Electric field correction

In these expressions, gi is the degeneracy of the initial state, n is the refractive index, and xl is the local correction to the electric field, accounting for the ion being less polarizable than the bulk medium. The local electric field correction may be taken as,... 

According to the macroscopic Maxwell approach, matter is treated as a continuum, and the field in the matter in this case is the direct result of the electric displacement (electric induction) vector D, which is the electric field corrected for polarization [7] ... 

There are many other attempts for incorporating the local electric field correction. I ao [37J used the finite-element analysis method for calculating the electrostatic interaction in a chain and found that the interaction force between a pair-particle can be expressed as ... 

Hq. (16) gives a slightly stronger force than that given hy hq. (17), and predicts 20% higher interparticle force than that given by the point-dipole approximation method with the local electric field correction [37]. Generally, a more universal form could be used to express the derived electrostatic force [38] ... 

The transverse fields of the fundamental modes in Table 14-1 contain no polarization effects due to the fiber. These effects are included in higher-order corrections through the expansions in Section 32-1. The second-order transverse electric field corrections satisfy the equation in Table 32-1, page 627. If we set f = R, substitute e or e,3 from Table 14-1 fore, and take = 51//A from Table 14-2, it is readily verified that the... 

The molecular quantities can be best understood as a Taylor series expansion. For example, the energy of the molecule E would be the sum of the energy without an electric field present, Eq, and corrections for the dipole, polarizability, hyperpolarizability, and the like ... 

The electric field can be incorporated in the Flamiltonian via a finite field term or approximated by a set of point charges. This allows the computation of corrections to the dipole only, which is generally the most significant contribution. 

The system of electric and magnetic fields or lenses is called the ion optics of the mass spectrometer. Electric lenses correct aberrations in the shape of the ion beam. 

Electric field measurement at the boundary of a metal container filled with charged material. Examples include pipelines and storage vessels. The electric field can be used to calculate charge density (3-5.1). Eield meters can also be lowered into containers such as silos to determine the local fields and polarities. Quantitative interpretation of the reading requires correction for field intensification and is sometimes accomplished using computer simulations. 

In order to find the correct quantum-mechanical energies for a nuclear quadrupole in an electric field gradient, we need to... 

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

The theoretical method, as developed before, concerns a molecule whose nuclei are fixed in a given geometry and whose wavefimctions are the eigenfunctions of the electronic Hamiltonian. Actually, the molecular structure is vibrating and rotating and the electric field is acting on the vibration itself. Thus, in a companion work, we have evaluated the vibronic corrections (5) in order to correct and to compare our results with experimental values. 

Moreover, for the observables depending on external electric field, its specific effect has to be investigated the electric field induces new terms in the nuclear Hamiltonian, due to the change of equilibrium geometry and the nuclear motion perturbation. Pandey and Santry (14) has brought to the fore this effect and calculated the correction which only concerns the parallel component. It is represented by the following expression ... 

Mulliken (41) distinguishes two kinds of polarization. He calls Coulomb polarization what we are concerned with in this paper the polarization produced by an electric field, and he calls valence polarization a kind of polarization du to quantum-mechanical valence forces. In order to correctly describe the chemical bond in H2, it is necessary to include the valence polarization function as soon as one calculates energy with the unperturbed function (i.e. the 2p orbital). 

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