Solutes charge distribution

To calculate AGgi c, we must take account of the work done in creating the charge distribi w ithin the cavity in the dielectric medium. This is equal to one-half of the electrostatic i action energy between the solute charge distribution and the polarised dielectric, amd S ... 

Note that Gp 0p of eq. (9) can be written in several equivalent but different looking forms, as is typical of electrostatic quantities in general. For example, it is often convenient to express the results in terms of the electrostatic scalar potential ( )(r) instead of the electric vector field E(r). In the formulation above, the dielectric displacement vector field associated with the solute charge distribution induces an electric vector field, with which it interacts. In the electrostatic... 

E-C. Electrostatics treated empirically, without reference to solute charge distribution. 

As mentioned above, the PCM is based on representing the electric polarization of the dielectric medium surrounding the solute by a polarization charge density at the solute/solvent boundary. This solvent polarization charge polarizes the solute, and the solute and solvent polarizations are obtained self-consistently by numerical solution of the Poisson equation with boundary conditions on the solute-solvent interface. The free energy of solvation is obtained from the interaction between the polarized solute charge distribution and the self-... 

The solute charge distribution derived from (2.2), which governs the interaction with the solvent, is expressed as... 

The difference between GB0 and Gsc resides in their second terms, which comprise the interaction free energy between the solute charge distribution and the solvent electronic polarization. In particular, the matrix elements of V are the cavity surface integrals... 

In words, s describes the interaction of the solute charge distribution component p, with the arbitrary solvent orientational polarization mediated by the cavity surface. The arbitrary weights p,, previously defined by (2.11), enter accordingly the definition of the solvent coordinates, and reduce, in the equilibrium solvation regime, to the weights tv,, such that the solvent coordinates are no longer arbitrary, but instead depend on the solute nuclear geometry and assume the form se<> = lor. weq. In equilibrium, the solvent coordinates are correlated to the actual electronic structure of the solute, while out of equilibrium they are not. 

Hence, one should expect that, along the ESP at sufficiently large inter-nuclear separation, the solvent will overcome the delocalizing effects of the electronic resonance coupling, and localize the solute charge distribution... 

Most of the theoretical works concerning dynamical aspects of chemical reactions are treated within the adiabatic approximation, which is based on the assumption that the solvent instantaneously adjusts itself to any change in the solute charge distribution. However, in certain conditions, such as sudden perturbations or long solvent relaxation times, the total polarization of the solvent is no longer equilibrated with the actual solute charge distribution and cannot be properly described by the adiabatic approximation. In such a case, the reacting system is better described by nonequilibrium dynamics. 

Applying this analysis to electrostatic perturbations in the solute charge distribution corresponding to different orders in the leading multipole indicates that the extent of cancellation decreases with increasing m, but in aeetonitrile it remains large, even for m = 3. ... 

The Maroncelh et al. result can easily be obtained from Eqs. (34) and (37). It corresponds to neglecting the center-of-mass translational velocity component of Eq. (37), which is reasonable for low-order multipolar perturbations (see Fig. 4) in the solute charge distribution. 

Only the former quantity is experimentally accessible, but the longitudinal component of the latter depends on the TCF of solvent charge density fluctuations, Fqq(k,ty9 a quantity that one would naturally associate with the solvent response to electrostatic perturbations. Indeed, the A -dependence of qq (k, t) resembles closely the leading multipolar order (w) in the solute charge distribution perturbation dependence of even for nondipolar liquids, so further... 

The primary area where classical PB equations find application is to biomolecules, whose size for the most part precludes application of quantum chemical methods. The dynamics of such macromolecules in solution is often of particular interest, and considerable work has gone into including PB solvation effects in the dynamics equations (see, for instance, Lu and Luo 2003). Typically, force-field atomic partial charges are used for the primary solute charge distribution. 

Of course, the response of a conductor to a solute charge distribution is complete , while that of a dielectric medium is not. So, in COSMO models, the more simply evaluated conductor-polarization free energy is scaled by a factor of 2(s — l)/(2e -f-1) after its computation (i.e., by the Onsager factor in the case of the SM5C model, however, the scaling factor is (e — l)/e - see Section 11.3.3). 

The relationship between spectroscopic and statistical functions has been exploited for a variety of phenomena related in different ways to the dynamical response of the medium. We cite as examples spectral line broadening, photon echo spectroscopy and phenomena related to TDFSS we are examining here. A variety of methods are used for these studies and we add here methods based on ab initio CS. The basic model is actually the same for all the methods in use ab initio CS has the feature, not yet implemented in other methods, of using a detailed QM description of the solute properties, allowing a description of effects due to specificities of the solute charge distribution. 

An ab initio version of the Mpller-Plesset perturbation theory within the DPCM solvation approach was introduced years ago by Olivares et al. [26] following the above intuitive considerations based on the fact that the electron correlation which modifies both the HF solute charge distribution and the solvent reaction potential depending on it can be back-modified by the solvent. To decouple these combined effects the authors introduced three alternative schemes ... 

To apply this picture to solvatochromism we have to consider that the responses of the microscopic constituents of the solvent (molecules, atoms, electrons) required to reach a certain equilibrium value of the polarization have specific characteristic times (CT). When the solute charge distribution varies appreciably within a period of the same order as these CTs, the responses of these constituents will not be sufficiently rapid to build up a new equilibrium polarization, and the actual value of the polarization will lag behind the changing charge distribution. 

Methods based on the solvent reaction field philosophy differ mainly in (i) the cavity shape, and (ii) the way the charge interaction with the medium is calculated. The cavity is differently defined in the various versions of models it may be a sphere, an ellipsoid or a more complicated shape following the surface of the molecule. The cavity should not contain the solvent molecules, but it contains within its boundaries the solute charge distribution. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

In the case of vibrations of solvated molecules the same two-term partition can be assumed, but in this case the slow term will account for the contributions arising from the motions of the solvent molecules as a whole (translations and rotations), whereas the fast term will take into account the internal molecular motions (electronic and vibrational) [42], After a shift from a previously reached equilibrium solute-solvent system, the fast polarization is still in equilibrium with the new solute charge distribution but the slow polarization remains fixed to the value corresponding to the solute charge distribution of the initial state. 

These findings indicate the complexity of the solvent polarization effect on the solute charge distribution, which shows differential trends depending on the nature of the solute. In conjunction with the free energy of solvation, the analysis of the solvent-induced changes in the solute s electron density should be valuable to shed light on the influence of solvation on the chemical reactivity of solutes. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

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