Self-consistent reaction field approach modelling solvent effects

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 isomeric equilibria of 2-acyl-2-nitroenamines with primary or secondary amino group are strongly solvent-dependent, as already seen for other enamines. An increase in the polarity of the solvent increases the population of the isomer(s) with Z-configuration, as deduced from the H-NMR spectra . In 3-amino-2-nitroacry-lic esters (567-574), the IR spectra show that an increase of solvent polarity increases the population of the ZE isomer , which has the highest calculated dipole moment. The effect of solvent polarity on the isomeric equilibria of some model 2-acyl-2-nitroenamines (554, R = H, Me R = Me, OMe R = R = H) has been qualitatively predicted by quantum-mechanical calculations using the self-consistent reaction field approach . 

During the last 40 years it has been possible to witness an important evolution on the way the environment around a solute molecule is described. The reaction field approach, the effect a continuous dielectric medium has on the charge distribution of a molecule that polarizes back the dielectric and generates a reaction potential, is a standard scheme to consider the solvent effects on many molecular properties. Most modem continuum models obtain through a self-consistent cycle the wave function of the molecule affected by the reaction potential thus the self-consistent reaction field acronym (SCRF). Solvatochromic effects have been more or less successfully explained using from Onsager s to more refined models like Nancy SCRF [44], Tomasi s polarizable continuum model (PCM) [45], Cramer and Tmhlar s SMx models [46]. 

These approaches date back to the classical papers by Onsager(9) and Kirkwood(lO). A self-consistent reaction field (SCRF) was developed and applied to several solvent effects with reasonable success(8, 11). However, it seems to become clear that these models where the solute and the solvent are represented by separated non-overlapping wave functions are too crude in some cases(12). Studies of solvent effects involving the interaction of the solute with a proton donor solvent (the so-called protic solvents) for instance usually leads to hydrogen bonds and therefore neglecting the overlap of the electron densities between the two subsystem is very difficult to justify. A similar difficulty is obtained for those absorptions where electron is trans-... 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

Proper inclusion of the solvent into the calculations is unfortunately quite difficult [46]. One can use classical molecular dynamics or Monte Carlo simulations, classical continuum models based on the Poisson-Boltzman equation, and quantum-chemical studies using various variants of the Self Consistent Reaction Field (SCRF) approach at the semiempirical or ab initio level. There are serious approximations associated with these methods. Continuous models neglect the specific solute-solvent interactions which are very important for polar solvent. Classical methods neglect the changes in the electronic structure of the solute due to the solvent effects. These uncertainties can be illustrated using the predicted solvation energy of adenine treated by various modem approaches. The calculated values vary from -8 to -20 kcal/mol [68]. 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

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