B3LYP/6-31G calculations for

FIGURE 3.26. Potential energy profiles (from B3LYP/6-31G calculations) for the cleavage of 4-cyanobenzyl chloride (a) 3- and 4-cyanobenzyl bromides (b and c) anion radicals in the gas phase (top) and in a solvent (middle and bottom) (from COSMO solvation calculations with a dielectric constant of 36.6 and 78.4, respectively). Dotted and solid lines best-fitting Morse and dissociative Morse curves, respectively. Adapted from Figures 4 and 5 of reference 43, with permission from the American Chemical Society. 

If you can afford it, use B3LYP/6-31G(d) for geometries and zero-poin corrections and B3LYP with the largest practical basis set for energ calculations. 

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

The one-electron oxidation of 1,2-dithiin 20 with 1.5 equivalent of SbCl5 under vacuum at room temperature gave a bright yellow solution that exhibited a nine-line ESR signal. The optimized structure obtained by theoretical calculations (B3LYP/6-31G(d)) for the radical cation 20 + was the one with a... 

In summary, transition structures with dioxirane and dimethyldioxirane are unsymmet-rical at the MP2/6-31G level, but are symmetrical at the QCISD/6-31G and B3LYP/6-31G levels. The transition states for oxidation of ethylene by carbonyl oxides do not suffer from the same difficulties as those for dioxirane and peroxyforaiic acid. Even at the MP2/6-31G level, they are symmetrical (Figure 17). The barriers at the MP2 and MP4 levels are similar and solvent has relatively little effect. The calculated barriers agree well with experiment . In a similar fashion, the oxidation of ethylene by peroxyformic acid has been studied at the MP2/6-31G, MP4/6-31G, QCISD/6-31G and CCSD(T)/6-31G and B3LYP levels of theory. The MP2/6-31G level of theory calculations lead to an unsymmetrical transition structure for peracid epoxidation that, as noted above, is an artifact of the method. However, QCISD/6-31G and B3LYP/6-31G calculations both result in symmetrical transition structures with essentially equal C—O bonds. 

The most convincing evidence for an essentially synchronous peracid epoxidation of simple alkenes came from a combined experimental and theoretical study by Singleton, Honk and coworkers. Experimental KIEs for the reaction of m-CPBA with 1-pentene, determined by the clever methodology developed by Singleton and Thomas utilizing the combinatorial high-precision determination of C and H KIEs at natural abundance, confirmed the symmetrical or nearly symmetrical nature of this epoxidation TS. These data were corroborated by B3LYP/6-31G calculations on propylene that supported a synchronous transition state for peroxyformic acid epoxidation. 

Cyclic allylic alcohols have different steric requirements than the acyclic substrates discussed above. Sarzi-Amade and coworkers addressed the mechanism of epoxida-tion of 2-cyclohexen-l-ol by locating all the transition structures (TSs) for the reaction of peroxyformic acid (PFA) with both pseudoequatorial and pseudoaxial cyclohexenol con-formers. Geometry optimizations were performed at the B3LYP/6-31G level, and the total energies were refined with single-point B3LYP/6-311- -G //B3LYP/6-31G calculations. 

MP2/6-31G bond distances are comparable to those from B3LYP/ 6-31G calculations, although errors for bonds involving one or more second-row elements are generally somewhat smaller. As stated earlier, it is difRcult to justify use of the more costly MP2/6-31G model (over B3LYP/6-31G ) for geometry determinations. 

Phenylcyclopropane radical cation (9 ) has divergent hyperfine coupling constants for the secondary cyclopropane protons (aptrans = 0.78 mT upcis = 0.07 mT CIDNP, B3LYP/6-31G calculations), apparently because the cis protons are located in a nodal plane. " Similarly, vinylcyclopropane radical cation is... 

Another more efficient catalytic version of the reaction consists of the interaction of ketones with chiral amines [6] to form enolate-like intermediates that are able to react with electrophilic imines. It has been postulated that this reaction takes place via the catalytic cycle depicted in Scheme 33. The chiral amine (130) attacks the sp-hybridized carbon atom of ketene (2) to yield intermediate (131). The Mannich-like reaction between (131) and the imine (2) yields the intermediate (132), whose intramolecular addition-elimination reaction yields the (5-lactam (1) and regenerates the catalyst (130). In spite of the practical interest in this reaction, little work on its mechanism has been reported [104, 105]. Thus, Lectka et al. have performed several MM and B3LYP/6-31G calculations on structures such as (131a-c) in order to ascertain the nature of the intermediates and the origins of the stereocontrol (Scheme 33). According to their results, conformations like those depicted in Scheme 33 for intermediates (131) account for the chiral induction observed in the final cycloadducts. 

The formation enthalpies for the C6()H2n hydrides were calculated from the results of the B3LYP/6-31G calculations using homodesmic reaction (4.4) with fullerene C60, adamantane C10H16 and cyclohexane C6H12 ... 

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