18 LIGHT AND LIFE 



lar orbitals pertinent for discussion of low-lying pyridine transitions. 

 The 77-orbital is shown in addition to the bonding and antibonding 

 TT-orbitals, which are similar to those in benzene. 



The 6 TT-orbitals in benzene can be represented analytically by 



'/'I = Vi(4>l + <^2 + <^3 + 04 + </>5 + 4»i) 



XJ/O = \/|(— <^l — h(t>2 + 03 + 04 + 205 ~ 20fi) 



^3 = 2(02 + 03 — 05 — 06) 



\p4 = VK01 ~ 202 — 503 + 04 — 505 ~ 206) 



^Po = ^("02 + 03 — 05 + 06) 



1^6 = 'y/U~4>l + 02 — 03 + 04 — 05 + 06) 



in increasing order of energy, where the 0's are 2p, orbitals on the six 

 carbon atoms. As indicated in Fig. 2, the pairs 2,3 and also 4,5 have 

 the same energy in benzene, "persubstituted," and symmetrically 

 trisubstituted benzene derivatives, but they have different energy if 

 the symmetry axis is reduced below three-fold, as in pyridine or the 

 mono- or di-substituted benzene derivatives. The reader may easily 

 verify that the analytical functions do indeed approximately represent 

 the TT and tt* orbitals in Fig. 2. In the schematic representation, how- 

 ever, no attempt was made to show details of the nonuniformities of 

 "orbital density," and thus electron density, around the ring. 



3. Geometry of Excited States of Molecules 



It was mentioned earlier that the geometry of an excited state of 

 a molecule is expected to be different from that corresponding to the 

 ground state if the bonding electron configuration is significantly 

 different in the two states. The geometry of the excited state may be 

 important in biochemical problems since the transfer of energy is 

 expected to be very sensitive to the crossing of potential energy sur- 

 faces, and the surfaces are defined in terms of an equilibrium geometry 

 of the molecule. The geometry of very simple molecules can be found 

 directly from an analysis of the rotational part of the electronic spec- 

 trum of the gas-phase molecule. If the molecide has more than three 

 or four atoms of the mass of carbon or greater, the direct evaluation 

 of excited-state geometry from the rotational structme becomes im- 

 practical, since the structure is not easily resolved. In a recent paper 

 (6), however, the rotational contours in the electronic spectrum of 

 naphthalene were "analyzed", and some inferences may be possible 

 concerning the geometry of the upper state. 



