Solvation SCRF model

As the plot of AE indicates, the energy difference between the two forms decreases in more polar solvents, and becomes nearly zero in acetonitrile. The left plot illustrates the fact that the IPCM model (at the B3LYP/6-31+G(d) level of theory) does a much better job of reproducing the observed solvent effect than the two Onsager SCRF models. In contrast, the Onsager model at the MP2 level treats the solvated systems more accurately than it does the gas phase system, leading to a poorer value for the solvent effect. ... 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

Given the diversity of different SCRF models, and the fact that solvation energies in water may range from a few kcal/mol for say ethane to perhaps 100 kcal/mol for an ion, it is difficult to evaluate just how accurately continuum methods may in principle be able to represent solvation. It seems clear, however, that molecular shaped cavities must be employed, the electiostatic polarization needs a description either in terms of atomic charges or quite high-order multipoles, and cavity and dispersion terms must be included. Properly parameterized, such models appear to be able to give absolute values with an accuracy of a few kcal/mol." Molecular properties are in many cases also sensitive to the environment, but a detailed discussion of this is outside the scope of this book. ... 

The comparisons made by Parchment et al. [271] illustrate the importance of combining electronic polarization effects with corrections for specific solvation effects. The latter are accounted for parametrically by the explicit simulation, but that procedure cannot explicitly account for the greater polarizability of tautomer 8. The various SCRF models do indicate 8 to be more polarizable than any of the other tautomers, but polarization alone is not sufficient to shift the equilibrium to that experimentally observed. Were these two effects to be combined in a single theoretical model, a more accurate prediction of the experimental equilibrium would be expected. 

These immediate and simple findings motivated me to accept Gerrit Schuiirmann s request and to implement COSMO as a new kind of SCRF model in the semi-empirical quantum chemistry package MOPAC [39]. Shortly afterwards, I met Jimmy Stewart, the author of the MOPAC package, in a European Computational Chemistry Workshop in Oxford, where he was available as a supervisor for a entire workshop. I gave a short presentation of my COSMO ideas and he was interested to get COSMO as the first solvation model in MOPAC. Therefore, he introduced me to some extend to the MOPAC program code, and we identified the places where COSMO would have to link in. 

Still within continuum solvation models, Wang et al. [5] have used an ab initio SCRF Onsager model to compute vibrational frequencies at different levels of the ab initio QM molecular theory, the G-COSMO model has been used by Stefanovich and Truong to calculate vibrational frequencies at the DFT level [6], and the multipole SCRF model, developed by the group of Rivail, has been extended to the calculation of frequency shifts at the HF, MP2 and DFT levels, including nonequilibrium effects [7],... 

Here we give an overview of the current status and perspectives of theoretical treatments of solvent effects based on continuum solvation models where the solute is treated quantum mechanically. It is worth noting that our aim is not to give a detailed description of the physical and mathematical formalisms that underlie the different quantum mechanical self-consistent reaction field (QM-SCRF) models, since these issues have been covered in other contributions to the book. Rather, our goal is to illustrate the features that have contributed to make QM-SCRF continuum methods successful and to discuss their reliability for the study of chemical reactivity in solution. 

It can be anticipated that the computation of A//soi and AAsoi is more delicate than the prediction of AGsoi, which benefits from the enthalpy-entropy compensation. Accordingly, the suitability of the QM-SCRF models to predict the enthalpic and entropic components of the free energy of solvation is a challenging issue, which could serve to refine current solvation continuum models. This contribution reports the results obtained in the framework of the MST solvation model [15] to estimate the enthalpy (and entropy) of hydration for a set of neutral compounds. To this end, we will first describe the formalism used to determine the MST solvation free energy and its enthalpic component. Then, solvation free energies and enthalpies for a series of typical neutral solutes will be presented and analyzed in light of the available experimental data. Finally, collected data will be used to discuss the differential trends of the solvation in water. 

Aleman, C. Solvation of cytosine and thymine using a combined discrete/SCRF model, Ghent. Phys. Lett. 1999, 302,461-470. 

Other semiempirical Hamiltonians have also been used within the BKO model. A Complete Neglect of Differential Overlap (CNDO/2) ° study of the effect of solvation on hydrogen bonds has appeared. o The Intermediate Neglect of Differential Overlap (INDO) °2 formalism has also been employed for this purpose.2011 Finally, the INDO/S model,which is specifically parameterized to reproduce excited state spectroscopic data, has been used within the SCRF model to explain solvation effects on electronic spectra.222,310-312 jhis last approach is a bit less intuitively straightforward, insofar as the INDO/S parameters themselves include solvation by virtue of being fit to many solution ultraviolet/visible spectroscopic data.29J... 

Given the diversity of different SCRF models, and tlie fact that solvation energies in... 

In the usual quantum-mechanical implementation of the continuum solvation model, the electronic wave function and electronic probability density of the solute molecule M are allowed to change on going firom the gas phase to the solution phase, so as to achieve self-consistency between the M charge distribution and the solvent s reaction field. Any treatment in which such self-consistency is achieved is called a self-consistent reaction-field (SCRF) model. Many versions of SCRF models exist. These differ in how they choose the size and shape of the cavity that contains the solute molecule M and in how they calculate t nf... 

The many body aspect of dispersion forces makes the computation of their role on a solvated molecule far more difficult than the intramolecular effects. Nevertheless the SCRF model can be adapted successfully to the evaluation of dispersion. The treatment is a generalization of Linder s theory [18] of van der Waals interactions in condensed media using reaction field techniques. 

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. 

Jaguar s solvation module uses a self-consistent reaction field (SCRF) model, which couples an accurate ab initio description of the charge distribution to a well-defined and realistic representation of the molecular cavity. The SCRF calculation is done by first calculating the gas phase wavefunction of the solute molecule, from which the electrostatic potential fitted charges are passed to an efficient finite element solver, which determines the reaction field by numerical solution of the Poisson-Boltzmann equations and represents the solvent as a layer of charges at the solute s molecular surface, which serves as the dielectric continuum boundary. The solvent point charges are incorporated in a subsequent wavefunction evaluation and the process is repeated until self-consistency is obtained. The cost is roughly twice that of a gas phase calculation. 

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]. 

The SM1-SM3 methods model solvation in water with various degrees of sophistication. The SM4 method models solvation in alkane solvents. The SM5 method is generalized to model any solvent. The SM5.42R method is designed to work with HF, DFT or hybrid HF/DFT calculations, as well as with AMI or PM3. SM5.42R is implemented using a SCRF algorithm as described below. A description of the differences between these methods can be found in the manual accompanying the AMSOL program and in the reviews listed at the end of this chapter. Available Hamiltonians and solvents are summarized in Table 24.1. 

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