The Hubbard model with bond alteration is used to calculate the hyperp
olarizability gamma of polymers. Exact numerical solutions are found f
or short chains of N sites. The hyperpolarizability is represented as
gamma is-proportional-to N(n). The exponent n is over six for no bond
alteration, and declines slowly with increasing bond alteration. This
behavior is compared with the measurements in polythiopehene.