The Effect of Silyl and Phenyl Functional Group End Caps on the Nonlinear Optical Properties of Polyynes: A Long-Range Corrected Density Functional Theory Study

The polarizabilities, alpha, second-hyperpolarizabilities, gamma, and gamma scaling factors, c, of polyynes [i-(Pr)(3) Si-(C C)(n)-Si i-(Pr)(3), H-(C C)(n)-Si i-(Pr)(3), H-(C C)(n)-Ph, and Ph-(C C)(n)-Ph: n = 1 to 8] end-capped with triisopropylsilarle (i-(Pr)(3) Si-; TIPS) and phenyl groups were calculated using HF and DFT using the recently developed LC-BOP and LCgau-BOP functionals. Comparison with the alpha and gamma values of the uncapped polyynes shows that the TIPS and phenyl end caps do not increase the alpha and gamma values by a simple additive constant, but instead seem to expand the effective conjugation length (n) of the polyyne backbone. Using a newly-proposed power-law function, gamma = a + b(n + Delta n)(c), we found that a single phenyl or TIPS end cap has the effect of increasing n by approximately Delta n = 1.35 or 0.83, respectively. In the case of the phenyl end caps, we confirm that this function gives a better fit to the data than the function gamma = a + bn(c), even with constant b and c values, determined from a fit to the uncapped polyyne gamma values (gamma = bn(c)). In the case of the TIPS end caps, the fit to gamma = a + b(n + Delta n)(c) gives a smaller Delta n, but the assumption of constant b and c is less accurate. We also compared our c values to experimental data using the commonly used function gamma = a + bn(c). Our results are consistent with the experimental c values, in that the c values of Ph-(C C)n-Ph are higher than those of i-(Pr)(3) Si-(C C)(n)-Si i-(Pr)(3). Finally, using the power-law, gamma = a + b(n + Delta n)(c) predict the, as yet undetermined, experimental c value of Luicapped polyynes using the experimental gamma values of Ph-(C C)(n)-Ph (Delta n = 2.7), to be similar to 4.88. (c) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2012-2022, 2009