Electronic charge density calculation

Most of the reports in the literature discuss electrophilic substitution of 1,3,6-triazacycl[3.3.3]azine (80) and the 2-methyl, 4-cyano and 4-ethoxycarbonyl derivatives. Electrophilic bromination occurs preferentially at the 4-position (if available), and subsequently at the 9- and 7-positions. These data support the electron charge density calculations (see Section 2.20.2) (73ACS3264). Nitrations are carried out using copper(II) nitrate and acetic anhydride. The central nitrogen is completely non-basic, and in the triazacycl-azines protonation occurs initially at position 6 (80) (77ACS(B)239). Ceder and Vernmark have reported that piperidine reacts with (81) via the aryne intermediate the A-E cine-substitution mechanism is an attractive alternative (equation 40). 

The different behavior of tertiary and quaternary carbon atoms seems to be due to either the complete neglect of overlap in these calculations or to polarization effects of the carbon-nitrogen bonds, Similar results are obtained for a series of 5-halouracils by plotting the 13C NMR chemical shifs versus 7r-electron charge densities calculated by the extended Hiickel theory [756], Though for several nitrogen heterocycles a better correla-... 

We anticipate two advantages of using the more realistic electron densities obtained by the AFDF methods. More reliable theoretical electronic charge densities calculated for each assumed nuclear geometry in the course of the iterative structure refinement process will improve the reliability of comparisons with the experimental di action pattern. In particular, AFDF electron densities are expected to serve as more sensitive and more reliable criteria for accepting or rejecting an assumed structure than the locally spherical or possibly elliptical electron density models used in the conventional approach. We also expect that the more accurate density representations within the QCR-AFDF framework will facilitate a more complete utilization and interpretation of the structural information contained in the observed X-ray diffraction pattern. 

Another approach for a stereochemical index Q encoding information on cis-trans isomerism in alkenes was described by Estrada on including a corrected electron charge density calculated with the MOP AC version 6.0, the following... 

It is interesting to know if there are other characteristics common for all Lewis acid-Lewis base interactions. It is difficult to point out general statements. Even for one type of La—Lb interaction, like for example for the hydrogen bond, it is difficult to indicate common characteristics. However few trends or mechanisms which most often are observed for the large part of La-Lb interactions could be listed. Few common characteristics are observed for the A-Y bond of the Lewis acid unit if this bond is in contact with the Lewis base center (in other words for the A-Y...B interactions, see Scheme 9.4). The increase of the polarization of the A-Y bond is the result of complexation (% of the electron charge density calculated at A-center) what comes from the increase of the positive charge of Y-atom and the increase of... 

Surface electron charge density can be described in tenus of the work fiinction and the surface dipole moment can be calculated from it ( equatiou (Bl.26.30) and equation (B1.26.31)). Likewise, changes in the chemical or physical state of the surface, such as adsorption or geometric reconstruction, can be observed through a work-fimction modification. For studies related to cathodes, the work fiinction may be the most important surface parameter to be detenuined [52]. 

Fig. 7. Maps of the electronic charge density in the (110) planes In the ordered twin with (111) APB type displacement. The hatched areas correspond to the charge density higher than 0.03 electrons per cubic Bohr. The charge density differences between two successive contours of the constant charge density are 0.005 electrons per cubic Bohr. Atoms in the two successive (1 10) planes are denoted as Til, All, and T12, A12, respectively, (a) Structure calculated using the Finnis-Sinclair type potential, (b) Structure calculated using the full-potential LMTO method.

Table 2.4 shows a comparison of the experimental and PPP-MO calculated electronic spectral data for azobenzene and the three isomeric monoamino derivatives. It is noteworthy that the ortho isomer is observed to be most bathochromic, while the para isomer is least bathoch-romic. From a consideration of the principles of the application of the valence-bond approach to colour described in the previous section, it might have been expected that the ortho and para isomers would be most bathochromic with the meta isomer least bathochromic. In contrast, the data contained in Table 2.4 demonstrate that the PPP-MO method is capable of correctly accounting for the relative bathochromicities of the amino isomers. It is clear, at least in this case, that the valence-bond method is inferior to the molecular orbital approach. An explanation for the failure of the valence-bond method to predict the order of bathochromicities of the o-, m- and p-aminoazobenzenes emerges from a consideration of the changes in 7r-electron charge densities on excitation calculated by the PPP-MO method, as illustrated in Figure 2.14. 

Some n-electron charge density differences between the ground and first excited states calculated by the PPP-MO method for 4-aminoazobenzene,... 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Seminario, J. M., J. S. Murray, and P. Politzer. 1991. First-Principles Theoretical Methods for the Calculation of Electronic Charge Densities and Electrostatic Potentials. In The Application of Charge Density Research to Chemistry and Drug Design. Plenum Press, New York. 

Our model of positive atomic cores arranged in a periodic array with valence electrons is shown schematically in Fig. 14.1. The objective is to solve the Schrodinger equation to obtain the electronic wave function ( ) and the electronic energy band structure En( k ) where n labels the energy band and k the crystal wave vector which labels the electronic state. To explore the bonding properties discussed above, a calculation of the electronic charge density... 

For azulene and its derivatives, the preference for the 1-position can be rationalized by considering the charge densities calculated for the various electronic states (Table 3, Pariser, 1954). 

Molecular orbital calculations have been performed on compounds 19 and 20 . The calculated PM3 equilibrium geometric structures show that these compounds are severely distorted from planarity in accordance with X-ray structural analysis (see Section 8.I2.3.I). On the other hand, PM3 calculations performed on both neutral and oxidized/reduced compounds show that oxidation and reduction induce a clear gain of aromaticity. Predictions using the nonempirical valence effective Hamiltonian (VEH) method have shown that the electronic charge density in the highest occupied molecular orbital (HOMO) is localized on the benzodithiin 19 or benzoxathiin 20 rings. 

The recent band calculations by Brooks et al. show indeed from charge density calculations that in stoichiometric UO2 a purely ionic picture is incorrect the oxygen ion is singly charged, the second electron not being retained by the Madelung potential. Simple considerations based on mechanical properties and spectroscopic evidence had already pointed at these conclusions. 

Figure 1.17. Electron charge density difference contour map for CO on Ni(100) and CO on Ni(100)/H in atop sites, derived from DFT calculations.

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