Decomposition perturbation schemes

Figure 8-3. Variational-perturbational scheme of interaction energy decomposition. The circles denote the consecutive levels of theory while the arrows designate the corresponding correction terms...

Despite the fact that the Kitaura Morokuma approach allows insight into the nature of interaction to be obtained, it has also a lot of limitations. One of the most important is that the binding energy and its components are not free of the basis set superposition error [39]. Another variation-perturbation scheme of the decomposition of the interaction energy was previously proposed [40]. The starting wave functions of the subsystems are obtained in this approach in the dimer-centered basis set (DCBS) hence, the following interaction energy components free of BSSE can be obtained ... 

Variational-perturbational energy decomposition scheme was successfully employed in a number of diverse phenomena investigations including the influence of mutations within enzyme active site54, the contribution of particular active site residues to catalytic effects55 and the connection between inhibitory activity and the interaction energy56-58. The latter will be presented in what follows. 

Pearson s linear correlation coefficient, 239 perturbation analysis, pairwise decomposition scheme Frobenius norm, 235 RTB Hessian matrix, 234 symmetric positive semidefinite (SPSD) matrix, 237... 

DePuy and coworkers " have established the same order of acidity for alkanes by examining the preferred modes of decomposition of the 5-coordinate silicon anions formed by the reaction of OH with (CH3)3SiR. By analogy with the reaction of F the initial step is believed to be formation of the complex 21 which can either expel CH3 or R. The exothermicity of the initial addition reaction is insufficient to allow expulsion of an alkyl anion and heterolysis of an Si—C bond results in the solvated ion 22a or 22b (Scheme 1). Rapid proton transfer within this ion-molecule complex leads to the irreversible formation of RH or CH4. Molecular orbital calculations show the five-coordinate silicon anion 21 (R = CH3) to be at a minimum and the transition structure for decomposition of 21 has CH3 almost completely removed while the proton of the OH group is only slightly perturbed. 

Charge transfer (CT) contributions are somewhat neglected by the formal elaborations of the perturbation theory. We know that they have an important role in the interpretation of many reactions (see. e.g. Fukui [17] and Klopman [18]) and represent an important factor in specific, albeit limited, classes of noncovalent interactions. The reason of this neglection of CT terms in the development of the symmetry-adapted version of the perturbation theory is due to the fact that attention has been focussed on small systems for which it was possible to consider the monomeric basis set as sufficient to describe all the aspects of the interaction. The definition of the charge-transfer contribution given by the K-M procedure is also open to criticism. An alternative decomposition scheme (Weinhold et al. [19]) in fact indicates this contribution in a modified version as one of the most important in determining the characteristics of non-covalent interactions. The Weinhold analysis in turn has been the object of several criticisms. In our opinion the occurrence of interpretative theories in competition is a positive fact science should benefit from this competition, unless one of the theories is decidedly inferior. 

For Inter Molecular Perturbation Theory (IMPT) see Hayes, I. C. Stone, A. J. An intermolecular perturbation theory for the region of moderate overlap, Mol. Phys. 1984, 53, 83-105 papers of this kind, however, contain a large amount of theoretical and mathematical detail and are not transparent to the uninitiated. For Symmetry-Adapted Perturbation Theory (SAPT) see e.g. Bukowski, R. Szalewicz, K. Chabalovski, C. F. Ab initio interaction potentials for simulations of dinitramine solutions in supercritical carbon dioxide with cosolvents, J. Phys. Chem. 1999, A103, 7322-7340, and references therein. The Morokuma decomposition scheme is described in Kitaura, K. Morokuma, K. A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation, Int. J. Quantum Chem. 1976,10, 325-340. 

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