Formation of a covalent bond is not necessarily associated with an increase in electron density in the bonding region. This can be established by analysis of the single electron density distributions ρ(r) with the aid of the assigned Laplace field ▽2ρ(r). For “bonds without bonding electron density ρ(r)”, it is decisive that the density ρ(r) actually present in the region between the atoms results in a decrease in the local energy density and, hence, produces a stabilizing effect.

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A detailed kinetic analysis of the complex reaction systems arising from the ozonolysis of C2H4 and (CH3)2CC(CH3)2 (TME), respectively, is carried out, using master equations and statistical rate theory. The thermochemical as well as the molecular data required are obtained from CCSD(T)/TZ2P and B3LYP/DZP calculations. It is shown that the primary ozonides are not collisionally stabilized under atmospheric conditions. In the reaction sequence for O3 + TME, the same is true for CH2C(CH3)OOH formed from (CH3)2COO, which completely dissociates to give OH radicals. However, in this system, a pressure dependence is predicted for the relative branching fractions of the reactions of the Criegee intermediate. Under atmospheric conditions, for both examples, the product yields obtained are in reasonable agreement with experimental results.

DFT calculations provide a reliable description of the Bergman reaction of (Z)-hex-3-ene-1,5-diyne 1 provided the following are considered. (a) Restricted DFT (RDFT) calculations along the reaction path have to be replaced by unrestricted DFT (UDFT) calculations at those locations where the former description becomes unstable. This is the case in the region of the p-didehydrobenzene biradical 2, which possesses significant multireference character. (b) LSD and pure GGA functionals are more stable than hybrid functionals, which can be directly related to the composition of these functionals. With increasing instability, RDFT calculations lead to increasing errors in the S−T splitting and the geometry of 2 as well as in the energetics of the Bergman reaction. (c) LSD and GGA functionals underestimate the energy barrier of the Bergman reaction of 1. This becomes obvious when the correct experimental barrier is considered, which was not done in previous DFT investigations. (d) The best description of the Bergman reaction is provided by a mixed RDFT/UDFT description using the B3LYP functional (average error of 2.7 kcal/mol). Although the B3LYP functional is rather unstable, its semiempirical calibration helps to compensate for the typical underestimation of barriers by GGA functionals, which demonstrates that the performance of a hybrid functional does not necessarily have to do with its stability. (e) Application of the sum formula to the UB3LYP energy of biradical 2 improves the description of the Bergman reaction so that the most reliable data are obtained at RB3LYP-UB3LYP(sum)/6-311+G(3df,3pd). Activation enthalpies at 470 K for forward and backward reaction are 29.9 and 21.4 kcal/mol, respectively (exptl values, 28.23 ± 0.5 and 19.75 ± 0.7 kcal/mol), while the calculated reaction enthalpy at 298 K is 8.5 kcal/mol (exptl value, 8.5 ± 1.0 kcal/mol) in reasonable agreement with experiment. The calculated S−T splitting is 2.6 kcal/mol (after correction, 4.9 kcal/mol; exptl value, 3.8 ± 0.5 kcal/mol at 298 K). It is shown that the UDFT description covers static correlation effects needed for the correct treatment of 2S. Total and on-top pair density reflect this, while Kohn−Sham orbitals and spin density have to be considered as physically not meaningful intermediates in line with the interpretation given by Perdew, Savin, and Burke (Phys. Rev. A 1995, 51, 4531).

Kinetic measurements as well as B3LYP/ and MP2/6-31G(d,p) calculations provide evidence that carbonyl oxides formed in the gas-phase ozonolysis of alkylated alkenes are an important source of OH radicals. In the gas-phase ozonolysis of propene, cis-2-butene, trans-2-butene, tetramethylethene, and isoprene, 18, 17, 24, 36, and 19% OH radicals (relative to reacted ozone, error margin ≤4%) are measured using CO as a scavenger for OH. The quantum chemical calculations show that OH radical production depends on syn positioned methyl (alkyl) groups and their interaction with the terminal O atom of a carbonyl oxide. For example, in the gas-phase ozonolysis of ethene only 5% OH radicals are measured while for a carbonyl oxide with syn-positioned methyl (alkyl) group, a much larger amount of OH radicals is formed. This is due to the fact that 1,4 H migration and the formation of an intermediate hydroperoxy alkene, that is prone to undergo OO bond cleavage, is energetically more favorable than isomerization to dioxirane. In the case of syn-methyl, dimethyl, and isopropenyl carbonyl oxide calculated activation enthalpies at 298 K are 14.8, 14.4, and 15.5 kcal/mol compared to the corresponding dioxirane isomerization barriers of 23.8, 21.4, and 23.0 kcal/mol, respectively. The OO cleavage reactions of the hydroperoxy alkenes formed in these cases are just 11, 12.8, and 10.3 kcal/mol.

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