Coulomb localization

The Auger spectra of CF4 and SiF4 have been analyzed in terms of the concept of Coulomb localization. Contributions from localized two-hole states were used to explain the presence of six r.ither than three main peaks... 

The origin of Coulomb localization for solids can be easily understood in physical terms. If U, the hole-hole repulsion, is larger than the electronic bandwidth, the separation is forbidden because the states lie in the bandgap,... 

While fragmentation is the dominant chemical reaction induced by core electron excitation of molecules in the gas phase, other reactions such as rearrangements can be expected, and this possibility needs to be investigated. The extent of a Coulomb explosion in a large molecule is not known, and the role of Coulomb localization in the chemistry of isolated molecules needs to be examined further. Electron-multiple ion coincidence experiments are essential in the study of the chemistry because it is necessary to relate specific electronic decay channels to particular fragmentation patterns as identified by the several ions that are produced. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

For large systems comprising 36,000 atoms FAMUSAMM performs four times faster than SAMM and as fast as a cut-off scheme with a 10 A cut-off distance while completely avoiding truncation artifacts. Here, the speed-up with respect to SAMM is essentially achieved by the multiple-time-step extrapolation of local Taylor expansions in the outer distance classes. For this system FAMUSAMM executes by a factor of 60 faster than explicit evaluation of the Coulomb sum. The subsequent Section describes, as a sample application of FAMUSAMM, the study of a ligand-receptor unbinding process. 

In addition to the entropy term we assume that there is an extra local coupling between the fields via and, in addition to the coulombic coupling which is long range, we assume the existence of a short-range non-local coupling via We can choose several functional forms to... 

It is seen that the symmetry of the non-coulombic non-local interaction in the bulk phase forces the symmetry of the localized interaction with the wall. If we omitted the surface Hamiltonian and set / = 0 we would still obtain the boundary condition setting the gradient of the overall ionic density to zero. The boundary condition due to electrostatics is given by... 

It is notable that pyridine is activated relative to benzene and quinoline is activated relative to naphthalene, but that the reactivities of anthracene, acridine, and phenazine decrease in that order. A small activation of pyridine and quinoline is reasonable on the basis of quantum-mechanical predictions of atom localization encrgies, " whereas the unexpected decrease in reactivity from anthracene to phenazine can be best interpreted on the basis of a model for the transition state of methylation suggested by Szwarc and Binks." The coulombic repulsion between the ir-electrons of the aromatic nucleus and the p-electron of the radical should be smaller if the radical approaches the aromatic system along the nodal plane rather than perpendicular to it. This approach to a nitrogen center would be very unfavorable, however, since the lone pair of electrons of the nitrogen lies in the nodal plane and since the methyl radical is... 

It is difficult to treat the effect of a heteroatom on the localization energies of aromatic systems, but Brown has derived molecular orbital parameters from which he has shown that the rates of attack of the phenyl radical at the three positions of pyridine relatively to benzene agree within 10% with the experimental results. He and his co-workers have shown that the formation of 1-bromoisoquinoline on free-radical bromination of isoquinoline is in agreement with predictions from localization energies for physically reasonable values of the Coulomb parameters, but the observed orientation of the phcnylation of quinoline cannot be correlated with localization ener-... 

According to a large number of experimental studies, the most stable phologen-erated species in the lowest excited stales of conjugated chains are electron-hole pairs bound by Coulomb attraction and associated to a local deformation of the backbone, i.e., polaron-excilons [18]. A good insight into the properties of these species can be provided by quantum-chemical calculations our recent theoretical... 

The small and weakly time-dependent CPG that persisLs at longer delays can be explained by the slower diffusion of excitons approaching the localization edge [15]. An alternative and intriguing explanation is, however, field-induced on-chain dissociation, a process that does not depend on the local environment but on the nature of the intrachain state. The one-dimensional Wannier exciton model describes the excited state [44]. Dissociation occurs because the electric field reduces the Coulomb barrier, thus enhancing the escape probability. This picture is interesting, but so far we do not have any clear proof of its validity. 

Besides its temperature dependence, hopping transport is also characterized by an electric field-dependent mobility. This dependence becomes measurable at high field (namely, for a field in excess of ca. 10d V/cm). Such a behavior was first reported in 1970 in polyvinylcarbazole (PVK) [48. The phenomenon was explained through a Poole-ITenkel mechanism [49], in which the Coulomb potential near a charged localized level is modified by the applied field in such a way that the tunnel transfer rale between sites increases. The general dependence of the mobility is then given by Eq. (14.69)... 

Fig. 10. Formation of the bipolaron (= diion) state in poly-p-phenylene upon reduction In the model it is assumed that the ionized states are stabilized by a local geometric distortion from a benzoid-like to a chinoid-Iike structure. Hereby one bipolaron should thermodynamically become more stable than two polarons despite the coulomb repulsion between two similar charges...

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

The first term is the familiar one-electron operator, the second term represents the Coulomb potential, and the third term is called exchange-correlation potential. HF and DFT differ only in this last term. In HF theory there is only a nonlocal exchange term, while in DFT the term is local and supposed to cover both exchange and correlation. It arises as a functional derivative with respect to the density ... 

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