Qx( 8 ). Replacement of the two central hydrogens by a metal ion
of appropriate size leads to theD4hgeometry and to degeneracy
the b2gand b3gorbitals (egorbitals in this point group), and only
one Q band is observed. The closer the degeneracy of the optical
transitions, the weaker the Q band. More sophisticated quan-
tum-mechanical calculations have shown the robustness of the
Gouterman model in describing the energy order and character
of the porphyrin molecular orbitals ( 9 ).
MO calculations for simple porphyrins, chlorins, and bacteri-
ochlorins show that, within the same series, the LUMOs are
nearly isoenergetic, that is, they do not change as the number
ofpelectrons is reduced from 22 to 20 and to 18 along the series.
However, the increasedD2hskeletal distortion destabilizes the
HOMOs, and their energies increase systematically (Fig. 3 (10)).
FIG. 3. Calculated energy levels of macrocycle HOMO1, HOMO,
LUMO, and LUMOþ1 in porphin, chlorin, and bacteriochlorin
complexes with Zn(II). For clarity, theD4hsymmetry labels of a1uand
a2uwere retained for all the macrocycles. Adapted from Ref. (10).
192 LUIS G. ARNAUT