Using density functional theory, the geometries and the vibrational frequencies of linear chain BC_2nB (n＝1～12, D_(h) have been investigated at the B3LYP/6-31G^* level. Time-dependent density functional theory (TD-DFT) has been used to calculate the vertical transition energies and oscillator strengths for transitions of BC_2nB with the cc-pvTZ and cc-pvDZ basis sets. At the B3LYP/6-311＋G^* level, the single-point energies of the clusters have been calculated in order to determine the first ionization energies. On the basis of present calculations, the explicit expressions for the size dependence of the excitation energy, the first adiabatic ionization energies (AIE) and vertical ionization energies (VIE) in linear carbon chains were suggested.

Key words: linear cluster BC_2nB, DFT and TD-DFT, electronic spectra, ionization energy, analytic expression