Empirical and Semiempirical Treatments of Solvent Effects

Explicit-Solvent versus Continuum-Solvent Methods 

Theoretical treatments of solvation can be categorized as either explicit-solvent approaches, in which many individual solvent molecules are explicitly included, or as continuum-solvent methods, where the solvent molecules are replaced by a continuous dielectric (Section 15.17). 

In an explicit-solvent treatment, one applies the molecular dynamics or the Metropolis Monte Carlo method (Sections 15.11 and 17.5) to a system of a solute molecule (or molecules if a chemical reaction is being studied) surrounded by hundreds or thousands of solvent molecules by suitable averaging, one obtains thermodynamic or kinetic properties. The solvent molecules are treated using an empirical force field. Some of the models used to represent water molecules are discussed in Leach, Section 4.14. The solute molecule(s) can be modeled using molecular mechanics or semiempirical quantum mechanics (the QM/MM method of Section 17.5). 

Continuum-solvent methods can be categorized as either classical or quantum-mechanical. 

The simplest and crudest continuum-solvent method is the solvent-accessible-surface area (SASA) model, which assumes that the standard free-energy of solvation AG i., can be expressed as 

Recall (Section 15.8) that the van der Waals surface of a molecule is the outer surface formed by intersecting atomic spheres with van der Waals radii. The solvent-accessible surface is the surface traced out by the center of a spherical solute molecule as its rolls on the molecular van der Waals surface. For H2Q, a sphere of radius 1.4 A is traditionally used in (16.103). A, is the solvent-accessible surface area of atom i or group 1, depending on whether an atom-based or group-based approach is used. The sum goes over all atoms (or groups) in the molecule. A, is that portion of the surface area of a sphere centered at atom i and having radius r, -1- rsoivent (where these quantities are the van der Waals radius of atom i and the solvent molecular radius) that is not contained 

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Section 16.7 Empirical and Semiempirical Treatments of Solvent Effects 681... 

Semiempirical methods are the middle ground between highly accurate ab initio methods and completely empirical molecular mechanical (MM) methods [155]. For the treatment of very large biomolecules, hybrid approaches have been developed where the reactive center is described by a semiempirical method and the inert rest of the molecule by a classical force field [3,156,157], This technique can also be applied for the description of solvent effects. The solvent molecules are then described by the MM method. If an even higher accuracy is required for the reactive center of the system, a hybrid approach of three different methods can be applied, e.g., in the ONIOM model by Vreven and Morokuma [158], Here the center is described at DFT or post-HF level, the nearest-neighbor atoms at semiempirical level, and the outer surrounding at MM level. There also exist hybrid schemes between semiempirical and DFT methods only [159],... 

Very often a specific semiempirical MO method was adopted to represent Hqu and a specific MM method was used for //mm and the coupling term / qm-mm introduced additional empirical parameters to allow the combined energy to reproduce experiments. Thus they are specific to the MO method and the MM method adopted at the initial definition of the method. The empirical valence bond approach has also been combined with MM for more complex systems. There have been other approaches attempting to incorporate different procedures which show the importance of combining these methods and the difficulty in doing so. Numerous QM/MM studies have been made in the past, including various versions, some applications, " the treatment of charges, application to zeolites and biochemistry, molecular dynamics, and solvent effects. These variations of the so-called QM/MM methods are treated in separate articles. 

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