G. WILSE ROlilXSON 19 



For more coiiiplicaicci mokciilcs, i^eonietry dianges can be louiul 

 througli a study ol (/) the inagniiiicle ol the vibrational irequencies 

 (10) and (//) the relative intensities ol the vibrational parts of the 

 electronic transition (1) . In both cases an analysis of the vibrational 

 structure must be made. The first method relies on the fact that the 

 frequencies of vibrations vary approximately as the square root of 

 the force constants, and the force constants in turn are roughly re- 

 lated to the bond orders and thus the interatomic distances. In this 

 sense, relative bond distances can be inferred from changes in vi- 

 brational frequencies between states. The second method relies on 

 the magnitudes of the so-called Franck-Condon overlap integrals (16) , 

 which are related to the displacement of the vibrational origins about 

 which small oscillations of the nuclei are described. Displacements 

 of these origins are caused by geometry changes. Assuming harmonic 

 oscillations, it is possible to compute the relative intensities of vi- 

 brational bands for various excited state geometries and to com- 

 pare them with the experimental intensities. Since the intensity pat- 

 terns are rather sensitive to geometry changes, reasonable estimates may 

 be made of the geometry of the excited state molecule. Both kinds 

 of calculations have been carried out for benzene (4, 10) , and the 

 two results agree fairly well. They shoAv that the C-C bond increases 

 by .037 A in the excited singlet state of the tt-tt* transition. One 

 of the 18 C-C bonding electrons is promoted to an antibonding or- 

 bital. The effect is spread over six bonds, so that an effective loss 

 per bond of ^ of a bonding electron occurs. One would predict 

 on this basis that the C-C bond increases by .035 A in this transition. 

 This is in excellent agreement with the observation. 



Almost without exception chemical bonds are weaker and longer 

 in excited state molecules. The greatest change expected for a one- 

 electron transition is that which occurs when a bonding electron is 

 excited to an antibonding orbital. This kind of a transition essentially 

 causes a triple bond to become double, a double bond to become 

 single, or a single bond to disrupt. The bond distance may increase 

 by 15 per cent or more. Bond angles may change by as much as 80° 

 because of changes in the degree of s-p hybridization, but no generaliza- 

 tion can be made concerning the direction of such changes without a 

 better knowledge of the electronic eigenfunctions.'^ 



'Molecules (ref. 13) such as CO,,, CS,., HCN, and acetylene arc linear in their 

 ground states but bent in their low excited states. Molecules such as XHo, HCO, 

 and possibly XO- are bent in liicir ground state but linear in their lowest excited 

 states. Often the change in bond angle is from around 100° to 180°, or vice versa. 



