Saturation of the second hyperpolarizability for polyacetylenes

Polyacetylene (PA) polymers -(-CH=CH-), lead to large second hyperpolarizabilities (y) that increase with N. For small N the increase is quite rapid, eventually saturating (becoming linear in N) for N > N& Both experimental and theoretical attempts have been made to estimate N,Y,,. In 1994 this led to two Science papers, one obtaining NA, = 20 (semiempirical theory) and the other obtaining N,,, y = 12.5 (experiment, but on a substituted disordered form of PA!). We report here ab initio calculations up through N = 49 (C,,H ,& and show that N,,, y = 45 + 5. The much larger experimental _ value, N,Y,, = 125, is explained in terms of the structural defects and disorder introduced by the synthetic method. There is a great deal of interest in developing organic non-linear optical (NLO) materials for use in optical processing, in storage of data and images, and in optically based telecommunications and computers [l]. Important for these applications are the hyperpolarizabilities, which describe how the dipole moment (~1 depends on an applied electric field (~9, /_Q( E) = pi + cqjEi + Pijk E,E, + yijk,EjEkEl + . . . . (1) Here (Y, /3, and y are the polarizability, first hyperpolarizability, and second hyperpolarizability, respectively. * Corresponding author. Fax: (818) 585 0918. The properties of most interest [ll are p and y which control: frequency doubling (better focus, more data), changes in refractive index (electro-optical switches for telecommunications), and frequency mixing. Currently LiNbO, is the material of choice for these applications [2]. However, polymers would provide great advantages in ease of processing and for tailoring the properties to match precise requirements [3]. The best such materials are charge-transfer type molecules [3] involving a polyene bridge linking between a donor and an acceptor. The nature of donor, acceptor, and bridge are chosen to optimize p or y. It is well known [4-71 that for polyenes, -(CH=CH-I,-, (Y and y increase rapidly with N for smaller N but saturate to increase only linearly with 0009-2614/%/$12.00 Copyright