Electron polarization, static electric fields

The application of a static electric field polarizes the electronic charge distribution and leads to changes in molecular magnetic susceptibility and nuclear... 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

For a long time the finite oligomer approach was the only method available for determining linear and nonlinear polarizabilities of infinite stereoregular polymers. Recently, however, the problem of carrying out electronic band structure (or crystal orbital) calculations in the presence of static or frequency-dependent electric fields has been solved [115, 116]. A related discretized Berry phase treatment of static electric field polarization has also been developed for 3D solid state systems... 

More recently, an alternative method has been developed which takes advantage of an applied static electric field designed to pull the muon and electron apart before they combine to form Mu near the end of the muon track [21]. The result of a typical experiment as a fimction of the applied field is shown in Figure 5 which gives the asymmetries (un-normalized polarizations) of Mu and D species in solid a-N2. It is obvious that the field interferes in the distribution of muons, and most remarkably, the behavior is not symmetric with respect to zero field. This means that the muon does not come to rest in the center of a... 

Molecules with polar groups possess a permanent dipole moment pp. In these molecules, a static electric field produces an orientation polarizability, in addition to induced atomic or electron polarization i.e., the most probable rest position for the permanent dipole lies preferentially in the direction of the field. Molecules with permanent dipoles thus often store more electrical energy than those with induced dipoles. 

The Stark-PNC form of interference is utilized in experiments with heavy atoms at Berkeley and Paris, and in many experiments with hydrogen. Here we present a qualitative sketch of the scheme used at Paris and Berkeley. The basic idea, originally pointed out by Bouchiat and Bouchiat, is that an electronic polarization (i.e., a nonzero expectation value of the electronic angular momentum ])) in the excited state of the atom is induced by absorption of a circularly polarized photon directed perpendicular to an applied static electric field. 

Nonadiabatic electronic transitions are of fundamental importance in chemistry. In particular, because a conical intersection (conical intersection) between two electronic states provides a very fast and efficient pathway for radiationless relaxation [117], there has been much interest in controlling transitions through a conical intersection. Indeed, several methods have already been proposed to control the dynamical processes associated with a conical intersection. One of these concerns the modification of electronic states involved in the conical intersection by environmental effects of polar solvents on the PES (potential energy hypersurface) through orientational fluctuations [6, 67, 68]. Another strategy is to apply a static electric field to shift the energy of a state of ionic character as in the Stark effect ]384, 482] (see Ref. ]403, 404] for the non-resonant dynamical Stark effect). More dynamical methods, which aim to suppress the transition either by preparing... 

High polarizability of electrons in Ceo is one of the reasons for which ions and polar molecules are stabilized when trapped in endohedral complexes [3,30]. The dipole polarizability (a) measures the electronic response to a static electric field of a constant strength. Experimental data on polarizability of Ceo or other fullerenes are currently lacking however, a lower bound to a equal to 442.1 au was established by Fowler et al. [31] with the help of ab initio electronic structure calculations carried out at the HF/6-3lG(d) level. Based on this result, one may conclude that, atom for atom, Ceo is at least as polarizable as benzene. A similar (but with a much worse basis set) estimate was obtained for the C70 cluster [32], which was found to be more polarizable than Ceo ... 

The frequency dependence explains why the dielectric permeability of water measured in a static electric field is 81, but at optic frequencies is only 1.77 in the first case all polarization mechanisms are participating in the polarization but in the latter case only electron polarization takes place. 

In the presence of a static, spatially uniform electric field Ea, the electronic cloud of atomic and molecular systems gets polarized. The energy, W, can be written as a Taylor series [1-3]... 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

The reaction between ammonia and methyl halides has been studied by using ab initio quantum-chemical methods.90 An examination of the stationary points in the reaction potential surface leads to a possible new interpretation of the detailed mechanism of this reaction in different media, hr the gas phase, the product is predicted to be a strongly hydrogen-bonded complex of alkylammonium and halide ions, in contrast to the observed formation of the free ions from reaction hr a polar solvent. Another research group has also studied the reaction between ammonia and methyl chloride.91 A quantitative analysis was made of the changes induced on the potential-energy surface by solvation and static uniform electric fields, with the help of different indexes. The indexes reveal that external perturbations yield transition states which are both electronically and structurally advanced as compared to the transition state in the gas phase. 

Applied electric fields, whether static or oscillating, distort (polarize) the electron distribution and nuclear positions in molecules. Much of this volume describes effects that arise from the electronic polarization. Nuclear contributions to the overall polarization can be quite large, but occur on a slower time-scale than the electronic polarization. Electronic motion can be sufficiently rapid to follow the typical electric fields associated with incident UV to near IR radiation. This is the case if the field is sufficiently off resonance relative to electronic transitions and the nuclei are fixed (see ref 5 for contributions arising from nuclear motion). Relaxation between states need not be rapid, so... 

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