Implicit Continuum Solvent Models

A wide variety of methods have been proposed to calculate AG and AG. . A common approach is to combine these terms and represent them by an equation of the form 

Within the scope of available ESMs, the explicit solvent simulations method is the most theoretically rigorous and most detailed approach to calculate AG, [7, 38,47, 48, 51,61-66]. The method is based on explicit simulation of a solute-solvent system 

Regardless of the level of theory used (MM, QM, or QM/MM), within the scope of the explicit solvent simulations approach the hydration (solvation) free energy can be calculated by four main groups of methods [52] (1) thermodynamic integration, (2) free energy perturbation, (3) probabihty densities, and (4) nonequihbrium work methods. 

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Generally, methods for calculating can be represented by two main categories implicit or explicit solvent models [38, 47-58]. The main difference between these two categories is the representation of the solvent strueture around the solute. Implicit Continuum Solvent Models (ICSMs) treat the solvent around the solvated molecule as a structureless polarizable medium characterized by a dielectric constant, e [49, 59,60]. In turn, in explicit solvent models (ESMs) both solute and solvent molecules in the solute-solvent systems are described at the atomistic level. There are two... 

Spassov, V.Z., Yan, L., Szalma, S. Introducing an implicit membrane in Generalized Bom/solvent accessibUity continuum solvent models. J. Phys. Ghem. B 2002,106, 8726-38. 

In contrast, there will be many cases where continuum solvent models are less useful. These include situations where one of the goals of the simulation is to obtain a detailed picture of solvent structure, or where there is evidence that a particular structural feature of the solvent is playing a key role (for example, a specific water-macromolecule hydrogen bond). In these situations, however, explicit representation of some water combined with implicit solvation may suffice. Another example is when molecular dynamics simulations are used to study kinetic, or time-dependent phenomena. The absence of the frictional effects of solvent will lead to overestimation of rates. In addition, more subtle time-dependent effects arising from the solvent will be missing from continuum models. Continuum solvent models are in effect frilly adiabatic, in the sense that for any instantaneous macromolecular conformation, the solvent is taken to be completely relaxed. For electrostatic effects, this implies instantaneous dielectric and ionic double layer relaxation rates, and for the hydrophobic effect, instantaneous structural rearrangement. An exception would be dielectric models that involve a frequency-dependent dielectric. Nevertheless, continuum solvent models should be used with caution in studying the time dependence of macromolecular processes. 

Solvation can be included in calculations implicitly (e.g., in PB-SCRF, PCM/DIR, SM2, and other continuum solvent models that emulate properties of bulk solvent at varying degrees of sophistication) or explicitly (by placing solvent molecules around the solute). The former approach is arguably more widely used, probably owing to the computational efficiency of implicit solvation and the avoidance of the compUcating issue of explicit solvent placement. Nevertheless, the sacrifice of atomic detail for the solvent is not always justified and recently, a hybrid explicit/implicit solvation method was proposed, treating the first solvation shell in atomic detail and the remainder of the solvent with a SCRF model [29]. 

Jinnouchi and Anderson, as well as Goddard and coworkers, have instead adopted a Poisson Boltzmann distribution of countercharge (Model 2b.4). These methods couple this distribution with an implicit continuum solvation model for the solvent (water). The continuum model extends the double layer consideration to the diffusion layer region. Jinnouchi and Anderson highlight that strongly bound water molecules must still be included... 

In Section III we described an approximation to the nonpolar free energy contribution based on the concept of the solvent-accessible surface area (SASA) [see Eq. (15)]. In the SASA/PB implicit solvent model, the nonpolar free energy contribution is complemented by a macroscopic continuum electrostatic calculation based on the PB equation, thus yielding an approximation to the total free energy, AVP = A different implicit... 

The mixed solvent models, where the first solvation sphere is accounted for by including a number of solvent molecules, implicitly include the solute-solvent cavity/ dispersion terms, although the corresponding tenns between the solvent molecules and the continuum are usually neglected. Once discrete solvent molecules are included, however, the problem of configuration sampling arises. Nevertheless, in many cases the first solvation shell is by far the most important, and mixed models may yield substantially better results than pure continuum models, at the price of an increase in computational cost. 

We present and analyze the most important simplified free energy methods, emphasizing their connection to more-rigorous methods and the underlying theoretical framework. The simplified methods can all be superficially defined by their use of just one or two simulations to compare two systems, as opposed to many simulations along a complete connecting pathway. More importantly, the use of just one or two simulations implies a common approximation of a near-linear response of the system to a perturbation. Another important theme for simplified methods is the use, in many cases, of an implicit description of solvent usually a continuum dielectric model, often supplemented by a simple description of hydrophobic effects [11]. 

In Section 11.4.6, the limitations of continuum models in their ability to treat non-equilibrium solvation, at least in their simplest incarnations, were noted and discussed. In principle, exphcit solvent models might be expected to be more appropriate for the study of chemical processes characterized by non-equilibrium solvation. In practice, however, the situation is not much better for the explicit models than for the implicit. 

Having identified the strongest points of the explicit and implicit solvent models, it seems an obvious step to try to combine them in a way that takes advantage of the strengths of each. For instance, to the extent first-solvation-shell effects are qualitatively different from those deriving from the bulk, one might choose to include the first solvation shell explicitly and model the remainder of the system with a continuum (see, for instance, Chahnet, Rinaldi, and Ruiz-Lopez, 2001). 

DFT was employed to study the mechanism of ammonolysis of phenyl formate in the gas phase, and the effect of various solvents on the title reaction was assessed by the polarizable continuum model (PCM). The calculated results show that the neutral concerted pathway is the most favourable one in the gas phase and in solution.24 The structure and stability of putative zwitterionic complexes in the ammonolysis of phenyl acetate were examined using DFT and ab initio methods by applying the explicit, up to 7H20, and implicit PCM solvation models. The stability of the zwitterionic tetrahedral intermediate required an explicit solvation by at least five water molecules with stabilization energy of approximately 35 kcalmol-1 25... 

While all implicit solvent models share the same advantage with respect to explicit ones, i.e. the very significant reduction in complexity achieved through the description of the solvent as a uniform continuum, they can be grouped in various ways according to the theoretical framework used to describe the solute, the solvent and the interface between them. 

A more sophisticated description of the solvent is achieved using an Apparent Surface Charge (ASC) [1,3] placed on the surface of a cavity containing the solute. This cavity, usually of molecular shape, is dug into a polarizable continuum medium and the proper electrostatic problem is solved on the cavity boundary, taking into account the mutual polarization of the solute and solvent. The Polarizable Continuum Model (PCM) [1,3,7] belongs to this class of ASC implicit solvent models. 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

Implicit solvent models have been the dominant class of multiscale continuum methods over recent years. However exciting new classes of multiscale continuum models have recently been developed. These new methods fall into the following categories, which are of similar definition and type to the interfaces used between the QM/MM and atomistic/CG levels ... 

Two-way embedded interfacing methods. These involve embedding an atomistic or CG model within a continuum representation. Implicit solvent models fall into this category. New multiscale methods, which capture hydrodynamic and mechanical effects have now also been developed. 

Continuum models can be directly interfaced with atomistic or coarse grain models using a two-way embedded interface. In this scheme, the atomistic or CG model is embedded within a continuum model. Implicit solvent methods, in which an atomistic or CG model of a solute is embedded within a continuum model of the solvent, are popular and well-established examples of this type of interface. Implicit solvent models represent the solvent as a dielectric continuum, and allow the electrostatics of the atomistic or CG solute to polarise the continuum, which then results in an electrostatic reaction field that returns to interact with the solute. Implicit solvent models have been reviewed in detail many times before, and enable the dynamic transfer of electrostatic information across the atomistic/ continuum or CG/continuum interfaces. Recently, new multiscale continuum methods have been developed that allow for the dynamic transfer of mechanical and hydrodynamic information across these interfaces. One example is the work by Villa... 

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