Electron densities, calculation

We have the makings of an iterative computer method. Start by assuming values for the matr ix elements and calculate electron densities (charge densities and bond orders). Modify the matr ix elements according to the results of the electron density calculations, rediagonalize using the new matrix elements to get new densities, and so on. When the results of one iteration are not different from those of the last by more than some specified small amount, the results are self-consistent. 

Electron-density calculations for quinazoline (which has no symmetry) vary markedly with the method used. The diagram (6) has the same bases as that given for pyrimidine above it will be observed that the 2- and 4-positions in quinazoline are comparable with the corresponding positions in pyrimidine and that the aromatic carbon atoms (C-5-C-8) in quinazoline are roughly comparable with C-5 in pyrimidine (67MI21300). The dipole moment of quinazoline does not appear to have been measured, but that of 2-methylquinazo-line is 2.2 D. 

Beyer synthesis, 2, 474 electrolytic oxidation, 2, 325 7r-electron density calculations, 2, 316 1-electron reduction, 2, 282, 283 electrophilic halogenation, 2, 49 electrophilic substitution, 2, 49 Emmert reaction, 2, 276 food preservative, 1,411 free radical acylation, 2, 298 free radical alkylation, 2, 45, 295 free radical amidation, 2, 299 free radical arylation, 2, 295 Friedel-Crafts reactions, 2, 208 Friedlander synthesis, 2, 70, 443 fluorination, 2, 199 halogenation, 2, 40 hydrogenation, 2, 45, 284-285, 327 hydrogen-deuterium exchange, 2, 196, 286 hydroxylation, 2, 325 iodination, 2, 202, 320 ionization constants, 2, 172 IR spectra, 2, 18 lithiation, 2, 267... 

MO calculations at the 6-3IG level have been done on both acrolein and aminoethylene. The resulting MOs were used to calculate charge distributions. Figure 1.26 gives the 7t-electron densities calculated for butadiene, acrolein, and aminoethylene. Inclusion of the hydrogen and a orbitals leads to overall charges as shown. These charge distributions result from a polarization which is counter to the n polarization. 

The electron density calculated from a wave function is given as the square of the function, The reduced density matrix of order y, is defined as ... 

FMO calculations using the MNDO method and electron-density calculations were performed to establish which calculations are in agreement with the experimentally observed regioselectivity of the SnH amination of some nitronaphthyridines (see Section III,B). 

Electron density calculations of the parent unsubstituted 1,2,4-tri-azolo[l,5-c]pyrimidine suggested that N4 and N6 caused a decrease of the... 

Two models of practical interest using quantum chemical parameters were developed by Clark et al. [26, 27]. Both studies were based on 1085 molecules and 36 descriptors calculated with the AMI method following structure optimization and electron density calculation. An initial set of descriptors was selected with a multiple linear regression model and further optimized by trial-and-error variation. The second study calculated a standard error of 0.56 for 1085 compounds and it also estimated the reliability of neural network prediction by analysis of the standard deviation error for an ensemble of 11 networks trained on different randomly selected subsets of the initial training set [27]. 

Owing to the relatively good crystallinity and the large number of OOZ reflections observed for the hydro calumite derivative, the electron density distribution along the c axis can be estimated using a series of OOZ reflections, in accordance with previous literature [82,83]. One-dimensional electron density calculations based on X-ray diffraction are often carried out to probe the structure of the intercalated species in two-dimensional inorganic hosts [33,84-86]. This yields specific information about the orientation and structure of the intercalated species or at least ehminates certain conformational possibihties, which are incompatible with the diffraction data. In LDH systems, however, such calciflations are usually impossible because the X-ray diffraction patterns of hybrid materials are often very ill defined [87,88]. 

Figure 11.1 Relief map of the electron density calculated for the charge-assisted dihydrogen complex H20H+- HBeBeH shown in the plane of the HBeBeH molecule. The electron density of the HBeBeH molecule is located on the left side of the figure, and the electron density of the H-0 bond, which is the proton-donating site, is shown on the right side. (Reproduced with permission from ref. 2.)...

Pp(r) is the electronic density calculated from the electronic wavefunc-tion -0,... 

Ab initio and PM3 semi-empirical methods have been used to optimize the geometry of the benzo[l,5-r 2,4-r ]-dithiolane 4 (R = H or Et). Electron density calculations predicted desymmetrization in the radical cation <1997PCB3665, 1997SM(86)1999>. 

An approach to chemical bonding that is currently attracting attention is that based on an analysis of electron densities calculated from quantum mechanics or measured using X-ray diffraction. Since the electron density shows how the electrons are distributed, it gives a better physical picture of the nature of chemical bonding than other models. It has been admirably described by Bader (1990) and, for inorganic solids, by Pendas et al. (1997, 1998) and Luana et al. (1997), but it is only necessary here to give a brief account of the approach to show why it is difficult to relate its concepts to those of the bond valence model. 

Fig. 1. n-Electron densities calculated for compounds 1-3.224 Values in parentheses are from... 

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