Numerical calculations energy parameters

The reliability of initial equations and regulations was proved with numerous calculations and comparisons. In particular, it was shown [8] that PE-parameter numerically equals the energy of valence electrons in a statistical atom model and is a direct characteristic of electron density in the atom at the given distance from the nucleus. 

Pressure dependent fs-CARS spectra for different colliding species are presented and successfully fitted by using the novel AECS scaling law for rotational energy transfer. The model provides as main fit parameter the relevant interaction time of the colliding molecules Tc, which is compared to a numerical calculation derived from the interaction potential. 

Numerical calculations of the dependences of the efficiency of tunnel electron transfer in triethylamine solutions of P on the concentration of mediator molecules calculated in Ref. [85] using Eq. (37), for various values of parameter A are presented in Fig. 15. From comparison of these results with the experimental data, it is seen that the best fit corresponds to A = 0.5 eV. So one can suppose that the nearest vacant level of CC14 in triethylamine is 0.5 eV distant from the energy of the tunneling electron. 

The parameters on p. 22 show that O is a better donor than Me, so it raises the energy of nco to a greater degree. Since MeO is an even better donor, we can deduce the order LUMO(ketone) [Pg.80]

The parameter y determines the distance at which the free energy of AB/s/ transforms to that of noninteracting B and A/s/. Numerous calculations in Refs. [52-55] have shown that, with a satisfactory accuracy, it can be accepted that... 

The activation barriers AE for dissociation and recombination belong to the same realm of relative energies as AQAB. For this reason, we shall not discuss here purely numerical calculations of AE. Remarkably, many authors tried to conceptualize their computational results in terms of simple analytic models, which have no direct relation to the computations. For example, the effective medium theory (EMT) is a band-structure model with a complex and elaborated formalism including many parameters (154). Nevertheless, while reviewing the numerical EMT applications to surface reactions, Norskov and Stoltze (155) discussed the calculated trends in the activation energies for AB dissociation in terms of a one-parameter model (unfortunately, no details were provided) projecting A b to vary as NJ, 10 - Nd), where Nd is the d band occupancy [cf. Eqs. (21a)—(21c) of the BOC-MP theory]. 

In the following section, the micellization model and the free-energy expression used in ref 6 are described. In section ID, the cmc and C t are calculated numerically for various values of o. Because the numerical calculations for a complete parametric study would be too lengthy, approximate, analytical relations for the two concentrations are developed in section IV. Computations based on these relations show that, of all the parameters, a is the only one which drastically affects the ratio between cmc and Cme The last section emphasizes again that Ccrit has a value close to the conventional cmc as long as the expression used for the free energy is a physically acceptable one. 

Photochemical initiation has often been used as an excellent method of studying radical and chain reactions.1 2 The primary step in many systems is followed by a sequence of steps, which may include conventional unimolecular processes of species having known or calculable energy. Examples are numerous and well known. In order to understand such systems, whether reaction is initiated photochemical ly or thermally, the typical characteristics of unimolecular reactions and their dependence on the energy parameters of the systems and on molecular structure must be clarified. This is the purpose of the present chapter, which will deal principally with the smaller hydrocarbon species below C6. 

We have a numerically calculated the dependence of the condensation energy Uo on the doping level using formula (6-9) and (5). We have carried out computer calculations of the condensation energy for the compounds Y0.5Ca02.Ba 2 Cu s07.xas a function of doping x. For our calculation we used the parameters Sf and / depended on the doping x, which we took from the Refs. [3, 13, 14]. 

A numerical calculation of the conductivity (195) has been performed in Refs. 149 and 150 at different sets of parameters. The energy of activation estimated in Ref. 149 varied from 0.288 to 0.32 x 10 19 J, while the experimentally obtained value was approximately 0.48 10 19 J. The better fit to the experimental data as mentioned in Ref. 149 could be possible if the additional short-range proton correlations would be taken into account. 

Kinetic parameters. The hterature contains numerous reports of the rate equations identified for particular crystolysis reactions, together with the calculated Arrhenius parameters. However, reproducible values of (Section 4.1.) have been reported by independent researchers for relatively few solid state decompositions. Reversible reactions often yield Arrhenius parameters that are sensitive to reaction conditions and can show compensation effects (Section 4.9.4.). Often the influences of procedural variables have not been carefully identified. Thus, before the magnitudes of apparent activation energies can be compared, attempts have to be made to relate these values to particular reaction steps. 

The next objective is to update Sji, Rf,R, and Qj to satisfy Equations 13.51 and 13.52. In the most general case all these parameters are variable, bringing the total number of variables to 4 /. The equations to be solved are N energy balances (Equation 13.51) and 3N specifications (Equation 13.52). The Newton method is used by numerically calculating the Jacobian matrix then inverting it to determine the corrections to the variables. The Jacobian elements are the partial derivatives of each of the residuals of Equations 13.51 and 13.52 with respect to each of the variables ... 

In the second-order approximation of the free energy, above T, Sa and Sb are both zero. Below T, the order parameters are non-zero. At T, the quadratic terms vanish. This formula illustrates the pseudo-second-phase-transition temperature vs. the molecular parameters that shows the same shapes as those of the numerical calculations of the N-I transition temperature Tc, mentioned above. 

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