Electron-topological matrix

Bersuker and Dimoglo (455) described a matrix-based approach that combines geometric and electronic features of a molecule, the electron-topological approach. For each molecule, an electron-topological matrix of congru-ity (ETMC) is constructed based on a con-former selected by conformational analysis. 

Figure 3.47. The electron-topological matrix of congruity (ETMC) for a 17-atom fragment proposed by Bersuker and Dimoglo (455) to encode geometrical and electronic features of molecules.

For each molecule with A atoms, the square symmetric Ax A matrix, called the electron-topological matrix of congruity ETMC, is defined as the following ... 

Electronic-Topological Matrix of Conjunction Electronic-Topological method... 

The Electronic-Topological Matrix of Gonjunction is calculated for each molecule in the data set. If a molecule is found in a few stable conformations, all of them are treated as a... 

The Electron-Conformational Approach (EGA) is based on the same procedure as the ET method [Chumakov, Terletskaya et al, 2000]. The main difference is the representation of molecules, which, in the framework of EGA, is defined in terms of a Set of Electronic and Conformational Parameters (SECPs) in place of the Electronic-Topological Matrix of Conjunction. Then, after choosing a compound as the reference, its SECPs are compared with the S ECPs... 

Given a series of N molecules with known biological activity or inactivity and provided that the conformations and electronic structure of these molecules can be determined, the essence of the ET method is as follows.For each molecule the so-called electron-topological matrix of congruity (ETMC) or, in the more sophisticated versions, a set of ETMC —the three-dimensional ETMC (TDETMC) —is constructed as shown schematically below. 

It is known that multivalued adiabatic electronic manifolds create topological effects [23,25,45]. Since the newly introduced D matrix contains the information relevant for this manifold (the number of functions that flip sign and their identification) we shall define it as the Topological Matrix. Accordingly, K will be defined as the Topological Number. Since D is dependent on the contour F the same applies to K thus K = f(F),... 

Single-valued potential, adiabatic-to-diabatic transformation matrix, non-adiabatic coupling, 49-50 topological matrix, 50-53 Skew symmetric matrix, electronic states adiabatic representation, 290-291 adiabatic-to-diabatic transformation, two-state system, 302-309 Slater determinants ... 

By comparing the ETMC matrices of all the active compounds with those of the inactive ones, the electron-topological submatrix of activity ETSA is derived which contains matrix elements that are present in all the active compounds and absent from the inactive ones. The information contained in this matrix allows the design of new active compounds as well as the screening of several compounds with respect to their activity. 

Then, one ofthe most active compounds is chosen as the reference molecule and its ETMC (the template) is compared with all other ETMCs. By this comparison those matrix elements that are present in all active compounds but are absent in the inactive ones (i.e., active features or pharmacophore) are derived and represented by the Electronic-Topological Submatrix of Conjunction (ETSC). 

Hall s formula (69) can be obtained from Eq. (74), because for AHs the topological matrix is of the form (31). In the case of NAHs A2 A-1 have non-zero diagonal elements Jt-electron distribution is thus not uniform and the dipole moments have values very different from zero. The rules governing the charge displacements in NAHs are discussed in Section VII. 

The modification of the CI(SD) denominator is performed in the most flexible way by introducing a topological matrix T which mediates the coupling of different electron pairs, thus allowing for individual denominators corresponding to different electron pairs. The CPF energy expression then reads... 

K. Ruedenberg, Quantum mechanics of mobile electrons in conjugated bond systems. III. Topological matrix as generatrix of bond orders, J. Chem. Phys. 34 (1961) 1884-1892. 

The D matrix plays an important role in the forthcoming theory because it contains all topological features of an electronic manifold in a region surrounded by a contour F as will be explained next. 

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