Fermi coupling

If the electronic properties of the semiconductor - the Fermi level, the positions of the valence and the conduction band, and the flat-band potential - and those of the redox couple - Fermi level and energy of reorganization - are known, the Gerischer diagram can be constructed, and the overlap of the two distribution functions Wox and Wred with the bands can be calculated. 

Consequently, the Hamiltonian of the dimer that involves Davydov coupling, Fermi resonances between the g excited state of the fast mode and the g first harmonics of the bending mode, together with the damping of is... 

The aim of this appendix is to show that the g ACF (304) involving Davydov coupling, Fermi resonances, and damping, may be viewed, after some simplifications, as formally equivalent to that used by Marechal [83] in his peeling-off approach of Fermi resonances. 

Spin density in s orbitals of an atom with a magnetic nucleus results in an isotropic hyperfine coupling (Fermi contact interaction of electron and nuclear spin). Proton s orbital spin densities are usually caused by spin polarization and are proportional to the spin density on the directly bound neighbor atom. Isotropic hyperfine couplings are thus related to the delocalization of the SOMO. 

P.-O. Lowdin. Studies in Perturbation Theory Part VIII. Separation of Dirac equation + Study of Spin-Orbit Coupling + Fermi Contact Terms. J. Mol. Spectrosc., 14(2) (1964) 131-144. 

In the Raman spectrum the modes should appear near 1594 cm , but because of a second-order coupling (Fermi resonance), the band spUts and the 1594 cm band is observed as a doublet. Thus the band in benzene is a split peak even though it arises from a degenerate band system (Figure 5.6). 

Several other examples of veiy strong intramolecular H bonding are known. For example, in tropolone the carbonyl band is essentially missing from the spectrum. The absorption that occurs near 1605 cm may involve some C—O displacement (Figure 7.9). f. Second-order coupling (Fermi resonance)... 

Chamma, D., and O. Henri-Roussean. 1999. IR theory of weak H-bonds Davydov coupling, Fermi resonances and direct relaxations. I. Basis equations within the linear... 

Many experimental techniques now provide details of dynamical events on short timescales. Time-dependent theory, such as END, offer the capabilities to obtain information about the details of the transition from initial-to-final states in reactive processes. The assumptions of time-dependent perturbation theory coupled with Fermi s Golden Rule, namely, that there are well-defined (unperturbed) initial and final states and that these are occupied for times, which are long compared to the transition time, no longer necessarily apply. Therefore, truly dynamical methods become very appealing and the results from such theoretical methods can be shown as movies or time lapse photography. 

The idea of having two distinct quasi-Fermi levels or chemical potentials within the same volume of material, first emphasized by Shockley (1), has deeper implications than the somewhat similar concept of two distinct effective temperatures in the same block of material. The latter can occur, for example, when nuclear spins are weakly coupled to atomic motion (see Magnetic spin resonance). Quasi-Fermi level separations are often labeled as Im p Fermi s name spelled backwards. 

It will be intriguing to theoretically examine the possibility of superconductivity in CNT prior to the actual experimental assessment. A preliminary estimation of superconducting transition temperature (T ) for metallic CNT has been performed considering the electron-phonon coupling within the framework of the BCS theory [31]. It is important to note that there can generally exist the competition between Peierls- and superconductivity (BCS-type) transitions in lowdimensional materials. However, as has been described in Sec. 2.3, the Peierls transition can probably be suppressed in the metallic tube (a, a) due to small Fermi integrals as a whole [20]. 

Gaussian computes isotropic hyperfine coupling constants as part of the population analysis, given in the section labeled "Fermi contact analysis the values are in atomic-units. It is necessary to convert these values to other units in order to compare with experiment we will be converting from atomic units to MHz, using the following expressions ri6ltYg ... 

The spin Hamiltonian operates only on spin wavefunctions, and all details of the electronic wavefunction are absorbed into the coupling constant a. If we treat the Fermi contact term as a perturbation on the wavefunction theR use of standard perturbation theory gives a first-order energy... 

The only term surviving the Bom-Oppenheimer approximation is the direct spin-spin coupling, as all the others involve nuclear masses. Furthermore, there is no Fermi-contact term since nuclei cannot occupy the same position. Note that the direct spin-spin coupling is independent of the electronic wave function, it depends only on the molecular geometry. 

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

A completely different type of property is for example spin-spin coupling constants, which contain interactions of electronic and nuclear spins. One of the operators is a delta function (Fermi-Contact, eq. (10.78)), which measures the quality of the wave function at a single point, the nuclear position. Since Gaussian functions have an incorrect behaviour at the nucleus (zero derivative compared with the cusp displayed by an exponential function), this requires addition of a number of very tight functions (large exponents) in order to predict coupling constants accurately. ... 

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

From an energetic point of view, the bands at higher wavenumbers can be assigned to the Ss rings. However, the intensities were found as ca. 0.65 1 (pure infected) instead of 2.8 1 which would be expected from the natural abundance of the isotopomers. These discrepancies were solved by applying the mathematical formalism utilized in the treatment of intramolecular Fermi resonance (see, e.g., [132]). Accordingly, in the natural crystal we have to deal with vibrational coupling between isotopomers in the primitive cell of the crystal [109]. 

The complete Hamiltonian of the molecular system can be wrihen as H +H or H =H +H for the commutator being linear, where is the Hamiltonian corresponding to the spin contribution(s) such as, Fermi contact term, dipolar term, spin-orbit coupling, etc. (5). As a result, H ° would correspond to the spin free part of the Hamiltonian, which is usually employed in the electron propagator implementation. Accordingly, the k -th pole associated with the complete Hamiltonian H is , so that El is the A -th pole of the electron propagator for the spin free Hamiltonian H . 

The expression for the rate R (sec ) of photon absorption due to coupling V beriveen a molecule s electronic and nuclear charges and an electromagnetic field is given through first order in perturbation theory by the well known Wentzel Fermi golden rule formula (7,8) ... 

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