External electric field additional energy

The latter term is gauge independent, i.e. does not contain the vector potential, and, therefore, fully deserves the interpretation of an additional potential term for the internal motion with the kinetic energy at Eq. (6). Apart from the constant the potential contains two coordinate dependent parts. The term linear in the coordinates — ] (K x B)r consists of two Stark terms one which is due to the external electric field E and a second one which is a motional Stark... 

The Hamiltonian of the crystal with possible ordering of the electric dipole moments [24] additionally to the traditional terms discussed above contains the energy of the polarized crystal, the electron-polarization interaction (similar to the electron-strain interaction), and the interaction with the external electric field. After... 

Care must be taken in using the expressions above for obtaining nonlinear optical properties, because the values obtained may not be the same as those obtained from Eq. [4]. The results will be equivalent only if the Hellmann-Feyn-man theorem is satisfied. For the case of the exact wavefunction or any fully variational approximation, the Hellmann-Feynman theorem equates derivatives of the energy to expectation values of derivatives of the Hamiltonian for a given parameter. If we consider the parameter to be the external electric field, F, then this gives dE/dP = dH/d ) = (p,). For nonvariational methods, such as perturbation theory or coupled cluster methods, additional terms must be considered. 

We now turn our attention to the outer, diffuse regions of the electronic system. The valence and core-valence basis sets considered so far are inadequate for the description of the difiuse electron distributions characteristic of anionic systems and excited states. In addition, these sets do not have the flexibility required for a proper description of interactions with external electric fields and hence the accurate calculation of dipole moments and polarizabilities. For such calculations, additional functions must be added in the outer valence region. Within the framework of correlation-consistent basis sets, we proceed by adding primitive functions to the standard cc-pVXZ sets, with exponents adjusted so as optimize the energy of atomic anions. Diffuse functions are added in groups, with one set of functions for each angular momentum present in the root set. This procedure leads to the augmented correlation-consistent polarized valence basis sets aug-cc-pVXZ [25], the composition and size of which are listed in Table 8.13. The number of functions in the aug-cc-pVXZ sets may be calculated as... 

In die presence of an electromagnetic field of energy of about our systems can undergo absorjDtive transitions from to E2, extracting a photon from die electric field. In addition, as described by Einstein, die field can induce emission of photons from 2 lo E (given E2 is occupied). Let die energy density of die external field be E(v) dren. 

As mentioned above, the interpretation of CL cannot be unified under a simple law, and one of the fundamental difficulties involved in luminescence analysis is the lack of information on the competing nonradiative processes present in the material. In addition, the influence of defects, the surface, and various external perturbations (such as temperature, electric field, and stress) have to be taken into account in quantitative CL analysis. All these make the quantification of CL intensities difficult. Correlations between dopant concentrations and such band-shape parameters as the peak energy and the half-width of the CL emission currently are more reliable as means for the quantitative analysis of the carrier concentration. 

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