Statistical electron correlation

The ab initio model potential for Age was used in molecular dynamics (MD) simulation of the thermal behavior of different isomers of Age in our studies The advantages of using such kind of potential in MD simulation studies are related to the reliability of the quantitative predictions obtained, due to the use of an accurate model potential at the electron correlation level and to the extended length of the simulation time (comparing with other ab initio MD approaches) during which a good statistics is collected. 

All told, the theory makes predictions for weakly doped cuprates for temperatures up to Tc which are in remarkable agreement with experimentation. Our end result is that high temperature superconductivity is primarily an electron correlation effect possibly supplemented by longer range polaronic attraction of the type discussed by Mott and Alexandrov (see [8] for other references). Indeed, it can be argued that this is a theory of unbound bipolarons on a cuprate layer where the Fermion statistics are strictly maintained. 

Investigation of replacement of the 5-methoxy group by substituents with different electronic and lipophilic properties and methylation of the indole nitrogen or its replacement by a sulfur atom was evidence for the shift of the 5-methoxy group to the 4-position of the indole nucleus led to the most active radical scavenger but much less effective as a cytoprotectant [135]. 5-alkoxy-2-(N-acylaminoethyl)indole (Fig. 15) appeared as the key feature to confer both antioxidant and cytoprotective activity to the structure. Antioxidant activity seems essential for cytoprotection, but it is not sufficient, and there is no statistically significant correlation between the two types of activity. 

The intermolecular electron correlation (the dispersion interaction) was calculated or estimated for some cation-ligand interactions using configuration interaction (Cl) calculations, perturbation theory or on the basis of a statistical model (see Table 4). Its contribution to the total interaction energy is less than 10% throughout. 

Several aspects of aromaticity have been studied <2002JOC1333> using statistical analyses of quantitative definitions of aromaticity. ASEs, REs, magnetic susceptibility exaltation (A), nucleus-independent chemical shift (NIGS), the harmonic oscillator model of aromaticity (HOMA), (/j) and (Aj), evaluated for a set of 75 five-membered 7t-electron systems and a set of 30 ring-monosubstituted compounds (aromatic, nonaromatic, and antiaromatic systems) revealed statistically significant correlations between the various aromaticity criteria, provided the whole set of compounds is used. The data in Table 9 have been found for arsole (AsH) 1 (E = As, R = H), its anion (As ), and protonated species (AsH2 ). 

These calculations are of special interest because Purcell and coworkers have been interested in the structure-activity relationships of this series of compounds for several years and have compared several approaches to structure-activity relationships with the same compounds. Earlier they (27, 28) reported on detailed studies of the effect of partition coefficients (benzene-water), electric moments, and electronic structures on the relative activity of the congeners. Purcell (28) used Huckel molecular orbital theory to calculate the net charges on all the atoms of each compound. The only apparent success was the apparent correlation of the net charge at the amide nitrogen atom with activity. This was later shown to be caused by the statistically significant correlation between the 7T value and the net charge on the nitrogen atom (29). 

This definition depends on the possibility to define a unique single configurational energy. As we have seen above, that might often not be possible if we do not want to fall back on the unsatisfactory UHF approach. We can as an alternative use the statistical definition of electron correlation. The electronic motion is uncorrelated if the probability to find electron one in a small volume element around xi and electron two around X2 is the product of the one-electron probability distributions ... 

An accurate representation of the electronic structure of atoms and molecules requires the incorporation of the effects of electron correlation, and this process imposes severe computational difficulties. It is, therefore, only natural to investigate the use of new and alternative formulations of the problem. Many-body theory methods offer a wide variety of attractive approaches to the treatment of electron correlation, in part because of their great successes in treating problems in quantum field theory, the statistical mechanics of many-body systems, and the electronic properties of solids. 

Moreover, Cheney (J) and collaborators have shown that these three structural classes possess similarity in their electronic structure as well, and that a statistically significant correlation exists between the energy of a low-lying unoccupied molecular orbital of members of all three series and the PCA activity. Structural similarity also exists between the phenylenedioxamic acids and the previously reported pyridoquinolinedicarboxylic acids It should be noted that the carboxyl-carboxyl dis-... 

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