Abstract: The geometries, bondings, and vibrational frequencies of C_2nH (n=3-9) and C_2n-1N(n=3-9) were investigated by means of density functional theory(DFT). The vertical excitation energies for the X²Π→²Π transitions of C_2nH(n=3-9) and for the X²Σ→²Π and the X²Π→²Π transitions of C_2n-1N(n=3-9) have been calculated by the time-dependent density functional theory(TD-DFT) approach. On the basis of present calculations, the explicit expression for the wavelengths of the excitation energies in linear carbon chains is suggested, namely, λ₀=[1240.6A/(2+√3n+6-√3n+3)](1-Be^-Cn), where A=3.24463, B=0.90742, and C=0.07862 for C_2nH, and A=2.94714, B=0.83929, and C=0.08539 for C_2n-1N. In consideration of a comparison of the theory with the experiment, both the expressions are modified as λ₁=0.92(λ₀+100) and λ₁=0.95(λ₀+90) for C_2nH and C_2n-1N, respectively.

Key words: DFT and TD-DFT, C_2nH, C_2n-1N, Electronic spectrum