Electron density modulation

The situation discussed here is equivalent to a periodic distortion of the lattice with a period 2a, as developed above. When the perturbation //per is given by lattice vibrations, that is mediated by electron-phonon interactions, the electronic density modulation is expressed in terms of a charge-density wave (CDW), while when electron-electron repulsions dominate the modulation is induced by SDWs (Canadell Whangbo, 1991). 

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. 

Gorecka E, Vaupotic N, Pociecha D (2007) Electron density modulations in columnar banana phases. Chem Mater 19 3027-3031... 

Modulation of the electron density on the frontier atomic orbitals centered on the active atom(s) with LUMO and HOMO character... 

At the start of each modulation pulse, a sharp peak in optical emission is seen. Similar SiH emission peaks in pulsed plasmas have been found by Scarsbrook et al. [516] and Howling et al. [321]. The sharp peak was claimed to be caused by a pulse of high-energy electrons. Overzet and Verdeyen [517] measured electron densities at a 2.9-MHz excitation frequency and modulation frequencies up to 20 kHz. The optical emission of a SQWM argon plasma was measured by Booth et al. [518], who also performed particle-in-cell modeling. 

Effect of diagonal-off-diagonal dynamic disorder (D-off-DDD). The polarization fluctuations and the local vibrations give rise to variation of the electron densities in the donor and the acceptor, i.e., they lead to a modulation of the electron wave functions A and B. This leads to a modulation of the overlapping of the electron clouds of the donor and the acceptor and hence to a different transmission coefficient from that calculated in the approximation of constant electron density (ACED). This modulation may change the path of transition on the potential energy surfaces. 

The effects of the modulation of electron density by local vibrations and polarization fluctuations are most pronounced for reactions involving transfer of weakly bound electrons. These effects were investigated in Ref. 16 for the transfer of weakly bound electrons from a donor Az to an acceptor BZ2 in a polar medium. 

Kinetic Parameters for the Symmetric Transition Taking Account of the Modulation of the Zeroth-Order Electron Densities (Beyond the Condon Approximation)... 

Based on the results obtained in the investigation of the effects of modulation of the electron density by the nuclear vibrations, a lability principle in chemical kinetics and catalysis (electrocatalysis) has been formulated in Ref. 26. This principle is formulated as follows the greater the lability of the electron, transferable atoms or atomic groups with respect to the action of external fields, local vibrations, or fluctuations of the medium polarization, the higher, as a rule, is the transition probability, all other conditions being unchanged. Note that the concept lability is more general than... 

Effect of Modulation of the Electron Density on the Inner-Sphere Activation... 

The effects of modulation of the electron density by the intramolecular vibrations on the process of inner-sphere activation... 

The termination module of surfactin synthetase is a 144 kDa four-domain enzyme responsible for the incorporation of the final amino acid (L-Leu) into the surfactin peptide and subsequent cyclization of the resulting product. The structure of the TE domain of this construct was previously solved. In the recently determined 2.6 A X-ray structure of the C-A-PCP-TE construct, the entire protein chain is evident in the electron density maps. " " The structural folds of the individual domains in this module are similar to structures of monomeric domains (Figure 13). The deviations observed in this multidomain structure include a slight difference in the hinge region of C domain subdomains and an orientation of the subdomains of the A domain that is not consistent with the open or closed conformations previously described. The A domain contains... 

The laser interferometer consists of two coupled resonators, one containing the laser, the other the plasma under investigation (Fig. 10). The laser radiation, reflected back from mirror A/s, which contains phase information about the refractive index of the plasma, interferes with the laser wave in cavity A, resulting in an amplitude modulation of the laser output 267). This modulation can be related to the refractive index and therefore to the plasma frequency and electron density. With a curved rather than a planar mirror, the sensitivity can be increased by utilizing transverse cavity modes 268). 

The isotropic shift. The isotropic shift is the sum of two contributions the contact and the dipolar contributions. The former is due to the presence of unpaired electron density on the resonating nucleus. The latter arises from the anisotropy of the magnetic susceptibility tensor, modulated by the distance between the unpaired electron and the resonating nucleus, and is also dependent on the orientation of the metal nucleus vector with respect to the principal axes of the magnetic susceptibility tensor. Some problems arise when the spin delocalization is taken into account in calculating the dipolar coupling, but we will not address this problem except when strictly necessary. 

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