BENSONs corrections

It is important to evaluate the surface distortion associated with the assymetric field at the surface, a difficult task often simplified by assuming that distortion is limited to the direction normal to the plane [64, 6S]. Benson and co-workers [6S] calculated displacements for the first five planes in the (100) face of sodium chloride and found the distortion correction to of about 100 ergs/cm or about half of itself The displacements show a tendency toward ion pair formation, suggesting that lateral displacements to produce ion doublets should be considered [66] however, other calculations yielded much smaller displacements [67]. 

The equivalency of sites required for the application of these equations is seldom found in practice, although many authors apply these corrections. Benson has described an alternative procedure in which the rate and equilibrium constants are... 

Almost all of the directly measured thermochemical data for the sulfoxides, sulfones, sulfites and sulfates are due to the work of Busfield and Mackle and their coworkers at the University of Leeds and The Queens University, Belfast1-14. This work involved measurement of enthalpies of combustion, fusion and vaporization. It is the basis of the subsequent compilations of Benson and coworkers15, Cox and Pilcher16 and Pedley, Naylor and Kirby11. The data given by the latter are used as the basic data set in the present work. Corrections and omissions are noted in the next section. Data on additional compounds were sought by searching the IUPAC Bulletin of Thermochemistry and Thermodynamics for the years 1980 198318, and by searches of Chemical Abstracts. 

By contrast, we do not use Benson group increments , a generally powerful thermochemical technique summarized in the volume by S. W. Benson himself, Thermochemical Kinetics, 2nd edition, Wiley, New York, 1976, and used in many thermochemical chapters throughout the Patai series. For the classes of compounds discussed in the current chapter, we believe the necessary number of parameters (included to reflect electrostatic interactions, proximity effects, steric repulsions and ring corrections) is excessive. 

In this section we have so far emphasized only the AH° and AH° of the reaction components. This is because the entropy change in many reactions is small and can often be neglected in comparison to the enthalpy change. When S° s are of interest, they too can be estimated by Benson s additivity rules. In order to calculate 5° for a molecule, the group S° contributions are added together just as they are for AHf, but now a correction for the overall rotational symmetry (a) of the molecule must be added. The correction is — R In a, where a is the product... 

See O Neal and Benson, in Free Radicals, J. K. Kochi, Ed., Vol. II, p. 337, for more detailed discussion of corrections and for data required to correct to other temperatures. 

Heats of formation assume resonance stabilizations 10.8 kcal mole-1 in ( CHaCN) 12.6 kcal mole-1 in (CH3CHCN) and in [(CH3)2CCN]. " Na = doubly bonded nitrogen in azo compounds. h This correction assumes that the barrier to rotation in the radical R is two-thirds the barrier in the corresponding alkane RH. See O Neal and Benson for further discussion of this point. AH° and to +2 cal mole-1 °K 1 for 5°. The following example shows how the table is used to calculate thermodynamic properties for the 2-butyl radical (12).41 H3C—ch—ch2—ch3 12 ... 

A well-known tool for the estimation of reactivity hazards of organic material is called CHETAH [5]. The method is based on pattern recognition techniques, based on experimental data, in order to infer the decomposition products that maximize the decomposition energy, and then performs thermochemical calculations based on the Benson group increments mentioned above. Thus, the calculations are valid for the gas phase, but this may be a drawback, since in fine chemistry most reactions are performed in the condensed phase. Corrections must be made, but in general they remain small and do not significantly affect the results. 

It is important to note that Benson s method may require the use of correction terms for molecules having rings, cis/trans or ortho/para isomers, 1,5-repulsions, or gauche interactions. The user is referred to Benson s book162 for a complete description of the method. Some pertinent notation used in this method is as follows ... 

This example shows how to determine the correct group value for AHf and S for C-(H)(Br)2(C) by considering known values in the sequence C-(H)3(C) to C-(Br)4. This example represents changes in the main/central group. Note that the entropy values for Benson groups such as C-(Br)4 have the symmetry contribution removed. The user must add in any symmetry contribution after the molecule is built with the complete set of Benson groups. For consistency in any interpolation scheme, one must remove the symmetry contribution from the entropy for the whole molecule. In this case, owing to the tetrahedral symmetry, an amount R In 12 (where R is the gas constant) was subtracted from the literature entropy value for C-(Br)4. 

The data necessary for thermodynamic estimates are available from experimental as well as computational methods. In many systems AGh can be approximated by experimentally accessible AGJ. The approximation is valid (to within 0.05-0.15 eV) if the radical coupling has no barrier (is diffusion limited) and the thermolysis is carried out under conditions selected to minimize the cage recombination [79]. The homolytic bond strengths can also be obtained in many cases from the Benson group-additivity tables [80] or semiempirical quantum or molecular mechanics calculations [81]. With appropriate entropy corrections [75f], relatively accurate AGh values can be obtained in that way. 

There is an intriguing report that C03" can be oxidized to C03 by triplet-state duroquinone in micellar solutions (264). From Benson s data we calculate A(G° = -171 16 kJ/mol for C03 in the gas phase (43). By applying a correction of 10 kJ/mol for hydration of C03 we obtain 0 = 2.3 + 0.2 VfortheC03/C03" couple, which shows that C03 is indeed a viable intermediate in the triplet duroquinone system. 

Despite a considerable amount of subsequent work, there has never been any real unanimity of opinion on the correctness of this mechanism or on the homogeneity of the reaction. Glissman and Schumacher in 1933 reported the most extensive series of studies, together with a very complex mechanism involving simultaneous atom and molecular paths and energy chains. They worked with both dilute and relatively concentrated ozone mixtures. Benson and Axworthy have repeated these studies and confirmed the experimental results but have shown that all of the known data, in both dilute and concentrated O3 systems, can be interpreted in terms of the following modified Jahn mechanism ... 

Subscript designates ligancy of atom, i.e., number of atoms bonded to central atom. The entropy contribution must be corrected by the addition of any electronic entropy, R In qny where qn is the electronic partition function. The quantity R n a must also be subtracted from the total entropy to correct for symmetry. symmetry number of the final species. Values taken from S. W. Benson and J. H. Buss, J. Chem, Phys., 29 (1958). These quantities are not to be used for cyclic structures such as benzene compounds. Estimates of Cp and are good to about 2 cal/mole- K for most species but may be poorer for heavily substituted species such as neopentane. They may also be poorer for very simple H-containing species such as NH3 and CH4. 

Gl. S. W. Benson, The foundations of chemical kinetics, McGraw-Hill, New York, 1960, updated and corrected reprint, Krieger, Melbourne, 1982, ISBN 0898741947, Chapters III and V. 

Interestingly, the product is head-to-head , i.e. it has one new C—C and Sb—Sb bond, as opposed to two new C—Sb bonds. Assume we were convinced of the more or less invariance of the Sb—Sb bond enthalpy and that we had a reliable value for the —Sb bond enthalpy (say from a more trustworthy measurement of the enthalpy of formation of triphenylstibine ). With judicious use of Benson increments and strain corrections, one could thus estimate the enthalpy of formation of the dimer, and accordingly derive a trustworthy value for the monomer. We would then have a handle on the aromaticity of antimonin. The enthalpy of reaction of bismin, CjHjBi, to form the analogous dimer has likewise been derived to be — 50kJmoCL However, this does not particularly help us since elemental bismuth is metallic, i.e. it is illogical to consider that Bi (s) is held together by covalent Bi—Bi bonds. 

All chemisorption experiments were single point measurements at 8.10 Pa. By measuring the adsorption isotherms from 10 -10 Pa for a few catalysts, it was checked that a relative comparison of the thus obtained chemisorption values was as justifiable as any other method based on other measuring points, or on extrapolation of measuring points to zero pressure, as advocated by Benson and Boudart (24). No corrections were made for chemisorption on the bare supports as such, because this was found negligible. 

Dean MF, Muir H, Benson PF, et al. Increased breakdown of glycosaminoglycans and appearance of corrective enzyme after skin transplants in Hunter syndrome. Nature 1975 257 609- 614. 

Our current estimates for a-allyl are currently based on calculations for CH3 with corrections to allyl based on Benson-type estimates (18). In addition, we have not yet estimated the stability of the TT-allyl species. Most important, we have not calculated the transition states and energy barriers for any of the steps. 

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