Electronic states from MOs

(c) The electronic states ranked approximately in relative energy. 

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A preliminary analysis of the absorption spectrum was given in Example 5.4-1 as an illustration of the application of the direct product (DP) rule for evaluating matrix elements, but the analysis was incomplete because at that stage we were not in a position to deduce the symmetry of the electronic states from electron configurations, so these were merely stated. A more complete analysis may now be given. The molecular orbitals (MOs)... 

Figure 1.6. Schematic representation of first-order configuration interaction for alternant hydrocarbons. Within the PPP approximation, conHgurations corresponding to electronic excitation from MO 4>i into and from MO., into are degenerate. The two highest occupied MOs (i =, k = 2) and the two lowest unoccupied MOs (f = r and k = 2 ) are shown. Depending on the magnitude of the interaction, the HOMO- LUMO transition

The total electron density contributed by all the electrons in any molecule is a property that can be visualized and it is possible to imagine an experiment in which it could be observed. It is when we try to break down this electron density into a contribution from each electron that problems arise. The methods employing hybrid orbitals or equivalent orbitals are useful in certain circumsfances such as in rationalizing properties of a localized part of fhe molecule. Flowever, fhe promotion of an electron from one orbifal fo anofher, in an electronic transition, or the complete removal of it, in an ionization process, both obey symmetry selection mles. For this reason the orbitals used to describe the difference befween eifher fwo electronic states of the molecule or an electronic state of the molecule and an electronic state of the positive ion must be MOs which belong to symmetry species of the point group to which the molecule belongs. Such orbitals are called symmetry orbitals and are the only type we shall consider here. 

The remarkable 19-electron molybdenum half-sandwich complex Mo(r 5-C5HPh4)(CO)2L2 (L2 = 2,3-bis(diphenylphosphino)maleic anhydride) (44) was prepared from [Mo(r)5-C5HPh4)(CO)3]2 and L2 and its structure in the solid state determined [65]. The average distance from molybdenum to the ring ligand is... 

For an electron removal from lower MO s, the situation is more complicated, because either an a-spin electron or a jS-spin electron can be removed. Hence, the ionized system formed can be in a singlet or a triplet state. 

For many years, investigations on the electronic structure of organic radical cations in general, and of polyenes in particular, were dominated by PE spectroscopy which represented by far the most copious source of data on this subject. Consequently, attention was focussed mainly on those excited states of radical ions which can be formed by direct photoionization. However, promotion of electrons into virtual MOs of radical cations is also possible, but as the corresponding excited states cannot be attained by a one-photon process from the neutral molecule they do not manifest themselves in PE spectra. On the other hand, they can be reached by electronic excitation of the radical cations, provided that the corresponding transitions are allowed by electric-dipole selection rules. As will be shown in Section III.C, the description of such states requires an extension of the simple models used in Section n, but before going into this, we would like to discuss them in a qualitative way and give a brief account of experimental techniques used to study them. 

In analogy to using a linear combination of atomic orbitals to form MOs, a variational procedure is used to construct many-electron wavefunctions from a set of N Slater determinants y, i.e. one sets up a N x. N matrix of elements flij = (d>, H d>y) which, upon diagonalization, yields state energies and associated vectors of coefficients a used to define (fi as a linear combination of A,s ... 

With six electrons and six MOs removed from the active space, one is left with 6 electrons in 20 orbitals, a calculation that could be performed easily. Several calculations were thus done with different space and spin symmetry of the wave function. The resulting ground state was found to be a septet state with all six electrons having parallel spin, and the orbital angular momentum was high with A = 11. Spin-orbit calculations showed that the spin and orbital angular momenta combined to form an O = 8 state. The final label of the ground state is thus yOg. 

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