Initial Detailed Molecular Orbital Calculations

Extended Huckel molecular orbital calculations were used to obtain an initial, qualitative picture of the electronic structure changes involved in two-electron transfer. EHMO calculations were carried out in D2h symmetry on H2P" bridged analogs of the [M2(p-PR2)2(CO)8] complexes using the CACAO program (50). Structural information and computational details are provided in reference 18. 

EPR spectrochemical experiments yield information about (i) the site of redox activity in the compound (ii) the contribution of various nuclei to the molecular orbital occupied by the unpaired electron that may then be checked against the results of theoretical calculations and (iii) the half-wave potentials of systems where direct measurement is difficult (usually as a result of slow electron-transfer rates). Examples of each of these have been taken from our investigations and are detailed below. Initially, however, the cell used in these experiments is described followed by a review of some other cell designs. 

H was the matrix-component of the Hiickel effective-Hamiltonian operator, effective between two basis atomic-orbitals, 4>r and 4>s, Srs was the overlap integral between 4>r and s, and H was set equal to a, H to / . This is how we developed the simple HMO-approach in Chapter Two. What Roothaan did was to show that a formally similar determinant is obtained in a full treatment of the re-electrons, but that it involves a somewhat more complicated expression for the matrix-elements, H . Furthermore, he showed that this more-complicated expression somehow had to take into account interactions between any one re-electron and all the other re-electrons. We do not go into the details of this here, except to say that, in order to find the LCAO-MO coefficients for one molecular orbital, it is necessary to know all the others, because all the others appear in the expressions for the equivalent terms, Hrs. This is a very familiar situation which mathematicians have long known how to deal with and which we encountered during our discussion of the self-consistent" Huckel-methods in 7.2—7.5 it is necessary to use an iterative scheme. An initial guess is made of all the orbitals except one and these are used to calculate the H -terms for the one orbital which has not yet... 

Both types of procedure typically adopt a self-consistent field (SCF) procedure, in which an initial guess about the composition of the LCAO is successively refined until the solution remains unchanged in a cycle of calculation. For example, the potential energy of an electron at a point in the molecule depends on the locations of the nuclei and all the other electrons. Initially, we do not know the locations of those electrons (more specifically, we do not know the detailed form of the wavefunctions that describe their locations, the molecular orbitals they occupy). First, then, we guess the form of those wavefunctions—we guess... 

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