SCRF model

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

Note that systems having a dipole moment of 0 will not exhibit solvent effects for the Onsager SCRF model, and therefore Onsager model (SCRF=Dipole) calculations performed on them will give the same results as for the gas phase. This is an inherent limitation of the Onsager approach. 

Next, we will consider the vibrational frequencies of formaldehyde in acetonitrile, using the Onsager SCRF model and the SCIPCM model. Acetonitrile is a highly polar solvent, with an e value of 35.9. In order to predict the vibrational frequencies, we ll first need to optimize the structure for formaldehyde in this medium. Thus, we ll be running these jobs ... 

As this table indicates, the SCRF facility in Gaussian produces very good agreement with experiment. The solvent produces fairly small but significant shifts in the locations of the major peaks, as predicted by both SCRF models. 

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. ... 

Compute the frequency associated with carbonyl stretch in solution with acetonitrUe for the carbonyl systems we looked at in the gas phase in Chapter 4. Run your calculations using RHF/6-31+G(d) with the Onsager SCRF model. Discuss the substituent effect on the predicted solvent effects. 

Compute the energies of the three structures using the SCI-PCM SCRF model and the B3LYP/6-31+G(d) model chemistry. ... 

Compute the energy difference between the anti (left) and syn forms of furfuraldehyde in a solution of dimethyl ether (e=12.0), using either the Onsager (MP2/6-31+G(d)) ortheSCIPCM (B3LYP/6-31+G(d)) SCRF models. The observed energy difference is -0.53 kcal-moT. ... 

J. B. Foresman, T. A. Keith, K. B. Wiberg, J. Snoonian and M. J. Frisch, Solvent Effects. 5. The Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on Ab Initio Reaction Field Calculations, J. Phys. Chem., submitted (1996). [Discusses the IPCM SCRF model.]... 

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... 

The spherical cavity, dipole only, SCRF model is known as the OnMger model.The Kirkwood model s refers to a general multipole expansion, if the cavity is ellipsoidal the Kirkwood—Westheimer model arise." A fixed dipole moment of yr in the Onsager model gives rise to an energy stabilization. 

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

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. ... 

Conceptually, the self-consistent reaction field (SCRF) model is the simplest method for inclusion of environment implicitly in the semi-empirical Hamiltonian24, and has been the subject of several detailed reviews24,25,66. In SCRF calculations, the QM system of interest (solute) is placed into a cavity within a polarizable medium of dielectric constant e (Fig. 2.2). For ease of computation, the cavity is assumed to be spherical and have a radius ro, although expressions similar to those outlined below have been developed for ellipsoidal cavities67. Using ideas from classical electrostatics, we can show that the interaction potential can be expressed as a function of the charge and multipole moments of the solute. For ease... 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

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. 

The SCRF models assume that solvent response to the solute is dominated by motions that are slow on the solute electronic motion time scales, i.e., Xp Telec. Thus, as explained in Section 2.1, the solvent sees the solute electrons only in an averaged way. If, in addition to the SCRF approximation, we make the usual Bom-Oppenheimer approximation for the solute, then we have xs Xelect-In this case the solute electronic motion is treated as adjusting adiabatically both to the solvent motion and to the solute nuclear motion. 

The SCRF models should be useful for any of the adiabatic cases, but a more quantitative treatment would recognize at least three time scales for frictional coupling based on the three times scales for dielectric polarization,... 

In the Onsager s SCRF model, the solute is placed in a cavity immersed in a continuous medium with a dielectric constant e. The molecular dipole of the solute induces a dipole in the solvent, which in turn interacts with the molecular dipole, leading to a net stabilization effect. 

Self-consistent reaction field (SCRF) models are the most efficient way to include condensed-phase effects into quantum mechanical calculations [8-11]. This is accomplished by using SCRF approach for the electrostatic component. By design, it considers only one physical effect accompanying the insertion of a solute in a solvent, namely, the bulk polarization of the solvent by the mean field of the solute. This approach efficiently takes into account the long range solute-solvent electrostatic interaction and effect of solvent polarization. However, by design, this model cannot describe local solute-solvent interactions. 

The results of the SCRF models depend strongly on the radius Rx used for the definition of the spherical interface between the solute and the solvent. Unfortunately, the dielectric theory does not provide an answer for the question of which value is appropriate for this radius. Owing to the implicit assumption of the dielectric continuum models that the electron density of the solute should be essentially inside the cavity, any value of Rx below a typical van der Waals (vdW) radius would not be meaningful. On the other hand, at least at the distance of the first solvent shell, i.e., typically at two vdW radii, we should be in the dielectric continuum region. However, there is no clear rationale for the right value between these two limits other than empirical comparison of the results with experimental data. Among others, the choice of spherical cavities which correspond to the liquid molar-solute volume has proved to be successful. 

Nevertheless, the use of spherical-cavity SCRF models finally led to a dead end, because no meaningful spherical cavities can be defined for non-spherical molecules. Even the attempt to overcome this problem by an extension of the Onsager model to ellipsoidal cavities did not really solve the problem, because this introduces additional fit parameters, while only a small portion of real molecules can still be considered as approximately ellipsoidal. Thus, the need for molecular-shaped SCRF models became more and more obvious. 

A problem of molecular-shaped SCRF models is the absence of an analytical solution for the reaction field. One line of development was the search for an approximate expression for the dielectric interaction energy of a solute in a molecular-shaped cavity, without the need for explicit calculation of the solvent polarization. These models were summarized as generalized Born (GB) approximations [22,30]. The most popular of these models... 

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. 

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