Explicit-implicit solvent models

In view of the results of the previous two sections, we can carry the practical development of quasi-chemical approximations further. We will initially consider cases for which the interactions are fundamentally short-ranged. For the principal contrary example, ions, the outer-shell term would represent the Bom contribution because it describes a hard ion stripped of any inner-shell ligands. But the balance of treatments of long-ranged interactions requires specific subsequent consideration. 

With that motivation and restriction, we identify the outer-shell term as an initial packing contribution 

This is a packing contribution of the type analyzed previously. Adopting the simplest of the preceding results, Eq. (7.30) p. 160, directly we have 

Returning to consider the inner-shell contribution, following a preceding section, the natural idea is to exploit the same self-consistent molecular field to approximate 

This notation [4 mf emphasizes that this is a functional of the enclosed material being subject to the molecular field Evaluation of the partition function Eq. (7.55) typically would not be a trivial task, but Chapter 5, p. 100, can be brought to bear because this is a standard form. 

---

Simonson T, Carlsson J, Case DA (2004) Proton binding to proteins pKa calculations with explicit and implicit solvent models. J Am Chem Soc 126 4167-4180. 

Bursulaya, B. D., and Brooks, C. L. (2000). Comparative study of the folding free energy landscape of a three-stranded /i-sheet protein with explicit and implicit solvent models./. Phys. Chem. B 104, 12378-12383. 

The weakest point of our approach is the treatment of the bulk solvent. The energies derived from an implicit solvent model like IPCM are mainly based on energy calculations on gas-phase structures and effects of explicit solvent molecules are not included. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

Desolvation free energies are computed using either explicit solvent or an implicit solvent model. While explicit solvent simulations are usually considered more accurate or at least more representative of the true molecular environment, simulations using implicit solvent are often chosen... 

Solvent effects can be incorporated into two kinds of solvation models, either those that consider each solvent molecule as an individual molecular species (explicit models), or those that deal with the averaged effect of the solvent molecules through use of a coarse-grained description of solvent (e.g., dielectric models, implicit solvent models, etc.). 

Relative Merits of Explicit and Implicit Solvent Models... 

The fundamental difference between the explicit and implicit solvent models is not that one has solvent and the other does not. Rather, the difference is that the implicit model employs a homogeneous medium to represent tlie solvent where the explicit model uses atomistically represented molecules. While tlie latter choice is clearly tlie more physically realistic, the practical limitations imposed by explicit representation dictate that it is not necessarily the best choice for a given problem of interest. This section compares and contrasts the relative strengths and weaknesses of tlie two models, including some illustrative applications. 

RELATIVE MERITS OF EXPLICIT AND IMPLICIT SOLVENT MODELS... 

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). 

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. 

Once the computational model of the molecule is created, it is of most interest to study its properties in the natural environment, in particular, water solvent. Surrounding the molecule with water, allows us to study the solvation process. Like molecules, the solvent may be also described with different levels of accuracy. Beginning with all-atom models of water,48,49 which allow for the studies of solvent structure around solutes but are time consuming and the results are model dependent, to continuous dielectric models,50- 52 which are faster but less accurate and give no knowledge about the solvent itself. Thus, the difference in the level of description for both models is either an advantage or a drawback. These models are commonly known as explicit or implicit solvent models, respectively. 

Zhang L, Gallicchio E, Levy RM (1999) Implicit Solvent Models for Protein-Ligand Binding, Insights Based on Explicit Solvent Simulations, (AIP Conference Proceedings, Simulation and Theory of Electrostatic Interactions in Solutions), 192 151 172... 

Shen M, Freed KF (2002) Long time dynamics of met-enkephalin comparison of explicit and implicit solvent models, Biophys J, 82 1791-1808... 

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. 

Similar to the AC determination work illustrated in Sect. 4.1, it is necessary to carry out a complete structural search for all significant chiral species present in order to extract the detailed information contained in the experimental spectra. In addition, one needs to consider solvent effects in these studies. As introduced in Sect. 3.2, currently there are two approaches to model the solvent effects the implicit solvent model and the explicit model where H-bonding intermolecular interactions are considered explicitly. An example VA and VCD simulation of ML in water with PCM with several different basis sets and functionals is shown in Fig. 10 [48]. Although the calculated VA spectrum with PCM shows a good... 

The solvent is a necessary part of the physical problem for computational studies of larger-scale structures in solution. But often the solvent is of secondary interest. Therefore, there has been extended attention to implicit solvent models for those computational studies, models that provide the proper statistical description of the macromolecule but without the solvent explicitly present (Roux and Simonson, 1999). Equation (3.38), p. 45, provides a fundamental basis for implicit solvent models. 

---