Typical UV spectra of aromatic hydrocarbons are shown in Figure 2.7. They contain absorption bands that fall into three categories according to their intensity:
Bands of the first type ('L,) are of low intensity ( E = lo2-I@), may be hidden by the other bands, and often possess a complicated vibrational structure.
Bands of the second type ('L, or 'B,) are moderately intense ( E = lo4); 'La bands usually show a regular vibrational structure;
Bands of the third type ('B,) are very strong ( E > I@) and have little vibra- tional structure.
The 'L,, 'La, 'B,, 'B, nomenclature originates in the perimeter model, dis- cussed in detail in Section 2.2.2.
Figure 2.8 shows how the experimentally observed wavelengths for two series of cata-condensed benzenoid hydrocarbons, the linearly annelated acenes and the angularly annelated phenes, change with increasing number of benzene rings. The shifts in the 'L, and 'B, positions are parallel to one another in both series, whereas the bathochromic shift of the 'L, band of acenes upon annelation is so pronounced that even in anthracene it masks the 'L, band.
These findings are difficult to understand on the basis of the simple HMO model. This model suggests that in the case of benzene a fourfold degenerate transition from the degenerate highest occupied MO into the equally degen- erate lowest unoccupied MO is to be expected instead of the observed three bands. In Example 1.9 it was shown that three bands of different symmetry are to be expected from group theoretical arguments, in agreement with ex- perimental observations.
2 ABSORPTION SPECTRA OF ORGANIC MOLECULES A I nml
Figure 2.7. Absorption spectra of naphthalene, anthracene, and tetracene as typical exariiples of the UV spectra of aromatic hydrocarbons (by permission from DMS-
UV-Atlas, 1966-71).
In general the HOMO and LUMO of condensed aromatic hydrocarbons are not degenerate, so simple theory gives a HOM-LUMO transition and a degenerate transition from the HOMO 4, into the second LUMO 4*., of from the second HOMO & into the LUMO +,..
As was shown in Section 1.2.4, the degenerate configurations and are split by configuration interaction (Pople, 1955; cf. Figure 1.6). The transition from the ground state into the lower of these states yields the 'L, band, and is forbidden within the PPP model. This is due to the fact that the transition moments and M,,,. between the ground configuration a.
and the singly excited configurations @I-2, and a,,. cancel one another exactly for that transition. The transition into the higher of these two states corresponds to the 'B, band and, in agreement with experimental data, is expected to be very intense since the individual transition moments MI,,, and M2,,, provided by its two constituents enhance one another.
2.2 CYCLIC CONJU~I'ED n SYSTEMS 73
100 ; I I I ,
2 3 4 5 6-I 001 1 2 3 4 5 6
Number of benzene rings Number of benzene rings
Figure 2.8. Wavelengths of 'L,, 'La, and IB, bands of condensed aromatic hydro- carbons plotted versus the number of benzene rings: a) linearly annelated aromatics (acenes); b) angularly annelated aromatics (phenes) (by permission from Badger, 1954).
Figure 2.9. Relation between HMO excitation energies A E = E , . - E, and observed excitation energies of the 'La band of various series of hydrocarbons (by permission from Koutecky, 1%5).
2.2 CYCLIC CONJUGATED n SYSTEMS 75
Figure 2.10. Relation between HMO excitation energies A E = E,. - E, = E , . - E,
and observed excitation energies of the 'L, and 'B, bands of condensed aromatic hydrocarbons (by permission from Kouteckg, 1965).
From these M O arguments it becomes apparent that the excitation energy of the 'La band is related t o the HOMO-LUMO energy difference. In fact, the relation between the experimental transition energy of the 'La band and the HMO excitation energies calculated a s orbital energy differences E,. -
is linear t o a fairly good approximation, a s is seen from Figure 2.9. From Figure 2.10 a similar linear relation between the transition energies of the 'L, band as well as the 'B, band and the orbital energy difference E,. - E, = E , . - E, is seen t o hold. This satisfactory proportionality between excitation energies and H M O orbital energy differences suggests that contributions of the electron repulsion terms t o the excitation energies are proportional t o orbital energy differences.
Example 2.3:
If the longest-wavelength transition corresponds to the 'La band, its excitation energy can be estimated easily from a model proposed by Dewar (1950). An even-alternant hydrocarbon can formally be considered as composed of two odd-alternant fragments, each of which must have a nonbonding orbital. When bonds are introduced that link the two fragments to form the total system, the two nonbonding orbitals interact to give one doubly occupied bonding orbital,
which will be the HOMO, and one antibonding orbital, the LUMO. From PMO theory the first-order splitting of the two nonbonding orbitals is given by
where 6 and are the LCAO coefficients of the nonbonding MOs of frag- ments R and S at atoms involved in the formation of a new p-a bond, and the Table 2.3 HOMO-LUMO Excitation Energies of Condensed Aromatic Hydrocarbons.
Comparison of Values (in cm-I) Calculated from the PMO Modela with Experimental Data for the 'L, Band (Adapted from Heilbronner and Bock, 1968)
Compound Chrysene (5)
3.4-Benzphenanthrene (6) 3.4-Benztetraphene (7) 1.2-Benztetraphene (8) Pentaphene (9)
1.2,-5.6-Dibenzanthracene (10) 1.2-7.8-Dibenzanthracene (11) Picene (12)
3.6-Benzchrysene (13)
IS 2 ABSORPTION SPECTRA OF ORGANIC MOLECULES 2.2 CYCLIC CONJUGATED n SYSTEMS 77 sum runs over all these new bonds. (Cf. Dewar and Dougherty, 1975.) In Table
2.3 wave numbers calculated from this relation using the regression line 5,dcm - = 8,200 - 22,000 A ~ l p
are collected for the condensed aromatic hydrocarbons 5-13, which can be
made up from benzyl, a-naphthyl, and Enaphthyl fragments, and compared with experimental data. Considering the very approximate nature of the model, the agreement is very good.
Triplet states of aromatics can be classified in a similar fashion as their singlet states. For instance, the 'La state is well described by the con- figuration. It is the lowest triplet state, even in those benzenoid hydrocar- bons in which 'L, rather than 'La is the lowest singlet, since the 'La-'La energy splitting is generally large, whereas the 'LAL, splitting vanishes in the first approximation. (Cf. Figure 6.18.)