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, α, second‐hyperpolarizabilities, γ, and γ scaling factors, c , of polyynes [ i ‐(Pr) 3 Si–(CC) n –Si i ‐(Pr) 3 , H–(CC) n –Si i ‐(Pr) 3 , H–(CC) n ‐Ph, and Ph–(CC) n –Ph: n = 1 to 8] end‐capped with triisopropylsilane ( 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 α and γ values of the uncapped polyynes shows that the TIPS and phenyl end caps do not increase the α and γ 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, γ = a + b ( n + Δ n ) c , we found that a single phenyl or TIPS end cap has the effect of increasing n by approximately Δ 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 γ = a + bn c , even with constant b and c values, determined from a fit to the uncapped polyyne γ values (γ = bn c ). In the case of the TIPS end caps, the fit to γ = a + b ( n + Δ n ) c gives a smaller Δ 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 γ = a + bn c . Our results are consistent with the experimental c values, in that the c values of Ph–(CC) n –Ph are higher than those of i ‐(Pr) 3 Si–(CC) n –Si i ‐(Pr) 3 . Finally, using the power‐law, γ = a + b ( n + Δ n ) c , we predict the, as yet undetermined, experimental c value of uncapped polyynes using the experimental γ values of Ph–(CC) n –Ph (Δ n = 2.7), to be ∼4.88. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009