Supermolecular model

Such supermolecular model has been successfully applied for investigation of chemo-, region- and stereoselectivity of dicyclopentadiene diepoxide (11) alkaline methanolysis [42, 43] and reaction of spirooxiranes (12-19) with methoxy anion [44]. 

There are certain instances where this approach may be regarded as an attractive option. For example, Cossi and Crescenzi (2003) found that accurate computation of NMR chemical shifts for alcohols, etliers, and carbonyls in aqueous solution required at least one explicit solvent shell, but that beyond that shell a continuum could be used to replace what would otherwise be a need for a much larger cluster. However, just as the strengths of the two models are combined, so are the weaknesses. A typical first shell of solvent for a small molecule may be expected to be composed of a dozen or so solvent molecules. The resulting supermolecular cluster will inevitably be characterized by a large number of accessible structures that are local minima on the cluster PES, so that statistical sampling will have to be undertaken to obtain a proper equilibrium distribution. Thus, QM methods require a substantial investment of computational resources. In addition, certain technical points require attention, e.g., how does one keep the first solvent shell from exchanging with the continuum since both, in principle, foster identical solvation interactions ... 

Let us now give examples of some characteristic forms of supermolecular organization arising through bifurcation in model or in laboratory systems. 

Regarding the parametrization of the Hamiltonian Eq. (7), the present approach relies on the parameters of the underlying lattice model Eq. (5). However, one could envisage an alternative approach, similar to the one described in Refs. [66-69] for small molecular systems, where a systematic diabatiza-tion is carried out based on supermolecular electronic structure calculations as described in Sec. 2.2. 

Nucleophilic vinylic substitutions of 4//-pyran-4-onc and 2,6-dimethyl-4//-pyran-4-one with a hydroxide ion in aqueous solution were calculated by the density functional theory (B3LYP) and ab initio (MP2) methods using the 6-31+G(d) and 6-31G (d) basis sets. The aqueous solution was modelled by a supermolecular approach, where 11 water molecules were involved in the reaction system. The calculations confirmed a different addition-elimination mechanism of the reaction compared with that in the gas phase or non-polar solution. Addition of OH- at the C(2) vinylic carbon of the pyranone ring with an activation barrier of 10-11 kcalmol-1 (B3LYP) has been identified as the rate-determining step, in good quantitative and qualitative agreement with experimental kinetics. Solvent effects increase the activation barrier of the addition step and, conversely, decrease the barrier of the elimination step.138... 

From the point of view of the Buckingham formula (Equation (2.23)) only the effect of long-range electrostatic and induction interactions crE of the solvent molecule with the reaction field is included in the traditional methods of the (n) group (continuum models). Contrary to that, the supermolecular approach (I) or combined MD/QM methods (III) includes the short-range term cra and the long-range crw and some of the [Pg.132]

A weakness of this model is that the separation of the electrostatic and the so-called specific solute-solvent interactions is not defined. In practice, two main approaches are used to account for solvent effects on the spin-spin coupling constants the continuum and the supermolecular methods. The combined MD/QM approach is rarely used for the purpose, since calculations of the spin-spin coupling constants are much more time consuming than those of the shielding constants and the MD/QM approach is too expensive for the former. 

Another study employing the MPE model (at the SCF computational level) is the calculation of spin-spin coupling constants in methyllithium and lithium dimethylamide [82], In this case, modelling of the solvent as supermolecular aggregates leads to far better agreement with experimentally measured liquid-state spin-spin coupling constants than... 

This model accounts only partially for the specific structure of liquid water, and to refine it, calculations within supermolecular and semicontinuum models were also performed. In these cases, the properties were computed for a cluster of five water molecules, simulating the inclusion of a first solvation shell. In the semicontinuum model, the cluster was immersed in the dielectric continuum. Because of the (prohibitive for the times) size of the cluster, it was possible to obtain only an uncorrelated result. On the other hand, a nonequilibrium solvation model was used in computing the orientational contribution of Equation (2.218). Finally, to determine mC(o>, T), an extensive property, a differential shell method was employed. 

This restriction rules out all discrete models exclusively based on semiempirical force fields, leaving among the discrete models the MC/QM and the MD/QM procedures, in which the second part of the acronyms indicates that the solute is described at the quantum mechanical (QM) level, as well as the full ab initio MD description, and some mixed procedures that derive the position of some solvent molecules from semiclassical simulations, replace the semiclassical description with the QM one, and repeat the calculation on these small supermolecular clusters. The final stage is to perform an average on the results obtained with these clusters. These methods can be used also to describe electronic excitation processes, but at present, their use is limited to simple cases, such as vertical excitations of organic molecules of small or moderate size. This limitation is due to the cost of computations, and there is a progressive trend toward calculations for larger systems. 

Current efforts in quantum-chemical modeling of the influence of solvents may be divided into two distinct approaches. The first, the supermolecular approximation, involves the explicit consideration of solvent molecules in quantum-chemical calculations. Another possibility for simulating solvent influence is to replace the explicit solvent molecules with a continuous medium having a bulk dielectric constant. Models of this type are usually referred to as polarized continuum models (PCMs). 

Accurate predictions of solute interactions with a limited number of solvent molecules are possible using the supermolecular approximation. This is an approach based on the consideration of the dissolved molecule together with the limited number of solvent molecules as the unified system. The quantum-chemical calculations are performed on the complex of the solute molecule surrounded by as many solvent molecules as possible. The main advantage of the supermolecular approximation is the ability to take into account such specific effects of solvation as hydrogen bonding between the selected sites of the solvated molecules and the molecules of the solvent. In principle there are only two restrictions for the supermolecular approximation. One of them is the internal limitations of the quantum-chemical methods. The second restriction is the limitation of the current computer technology. Because of such restrictions this approximation coupled with ab initio molecular dynamics is possible only for small model systems.46-50... 

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