Supermolecular approximation

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... 

The development of the theoretical models and computational methods, which can accurately account for the solvent effects on the NLO properties of molecular systems is one of the largest challenges in the contemporary quantum chemistry. The important conceptional and computational difficulty arises from the fact that the nature of the solute-solvent interaction in the condensed phase is extremely complicated. In modern quantum chemistry the solute-solvent interactions are modeled by a number of different approaches that can be divided into three main groups supermolecular approximations, discrete simulations and continuum models. 

The supermolecular approximation provides a more appropriate description of specific solvation and reaction mechanisms, where solvent molecules are considered to be reagents. Successful apphcation of the supermolecular approach requires... 

It should be noted that the activation barrier for the reaction of endo isomer (7), calculated in the supermolecular approximation, is lower by 9.62 kJ/mol than the corresponding barrier calculated for exo isomer (8). Comparison of these results with those obtained by in vacuo calculations shows that steric factor is actually determinative for the reactivity of strained epoxynoibomanes (7,8). Only this factor is taken into account in terms of the supermolecular approach, where solvent molecules are included in the explicit form. As a result, the effective volume of the reagent considerably increases (Fig. 10.5). 

Fig. 10.5 Structure of transition states in the methanolysis of stereoisomeric epoxynorbornanes (7, 8), calculated in the supermolecular approximation (n = 4, m = 1)...

The most correct approach to the solution of the first problem involves the so-called supermolecular approximation in which the molecules of the reactants and the greatest amount of the solvent molecules admissible by the calculational scheme and computer capacity are merged into the unified system of a supermolecule (Sect. 3.4). The reliability of this approximation is determined by the accuracy of the quantum chemical scheme of calculation and also by the number of the solvent molecules taken into account. Of course, by far not all the potentialities of this method can currently be implemented because of calculational difficulties, in particular, excessive demands on computer time. 

The following effects can be described in terms of the supermolecular approximation the degree of charge transfer between a solute molecule and the molecules of the solvent, changes in the electron and geometry structure of the molecule incorporated into solution, the influence a solvent has on the mechanism of chemical reaction. 

The effect which a solvent has on the rate and character of the 8, 2 reactions is enormous [1,11,15,52]. Some important theoretical results were obtained in the supermolecular approximation with various degrees of completeness in regard to reproduction of the solvation shell. 

Thus, the first results of the Monte Carlo modelling of reactions in solution call for cautious attitude towards the conclusions based on calculations in supermolecular approximation. 

The following SnI reactions were calculated more rigorously than others, with the solvent (S) effect taken into account using the supermolecular approximation [67-70] ... 

The first solvation shell of the methyl cation in water and HF can satisfactorily be represented by five and that of the fluorine anion—by six solvent molecules, i.e., the total number of the solvent molecules included in the supermolecular approximation is 11. The C—X distance was taken as the reaction coordinate and all other geometry parameters, includingg those of the solute environment, were optimized. The most important result of the calculations of Eq. (5.7) by the CNDO/2 and ab initio (STO-3G basis set) methods is the detection of three minima along the MERP. The first of these characterized by the distance r( p= 1.388 A corresponds to the hydrated undissociated molecule CH3F. The second minimum corresponds to rcp = 3.480 A. There are no solvent molecules between the ions CHj and F , hence they are located in one cage and may be structurally described as a contact ion pair of type IV. The third minimum corresponds to a completely dissociated system (r< p = 5.463 A), i.e., the solvent-separated ion pair V with each ion surrounded by its own solvation shell with n = 11, j = 5, and k = 6 in Eq. (5.7). 

The constant advancement of supercomputer technology currently allows one to apply the same levels of computational methodology to DNA basis, which four or five years ago were possible only for small model compounds. Indeed, this possibility has opened a new way of investigations of the various properties of the DNA fragments, because now the system of interest can be extended and directly related to the DNA base or even the whole nucleotide. So, one may not only study the tendencies which were predicted during the investigations of the model molecules, but also may see the variations related to the differences in the structures of various DNA bases. Below we review the available literature on the influence of hydration on properties of the DNA bases. We restricted the review primarily to the results of the supermolecular approximations because the studies performed in the framework of the several continuum models are covered in the contributions of Orozco et al. [118]. 

Obviously, the situation will be more difficult when additional approximations have to be employed, e.g., the divide-and-conquer scheme, an effective Hamiltonian or a perturbation approach. A central open question is which electronic states of the fragments have to be included so that reliable results, as compared with supermolecular calculations, can be provided. In any case, accounting for just one state per base pair will yield only semi-quantitative results. A careful analysis of this point is highly desirable for DNA-related systems. 

We assume that the absorbing gas is of a uniform composition and in thermal equilibrium. The absorption coefficient, which is defined by Lambert s law, Eq. 3.1, is expressed in terms of the probabilities of transitions between the stationary states of the supermolecular system, in response to the incident radiation. Assuming the interaction of radiation and matter may be approximated by electric dipole interaction, i.e., assuming the wavelengths of the radiation are large compared with the dimensions of molecular complexes, the transition probability between the initial and... 

Keywords intermolecular forces, Born-Oppenheimer approximation, supermolecular method, polar-... 

In order to obtain more information on the solvation process Yang and Cui performed a so called natural energy decomposition analysis (NEDA) on monomethyl phosphate ester (MMP) solvated in water. They used a supermolecular approach where the solute plus a number of water molecules (up to 34) were treated quantum-mechanically. A further set of water molecules was treated with a force-field model. Their results indicate that there is a substantial charge transfer between the solute and the nearest solvent molecules. The interaction energy due to this transfer was found to amount to some 70-80% of that of the electric interactions. Since MMP forms hydrogen bonds with the water molecules, all results together suggests that for such a system it is important to include the nearest solvent molecules in the quantum-mechanical treatment, whereas a continuum approximation or a force field may not be sufficiently accurate. 

We mention that, by contrast, the more familiar Raman spectra arising from the permanent polarizabilities of the individual (noninteracting) molecules of the complex are not considered a part of the supermolecular spectra, or of CILS. In ordinary Raman spectroscopy of rarefied gases the invariants of the permanent molecular polarizability tensor are conveniently considered to be not affected by intermolecular interactions, an approximation that is often justified because induced spectral components are usually much weaker than ordinary allowed Raman bands. 

Fig. 2. Accuracy of approximations to —9 spa PB ° a ne(l fr°m gradient expansion approximation (zeroth- or second-order GEA) for the HF...HF dimer at various intermolecular separations (d(FF)). The difference between the Coulomb energy (J) obtained using approximate -Ta in Eqs. 31-32 and that (Jref) obtained from supermolecular Kohn-Sham calculations, which do not...

Fig. 7. Accuracy of different gradient-dependent approximations to —2— f°r HF...NCH dimer at various intermolecular separations (d(FN)). The considered approximations differ in the analytic form of the enhancement factor used in Eq. 77. The accuracy of each approximation is measured as the difference between the Coulomb energy derived from a given approximation and that obtained from supermolecular Kohn-Sham calculations which do not depend on 6T d pA,PB ...

The lower part of Table 33.2 shows the SAPT correlation contributions to the three-body energy of the water trimer. These contributions include the electron correlation effects at the level approximately comparable to the supermolecular many-body... 

---