Charge density analysis, calculations

Thus, while the X-ray method of charge density analysis does not suffer from some of the ambiguities of the theoretical calculations, the measurements give information on a molecule in a particular environment and not on the isolated state commonly treated in theoretical work. Nevertheless the absence of strong interactions in the FeTPP crystal leads to the conclusion that the ground state of this molecule in its isolated state is close to the 3 ... 

Koritsanszky, T. S. Coppens, P. Chemical applications of X-ray charge-density analysis, Chem. Revs. 2001, 101, 1583-1627 Volkov, A. Coppens, P. Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning, J. Comp. Chem. 2004, 25, 921-934 Suponitsky, K. Y Tsirelson, V. G. Fell, D. Electron-density-based calculations of intermolecular energy the case of urea, Acta Cryst. 1999, A55, 821-827. 

Following Vincent and Radom s comprehensive ab initio study (1978), Escudero et al. (1985) also performed ab initio calculations at the STO-3G level for seven 4-substituted benzenediazonium ions. For the unsubstituted benzenediazonium ion, the optimized geometries are the same as in Figure 4-1 (I). For charge density calculations another population analysis method was used (Escudero and Yanez, 1982), and this gave results different from those of Vincent and Radom. However,... 

In characterizing layered silicate, including layered titanate (HTO), the surface charge density is particularly important because it determines the interlayer structure of the intercalants as well as the cation exchange capacity (CEC). Lagaly proposed a method of calculation consisting of total elemental analysis and the dimensions of the unit cell [15] ... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

On the basis of NMR results, an intriguing anion within the trianion structure was proposed for S ". Such a structure would require 3.0 ee excess in the rim, and 1.0 ee excess in the hub, as compared to neutral 8. Analysis of the charge densities calculated at both semiempirical AMI and ab initio levels, however, predict the hub atoms to gain only about 0.5 ee, while the rim atoms bear more of the charge at 3.5 ee. ... 

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. 

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