Empirical values

Note that agreement with Pariser and Parr s empirical value is better for Y13 than for Yn ) Use Salem s values to calculate election densities on the three carbon atoms of the allyl anion for one iteration beyond the initial Huckel values, as was done in Exercise 8.9.1. Comment on the results you get, as to the qualitative picture of the anion, the influence of election repulsion on the charge densities, and agreement or lack of agreement with the results already obtained with the Pariser and Parr parameters. 

The principal semi-empirical schemes usually involve one of two approaches. The first uses an effective one-electron Hamiltonian, where the Hamiltonian matrix elements are given empirical or semi-empirical values to try to correlate the results of calculations with experiment, but no specified and clear mathematical derivation of the explicit form of this one-electron Hamiltonian is available beyond that given above. The extended Hiickel calculations are of this type. 

The algorithms in ZINDO/S are almost the same as those in ZINDO/1, except of the one-center two-electron integral, F . ZINDO/S uses empirical value of F instead of using ab initio value in terms of the Slater orbitals. 

Two now classical papers 61MI40400, 62JCS2927) contain almost all the experimental thermochemical data on pyrazole and indazole. Heats of combustion determined by Zimmerman (61MI40400) have been used by Dewar to calculate the heats of atomization (Table 25) (69JA796). Quantum mechanical calculations, carried out by Dewar (69JA796) or Olivella 81JHC1189), gave accurate empirical values. 

To date, there has been relatively little work reported on the mesophase pitch rheology which takes into account its liquid crystalline nature. However, several researchers have performed classical viscometric studies on pitch samples during and after their transformation to mesophase. While these results provide no information pertaining to the development of texture in mesophase pitch-based carbon fibers, this information is of empirical value in comparing pitches and predicting their spinnability, as well as predicting the approximate temperature at which an untested pitch may be melt-spun. 

Calculations have been done at the STO-3G and 4-3IG levels, and the resulting substituent constants correlate well with empirical values derived from ground-state structural parameters, such as C-NMR chemical shifts and IR absorption frequencies. 

Where there is no mechanical supply or extract, factors are used to estimate possible natural infiltration rates. Empirical values may be found in several standard references, and the CIBSE Guide ([2], A4) covers this ground adequately. 

ICso, the concentration (usually molar) of an inhibitor (receptor, enzyme antagonist) that blocks a given predefined stimulus by 50%. It is an empirical value in that its magnitude varies with the strength of the initial stimulus to be blocked. 

We assume that the double bonds in 1,3-butadiene would be the same as in ethylene if they did not interact with one another. Introduction of the known geometry of 1,3-butadiene in the s-trans conformation and the monopole charge of 0.49 e on each carbon yields an interaction energy <5 — 0.48 ev between the two double bonds. Simpson found the empirical value <5 = 1.91 ev from his assumption that only a London interaction was present. Hence it appears that only a small part of the interaction between double bonds in 1,3-butadiene is a London type of second-order electrical effect and the larger part is a conjugation or resonance associated with the structure with a double bond in the central position. 

It was stated (l.c.) that (8) gives very accurate results with empirical values of 7, A, and B. Bertrand found, however, that these values do not even approximately agree with those calculated from A = C/R, y = ( Cv —C )/R, except in the case of steam. 

The water elimination reactions of Co3(P04)2 8 H20 [838], zirconium phosphate [839] and both acid and basic gallium phosphates [840] are too complicated to make kinetic studies of more than empirical value. The decomposition of the double salt, Na3NiP3O10 12 H20 has been shown [593] to obey a composite rate equation comprised of two processes, one purely chemical and the other involving diffusion control, for which E = 38 and 49 kJ mole-1, respectively. There has been a thermodynamic study of CeP04 vaporization [841]. Decomposition of metal phosphites [842] involves oxidation and anion reorganization. 

The empirical values of the parameter F2 found using uncorrected Rayleigh ratios or turbidities should be angle-dependent and do not necessarily represent the customary thermodynamic parameter F2. 

The above-described theory, which has been extended for the transfer of protons from an oxonium ion to the electrode (see page 353) and some more complicated reactions was applied in only a limited number of cases to interpretation of the experimental data nonetheless, it still represents a basic contribution to the understanding of electrode reactions. More frequently, the empirical values n, k° and a (Eq. 5.2.24) are the final result of the investigation, and still more often only fcconv and cm (cf. Eq. 5.2.49) or the corresponding constant of the Tafel equation (5.2.32) and the reaction order of the electrode reaction with respect to the electroactive substance (Eq. 5.2.4) are determined. 

Lutz, J. and E. Pemicka (1996), Energy dispersive X-ray fluorescence analysis of ancient copper alloys Empirical values for precision and accuracy, Archaeometry 38, 313-323. 

The natural van der Waals radii of Table 1.1 are generally found to be in good correspondence to empirical values. However, one can establish that the van der Waals surface of a bonded atom is generally somewhat ellipsoidal (rather than spherical), with major and minor axes respectively transverse and longitudinal to the bond direction. One can also evaluate the hardness (radial derivative of steric energy), charge dependence, and temperature dependence of van der Waals radii, thereby obtaining many quantitative refinements of empirical steric concepts. 

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