Benzene cycle index

As an illustration, the generating function c(x) = - - substituted in the benzene cycle index of Eq. [5] gives the counting series ... 

The benzene cycle index derivation considers the symmetry elements indicated in Figure 4, corresponding to the permutations and cycle index terms presented in Table 17. 

From Figure 3 and Table 1, it is easy to verify that the cycle index of benzene is... 

The number of benzene substitution isomers with formula C6Hg, tXt is obtained by substituting equation (87) in the cycle index for benzene, equation (89). This substitution gives the counting polynomial ... 

The application of P6lya s theorem can be illustrated by its use for the counting of substituted benzene isomers. The cycle index (equation S) of the planar hexagonal skeleton can be written as follows using the permutation group ... 

Capello et al.16 applied LCA to 26 organic solvents (acetic acid, acetone, acetonitrile, butanol, butyl acetate, cyclohexane, cyclohexanone, diethyl ether, dioxane, dimethylformamide, ethanol, ethyl acetate, ethyl benzene, formaldehyde, formic acid, heptane, hexane, methyl ethyl ketone, methanol, methyl acetate, pentane, n- and isopropanol, tetrahydrofuran, toluene, and xylene). They applied the EHS Excel Tool36 to identify potential hazards resulting from the application of these substances. It was used to assess these compounds with respect to nine effect categories release potential, fire/explosion, reaction/decomposition, acute toxicity, irritation, chronic toxicity, persistency, air hazard, and water hazard. For each effect category, an index between zero and one was calculated, resulting in an overall score between zero and nine for each chemical. Figure 18.12 shows the life cycle model used by Capello et al.16... 

Among the multitude of organic compounds, there is a small number of objects with p 0 (all types of acyclic compounds most topologically relevant to n-alkanes). The increase in number of cycles in the molecules leads to the increase of p up to 0.3-0.5 (cycloalkanes, arenes, etc.), 0.5-0.8 (naphthalenes, biphenyl, etc.), and 1.0 and more retention index units per degree (i.u./deg) for tri- and polycyclic structures. Hence, it is not surprising that RI data for isoalkanes, ethers, esters, etc. being measured at different conditions, are in good accordance with each other (standard deviations of randomized interlaboratory values are not more than 1-3 i.u.). The same statistical characteristics for substituted benzenes is about 8 i.u., and for naphthalenes and other condensed arenes, it may exceed 10-15 i.u. 

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