Size Dependence of Electronic Excitation Energy in Linear C_(2n)H and C_(2n-1)N

The geometries, bondings, and vibrational frequencies of C 2n H ( n =3-9) and C 2n -1 N( n =3-9) were investigated by means of density functional theory(DFT). The vertical excitation energies for the X 2Π→ 2Π transitions of C 2n H( n =3-9) and for the X 2Σ→ 2Π and the X 2Π→ 2Π transitions of C 2n -1 N( 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, λ 0=[1240 6A/(2+[KF(]3n+6-3n+3)](1-B e -Cn ), where A=3 24463, B=0 90742 , and C = 0 07862 for C 2n H, and A=2 94714, B=0 83929 , and C =0 08539 for C 2n -1 N. In consideration of a comparison of the theory with the experiment, both the expressions are modified as λ 1=0 92( λ 0+100) and λ 1= 0 95( λ 0+90) for C 2n H and C 2n -1 N, respectively. (1-B e -Cn ), where A=3 24463, B=0 90742 , and C = 0 07862 for C 2n H, and A=2 94714, B=0 83929 , and C =0 08539 for C 2n -1 N. In consideration of a comparison of the theory with the experiment, both the expressions are modified as λ 1=0 92( λ 0+100) and λ 1= 0 95( λ 0+90) for C 2n H and C 2n -1 N, respectively.