Total electric field, definition

In Eq. (3), is the relevant molecular transition frequency, y is a dam >ing rate, is a polarizability, and (/) is the z-component of the total electric field in the vicinity of the molecule. If (t) were simply of the form i)Cos(fijr), then Eq. (3) is the well-known phenomenological Lorentzian oscillator model of absorption which leads to an approximate Lorentzian form for the absorption cross section [1]. Similar remarks hold for the SP dipole, fi/f), if E t) = ocos(mr), where E t) is the z-component of the total electric field near the SP dipole. The parameters 04,74 and a, in this case are chosen such that the resulting Lorentzian cross section proximates the known exact sur ce plasmon absorption cross section or its appropriate form in the quasistatic (a A=2 tic/cs) limit. Note that I am using a simplified notation compared to the various notations of Refs. [13-15]. (Relative to Ref. [13], for example, my definitions of surface plasmon dipole... 

In Chapter 32 we derived the governing equation which relates the total electric field E of a weakly guiding waveguide to current sources of density J within the waveguide. Using the waveguide parameter definition inside the back cover, Eq. (32-52) is expressible as... 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

Quadratic terms in die property expansions are considered to be first-order in electrical anharmonicity, cubic terms are taken to be second-order, etc. Similarly, cubic terms in the vibrational potential are considered to be first-order in mechanical anharmonicity, quartic terms are second-order, and so forth. The notation (n, m) is used hereafter for the order of electrical (n) and mechanical (m) anharmonicity whereas the total order (n -I- m) is denoted by I, II,. Although our definition of orders is reasonable other choices are possible. Two key questions are (1) How important are anharmonicity contributions to vibrational NLO properties and (2) What is the convergence behavior of the double perturbation series in electrical and mechanical anharmonicity Both questions will be addressed later. Here we note that compact expressions, complete through order II in electrical plus mechanical anharmonicity, have been presented [19]. The formulas of order I contain either cubic force constants or second derivatives of the electrical properties with respect to the normal coordinates. Depending upon the level of calculation at least one order of numerical differentiation is ordinarily required to determine these anharmonicity parameters. For electrical properties, the additional normal coordinate derivative may be replaced by an electric field derivative using relations such as d p./dQidQj = —d E/dldAj.ACd, = —dk,/rjF where F is the field and k j is... 

As for the electric field, this leads to the definition of the dipole and magnetizability as first and second derivatives of the total energy with respect to the magnetic field. 

The total number of bonds with solvent and ligand molecules in the first coordination sphere is the coordination number (CN) of the ion. The first solvation number (Ns) is the number of solvent molecules in the first coordination sphere. Such a time-independent definition needs, however, a complementary time-dependent definition of the first coordination sphere. Therefore, a solvent molecule in the first coordination sphere may be defined as having a long residence time in comparison to its correlation time in subsequent coordination spheres or in the bulk. Undoubtedly, the solvation residence time varies with the lability of the metal ion. The solvation number (S) is defined as the number of solvent molecules under the influence of the electric field generated by the central ion, and following the ion s motion in the solution. 

At this time, one should ask what is the migration velocity Ui of the ith ionic species exposed to an electrical field V

ionic flux AT, From definitions (3.1.82) and (3.1.84b),... 

The determination of a property density at some point in a molecule by the total distribution of particles in the system is essential to the definition of atomic contributions to the electric and magnetic properties of a system. The densities for properties resulting from the molecule being placed in an external field must describe how the perturbed motion of the electron at r depends upon the field strength everywhere inside the molecule, a point that has been emphasized by others (Maaskant and Oosterhoff 1964). This requirement is met by the definition of an atomic property as determined by the theory of atoms in molecules. Property densities for a molecule in the presence of external electric and magnetic fields have been defined and discussed by Jameson and Buckingham (1980) and the present introduction follows their presentation. 

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