Reactivity indices calculation

In the third type of correlation (C), experimental rate or equilibrium data are compared with reactivity indices calculated by some (usually) semiem-pirical method of theoretical chemistry. The main problem here is in the design of a suitable molecular model as the basis for calculation. 

Recently, a series of models of 16 polynuclear pyridine-like heterocycles (Fig. 9 shows formulas of eleven of these) were treated using the HMO approximation7 (SN = 0.6, inductive effect not allowed for) and the following reactivity indices calculated 77-electron densities (q), bond orders (p), free valences (F, N x = Wheland s atom localization energies (A(,Ar,An), and superdelocalizabilities, both exact (Se,Sr,Sn) and approximate (S e,S r,S n). Atom-atom polarizabilities150 (773) had been calculated earlier.151 Some of the indices calculated are presented in Section VI, B. 

In this communication we have so far performed ground state reactivity index calculation, excited state calculation with Cl method whose credibility is vaUdated... 

The reactivity index is the conventional theoretical quantity which is used as a measure of the relative rate of reactions of similar sort occurring in different positions in a molecule or in different molecules. As has already been mentioned in Chap. 2, most reactivity indices have been derived from LCAO MO calculations for unicentric reactions of planar n electron systems as). The theoretical indices for saturated molecules have also been put to use B0>. In the present section the discussion is limited to the indices derived from the theory developed in the preceding sections, since the other reactivity indices are presented in more detail than the frontier-electron theory in the usual textbooks 65,86) jn this field. 

The detailed model was constructed as described by Carslaw et al. (1999, 2002). Briefly, measurements of NMHCs, CO and CH4 were used to define a reactivity index with OH, in order to determine which NMHCs, along with CO and CH4, to include in the overall mechanism. The product of the concentration of each hydrocarbon (and CO) measured on each day during the campaign and its rate coefficient for the reaction with OH was calculated. All NMHCs that are responsible for at least 0.1% of the OH loss due to total hydrocarbons and CO on any day during the campaign are included in the mechanism (Table 2). Reactions of OH with the secondary species formed in the hydrocarbon oxidation processes, as well as oxidation by the nitrate radical (NO3) and ozone are also included in the... 

Chatteijee, A. 2005. Application of localized reactivity index in combination with periodic DFT calculation to rationalize the swelling mechanism of clay type inorganic material. J. Chem. Sci. 117 533-539. 

Also other Type B and C series from Table II are consistent with the above elimination mechanisms. The dehydration rate of the alcohols ROH on an acid clay (series 16) increased with the calculated inductive effect of the group R. For the dehydrochlorination of polychloroethanes on basic catalysts (series 20), the rate could be correlated with a quantum-chemical reactivity index, namely the delocalizability of the hydrogen atoms by a nucleophilic attack similar indices for a radical or electrophilic attack on the chlorine atoms did not fit the data. The rates of alkylbenzene cracking on silica-alumina catalysts have been correlated with the enthalpies of formation of the corresponding alkylcarbonium ions (series 24). Similar correlations have been obtained for the dehydrosulfidation of alkanethiols and dialkyl sulfides on silica-alumina (series 36 and 37) in these cases, correlation by the Taft equation is also possible. The rate of cracking of 1,1-diarylethanes increased with the increasing basicity of the reactants (series 33). 

Recently, a new reactivity index has been proposed (80H(14)1717> which predicts accurately the site selectivity of photocyclization of substituted cycloheptatrienes to their bicyclic valence tautomers. Unfortunately, application of the method to substituted lH-azepines is far less successful. For example, for 2-methyl-l-methoxycarbonyl-lH-azepine (37 R = 2-Me) AGrs values for C-2—C-5 and C-4—C-7 cyclization are calculated as 0.093 and 0.040 kJ mol-1, respectively, i.e. predicting the 1-methyl isomer (39) as the major product. Experimentally, however, the reverse is true, the yields being 93.5% for 3-methyl (38 R = Me) and 6.5% for 1-methyl (39 R = Me). The corresponding photoinduced valence isomerizations of 1-benzazepines to 3,4-benz-2-azabicyclo[3.2.0]hepta-3,6-dienes (38a) have been recorded (80JOC462). These isomerizations have also been achieved thermally in the presence of silver ion (80TL3403). 

Yokono et al. [85] have suggested that the results obtained by Lewis and Edstrom [84] can be understood in terms of the maximum value of the index of free valence as calculated by the HMO method. However, as Herndon [30] has shown, some discrepancies occur when the free valence approach is applied to the experimental findings. He found that the structure count ratio for the single position in each compound that would give rise to the most highly resonance stabilized radical is a reliable reactivity index to correlate and predict the qualitative aspects of the thermal behaviour of benzenoid hydrocarbons. 

Reactivity indexes and 7r-electron densities of 4-aryl-l,3-dithiolylium ions have also been calculated by the Hiickel MO method (70CPB865, 65ZC23). 

Benzo[(i]quinolines, 1,2,3,4,4a,5,6,1 Ob-octahydro-, stereoisomers, 57, 57 Benzoquinolizinium (ions/salts) reactivity indexes, 55, 344 reactivity with nucleophiles, 55, 346 Benzo[a]quinolizinium (ions/salts) calculated electron densities, 55, 275 calculated electronic spectrum, 55, 324 nitration, 55, 342 synthesis, 55, 282 Benzo[a]quinolizinium (ions),... 

Following a similar approach but using a smaller data set of 369 compounds, Ivanciuc et al. correlated their liquid viscosity (10 Pa s) at 298 K with a mixed set of descriptors to obtain Eq. [48]. This involves three QM descriptors, one topological, and one constitutional descriptor. The QM descriptors were calculated with the AMI Hamiltonian in AMPAC, and CODESSA was used to calculate the descriptors and perform the statistical analyses. The HDCA2 parameter is the same HBD charged surface area used in Eq. [46]. The maximum electrophilic reactivity index, Ep, for a carbon atom is defined by X/ lumo,/A lumo+ 10), with the summation over the valence AOs on a carbon atom in the LUMO. The maximum AO electronic population, Y, models the molecular nucleophilicity and is defined by... 

There are many ways to measure the reactivity index, and all of them are feasible in such a study. By finding one that works—i.e., gives significant statistics in Equation 1—statements may be formulated regarding possible mechanisms. In this type of work, it must be remembered that it is not valid to imply causality to a correlation. However, from a pragmatic point of view, it is possible to set up models that can be tested by further synthesis. The measurements used for the reactivity index in the following examples include hydrolysis constants and molecular orbital calculations. 

A reactivity index suitable for use in Equation 1 was calculated by using the simple molecular orbital techniques described by the Pullmans (14). Many indexes may be deduced from this type of procedure. The one that seemed to have the most significance for the correlation was the energy of the highest occupied molecular orbital (HOMO). This index is a relative measure of the ability of an electron to be transferred to an acceptor molecule. The calculations were performed on the substituted phenol in the imidazoline structure. This simplification was made since it could be assumed that any perturbation caused by the imidazole would be insulated from the rest of the molecule by the methylene group. 

The calculation of the Reaction Potential Maps (RPM) [215] is a new kind of molecular reactivity index which is very helpful in elucidating the site selectivity observed in some chemical reactions. This was a development of the original calculation of electrostatic potential maps (EPM) by Bonaccorst and co-workers [216]. 

The amount of AG that is covalently bound to protein is dependent both on the concentration of AG and the degree of reactivity to form protein and peptide adducts. Historically, AG reactivity has been expressed as the percentage of total AG that is involved in the reaction with protein [26,27]. For this technique, the AG reactivity is calculated as reactivity index, C%, which is the ratio of ion current peak areas of AG peptide adducts (peak area a + b in Figure 10.15 A) to those that correspond to AGs from the same sample (peak area a -F b -F c in Figure 10.14A) multiplied by 100. The C% for DCL-AG was determined to be 0.88%. The AG reactivities of the seven drugs were ranked based on their C% (Table 10.3). 

Jt-Electron densities and reactivity indexes of 4-aryl-l,3-dithiolium ion have been calculated by the HMO method.Jt-Electron densities at the C-2 positions of different cations showed a linear correlation with experimental p. R+ values, and an excellent correlation between pKg and the Hanunett constants was established. ... 

The perturbational MO method of Longuet-Higgins (11) and Dewar (12), which was thoroughly reviewed by Dewar and Dougherty (6), has been the pencil-and-paper method of choice in numerous applications. More recently, a modified free-electron (MFE) MO approach (13-15) and a valence-bond structure-resonance theory (VBSRT) (7, 16, 17) have been applied to several PAH structure and reactivity problems. A new perturbational variant of the free-electron MO method (PMO F) has also been derived and reported (8, 18). Both PMO F and VBSRT qualify as simple pencil-and-paper procedures. When applied to a compilation of electrophilic substitution parameters (ct+) (19-23), the correlation coefficients of calculated reactivity indexes with cr+ for alternant hydrocarbons are 0.973 and 0.959, respectively (8). In this case, the performance of the PMO F method rivals that of the best available SCF calculations for systems of this size, and that of VBSRT is sufficient for most purposes. 

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