Radicals calculating

Semiempirical programs often use the half-electron approximation for radical calculations. The half-electron method is a mathematical technique for treating a singly occupied orbital in an RHF calculation. This results in consistent total energy at the expense of having an approximate wave function and orbital energies. Since a single-determinant calculation is used, there is no spin contamination. 

TABLE 1. Characteristics of the orbital containing the unpaired electron in sulfonyl radicals calculated from 33S splittings... 

It wiU be seen below that the actual geometrical structures of these radicals calculated using the dynamic theory support these conclusions. 

Based both on the determined isotopic shifts and the comparison of the radical IR spectrum with the spectra of various substituted benzenes, the bands have been assigned to the normal modes and the force field of the benzyl radical calculated (Table 8). 

Figure 13.2 Combination of three atomic p orbitals to form three n molecular orbitals in the allyl radical. The bonding n molecular orbital is formed by the combination of the three p orbitals with lobes of the same sign overlapping above and below the plane of the atoms. The nonbonding n molecular orbital has a node at C2. The antibonding n molecular orbital has two nodes between Cl and C2, and between C2 and C3. The shapes of molecular orbitals for the allyl radical calculated using quantum mechanical principles are shown alongside the schematic orbitals.

Kuppermann and Belford (1962b) also performed 2-radical calculations using a reaction scheme and numerical procedure similar to Dyne and Kennedy however, their stated purpose was not the obtaining of agreement... 

Oxidation rate constant k, for gas-phase second order rate constants, k0H for reaction with OH radical, kN03 with N03 radical and k0j with 03 or as indicated, data at other temperatures see reference k = 4 x 107 M-1 h-1 for singlet oxygen and k = 5 x 103 M-1 h-1 for peroxy radical (calculated, Mabey et al. 

These reactions are very important in the oxidation of carbon-chain polymers (see Chapter 19). The available experimental data on the rates of such reactions are summarized in Table 2.9. The parameters for intramolecular hydrogen transfer in peroxyl radicals calculated by the IPM are presented in Table 6.12. 

Enthalpies, Activation Energies, and Rate Constants of Intramolecular Hydrogen Atom Transfer in Peroxyl Radicals Calculated by the IPM Method [36], (Ais Increment of Polar Interaction in the Transition State)... 

FIGURE 16.1 The dependence of activation energy E on reaction enthalpy A He for reaction of hydrogen atom abstraction by aminyl radical from the C—H bond of alkylperoxyl radical and O—H bond of hydroperoxyl radical calculated by IPM method (see Chapter 6). The points fix the reactions with minimum and maximum enthalpy among known aromatic aminyl radicals. 

The activation energies and rate constants for the discussed reactions of the diphenylaminyl radical with various peroxyl radicals calculated in this way are presented below [22]. 

Since the number of free radicals calculated from the dilference in nitrogen uptake (1.13 102 /gm) agreed well with the number of unpaired electrons as determined by e.s.r. (0.80-10 /gm), the aroxylic structure seemed very likely. The reaction of oxidized carbon black with styrene can be explained on this basis 102). 

These ideas have been illustrated in a recent study of the co-crystalline complex of 1-meCyt 5-FUra [19]. Using model calculations, it was shown how the hydrogen-bonding network of the crystal is able to sustain a proton shuttle which leads to the selective formation of certain radicals. Calculations predict that the site of reduction would be the cytosine base, yielding the N3 protonated cytosine anion, Cyt(N3-I-H), while the uracil base would be the site of oxidation, yielding the N1 deprotonated uracil cation, Ura(Nl—H) ... 

The parameters for intramolecular hydrogen transfer in peroxyl radicals calculated by the IPM are presented in Table 6.12. 

It is evident from Table 16.3 that quinones react rapidly with the hydroperoxyl radicals. Calculation shows that the change in the enthalpy of this reaction is relatively small. The dissociation energy of the —H bond in the semiquinone radical 4- 40 is 228.1 kJ mol 1 and the enthalpy of the reaction Q + H02 is A// 220.0 228.1 8.1 kJ mol. ... 

For nonaltemant hydrocarbons the energies of the bonding and antibonding orbitals are not equal and opposite and charge distributions are not the same in cations, anions, and radicals. Calculations are much more difficult but have been carried out.121... 

In Tables 10 to 12 we show the heats of formation calculated by the various methods, together with their deviation from the experimentally observed values for alkanes and cycloalkanes, alkenes and cydoalkenes, and acetylenes and aromatic compounds. Table 13 shows a comparison of heats of formation of hydrocarbon radicals calculated by the MINDO methods. Finally, in Tables 14 and 15 we show the results of MINDO/1 calculations on a selection of oxygen- and nitrogen-containing compounds. 

Table 13. Heats of formation of hydrocarbon radicals calculated by MINDO/1 and MINDO/2...

Fig. 2. Yield of chain breaks for the reaction of hydroxyl radicals, calculated using Equation (9).

TABLE 6.11 Harmonic and Anharmonic Contributions to hcc of Vinyl Radical Calculated at the PBE0/EPR-I1//PBE/6-311 + G(d,p) Level... 

---