Solvation supermolecule

The first result to comment about is the evidently different description obtained for the isolated and the solvated supermolecules. In absorption, the result obtained in the isolated supermolecule is even blue-shifted with respect to cyclohexane, while in emission, the red-shift is recovered, but is very small. Only by adding the effect of the bulk with the PCM, the correct behavior is obtained with a net red-shift both in absorption and emission. On the emission, however, the correction introduced with the two explicit water molecules is not sufficient to get a real quantitative agreement with the experiments. Once again, a possible source of inaccuracy is the TDB3LYP description of the excited state geometry, which is here complicated by the presence of the H-bonded water molecules. 

The results are reported in Fig. 2.1 in which z is the coordinate perpendicular to the interface. The limit values (z - oo) refer to bulk cyclohexane and bulk water in the latter case, the result obtained for the solvated supermolecule is also reported (in red). In the same graph, we also report the position-dependent value of the dielectric constant used to mimic the diffuse interface. 

The continuum models represent a real alternative to the supermolecule approach. In this cases the solvation energy Esolv is assumed to be a sum of individual terms which can be calculated separately (see Eq. (6)). 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

In Ref.125) the calculation of an activation barrier for reaction (21) in the gas phase is considered to be an error of the MINDO/3 method and the process is assumed to be activationless. But in respect to the medium effect a barrier of 54 k J mol-1 is obtain-ed which agrees again with the results from Huron-Claverie calculations. Bertran et al. calculated the influence of the solvation on the electrophilic attack of a proton 133) or a methyl cation 134,135) on ethene using a MINDO/3 supermolecule model. Smaller reaction enthalpies also result in solution than in the gas phase in addition to the appearance (H+ + ethene) or the increase (CH 4 + ethene) of an activation barrier1361. 

The alternative theoretical scheme for studying chemical reactivity in solution, the supermolecule approach, allows for the investigation of the solvation phenomena at a microscopic level. However, it does not enable the characterization of long-range bulk solvent forces moreover, the number of solvent molecules required to properly represent bulk solvation for a given solute can be so large that to perform a quantum chemical calculation in such a system becomes prohibitively expensive. ... 

Figure 6 Typical supermolecule used in the QM calculations. This illustration shows the /3-carotene surrounded by 50 first-neighbor acetone molecules corresponding to the first solvation shell as defined by the nearest-neighbor RDF, Gx-Nearest(r)-...

Space does not permit the inclusion of any of the papers dealing with hydrogen bonding188 or solvation phenomena,189 and the reader is referred to the above references for more details. It is clear, however, from recent work that it is feasible to include the interaction with several solvent molecules using the supermolecule approach, and very interesting and informative results have been obtained in this way. 

In particularly thorough examples of the traditional physical organic approach, Parker (1969) and Abraham (1974) interpreted solvent effects on Walden inversion reactions by using thermodynamic transfer functions. However, in order to explain the reaction rate decrease upon solvation from a microscopic point of view, quantum mechanical electronic structure calculations must be carried out. Micro-solvated Sn-2 reactions were initially studied in this way, with the CNDO/2 semiempirical molecular orbital (MO) method, by using the supermolecule... 

In the second family of approaches, explicit solvent molecules are placed around the gas phase stationary point structures. In some cases, the gas phase geometries are held constant and only the geometries and/or positions of the surrounding solvent molecules are optimized, and in other cases, the structure of the whole system (often called a supermolecule 32) is optimized. The supermolecule approach generally only involves explicit solvent molecules from the first (and occasionally second) solvation shell of the solute. 

Much effort has been devoted to other electrostatic representations of molecular interactions [89] using ab initio calculations based on the understanding that this component is the largest portion of the interaction energy [90]. A major application of the detailed analysis of intermolecular interactions provided by ab initio formulations has been an approximate expansion in terms of analytical functions that allow practical calculation for many different intermolecular distances [97], Alarge scale simulation of potential functions for solvated amino acids has been derived from supermolecule calculations based on one interacting water molecule [92],... 

Supermolecule model. By a "supermolecule" we imply a model consisting of the solute molecule surrounded by a certain number of solvent molecules. Pair complexes solute-solvent and solvent-solvent may be considered the simplest supermolecules. Since the cost of the supermolecule approach becomes prohibitive as the number of solvent molecules is increased, in most treatments only the first solvation shell is assumed. Such small clusters cannot of course provide a realistic model of a liquid but rather they give us a theoretical picture of what is referred as to "the solvation in the gas phase". As with the approach dealt with in the last paragraph, the ab initio calculation on the supermolecule should be followed by a statistical thermodynamic treatment. The use of the standard statistical thermodynamic is straightforward, in which case the supermolecule approach becomes e-quivalent to treatment of common chemical equilibria dealt with In Section 5.F. The calculations presented in Table 5.17 are just of this... 

It does not appear that any attempt has been made to couple this BKO model to a means by which to calculate the CDS components of solvation, and this limits the model s accuracy, especially for solvents like water, where the CDS terms are not expected to be trivial. For water as solvent, studies have appeared that surround the solute with some small to moderate number of explicit solvent molecules, with the resulting supermolecule treated as interacting with the surrounding continuum. 23,230 Although such a treatment has the virtue of probably making the calculation less sensitive to the now-large cavity radius, it suffers from the usual explicit-solvent drawbacks of the size of the system, the complexity of the hypersurface, and the need for statistical sampling. 

As mentioned earlier, various workers have attempted to remove some of the strong dependence on the cavity radius by going to supermolecule systems incorporating explicit solvent molecules.222,230,311,312 jhis approach has the additional benefit of including directional components of local solvation effects, which may be important in spectroscopy, 2 albeit at the expense of rapidly complicating the hypersurface. 

Heard, G. L., Yates, B. F. Hybrid supermolecule-polarizable continuum approach to solvation application to the mechanism of the Stevens rearrangement. J. Comput. Chem. 1996, 17, 1444-1452. 

It came out immediately clear that the supermolecule approach cannot represent the method to be used in extensive studies of solvent effects. The computational costs increase in the ab initio versions with more than the fourth power of the number of basis set functions, at a given nuclear geometry of the supermolecule. Even more important it has been the recognition that, when the size of the solvation cluster exceeds some very low limits, the number of different nuclear conformations at an equivalent energy increases exponentially computational costs increase in parallel, and the introduction of thermal averages on these conformations becomes necessary. These facts, and some attempts to overcome them, are well summarized in a dementi s monograph (Clementi, 1976). The problem of multiple equivalent minima still plagues some discrete solvation models. 

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