How long are the ends of polyene chains?

In this work we study conjugation in all-trans polyene chains H[Single Bond](HC[Double Bond]CH)(n)[Single Bond]H with a view to establishing the length scale for the interaction between conjugated double bonds. As a polyene oligomer is made longer, bond length alternation between formal carbon-carbon single and double bonds diminishes toward the middle of the chain, eventually reaching a constant value characteristic of an "infinite" chain. However those bonds near the end of the chain continue to be influenced by the end, even in the long-chain limit. We have determined optimized geometries for polyene oligomers with up to n=11 repeat units at the MP2/cc-pVTZ level. At this length the central-most bonds are almost converged to the long chain limit, for which we estimate R(C[Double Bond]C)=1.3652 A and R(C[Single Bond]C)=1.4238 A. In contrast, the endmost double bond has a length of 1.3442 A and the endmost single bond has a length of 1.4425 A. We find that a given bond is significantly influenced by conjugation paths through up to six neighboring conjugated double bonds. End effects can also be monitored by examining the energy increment per added monomer as the oligomer length is increased. This analysis also indicates that significant conjugation effects extend out through approximately six neighboring double bonds. From the energy per monomer of the longest chains we extract a value of about 8 kcal/mol for the extra stabilization energy per monomer due to conjugation in long chains.