Computational Quantum Chemical Considerations

For the present case-study 12 aromatic compounds are considered, namely benzene, aniline, phenol, naphthalene, a-naphthol, p-naphthol, a-naphthylamine, P-naphthylamine, pyridine, pyrimidine, N,N -dimethyl p-aminoaniline, and monochlorohydrate of N,N -dimetiiyl p-aminoaniline. Among these molecules, some of them present symmetry features, which can be used to lower the degree of the secular determinant obtained in the HMO method (Hiickel, 1931 Mandado et al., 2007). However, to compute the determinant of these aromatic compounds the computational technique has been considered using the data from Table 4.1 the present discussion follows (Putz et al, 2010) 

TABLE 4.1 The Parameters Values Considered for the Conjugated Systems (HMO method) (Putz et al., 2010) 

Employing the Hiickel matrices, the eigenvectors, the ti levels of energy, the total ground state energy E, the delocalization energy/tr electrons ( ), the charge densities q), the bond orders pj and the free valence (F = 1.732 - Zp ) been calculated. 

For the DFT computations, the present based molecular computations employ the sum of the exchange and correlation contributions in the mixed functional of Eq. (4.1) 

For the exchange term was used the Becke s functional via the so called semiempirical (SE) modified gradient-corrected functional (Becke, 1986)  

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As is evident from these examples, computational quantum mechanics, semiempirical and ab initio methods alike, represent important new tools for the estimation of rate parameters from first principles. Our ability to estimate activation energies is particularly significant because until the advent of these techniques, no fundamentally based methods were available for the determination of this important rate parameter. It must be recognized, however, that these theoretical approaches still are at their early stages of development that is to say, computational quantum chemical methods should only be used with considerable care and in conjunction with conventional methods of estimation discussed earlier in this article, as well with experiments. 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Beyond its ability to account for what is known, the second important consideration in the selection of an appropriate molecular mechanics or quantum chemical model is its cost . It is really not possible to estimate precisely how much computer time a particular calculation will require, as many factors remain uncertain. In addition to the size of the system at hand and the choice of model (both of which can be precisely defined), there are issues the quality of the guess (which in turn relates to the experience of the user) and the inherent difBculty of the problem (some things are easier than others). It is possible, however, to provide representative examples to help distinguish applications which are practical from those which are clearly not. 

We reiterate that both homoaromaticity and aromaticity are more pronounced in ions than in related neutrals. In the tour-de-force of computational theory, S. Sieber, P. v. R. Schleyer, A. H. Otto, J. Gauss, F. Reichel and D. Cremer [7. Phys. Org. Chem., 6,445 (1993)] document considerable homoaromatic stabilization of the cyclobutenyl cation. Yet the difference of the enthalpy of formation they calculate from their quantum chemical cations, 1021 kj mol-1, is only 54 kJmol-1 lower than that archivally recommended for the cyclopropenium ion [S. G. Lias,... 

The topic of interactions between Lewis acids and bases could benefit from systematic ab initio quantum chemical calculations of gas phase (two molecule) studies, for which there is a substantial body of experimental data available for comparison. Similar computations could be carried out in the presence of a dielectric medium. In addition, assemblages of molecules, for example a test acid in the presence of many solvent molecules, could be carried out with semiempirical quantum mechanics using, for example, a commercial package. This type of neutral molecule interaction study could then be enlarged in scope to determine the effects of ion-molecule interactions by way of quantum mechanical computations in a dielectric medium in solutions of low ionic strength. This approach could bring considerable order and a more convincing picture of Lewis acid base theory than the mixed spectroscopic (molecular) parameters in interactive media and the purely macroscopic (thermodynamic and kinetic) parameters in different and varied media or perturbation theory applied to the semiempirical molecular orbital or valence bond approach [11 and references therein]. 

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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