20 LIGHT AND LIFE 



Little is known about geometry differences in polyatomic molecules 

 between singlet states and triplet states having the same electron 

 configuration, except what can be implied from the vibrational part 

 of the electronic spectrum. The difference between the states is caused 

 by the fact that, in the triplet state, the electron spins are parallel, 

 while in the singlet they are antiparallel. One could hardly believe 

 that small magnetic effects can have very much to do directly with 

 the equilibrium geometry of the molecule, and on the basis of the 

 orbital approximation it is expected that the geometry differences 

 would be insignificant. Actually, the orbital apj^roximation does not 

 take into account the repulsive interactions between electrons, and 

 it is just this contribution which causes by far the major differences 

 in energy and geometry between states having the same configura- 

 tion. Electron-electron repulsion energy is greater in the singlet 

 state than the triplet essentially because of the restrictions brought 

 about by the Pauli exclusion principle. In effect, this principle re- 

 quires that in the triplet state, unlike the singlet, two electrons which 

 have the same spin cannot simultaneously occupy the same space 

 part of the electron cloud. Thus electron-electron repulsion energy 

 is decreased. Because of this, the triplet state lies below the correspond- 

 ing singlet, and bonding properties and geometry are affected to some 

 extent. 



In the simple molecule formaldehyde, the geometry of the lowest- 

 lying singlet and triplet excited states was ascertained from an analysis 

 of the rotational structure in the electronic transition (8, 32). These 

 states are the excited states of the w-tt* singlet-singlet and singlet- 

 triplet transitions. Since, in the transition, one non-bonding electron 

 becomes antibonding in the C=0 bond, this bond becomes essentially 

 a 3-electron rather than a 4-electron bond. The bond length (~ 1.3 

 A) is expected, and found, to be half-way between single (~ 1.2 A) 

 and double (~ 1.4 A) bond carbon-oxygen distances. The molecule 

 is planar in the ground state but non-planar (about half-way toward 

 tetrahedral bonding) in both excited states. In the triplet state the 

 carbon-oxygen bond distance is 1.312 A while it is 1.326 A in the 

 singlet state, so there is slightly tighter bonding in the triplet state. 

 This is further characterized by the higher carbon-oxygen vibrational 

 frc(juency in the triplet state. The non-planarity is greater in the 

 tri|)lct state, and the energy difference between the planar and equili- 

 brium non-planar forms is also greater in the triplet than the excited 

 singlet state. 



While formaldehyde is the only case where a really precise de- 



