Electron-ion interaction

The second important approximation that enables the resolution of Eq. (1.6) consists in considering that every electron is subject to an effective interaction potential V(ri), which takes into account the full attractive electron-ion interactions as well as somehow a part of the repulsive electron-electron interactions. Ideally we would like to express Hq in the form ... 

Prigodin VN, Hsu EC, Park JH, Waldmann O, Epstein AJ (2008) Electron-ion interaction in doped conducting polymers. Phys Rev B 78 035203... 

It is important to remark here that the periodicity of the cation sublattice in the chain direction z just coincides with 2kF periodicity in the case of TEA(TCNQ)2, and with 4kF periodicity in the case of MEM(TCNQ)2. This fact would suffice by itself to account, in terms of electron-cation interaction and commensurability effect, for the intrinsic chain tetramerization of TEA(TCNQ)2 and for the intrinsic chain dimerization of MEM(TCNQ)2, in particular for the residual dimerization still above 335 K. However, the cation subsystem certainly has a more direct, steric influence than through only the electron-ion interaction discussed above on the overall structural properties of the organic salts. 

Using 51-nucleotide sequence windows, Nair et al. (1994) devised a neural network to predict the prokaryotic transcription terminator that has no well-defined consensus patterns. In addition to the BIN4 representation (51 x 4 input units), an EIIP coding strategy was used to reflect the physical property (Le., electron-ion interaction potential values) of the nucleotide base (51 units). The latter coding strategy reduced the input layer size and training time but provided similar prediction accuracy. 

The electronic properties of amino acid side chains are summarized in Table 3, and they represent a wide spectrum of measures. The NMR data are derived experimentally (37). The dipole (38), C mull, inductive, field, and resonance effects were derived from QM calculations (15). The VHSE5 (39) and Z3 (25) scales were developed for use in quantitative structure-activity relationship analysis of the biologic activity of natural and synthetic peptides. Both were derived from principal components analysis of assorted physico-chemical properties, which included NMR chemical shift data, electron-ion interaction potentials, charges, and isoelectric points. Therefore, these scales are composites rather than primary measures of electronic effects. The validity of these measures is indicated by their lack of overlap with hydrophobicity and steric parameters and by their ability to predict biologic activity of synthetic peptide analogs (25, 39). Finally, coefficients of electrostatic screening by amino acid side chains (ylocal and Ynon-local) were derived from an empirical data set (40), and they represent a composite of electronic effects. 

Selloni et al. [48] were the first to simulate adiabatic ground state quantum dynamics of a solvated electron. The system consisted of the electron, 32 K+ ions, and 31 Cl ions, with electron-ion interactions given by a pseudopotential. These simulations were unusual in that what has become the standard simulating annealing molecular dynamics scheme, described in the previous section, was not used. Rather, the wave function of the solvated electron was propagated forward in time with the time-dependent Schrodinger equation,... 

However, plane wave basis sets also have disadvantages. The first one is probably the very large number of basis set elements which can range from a few 10000 to a few 10 . To avoid this number of basis set elements to become even higher so that calculations would become untractable it is absolutely necessary to employ pseudopotentials Only valence electrons are considered, not core electrons it results from this that the electron-ion interactions are not simply the fundamental coulomb attraction. 

Our aim in the present section is to examine the nature of vibrations in several exotic carbon structures, and we begin with the Ceo itself. The calculations to be described here were based on first-principles techniques in which the electron-ion interaction was handled using pseudopotentials in conjunction with a mixed basis including both plane wave states and localized s- and p-orbitals associated with the carbon atoms (Bohnen et al. 1995). As has already been made clear, to... 

By making a Fourier transformation of Ve j and using a plane wave basis k> for the electrons, we can consider the electron-ion interaction in the usual scattering terms in which we consider the amplitude Mq to transfer momentum q to the electron state k> "scattering it into state k + q>. The corresponding diagram for this process in Figure 1. 

Frohlich (10) showed how second order perturbation theory could be applied to derive an effective interaction between electrons from the direct electron-ion interactions. The physical idea is that as one electron scatters from a nuclear center it distorts the lattice, this distortion is felt by another electron, and thus the electrons experience an indirect interaction. The result is that we can think of the electrons as exchanging phonon momentum q in an electron-electron scattering process shown in Figure 2. The effective potential of interaction between the electrons for a scattering involving a change in momentum q is (11),... 

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