Electron deformation density patterns

So far we have discussed 2D density modulated phases that are formed by deformation or breaking of the layers. However, there are also 2D phases with more subtle electron density modulations. In some cases additional peaks observed in the XRD pattern (Fig. 10) are related to a double layer periodicity in the structure. As double layer periodicity was observed in the bent-core liquid crystals formed by the asymmetric as well as symmetric molecules [22-25] it should be assumed that the mechanism leading to bilayers must be different from that of the pairing of longitudinal dipole moments of molecules from the neighboring layers, which is valid for smectic antiphases made by asymmetric rod-like molecules. 

J. Gu et al., H-bonding patterns in the platinated guanine-cytosine base pair and guanine-cytosine-guanine-cytosine base tetrad An electron density deformation analysis and aim study. J. Am. Chem. Soc. 126, 12651-12660 (2004)... 

Under equal circumstances, the X-ray diffraction pattern shows an intensity proportional to ZtZ2 and by far the larger part of the intensity is due to the electrons in inner shells. It is very difficult to obtain reliable values for the density of the valence electrons 51) and even in the very favorable case of diamond (where only a-third of the electrons are in inner shells) the electron density around each C+4 core is almost exactly spherical, and certainly not four sausages connecting the closest neighbor atoms. For group-theoretical reasons, the first deviation from spherical symmetry allowed 16 > has octupole symmetry (proportional to xyz) but the strength of this deformation is only a few percent of the spherically symmetric density. 

Theoretical and experimental approaches to understanding structure and properties of cyclophosphazenes have appeared. The most significant of these is a report of the observed (x-ray diffraction) and calculated (ab initio) deformation electron densities in the benzene solvate of hexa(aziridinyl)-cyclotriphosphazene. The electron densities in the phosphazene clearly show the classic island model pattern with nodes in the n system at nitrogen. The dual system is also clearly... 

Fig. Y.l. Coin)arison of the Pauli deformation for two hydrogen atoms and for two helium atoms, (a) Two hydrogen atoms. Visualization of p — calculated in the plane containing the nuclei (the net result is zero). One of the protons is located at the origin, and the other has the coordinates (0, /f, 0), with / = 1.4 a.u. (the distance close to the equilibrium). For this distance, the overly integral (see Appendix R available at booksite.elsevier.com/978-0-444-59436-5, p. el37) 5 = (1 + / + )exp —R) amounts to 0.752943. As we can see, the electronic density has flown from the nuclei to the bond, (b) Two helium atoms. The only difference with respect to (a) is that two electrons have been added. But the visualization of p — p( reveals a completely different pattern. This time, the electronic density has been removed from the bond region and increased in the region of the nuclei.

This makes out of computational chemistry a quite unique tool allowing to give the answer about the energy and electronic density distribution (bond pattern) for any system and for any deformation of the system we imagine. This powerful feature can be used not only to see what happens for a particular experimental situation, but also what would happen if we were able to set the conditions much beyond any imaginable experiment. 

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