Molecular orbital theory, single-determinant

Hiberty40 used the single determinant ab initio molecular orbital theory to study the unimolecular HC1 elimination from ethyl chloride. The calculations of three potential energy surfaces corresponding to -elimination, planar //-elimination, and nonplanar anti-elimination were performed and the dehydrochlorination process was predicted to be syn, and to proceed via a planar four-membered transition state. According to these estima-... 

Single determinant ab initio LCAO-SCF molecular orbital theory is used throughout this study (6,7), Molecular geometries were optimized with the minimal STO-3G basis set (8,9), and where possible the energy of the final structure was recalculated with the extended 4-31G basis set (9,10), Such a procedure has been shown to provide a reasonable description of the structures and energies of neutral organic molecules (11) and carbocations (12), The potential surface for the concerted elimination of hydrogen chloride from ethyl chloride also has been studied successfully (13) with this technique. 

The models for the bonding in small ring hydrocarbons based on single determinant molecular orbital theory are suitable in a qualitative and quantitative sense to interprete their PE spectra. 

The molecular orbital theory (MOT) is widely used by chemists. It includes both the covalent and ionic character of chemical bonds, although it does not specifically mention either. MOT treats the electron distribution in molecules in very much the same way that modem atomic theory treats the electron distribution in atoms. First, the positions of atomic nuclei are determined. Then orbitals aroimd nuclei are defined these molecular orbitals (MO s) locate the region in space in which an electron in a given orbital is most likely to be found. Rather than being localized arormd a single atom, these MO s extend over part or all of the molecule. 

Having formed a set of N linearly independent molecular orbitals, these orbitals must then be occupied to form the wave function. In ab initio molecular orbital theory the wave fimction is formed as the determinant of a matrix, which for an re-electron closed-shell system [ie, re is even (If re were odd, and the system was a doublet species (having one unpaired electron), we could instead form (re +1)/2 orbitals, one of which would be singly occupied. The treatment of open-shell systems is discussed in more detail below.)] might be written as follows. 

P. C. Hariharan and J. A. Pople, Accuracy of AH j equilibrium geometries by single determinant molecular orbital theory, Mol. Phys. 27 209 (1974). 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

The usual first ah initio approximation to the wave function leads to the Hartree-Fock theory, where V molecular spin orbitals (. with one for each electron. Then, asking the question what is the single determinant solution with the lowest possible energy, we obtain the Hartree-Fock equations and density, ... 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

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