Alternant hydrocarbons, degenerate

FIGURE 2.7 Energy levels in odd- and even-alternant hydrocarbons. The arrows represent electrons. The orbitals are shown as having different energies, but some may be degenerate. 

Some rules have been put forward to design molecules with degenerate NBMO s. Following the proposal of Longuet-Higgins, an alternant hydrocarbon has at least N-2T singly occupied NBMO s, where N is the number of carbon atoms and T is the maximum number of double bonds occurring in any resonance structure [383, 396]. These rules have later been unproved on the... 

The outstanding feature of replacing a carbon by a nitrogen atom is an increase in the stength of an a band. As stated previously, in the case of the alternant hydrocarbons, the degenerate pair of transitions (HOMO-next-LUMO and next-HOMO-LUMO) splits into two components by the Cl procedure. If , and u2 denote the transition moments of these two transitions, respectively, the transition moments of the two components (MH and ML) can be written as weighted sums of w, and u2 as follows ... 

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

Transition. See also Electronic transition 0-0, 37, 261-62 allowed and forbidden, 27 charge-transfer, 123-26 degenerate, 158 electric dipole. S quadrupole, 5 intensity. 21-27 longest-wavelength, alternant hydrocarbons, 74-75 magnetic dipole, 5 n- jr, 118-23... 

Figure 1.6. Schematic representation of first-order configuration interaction for alternant hydrocarbons. Within the PPP approximation, configurations corresponding to electronic excitation from MO into and from into are degenerate.

Cyclopentadienyl is an odd non-alternant hydrocarbon. Being cyclic, it has degenerate energy levels, but they do not show the pairing property nor is there a non-bonding orbital. The energy levels are shown in Fig. 1.24. 

Chirality can also be introduced when one or more chiral carbons are incorporated in the molecules, for example in the hydrocarbon terminal chains [67, 68], within the bent-core [69], or by addition of chiral dopants [6, 70], It was noted during the early research that the handedness of the homochiral structures is very sensitive to chiral dopants [6], or even on chiral surfaces [71]. On the other hand, it was observed that banana-smectics made of enantiomeric chiral molecules form synclinic - antiferroelectric [44] and anticlinic ferroelectric [67] domains. This combination of tilt and polar order implies that the phase is racemic, with a rigid alternation of right- and left-handed chiral layers. This shows that the molecular chirality has no or minor effect on deciding about anticlinic or synclinic packing (which is mainly determined by entropic reasons), but it can bias the otherwise degenerate tilt directions. 

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