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
Date of Award
Doctor of Philosophy (PhD)
Professor R.F.W. Bader
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.
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.
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.
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.
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.
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.
Stephens, Michael Edwin, "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" (1975). Open Access Dissertations and Theses. Paper 838.