Crystal, electron distributions

Significant progress in the optimization of VDW parameters was associated with the development of the OPLS force field [53]. In those efforts the approach of using Monte Carlo calculations on pure solvents to compute heats of vaporization and molecular volumes and then using that information to refine the VDW parameters was first developed and applied. Subsequently, developers of other force fields have used this same approach for optimization of biomolecular force fields [20,21]. Van der Waals parameters may also be optimized based on calculated heats of sublimation of crystals [68], as has been done for the optimization of some of the VDW parameters in the nucleic acid bases [18]. Alternative approaches to optimizing VDW parameters have been based primarily on the use of QM data. Quantum mechanical data contains detailed information on the electron distribution around a molecule, which, in principle, should be useful for the optimization of VDW... 

A few years ago3 71 proposed an electroneutrality principle—the postulate that the electron distribution in stable molecules and crystals is such that the electrical charge that is associated with each atom is close to zero, and in all cases less than 1, in electronic units. In a molecule involving single bonds we expect a transfer of charge from atom to... 

Since every atom extends to an unlimited distance, it is evident that no single characteristic size can be assigned to it. Instead, the apparent atomic radius will depend upon the physical property concerned, and will differ for different properties. In this paper we shall derive a set of ionic radii for use in crystals composed of ions which exert only a small deforming force on each other. The application of these radii in the interpretation of the observed crystal structures will be shown, and an at- Fig. 1.—The eigenfunction J mo, the electron den-tempt made to account for sity p = 100, and the electron distribution function the formation and stability D = for the lowest state of the hydr°sen of the various structures. 

The ground term of the cP configuration is F. That of is also F. Those of and d are " F. We shall discuss these patterns in Section 3.10. For the moment, we only note the common occurrence of F terms and ask how they split in an octahedral crystal field. As for the case of the D term above, which splits like the d orbitals because the angular parts of their electron distributions are related, an F term splits up like a set of / orbital electron densities. A set of real / orbitals is shown in Fig. 3-13. Note how they comprise three subsets. One set of three orbitals has major lobes directed along the cartesian x or y or z axes. Another set comprises three orbitals, each formed by a pair of clover-leaf shapes, concentrated about two of the three cartesian planes. The third set comprises just one member, with lobes directed equally to all eight corners of an inscribing cube. In the free ion, of course, all seven / orbitals are degenerate. In an octahedral crystal field, however, the... 

Brown, A.S., Spackman, M.A. and Hill, R.J. (1993) The electron distribution in corundum. A study ofthe utility of merging single-crystal and powder diffraction data, Acta Cryst., A49, 513-527. 

The linear and nonlinear optical properties of the conjugated polymeric crystals are reviewed. It is shown that the dimensionality of the rr-electron distribution and electron-phonon interaction drastically influence the order of magnitude and time response of these properties. The one-dimensional conjugated crystals show the strongest nonlinearities their response time is determined by the diffusion time of the intrinsic conjugation defects whose dynamics are described within the soliton picture. 

Two- and three-dimensional crystals.In two-dimensional (2D) systems the critical regions are of two kinds points at energy Eo at the edge of the B.Z. reminiscent of ID patterns in the electron distribution with a contribution in x and x as given by (7) and lines at energy Ej intrinsic to the 2D system. The effect... 

An EPR and ENDOR investigation of the planar copper complex 63Cu(sal)2 (Fig. 30) substituted into a single crystal of Ni(sal)2 has been reported by Schweiger et al.62,65). The aim of this work was to determine the structure of the internal H-bond occuring in Cu(sal)2, and to draw a detailed picture of the unpaired electron distribution on the... 

One important aspect not discussed above is the change in atomic structure at a surface. Contrary to the schematic picture of the Si(lll) surface shown in Fig. 14.6, a solid surface is usually not just the end of a perfect crystal. Surfaces reconstruct in response to the changes in the electronic distribution caused by the surface itself. Again, all these changes occur selfconsistently, and in principle, if the total energy for various configurations of atomic structures at a surface could be evaluated, the shifts in the positions of the atoms and the electronic structures of the surface could be determined theoretically. This approach will be discussed in the next section, but the first calculations for reconstructed surfaces were done using experimental determinations of the atomic positions. 

The mechanism by which electrons interact with crystals is different from that of X-rays. X-rays detect electron density distribution in crystals, while electrons detect electrostatic potential distribution in crystals. Electron crystallography may be used for studying some special problems related to potential distribution such as the oxidation states of atoms in the crystal. 

A major application of QED is the accurate determination of crystal charge density. The scientific question here is how atoms bond to form crystals, which can be addressed by accurate measurement of crystal structure factors (Fourier transform of charge density) and from that to map electron distributions in crystals. 

As mentioned above, the number of projections, or zone axes, which need to be collected depends on the symmetry of the crystal and distribution of strong reflections. In order to determine which zone axes should be chosen for collecting HREM images, a nearly complete 3D electron diffraction data set needs to be collected. 

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