Linear and nonlinear feature of electronic excitation energy in carbon chains HC2n+1H and HC2nH

Density functional theory has been used to investigate the geometries, bonding, and vibrational frequencies of HC_2nH (n = 1–13) and HC_2n+1H (n = 2–12). Vertical excitation energies for the X¹Σ → 1¹Σ transition of HC_2nH (n = 1–5) and for the X³Σ → 1³Σ transition of HC_2n+1H (n = 2–5) have been calculated by the time‐dependent density functional theory and ab initio second‐order multiconfiguration perturbation method, respectively. On the basis of the present calculations, explicit expressions for the size dependence of excitation energy in linear polyynes HC_2n+1H and HC_2n+1H are suggested. Such analytical λ ? n relationships show good agreement with experimental observations. Theoretical investigations of relevant excited states demonstrate that distinct linear and nonlinear spectroscopic features in such polyynes can be ascribed to similarity and difference in bonding between the ground and excited states in HC_2n+1H and HC_2nH. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004