Charge flux parameters

Atomic Charges and Charge Flux Parameters from the Atomic Multipolar Tensors. The Planar Case... 

The atomic charges and charge flux parameters are thus all contained in the atomic polar tensor, and are readily available from ab initio calculations. 

ATOMIC CHARGES AND CHARGE FLUX PARAMETERS FROM THE ATOMIC MULTIPOLAR TENSORS. THE PLANAR CASE... 

Given this result the charge flux parameters can now be determined in the following way ... 

Thus, the in-plane charge flux parameters are the crossed second derivatives of the molecular dipole moment, a well-defined computational observable. 

Figure 1 The forces on the two nuclei of CO that are exerted by an incoming point charge of q-O.I e. The lines are interpolations between ab initio results (6-31G /MP2), the squares denote force field calculations that include FR atomic charges q and charge flux parameters j >, and the circles denote force field calculations which include also FR atomic dipoles m and dipolar flux j ". (From Ref. 4, rqtFoduced by permission of the American Chemical Society)...

Relations between effective atomic charges, charge flux parameters and atomic polar tensors for AB2 and AB2 (C2v) molecules (Reprinted from Ref [117] with pomission)... 

If there are more charge parameters than conditions the extra constraint of minimal charge flux may be used by introducing Lagrange multipliers for conditions (2) and... 

Thus the dipole moments do not constitute additional data but are included in the APT. From the empirical force field point of view there are N — 1 charges and (N — 1)[3(N — )] flux parameters (where charge conservation and translational invariance are taken into account), i.e., a total of (N — l)(3N -2) parameters. Therefore, in the most general case there are many more atomic parameters than ab initio) data points. This means that some modeling and approximations must be invoked. For example, one may expect that fluxes between nonbonded atoms that belong to the same molecules may be neglected, and thus reduce the number of parameters. 

In kcal mol /A. y and 7 denote, respectively, the charge and dipolar flux parameters. 

As early as 1972 it was recognized that an explicit inclusion of terms associated with the charge-flux effects accompanying molecular vibrations may offer an opportunity for better understanding of the physical significance of parameters in infi-ared intensity models based on the bond moment concept [42]. 

The bond charge parameter formulation developed by Van Straten and Smit [92] describes infi-ared intensities in terms of static bond charges and bond charge fluxes induced by vibrational distortions. In the mathematical procedure many common features with the )paratus of the valence-optical theory are present. 

It should be emphasized that the charge-flux effects are implicidy included in electro-optical parameters of the type dpj dRj that appear in the first-order bond moment model [72]. Thus, in standard applications to various molecules it does not seem necessary to extend the original formulation since this would result in further increase in intensity parameters. 

Similar formulation, based on representing a molecular difKile moment in terms of effective atomic charges, has been put forward by Aleksanyan el al. [107,110]. Basically the treatment refers to analogous intensity parameters. These are effective atomic charges and atomic charge fluxes expressed in the space of atonuc Cartesian displacement... 

In contnst to atcMoic polar tensors, txmd polar parameters need not be furtber transfimned into effective charges, bond moments, charge fluxes, etc. These should be considered as quantities influmced all kinds of flu t and long distance intramolecular... 

Figure 23. Comparison of calculated current-voltage characteristics of n-type semi-conductor-electroiyte junction device under illumination of 1 mA cm (equivalent) photon flux. Parameters used are Ld = 0.5 x 10 cm, N = 10 cm , a = 3 X 10 cm , n, = 10 cm , e = 12, A Vj. = 0.7 V, t = 10 sec, and the electron and hole exchange current parameters are 10 mA cm and 10 mA cm , respectively. (a) Gartner s (Butler s) model [Eq. (103)]. (b) Reichman s model considering both electron and hole currents but neglecting the space charge recombination, (c) Reichman s model with the space charge recombination, (d) As (b) but in dark.

In silane discharges several ions are observed to be involved in a charge exchange process, and therefore maxima in their ion energy distribution at distinct energies are observed. The charge carrier density and the plasma potential that result from the fit of the lED allow for the quantification of the related parameters sheath thickness and ion flux. This method has been be used to relate the material quality of a-Si H to the ion bombardment [301. 332] see also Section 1.6.2.3. 

The number of charge carriers generated in the SCR depends on the absorbed flux of incident photons per unit area P, the width W of the SCR and the wave-length-dependent absorption coefficient a of bulk Si. The latter parameter is shown in Fig. 7.6, while the resulting penetration depth for light of different wavelengths is shown in Fig. 10.4a. 

Dungan et al. [186] have measured the interfacial mass transfer coefficients for the transfer of proteins (a-chymotrypsin and cytochrome C) between a bulk aqueous phase and a reverse micellar phase using a stirred diffusion cell and showed that charge interactions play a dominant role in the interfacial forward transport kinetics. The flux of protein across the bulk interface separating an aqueous buffered solution and a reverse micellar phase was measured for the purpose. Kinetic parameters for the transfer of proteins to or from a reverse micellar solution were determined at a given salt concentration, pH, and stirring... 

---