its dielectric constant. Electrostatic effects usually constitute the dominating part of the solute - solvent interaction but in some cases explicit solute-solvent (or solute-solute)... 

Equation (3.21) shows that the potential of the mean force is an effective potential energy surface created by the solute-solvent interaction. The PMF may be calculated by an explicit treatment of the entire solute-solvent system by molecular dynamics or Monte Carlo methods, or it may be calculated by an implicit treatment of the solvent, such as by a continuum model, which is the subject of this book. A third possibility (discussed at length in Section 3.3.3) is that some solvent molecules are explicit or discrete and others are implicit and represented as a continuous medium. Such a mixed discrete-continuum model may be considered as a special case of a continuum model in which the solute and explicit solvent molecules form a supermolecule or cluster that is embedded in a continuum. In this contribution we will emphasize continuum models (including cluster-continuum models). 

Molecular dynamics (MD) and Monte Carlo (MC) are in most cases associated with a discrete description of the solvent and with classical representations of the solute and/or solvent Hamiltonians. However, the same type of sampling engines can be coupled to continuum methods, which implies a loss of detail in the representation of individual solute-solvent interactions, but present two main advantages (i) calculation can be faster since no explicit sampling of solvent is needed, (ii) sampling efficiency of solute movements can be very high because of the neglect of solvent friction. 

The main advantage of the MFA is that it permits one to dramatically reduce the computational requisites associated with the study of solvent effects. This allows one to focus attention on the solute description, and it consequently becomes possible to use calculation levels similar to those usually employed in the study of systems and processes in the gas phase. Furthermore, in the case of ASEP/MD this high level description of the solute is combined with a detailed description of the solvent structure obtained from molecular dynamics simulations. Thanks to these features ASEP/MD [8] enables the study of systems and processes where it is necessary to have simultaneously a good description of the electron correlation of the solute and the explicit consideration of specific solute-solvent interactions, such as for VIS-UV spectra [9] or chemical reactivity [10]. 

If one wants to consider explicitly the electron polarization of the solvent it is necessary to add to Eq. (6-22) the energy spent in polarizing the solvent dipoles. In a previous work [36], we have shown that for a polarizable solvent, the final expression that the solute-solvent interaction energy takes is... 

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

In the continuum model, the solvent effect is accountable for in two ways. Either one evaluates the solvation energy by means of explicit formulas derived in the classical theories noted above, or, preferably, one may introduce the term for the solute-solvent interaction directly into the Hamiltonian "" , The latter approach provides not only the solvation energy but also the wave function of the... 

According to Ekj. (7), it is the dielectric dynamics of the homogeneous solvent, as expressed in C (fc, ), that is the source of the time dependence of the estimate Z t) of the solvation tcf. In the RDT approximation the effect of the solute-solvent interactions is carried by the static coupling function B (fc). This factorization (to a function of the homogeneous solvent dynamics times a function of the static solute-solvent structure) is a characteristic feature of the RDT theory. The renonnalized character of the coupling function allows us to bypass the two-time many-point correlation functions that would necessarily appear in a dynamical theory that explicitly addressed the inhomogeneity of the solvent in the neighborhood of the solute particle. 

It may not surprise that the importance of the inclusion of explicit water molecules increases when strong solute-solvent interactions exist. In some cases, with the C03 ion being special, the inclusion of more explicit water molecules could be important. The case of C03 was studied in some details by Kelly et who considered the three arrangements of Fig. 13. In this case, the accuracy depended not only on the number of explicit water molecules but also on the precise form of the solvent model. 

Specific solute-solvent interactions, which are not explicitly taken into account in continuum models, can play a significant role especially for charged species. A typical cluster formed by the glycine anion radical with four water molecules is shown in figure 16. The analogous supermolecule obtained for the neutral form is quite similar, except for the much weaker interaction energies involved in the neutral species. The number and the position of the solvent molecules are determined by molecular dynamics simulations performed by the AMBER force field [141]. 

The term solvatochromism is used to describe the change of position, intensity and shape of the UV-Vis absorption band of the chromophore in solvents of different polarity [1, 2], This phenomenon can be explained on the basis of the theory of intermolecular solute-solvent Interactions in the ground g) and the Franck-Condon excited state e). We will consider only the effect of the solute-solvent interaction on the electronic absorption and nonlinear optical response of a dilute solution of the solute. This way we avoid the explicit discussion of the solute-solute interaction, which significantly obscures the picture of the solvatochromism phenomenon. 

---