ABSORPTION SPECTRA OF THE CAROTENOIDS 663 



conjugated chain, the absorption bands are shifted regularly toward longer 

 wave length, and their intensity becomes greater. 



These simple relations between color and molecular structure make polyene dyes 

 particularly suitable objects for theoretical studies. This problem was treated by Paul- 

 ing (1939), who used the method of atomic orbitals and the concept of resonance, and by 

 Mulliken (1939, 1941), who used the method of molecular orbitals. According to Paul- 

 ing, the fundamental resonance possibilities of polyene molecules are provided by the 

 shifting of the double bonds, which results in the transfer of an electron from one end of 

 the molecule to the other. If we consider, e. g., a straight conjugated chain with an 

 even number of carbon atoms {A), the shift of all double bonds to the left will produce 

 structure B and a shift to the right, structure C: 



{A) CH3CH=CHCH CHCH=CHCH3 



(B) +CH3=CHCH=CH CH=CHCHCH3 



(C) CHaCHCH^CH CH=CHCH=CH3 + 



Each of the states B and C has a large dipole moment; but, since the two moments 

 have opposite directions, and B and C have equal probabilities, the molecule will show 

 no dipole moment at all, both in the ground state of the molecule and in the lowest ex- 

 cited states formed by resonance between the same three structures. However, the 

 transition from the normal state to an excited state of this type lias a "transition mo- 

 ment" whose order of magnitude is that of the dipole moment of the individual structures 

 B and C This is a very large moment, and it increases with length of the chain. In 

 wave mechanics, the probability of a spectroscopic transition between two states {i. e., 

 the intensity of the corresponding absorption hne or band) is determined by the magni- 

 tude of the "transition moment." This explains why polyene molecules have strong 

 absorption bands, and why their intensity increases with the greater chain length. 



The second approach to the same problem is that of the theory of "molecular orbi- 

 tals." It considers the actual state of the molecule without decomposing it into imagi- 

 nary resonating components. It tries to assign the electrons not to definite atoms or 

 bonds, but to definite lA-functions (orbitals) of the molecule as a whole. In a long chain 

 of conjugated double bonds, some of these orbitals include the nuclei of all atoms in the 

 chain, and electrons assigned to them can be considered as moving freely through the 

 whole chain (this being the counterpart to the "shifting of double bonds" in the reso- 

 nance theory). A conjugated double bond chain has, in this theory, a certain similarity 

 to a metallic wire. 



An investigation of a molecule by this theory consists in the determination of the 

 qualitative characteristics of available orbitals and the evaluation of the relative ener- 

 gies of the states obtained by different assignments of the electrons to the orbitals. 



Let us consider (Mulliken 1939) a straight chain of n carbon atoms (n = even num- 

 ber) and n/2 double bonds (the presence of symmetrical end groups on both ends of this 

 conjugated chain — which is common in carotenoids — does not alter the problem). It 

 contains n "unsaturation orbitals," sweeping over the whole conjugated chain, of which 

 n/2 are "bonding" (i. e., electrons assigned to them stabilize the molecule), and n/2 

 "antibonding." Each orbital can, as usual, hold two electrons, so that the n available 

 "unsaturation electrons" are just enough to fill the n/2 bonding orbitals, thus giving a 

 singlet normal state. The transfer of any one of these electrons into any one of the n/2 

 antibonding orbitals leads to an excited state; there are therefore nV4 groups of ex- 

 cited states. Each group consists (because of the interaction of orbitals with the elec- 

 tron spin) of one triplet and one singlet state; however, because of the prohibition of 



