Electronic excitations in finite and infinite polyenes

We study electronic excitations in long polyenes, i. e. , in one-dimensional strongly correlated electron systems which are neither infinite nor small. The excitations are described within Hubbard and Pariser-Parr-Pople (PPP) models by means of a multiple-reference double-excitation expansion P. Tavan and K. Schulten, J. Chem. Phys. 85, 6602 (1986). We find that quantized ``transition'' momenta can be assigned to electronic excitations in finite chains. These momenta link excitation energies of finite chains to dispersion relations of infinite chains, i. e. , they bridge the gap between finite and infinite systems. A key result is the following: Excitation energies E in polyenes with N carbon atoms are described very accurately by the formula E^=E₀^+^k (N) q, q=1, 2,. . . , where denotes the excitation class, E₀^ the energy gap in the infinite system ^k (N) >0, and k (N) the elementary transition momentum. The parameters E₀^ and ^ are determined for covalent and ionic excitations in alternating and nonalternating polyenes. The covalent excitations are combinations of triplet excitations T, i. e. , T, TT, TTT,. . . . The lowest singlet excitations in the infinite polyene, e. g. , in polyacetylene or polydiacetylene, are TT states. Available evidence proves that these states can dissociate into separate triplets. The bond structure of TT states is that of a neutral soliton-antisoliton pair. The level density of TT states in long polyenes is high enough to allow dissociation into separate solitons.