SMx solvation models

SMx Solvation model x (a name we give to our own parameterized GB/ST models)... 

Various SMX solvation models are available in many quantum-chemistry programs. For listings, see comp.chem.umn.edu/solvation. 

Equations [305]-[310] are strictly valid only for thermodynamic species, which are ordinarily associated with stationary points on the potential energy surface V(R), where R denotes the full set of solute coordinates. However, we also use the SMx solvation models to calculate potentials of mean force, which are called W(R,T). The gradient of W(R,T) gives the force on the solute molecule averaged over a canonical ensemble of solvent molecules and is a generalization of the one-dimensional radial potential of mean force that appears in Debye-Hiickel theory. Thus, we write... 

In common with similar approaches that relate solvent accessible surface to cavity free energy90-93, the simple SMI model required careful parameterization, and assumed that atoms interacted with solvent in a manner independent of their immediate molecular environment and their hybridization76. In more recent implementations of the SMx approach, ak parameters are selected for particular atoms based on properties determined from the SCF wavefunction that is evaluated during calculation of the solute and solvent polarization energies27. On the other hand, the inclusion of more parameters in the solvation model requires access to substantial amounts of experimental data for the solvation free energies of molecules in the training set94 95. 

Tables 1 and 2 provide a list of recently proposed solvation models and classifies them according to the above scheme. For convenience, each row of the table is given a label. In some cases the label is based on a well established name or acronym (e.g., PCM, SMx), or an acronym to be used in this chapter. The acronyms to be used in labels are as follows ...

Solvation models (SMx) are semi-empirical models that introduce into calculations the effects of solvents, for example water [43. 48-52], alkanes [53, 54], chloroform [46], and others [44]. They were developed by Donald G. Truhlar,... 

Unfortunately, a detailed comparison of the continuum models is available only at the semiempirical level.54,55 Because the SMx models are specially parametrized to describe free energy of hydration, it is not surprising that they are the best for reproducing this value. A detailed discussion of the advantages and limitations of different types of solvation models with regard to the various types of approximations and different types of organic molecules can be found in references 53-55. 

Cramer considers the development of the SMX models as his most important scientific contribution. This work drove the field forward. Tomasi and Barone moved to put in non-electrostatic components in a more accurate way, Cramer claims. He is somewhat disappointed in the limited use of the SM models by other computational chemists. What s driving the train is that people use what s in the code that they bought. To the extent that PCM is a very successful solvation model, it s in part because it is in Gaussian. The SMX models sadly have never been available in Gaussian. ... 

The SMx Approach Generalized Born Electrostatics Augmented by First-Hydration-Shell Effects Each of the foregoing solvation models, when implemented at the semiempirical level, resembles closely its implementations employing ah initio molecular orbital theory—indeed, the ab initio versions often predate the semiempirical. On the other hand, the generalized Born model, discussed with respect to Equation [16] for the case of molecular mechanics,has certain properties that make it particularly appropriate i" to the semiempirical level. 27,202,203 Qur own SMx models, where SM denotes solvation model, take advantage of this, and we now review these models. 

The SMx aqueous solvation models, of which the most successful are called AM1-SM2,27 AMl-SMla, and PM3-SM3, °- adopt this quantum statistical approach, which takes account of the ENP and CDS terms on a consistent footing. The NDDO models employed are specified as the first element (AMI or PM3) of each identifier. It is worth emphasizing that the SMx models specifically calculate the absolute free energy of solvation—a quantity not easily obtained with other approaches. We have reviewed the development and performance of the models elsewhere.203 We anticipate our further observations later in this chapter by noting that the mean unsigned error in predicted free energies of solvation is about 0.6-0.9 kcal/mol for the SMx models for a data set of 150 neutral solutes that spans a wide variety of functionalities. A number of examples are provided later in this chapter. 

In the SCRh model the full polarization is taking into account, i.e. the initial dipole Model (COSMO) and Solvation Models (SMx, x—l -5) also employ molecular shaped... 

RestrirteH Open-shell Hartree-Fock (ROHFl Solvation Models (SMx), 397 Trajectory, 3 /6 Verlet algorithm, for molecular dynamics, 384... 

Generalized Bom (GB) approach. The most common implicit models used for small molecules are the Conductor-Like Screening Model (COSMO) [77,78], the DPCM [79], the Conductor-Like Modification to the Polarized Continuum Model (CPCM) [80,81], the Integral Equation Formalism Implementation of PCM (IEF-PCM) [82] PB models, and the GB SMx models of Cramer and Truhlar [23,83-86]. The newest Minnesota solvation models are the SMD universal Solvation Model based on solute electron density [26] and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [87-89] with semiempirical terms that account for local electrostatics [90]. Further details on these methods can be found in Chapter 11 of Reference [23]. 

A series of continuum solvation models (SMx, x = 1-5) has been developed by Truhlar and co-worker (Cramer and Truhlar [79]), based on the Generalized Born/Surface Area (GB/SA) model (Still et al. [86]). Recall that in the GB approach the molecular shape is taken into account as the solute charge is distributed over a set of atom-centered spheres. For this GB/SA model, the polarization free energy is given by... 

Cramer, Truhlar, and co-workers developed a series of semiempirical continuum solvation models SMr, where SM stands for solvation model and x = 1,2,3,4,5 is the version number. The SMx methods are quantum-mechanical versions of Still s GB/SA... 

To date the SMx family is probably the best parametrized model for calculations of the energy of hydration, especially in the case of local minima. Nevertheless, the last versions of the PCM and SCRF models which do not contain the parametric expressions, at least for the electrostatics, look very promising. For the choice of the most efficient application, a careful comparison of the results of these three versions of solvation models is needed. 

The same formalism, with opportune changes, has been adopted by Cramer and Truhlar in a class of QM-continuum dielectric models, called SMx where x denotes the specific parametrization of particular solvation models. In these models... 

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