Hybridization parameter

In this expression, the hybridization parameter A, varies between 0 (pure s) and oo (pure p), with any integer or non-integer value in this range being physically allowed. The general relationships between k and percentage s and p characters are given by... 

We can also verify that the usual ECAO-MO description (3.2) and (3.4) leads to predicted hybridizations that are generally consistent with the donor-acceptor estimates (3.8). Suppose that each H atom is associated with a valence spin-orbital of hybridized form (3.6). According to Eq. (3.2), the optimal electronic energy of bond formation is obtained by choosing the hybridization parameter k to maximize the magnitude of the interaction element... 

How accurate are the sum rules (3.37a) and (3.37b) for the molecules considered in Example 3.1 The table below summarizes the hybridization parameters A.,- and sum-rule values for C in each species ... 

Exercise Estimate the hybridization parameters (A.nb) for the sigma lone-pair hybrids h b of NH3, H2O, and HF. 

The hybridization parameter X can be estimated at each R by expressions such as (3.1 lb), which in turn are related to visual plots of the s-pz overlap. A procedure for numerically estimating X will be given at the end of this section. For present purposes, we need only recognize from the percentage s characters that the relative energies of the starting atomic hybrids satisfy... 

For the more general case of mequivalent spd hybrids, the expressions have to be modified to allow for different hybridization parameters on the two hybrids, namely A,i and /ii for hi and X2 and /x2 for h2. The general (hx h2) overlap integral now takes the form... 

The hybridization parameter a is to be chosen so as to make the energy of the molecule a minimum, that is, to make the bond energy B have its maximum value. Hence we differentiate B with respect to a and equate to zero, to obtain the equation... 

At the heart of molecular mechanics is a force field [89] and the ultimate force field should be fully transferable between all types of molecule. However, progress towards comprehensive force fields, such as the Universal Force Field of Casewit and Rappe [90], is invariably accompanied by an almost exponential increase in the number of parameters. The effort to reformulate molecular mechanics in terms of valence-bond concepts [91] reduces the number of formal parameters, but at the expense of almost the same number of hybridization parameters, which the authors [92] describe as follows ... 

One can define four coefficients or hybrid parameters hu, / 12, h2i, and I122 and assume a linear dependence of the emitter voltage vE and the collector current ic on the emitter current iE and the collector voltage vCr as follows ... 

The energy of each electron, in the Bond Orbital Approximation, is obtained by using hybrid parameters in Eq. (3-12) ... 

Tlie bands have long been interpreted as LCAO d bands, crossed by and hybridized with a free-electron-like band (Saffren, 1960 Hodges and Ehrenreich, 1965 and Mueller, 1967). By including some eleven parameters (pseudopotential matrix elements, interatomic matrix elements, orthogonality corrections, and hybridization parameters), it is possible to reproduce the known bands very accurately. We shall also make an LCAO analysis of the bands but shall take advantage of recent theoretical developments to reduce the number of independent parameters to two for each metal, each of which can be obtained for any metal from the Solid State Table. These two parameters will also provide the basis for understanding a variety of properties of the transition metals. 

In this way, we see that little hybridization on F originates an atomic dipole ( /xA = O.lOeao) which reduces the formal charge S by about 14%. This reduction is expected to be even larger with larger values of the hybridization parameter. 

The hybridization parameter < >, arbitrary so far, is best chosen so as the bond hybrids bi and b2 point in the direction of the two O—H bonds, giving in this way strongest bonding with His orbitals and satisfying the principle of maximum overlap. According to Equation (2.214), 26 = 105° gives o)Ki 40°, and we obtain the set (Figure 2.21) ... 

The range of small wavevectors k 1 /A -C 1/-R is of special interest as excitons with such wavevectors may be created straightforwardly by light of wavelength A. To leading order kR -C 1, the hybridization parameter F(/. ) of eqn (13.45) has the following form... 

The terminal half-life is a hybrid parameter, and its determinants need to be acknowledged. It is either a hybrid PK parameter determined by both clearance and distribution of the substance or, when there is a flip-flop, a PK characteristic of the drug product depending on bioavailability factors (rate and extent of absorption). In this latter case, the terminal half-life does not reflect the intrinsic rate of substance elimination. Whatever the biological factors controlling the terminal half-life, T1/2 should be considered to select an optimal interval between dose administrations. This is clear if one considers a threshold plasma concentration required for AMD efficacy a long terminal half-life will result in a longer time for plasma concentrations to decline to the threshold concentration. 

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