22 LIGHT AND LIFE 



The first term in the parenthesis is repulsive and the second is 

 attractive. The spectral shift is accordingly given by 



A£ 



-^{^.-'i) (2) 



where /\A andA^ are differences of repulsive and attractive co- 

 efficients in the two electronic states, and the sum is over all neighbors. 

 In Eq. 1, e is the intermolecular binding energy and o" is a parameter 

 of size at which attractive and repulsive contributions are equal. The 

 sum is justified here since the interactions are known to be approxi- 

 mately additive. The binding energy in the liquid or solid is thereby 

 increased by a factor of 8 to 14 over that of the binary interaction. 

 For ground states of molecules, the parameters for pure substances 

 can be determined from solid state data, thermodynamic virial co- 

 efficients or transport properties of gases. ^ For two different interacting 

 partners (solvent and solute) , the parameters are approximately 

 obtained as mean values of the parameters for each of the pure 

 substances. The attractive interactions are derived from the London 

 dispersion forces. For spherically symmetric molecules as a first 

 approximation these are given by induced-dipole — induced-dipole 

 interactions. They depend upon the molecular polarizability which 

 increases with the electron density in the molecule. In large mole- 

 cules it is the local polarizability and not the overall molecular 

 polarizability which is important in the discussion of spectral shifts. 

 The repulsive interactions are derived primarily from exchange forces 

 (non-bonded repulsion) as the electrons of one molecule try to crowd 

 into the filled orbitals of a neighboring molecule. Attractive dis- 

 persion interactions generally have a larger coefficient in the excited 

 state than in the ground state because of the larger polarizability of 

 the more diffuse electron cloud. Repulsive interactions have a larger 

 coefficient in excited states because of the increase in orbital "size." 

 The interaction coefficients for the excited states of simple mole- 

 cules can be estimated quantitatively by extending the London theory 

 to excited molecules (18) . Because of the increased magnitude of the 

 excited state intermolecular parameters, solvent-solute attractive in- 

 teractions result in a shift of the spectrum to lower energy (red 

 shift), while repulsive interactions cause a blue shift. The latter situa- 

 tion is not too common. It might result when a large molecule is 

 dissolved in a small-molcculc solvent, the strong intermolecular 

 solvent-solvent interactions essentially squeezing the solute molecule 



" For details see ref. 15. 



