Molecular orbital nondegenerate

The majority of photochemistry of course deals with nondegenerate states, and here vibronic coupling effects aie also found. A classic example of non-Jahn-Teller vibronic coupling is found in the photoelection spectrum of butatiiene, formed by ejection of electrons from the electronic eigenfunctions [approximately the molecular orbitals). Bands due to the ground and first... 

In the four-orbital model (1 ), low-lying ir-ir states of free-base porphyrins (symmetry D2h) are considered as resulting from single electron excitation from a pair of nondegenerate highest occupied molecular orbitals (bi, bo) to a pair of nondegenerate lowest unoccupied molecular orbitals (ci, cg). In the case of symmetry D2h mutually perpendicular electric transition dipoles X and Y are not equivalent and, therefore, in the visible absorption spectra of free-base porphyrins two different electronic bands Qx(0>0) and Qy(0,0) are observed (Table 1 and Fig. 10). 

Thus, let us assume that two different external potentials can each be consistent with the same nondegenerate ground-state density po- We will call these two potentials Va and wj, and the different Hamiltonian operators in which they appear and Ht,. With each Hamiltonian will be associated a ground-state wave function Pq and its associated eigenvalue Eq. The variational theorem of molecular orbital theory dictates that the expectation value of the Hamiltonian a over the wave function b must be higher than the ground-state energy of a, i.e.. 

The anion diradical (BQNN)- has two nondegenerated single occupied molecular orbitals (SOMOs). One is delocalized over the entire molecule and the other (SOMO ) is localized within the NN group. 

Disilyne 76 is emerald green in the solid state and shows two allowed n- n absorption bands in hexane at 259 (e 10300) and 328 (e 5800) nm and two forbidden n- n absorption bands at 483 (e 120) and 690 (e 14) nm.41 Theoretical calculations for 76 at the HF/6-311G(d)//B3LYP/6-31G(d) level have shown that HOMO and HOMO-1 are two split n orbitals and LUMO and LUMO+ 1 are two split lowest 7i orbitals. The out-of-plane n orbitals HOMO and LUMO+ 1 are represented by pure (p -p )7i orbitals, whereas the in-plane n orbitals HOMO-1 and LUMO are represented mainly by (py-py)n orbitals with a weak contribution of the a (Si-Si) orbital of the central bond. The presence of the nondegenerate n and ti molecular orbitals in 76 is responsible for the UV-vis absorption band feature of 76. 

This type of interaction determines above all the optical properties of lowdimensional organic conductors in the middle infrared region. It leads to activation of modes that are normally nonactive in the IR. For the tetra-cyano-p-quinodimethane (TCNQ), tetrathiafulvalene (TTF), and other symmetrical molecules, tt molecular orbital occupied by the radical electron are nondegenerate, so linear e-mv coupling is possible only for the totally symmetric (ag) modes. For example, TCNQ molecule has 54 normal modes, among which only 10 are the ag modes. They cover a range of frequencies from about 130 cm-1 to about 3050 cm-1 [16], while TTF molecules has seven totally symmetric modes of the range 250 cm-1 < toa < 3100 cm-1... 

We now consider the orbital degeneracy of molecular electronic terms. This is degeneracy connected with the electrons spatial (orbital) motion, as distinguished from spin degeneracy. Thus 11 and 11 terms of linear molecules are orbitally degenerate, while and 2 terms are orbitally nondegenerate. Consider an operator P that commutes with the molecular electronic Hamiltonian and that does not involve spin we have... 

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