Theoretical Studies of the Spin and Charge Distributions in Molecules. Part A: Reaction Mechanisms of the Cycloaddition of Singlet and Triplet Atomic Oxygen to Olefins. Part B: Electron Correlation and Localization

Abstract

<p>Potential surfaces for the cycloaddition of singlet and triplet atomic oxygen to ethylene to form ethylene oxide were constructed. The singlet species was found to energetically favour a symmetric attack on the ethylene along the right bisector of the carbon-carbon axis in a place perpendicular to the plane of the nuclei, with an activation energy of the order of 10kcal/mole. The triplet species was found to prefer an asymmetric attack yielding an open-ring transition state geometry of energy 36 kcal/mole above the energy of the separated reactants. From this geometry, spin inversion and subsequent ring closure result in the formation of the singlet ethylene oxide product.</p> <p>Experimentally observed retention/loss of cis-trans stereo-chemistry of olefins added to by singlet/triplet oxygen are attributed to the concerted formation of ring bonds in the singlet case, and non-concerted ring bond formation in the triplet case with free rotation around the carbon-carbon axis in the intermediate transition state.</p> <p>Spin "uncoupling" and "transfer" mechanisms (originally developed elsewhere in a study of the varying tendencies of singlet and triplet oxygen to insert into or abstract a proton from hydrocarbon CH bonds) are also shown to explain the observed triplet asymmetric attack, non-concerted bond formation, and loss in product stereospecificity.</p> <p>The formalism of two statistical measures of the information content of a quantum mechanical wavefunction, the "missing information function", I and "population fluctuation", Λ, are developed. The formal coordinate-space quantum description of the distrbution of "event probabilities" of observing various numbers of electrons in various spatial regions of a molecule is shown to be related to intuitive concepts of the localizability of primariliy intra-correlated groups of electrons within non-overlapping volumes.</p> <p>The effects of the Fermi correlation described by a Hartree-Fock wavefunction were studied. Several small hydride molecules, LiH+, LiH, BeH(X), BH, BeH2, BH3, BH4‾, and CH4, were found to be partitionable (by criteria based on I and on Λ) into volumes corresponding to intuitive notions of "core", "bonding", and "non-bonding" regions of a molecule, each containing a population of two primarily intra-correlated electrons. For several other molecules, BeH(A), NH3, H2O, N2, and F2, only core pair populations were found to be well-localized. The valence density in these cases was found to be unpartitionable.</p> <p>The formalisms developed here provide a useful method of computing the effects of correlation on particle localizability described by any form of wavefunction. The techniques also permit evaluation of the likelihood of accurate wavefunction decomposition into a product of wavefunctions each incorporating a description of the internal group particle correlation. Finally, one can assess the probability of an accurate partitioning of a quantum system into nearly independent subsystems.</p>