Methyl radicals calculation methods

Several other methods have been employed to access the conditions of bubble collapse. Misik et al. studied H20—D20 mixtures and through measurements with the use of spin traps, were able to determine the temperature from the relative rates of O—H and O—D cleavage [21]. They reported temperatures ranging from 2,000 to 4,000 K. Hart et al. developed a method based on the gas phase recombination of methyl radicals (MRR method), formed from the decomposition of methane [22]. They calculated temperatures of 2,000-2,800 K depending on the methane concentration. 

Tmax—bubble temperature on collapse T , and are solution temperature and pressure, respeetively, Py is pressure inside the bubble and y is heat capacity ratio of the gas inside the bubble. A theoretical temperature of about 12,700 K could be calculated by using y = 1.66 (ideal gas), T , = 298 K, P , = 2 atm, Py = 0.031 atm. Replacing y of an ideal gas by that of water (1.32), the temperature drops to 6150 K highlighting the importanee of the heat capacity ratio of the gas contained in the collapsing bubbles. Susliek and coworkers [46, 47] have used sonoluminescence spectra to calculate bubble temperatures in multibubble systems and found to be in the order of 1000-5000 K. Henglein and coworkers [48] have used methyl radical recombination method and determined the cavitation bubble temperatures to be in a... 

Opposing reactions. Use the data on the right side of Table 3-2, concerning the triphenyl methyl radical, to calculate ki. This experiment refers to the concentration-jump method in which the parent solution was diluted with solvent to twice its initial volume. 

The calculation of an activation barrier for the reactions (21) and (22) must not necessarily be considered as an error of the method. For example, the MINDO/3 calculated activation barrier for the attack of a methyl radical on ethene 137-138) which is comparable to the former reactions was confirmed by experiments 139). In contrast to a free proton (Eq. (20)) the methyl radical as well as the ethyl cation possess steric space need. For this reason, the calculation of repulsive interactions which are able to overcome the attractive forces at certain distances cannot be seen without doubt as faulty. 

After the first unsuccessful attempts to record a matrix IR spectrum of the methyl radical, reliable data were obtained by the use of the vacuum pyrolysis method. IR spectra of the radicals CH3 and CD3 frozen in neon matrices were measured among the products of dissociation of CH3I, (CH3)2Hg and CD3I (Snelson, 1970a). The spectra contained three absorptions at 3162 (1 3), 1396 V2) and 617 cm (I l) belonging to the radical CH3 and three bands 2381, 1026 and 463 cm assigned to the radical CD3. Normal coordinate analysis of these intermediates was performed and a valence force field calculated. In accordance with the calculations, methyl radical is a planar species having symmetry >31,. 

Generated from diacetyl peroxide, methyl radicals attack 2-methylfuran at position 5 preferentially if both 2- and 5-positions are occupied as in 2,5-dimethylfuran there is still little or no attack at the 3(4)-position. If there is a choice of 2(5)-positions, as in 3-methylfuran, then that adjacent to the methyl substituent is selected.249 These orientation rules are very like those for electrophilic substitution, but are predicted for radical attack by calculations of superdelocalizability (Sr) by the simple HMO method. Radical bromination by IV-bromsuccinimide follows theory less closely, presumably because it does not occur through a pure radical-chain mechanism.249... 

RSEs for a broader selection of substituted methyl radicals, as well as MADs and MDs from experiment and CBS-RAD values, are presented in Tables 6.12 and 6.13. We noted in the previous section that our highest-level procedure, namely Wl, gives accurate BDEs, and this observation carries over to the RSEs calculated at this level. The MAD from experiment for the Wl method is 3.1 kJ/mol. The Wl RSEs tend to be slightly lower than those determined from experimental data [MD(Exp.) of -2.2 kJ/mol]. 

Table 6.13 Comparison of experimental radical stabilization energies at 0 K (k J/mol) of substituted methyl radicals with those calculated with DFT-based electronic structure methods.

Table 6.15 Comparison of experimental barriers at 0 K (kJ/mol) for the addition of methyl radical to alkenes CH2=CXY with those calculated with wavefunction-based methods.

As no clear-cut conclusion can be drawn from the analysis of these ab initio calculations it is not surprising that further attempts have been made to answer the question of the existence of a special captodative effect by improving the calculational methods. Clark (Clark, 1988) has carried out extensive calculations for the cyanomethyl-, amlnomethyl- and aminocyano-methyl-radical system by perturbational methods including different amounts of correlation. The results using the isodesmic reactions (5)-(8) are shown in Table 5. 

Termination rate constants for alkyl and benzyl radicals in solution range between 109 and 1010 M 1 sec-1.85 These rates correspond quite closely to that calculated for a diffusion-controlled reaction, about 8 x 109 M x sec-1 for the common solvents at room temperature.86 Gas-phase rotating sector results are similar a newer method, however, shows that in the gas phase the rotating sector technique overestimates termination rates. Recombination is fastest for methyl radicals (1010,5 M-1 sec-1) and slower for others (-CF3, 109-7 at 146°C ... 

A. F. Trotman-Dickenson has employed this method to calculate the preexponential factors of a number of free radical reactions. For checks on the calculated entropies of methyl radicals he compares his values with the entropies of similar molecules. Thus the standard entropies (25 C, 1 atm) of CH4, 44.5 cal/mol- K, and NII3, 45.9 cal/mol-°K, are compared to a calculated value for CH3 of 45.5 (neglecting electronic degeneracy), ... 

With this information in hand, it seemed reasonable to attempt to use force field methods to model the transition states of more complex, chiral systems. To that end, transition state.s for the delivery of hydrogen atom from stannanes 69 71 derived from cholic acid to the 2.2,.3-trimethy 1-3-pentyl radical 72 (which was chosen as the prototypical prochiral alkyl radical) were modeled in a similar manner to that published for intramolecular free-radical addition reactions (Beckwith-Schicsscr model) and that for intramolecular homolytic substitution at selenium [32]. The array of reacting centers in each transition state 73 75 was fixed at the geometry of the transition state determined by ah initio (MP2/DZP) molecular orbital calculations for the attack of methyl radical at trimethyltin hydride (viz. rsn-n = 1 Si A rc-H = i -69 A 6 sn-H-C = 180°) [33]. The remainder of each structure 73-75 was optimized using molecular mechanics (MM2) in the usual way. In all, three transition state conformations were considered for each mode of attack (re or ) in structures 73-75 (Scheme 14). In general, the force field method described overestimates experimentally determined enantioseleclivities (Scheme 15), and the development of a flexible model is now being considered [33]. 

---