Polarization coefficient

The fluorine sp3,77 hybrid [with 78.95% p character see Example 2.2] also has weak d-orbital contributions [0.12%] that can usually be ignored.) The polarization coefficients indicate that about 77.6% of the electron density is polarized toward the more electronegative F atom. 

Of course, there is intrinsically no sharp physical distinction between a strongly delocalized lone pair and a highly polarized dative bond. As shown by Eq. (1.31a), a general NBO allows smooth variations of polarization coefficients between the single-center ionic (ca = 0, cb = 1) and two-center covalent (ca = cb) limits. 

For a normalized bond orbital, the relationship between polarization coefficients cA and cB and fractional ionicity zAB can be expressed as (cf. Eq. (1.41a))... 

The accuracy of this approximation is shown in the entries of Table 3.8. Furthermore, the polarization coefficients cA and c in (3.54) are simply related to the bond... 

Exercise Estimate the polarization coefficients of the sigma and pi bonds of N=As. Solution From Table 3.11 the pi-electronegativities of N and As are... 

These estimates compare reasonably with the calculated polarization coefficients in the actual 7TNas NBOs of N=As,... 

The accuracy of alternative Lewis structures can be assessed by specifying the number and locations of lone pairs and two- and three-center bonds with a SCHOOSE keylist (a standard option of the NBO program). (The directed SCHOOSE list replaces the usual NBO search over all possible Lewis structures, but the hybrids and polarization coefficients of CHOOSE structures are optimized in the usual way.) The increased non-Lewis density measures the larger error of the CHOOSE structure compared with the optimal NBO structure. 

Recently the data concerning to interaction of propanthiole with chlorine dioxide in 8 solvents have been published [1], In this work it was shown, that the dependence of process rate from solvents properties is satisfactory described for seven solvents, after the exclusion of data for ethyl acetate, by the Koppel-Palm four parameters equation (coefficient of multiple correlation R 0,96) at determining role of medium polarity (coefficient of pair correlation between lg(k) and (s - l)/(2e + 1) - r 0.90). Chemical mechanism of the reaction including the formation of ion-radical RS H and radical RS has been proposed by authors [ ] ... 

Now the magnitude of the polarization depends on the direction of displacement (Figure 14). For the covalent (e.g. titanyl or vanadyl) M=0 bond, in general, one expects that the electron cloud would be more easily polarized towards the oxygen atom. This direction dependency means that the polarization coefficients must be described using tensor quantities. 

This expression disentangles the properties of the light polarization (coefficients /9, ( 1)), the geometry of two-electron emission (coefficients B t2(Ka, Kb)) and the dynamical parameters of the double photoionization process (coefficients A(ku k2, k)). The pkq(El) are the statistical tensors of the incident light which describe its polarization properties in the electric dipole approximation represented by 1. For linearly polarized light in which the electric field vector defines the z-axis of the coordinate frame, one has only two non-vanishing components given by (see equ. (8.99b))t... 

Material polarization coefficient or dielectric susceptibility such that polarization density P = soxmks E in mks ("SI") units or /cgs E in cgs ("Gaussian") units. 

Concentration and temperature polarization can be reduced by the presence of spacers that are mrbulence promoters, which enhance the mass flux by increasing the film heat transfer coefficient. Spacers also change the flow characteristics and promote regions of turbulence thus improving boundary layer transfer [106]. DCMD in spacer-filled channels have been shown to improve flux by 31% 1% than that without spacers. The temperamre polarization coefficients are substantially increased and approach unity when the spacers are used in the channels. 

Upon operation, we can obtain both polarization coefficients ... 

The three typical molecular configurations and the associated second and third NLO polarization coefficient summary are shown in Figure 6.30. Those with the center symmetry have no second NLO property. However, they may have a non-zero value if an electric field destroys the up and down symmetry of molecular orientation. 

Figure 7.1 presents contour diagrams for the Lewis-type NBOs of formaldehyde (panels a, c, e, g, h), calculated at the B3LYP/6-311-H-G""" level of hybrid density functional theory (DFT). As is immediately apparent, the bonding Gch, and Kcq NBOs exhibit the familiar sigma and pi shapes of idealized textbook depictions. The resemblance to expected textbook forms is further emphasized when each A-B bond is written as a linear combination (LC) of its constituent natural hybrid orbitals (NHOs) and with polarization coefficients and Cg, namely. 

The upper entries in Table 7.1 summarize details of the LC-NHO expansions for valence Lewis-type NBOs of formaldehyde at the B3LYP/6-311-H-G""" level. The carbon and oxygen hybrids of a o and Gch have the expected sp -like composition, and the polarization coefficients vary in the expected way with elec-... 

In this relation, M and fi are mass and polarization coefficients of colliding atoms, and Tq is the gas temperature. The ion-conversion effect takes place as a preliminary stage of recombination not only for simple atomic ions but also for some important molecular ions. Polyatomic ions have very high recombination rates (see Table 2-2), often exceeding 10 cm /s at room temperature, which results in an interesting fact recombination of... 

It seems quite reasonable that the ratio of the hydrogen bonding to the polarity coefficients (b/s) in the solvatochromic equations should be higher for the pmr shift of the hydrogen bonded proton than for the C nmr shift, involving an atom once removed from the hydrogen bonding site. 

He et al used a binary mixture-based film model to perform a theoretical analysis on the concentration polarization in a generic membrane. They defined a concentration polarization coefficient for both the two species involved in the separation as the ratio of the actual flux to the ideal one (without polarization), quantifying the polarization effect by means of the ratio of the actual fluxes of the components. Although this is a simplified approach that cannot be generalized to multi-component systems, nevertheless, under some operating conditions, the authors predicted a significant influence of the external mass transfer on the process. 

In the following sub-section, concentration polarization coefficient (CPC) and inhibition coefficient (IC) will be introduced separately in order to show their different contribution on the overall permeance reduction. 

In order to provide a quantitative indication of the polarization level, several different concentration polarization coefficients can be found in the literature. The most used definitions are summarized in Table 14.1. The first thing to... 

Table 14.1 The most common concentration polarization coefficients in literature...

Wang et alP uses a similar approach to define a concentration polarization coefficient, with the only difference that in their definition the coefficient is close to zero when the polarization is negligible. 

All of the considerations made in the previous section lead to the necessity of defining a concentration polarization coefficient that could be directly connected to specific permeation quantities.Here, this approach will be direct to hydrogen permeation through Pd-based membranes. 

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