Electron density, calculation by molecular

H.H. Jaffe, Correlation of Hammett s (5-values with electron densities calculated by molecular orbital theory, J. Chem. Phys. 20 (1952), pp. 279-284. 

The electron-withdrawing effect of pentazole is similar to a nitro group and the H NMR shifts of nitrophenyl and pentazolylphenyl compounds are similar <2002ZFA1933>. The 7i-electron densities calculated by the Hiickel molecular orbital (HMO) method show a linear correlation with 111, 13C, and 14N NMR chemical shifts in the azole series <1977IJB168>. The 1SN NMR chemical shifts of the following compounds have been reported cesium/tetramethyl ammonium (TMA) pentazolylphenolate (8 —81.1 (N-l), —29.7 (N-3/N-4), 1.9 (N-2/N-5)) <2002AGE3051> ... 

The critical point is the point at which the gradient vector field for the charge density is zero, that is, either a maximum or minimum along N. The condition Vp(r) N(r) = 0 applied to other paths between two atoms defines a unique surface that can represent the boundary of the atoms within the molecule. The electron density within these boundaries then gives the atomic charge. The combination of electron density contours, bond paths, and critical points defines the molecular graph. This analysis can be applied to electron density calculated by either MO or DFT methods. For a very simple molecule such as Hj, the bond path is a straight line between the nuclei. The... 

Electrophilic Aromatic Substitution. The Tt-excessive character of the pyrrole ring makes the indole ring susceptible to electrophilic attack. The reactivity is greater at the 3-position than at the 2-position. This reactivity pattern is suggested both by electron density distributions calculated by molecular orbital methods and by the relative energies of the intermediates for electrophilic substitution, as represented by the protonated stmctures (7a) and (7b). Stmcture (7b) is more favorable than (7a) because it retains the ben2enoid character of the carbocycHc ring (12). 

These slight differences are mainly due to the smearing of electron density caused by thermal vibration of the Co atom in crystals. Johansen has also calculated the theoretical deformation density of Co0610 by the ab initio molecular orbital method (39), on the assumption of a regular octahedral geometry with high-spin state (t2g )Heg)2. The as-phericity of 3d electron density is similar to that observed for [Co(N02)6]3. ... 

Finally, in careful comparative studies of the molecular electron densities generated by HF, correlated ab initio, and pure, self-interaction corrected, and hybrid DFT calculations, Cremer et al have made a very interesting observation [72, 73]. They found that the pure DFT generated densities differed from those obtained with accurate ab initio methods in a particular way, and that both hybrid, and self-interaction corrected DFT methods, yielded densities closer to the correct ones. Based on this observation, they suggested that mixing in of exact exchange in hybrid functionals serves as a proxy for the self-interaction correction. 

Apart from serving to partition crystallographically measured electron densities, the atoms-in-molecules procedure is also used to derive molecular properties from isolated-molecule densities, calculated by ab initio methods. Discrepancies between sum-over-atoms and whole-molecule calculations,... 

The electronic state calculation by discrete variational (DV) Xa molecular orbital method is introduced to demonstrate the usefulness for theoretical analysis of electron and x-ray spectroscopies, as well as electron energy loss spectroscopy. For the evaluation of peak energy. Slater s transition state calculation is very efficient to include the orbital relaxation effect. The effects of spin polarization and of relativity are argued and are shown to be important in some cases. For the estimation of peak intensity, the first-principles calculation of dipole transition probability can easily be performed by the use of DV numerical integration scheme, to provide very good correspondence with experiment. The total density of states (DOS) or partial DOS is also useful for a rough estimation of the peak intensity. In addition, it is necessary lo use the realistic model cluster for the quantitative analysis. The... 

In this review, we describe the basic steps in theoretical (molecular, nonperiodic) calculations to study the H-H bonding interactions. For the analysis of electron density obtained by high-resolution low-temperature X-ray diffraction experiments coupled with multipolar refinement [125], the reader is referred to the literature [65, 66]. 

Figure 10 (a) Schematic structure of the molecule Ni(C4N4H2)2 and (b)-(d) difference electron densities obtained by subtracting superposed atomic densities from the molecular density, (b), (c), and (d) were obtained from experiment, from Hartree-Fock calculations, andfrom LDA calculations, respectively (Reproduced by permission of the American Chemical Society from ref. 56)... 

In the course of the pharmacophore identification process, clearly two different steps have to be taken in succession. First, a conformational analysis has to be carried out. After this initial step, a common three-dimensional arrangement of functional groups is determined through a superpositioning procedure. During the second step this preliminary sterical pharmacophore model has to be checked and consolidated by electron density calculations and establishment of the corresponding molecular electrostatic potentials (MEPs). 

In benzenium ions the greatest deficit of jc-electron density, according to molecular-orbital calculations, manifests itself at the 2-, 4-, and 6-positions. Accordingly, in protonating mesitylene, out of two possible isomers, (6) and (7), only 2,4,6-trimethylbenzenium ion (6) is detected by the PMR method... 

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