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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.

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler᎐Lagrange equations for molecular fragments n described by internal parameters . An internal mode is localized in a molecular n fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k , adiabatic force constants. a Minimization of the kinetic energy of the vibrating fragment yields the adiabatic mass n Ž . m corresponding to 1rG of Wilson's G matrix and, by this, adiabatic frequencies . a n n aAdiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates.

For the first time, a complete implementation of coupled perturbed density functional theory ͑CPDFT͒ for the calculation of NMR spin-spin coupling constants ͑SSCCs͒ with pure and hybrid DFT is presented. By applying this method to several hydrides, hydrocarbons, and molecules with multiple bonds, the performance of DFT for the calculation of SSCCs is analyzed in dependence of the XC functional used. The importance of electron correlation effects is demonstrated and it is shown that the hybrid functional B3LYP leads to the best accuracy of calculated SSCCs. Also, CPDFT is compared with sum-overstates ͑SOS͒ DFT where it turns out that the former method is superior to the latter because it explicitly considers the dependence of the Kohn-Sham operator on the perturbed orbitals in DFT when calculating SSCCs. The four different coupling mechanisms contributing to the SSCC are discussed in connection with the electronic structure of the molecule.

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