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Extra resources for Electronic Absorption Spectra and Geometry of Organic Molecules. An application of molecular orbital theory
Example text
5. In the ground electron con figuration all the bonding π orbitals, ψ+1, ψ+2, and ψ+3, are doubly occupied. That is, the ground electron configuration is expressed as ψΧιψ+2ψ+3 · Ψ+1Ψ+2 and ψ+3 are closed shells. Every closed shell remains unchanged under all the symmetry operations of the group, that is, it belongs to the totally symmetric representation of the group. The ground electron configuration of benzene is, of course, a closed-shell configuration, and belongs to symmetry species Alg of point group D6h .
Rotation about an axis of symmetry by an angle 2π/η. The axis is called an «-fold symmetry (or rotational) axis. The symmetry axis with the largest value of n in a figure is called the principal axis of symmetry of the figure and is usually taken as the z coordinate axis. Reflection in the plane of symmetry perpendicular to the principal axis, that is, the "horizontal" symmetry (or mirror) plane. Reflection in the plane of symmetry containing the principal axis, that is, the "vertical" symmetry (or mirror) plane.
69) gives a simple equation of the nth order in E. By solving this equation we can obtain n values of E. 68) and solving the resulting n simultaneous homogeneous linear equations in n unknowns, we can determine the ratios of all the n coefficients cri to one of them, for example, crk . When the ratio of cri to crk is denoted by kri, the coefficient cri can be expressed as Nrkri. * That is, from the normalization condition, (V r 2 dr = 2 Σ cricrjSi3. 73) the constant Nr is given by Nr= (llKiKiSilf112- (2-74) The Nr is the so-called normalization factor.