Abstract: Density functional theory with the B3LYP functional is used to determine the geometries and vibrational frequencies of HC 2nH (n=1～13). The  vertical transition energies of HC 2nH (n=1～5) have been estimated by TD-B3LYP/cc-PVTZ calculations.On the basis of theoretical calculations,a generally analytic expression for the chain-size n dependence of the vertical transition energy was suggested,which can predict excellent excitation energies in comparison with available observed bands.Current calculations reveal that a nonlinear behavior for the even-numbered HC2nH between the excitation energy and the number of carbon atoms.

Key words: Polyynes, TD-B3LYP, Electronic spectra, Analytic expression