Chemical Bonding and Size Scaling of Nonlinear Polarizabilities of Conjugated Polymers

Using sum rules for spectral moments of linear and nonlinear absorption we show that the jth order off-resonant polarizabilities of polyacetylene chains scale as $\sim j{\Delta }^{-j}{N}^{j+1\mathrm{}}/(N+L{)}^j$; $N$ is the number of carbon atoms, $\Delta$ the bond-length alternation, and $L\left(\Delta \right)$ the exciton coherence size. This result is in excellent agreement with time-dependent Hartree-Fock calculations performed for chains with up to 200 carbon atoms.