Size Dependence of Electronic Excitation Energy in Linear C2nH and C2n－1N

The geometries, bondings, and vibrational frequencies of C2nH (n = 3—9) and C2n-1N(n= 3—9) were in-vestigated by means of density functional theory (DFT). The vertical excitation energies for the X^2Ⅱ→^2Ⅱ transitions of C2nH(n= 3—9) and for the X2∑→^2Ⅱ and the X^2Ⅱ→^2Ⅱ transitions of C2n-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 C2nH, and A=2. 94714, B=0. 83929, and C=0. 08539 for C2n-1N. In consid-eration 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 C2nH and C2n-1N, respectively.

Size Dependence of Electronic Excitation Energy in Linear C2nH and C2n-1N

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.