Theoretical Studies On The Structures And Electronic Spectra Of Linear Carbon Clusters Mc₂nh (m = Mg, Al; N = 1-5) And HC_nh⁺ (n = 4-16)

Complete active space self-consistent-field (CASSCF) approach has been used for the geometry optimization of the X²Î£⁺ and A²Î electronic states for the linear magnesium-containing carbon chains MgC_2nH (n = 1–5). Multireference second-order perturbation theory (CASPT2) has been used to calculate the vertical excitation energies from the ground to selected seven excited states, as well as the potential energy curves of two ²Î£⁺ and two ²Î electronic states. The studies indicate that the vertical excitation energies of the A²Î â†X²Î£⁺ transition for MgC_2nH (n = 1–5) are 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respectively, showing remarkable linear size dependence. Compared with the previous TD-DFT and RCCSD(T) results, our estimates for MgC_2nH (n = 1–3) are in the best agreement with the available observed data of 2.83, 2.78, and 2.74 eV, respectively. In addition, the dissociation energies in MgC_2nH (n = 1–5) are also been evaluated.Geometries and stabilities of the linear aluminium-bearing carbon chains AlC_2nH (n = 1–5) in their ground states have been explored by the DFT-B3LYP and RCCSD(T) methods. Structures of the X¹Î£⁺ and 11Πelectronic states have also been optimized by the CASSCF approach. The studies indicate that these species have single-triple bond alternate pattern, Al–C≡C–C≡C···C≡C–H, and the electronic excitation from X¹Î£⁺ to 11Πleads to the shortening of the Al–C bonds. The vertical excitation energies of the 11Π←X¹Î£⁺ and 21Π←X¹Î£⁺ transitions for AlC_2nH (n = 1–5) have been investigated by the CASPT2, EOM-CCSD, and TD-B3LYP levels of theory with the cc-pVTZ basis set, respectively. CASPT2-predicted 11Π←X¹Î£⁺ transition energies are 3.57, 3.44, 3.33, 3.26, and 3.21 eV, respectively. For AlC2H, our estimate agrees very well with the experimental value of 3.57 eV. In addition, the Al–C bond dissociation energies and the exponential-decay curves for these vertical excitation energies are also discussed.The B3LYP, CAM-B3LYP, and RCCSD(T) calculations have been used to determine the ground-state geometries of the linear polyyne cations HC_2nH⁺ (n = 2–8). The CASSCF method has also been used to optimize the ground and first excited states. The present results indicate that these linear cations generally have an acetylenic structure, H–C≡C–C≡C···C≡C–H⁺, with the ground state of X²Î g for even-numbered n or X²Î u for odd-numbered n. Moreover, the bond length alternation (BLA) of HC_2nH⁺ is less pronounced than the corresponding one of the neutral polyyne chains HC_2nH. The CASPT2 approach has been employed to estimate the vertical excitation energies for the dipole-allowed (A,B,D)²Î _u/g←X²Î _g/u and dipole-forbidden C2Φu/g←X²Î _g/u transitions in HC_2nH⁺ (n = 2–8) clusters. The predicted A²Î _u/g←X²Î _g/u transition energies in the gas phase are 2.62, 2.14, 1.81, 1.52, 1.35, 1.22, and 1.10 eV, respectively, in excellent agreement with the corresponding observed values of 2.45, 2.07, 1.75, 1.52, 1.34, 1.20, and 1.08 eV. The present calculations show that the absorption wavelengths for the A²Î _u/g←X²Î _g/u transitions exhibit notably linear size dependence as shown in previous experimental studies, quite different from the nonlinearλ-n relationship for origin bands in HC_2nH.In this work, the odd-numbered linear hydrocarbon cations HC_2n+1H⁺ (n = 2–7) have been investigated with the B3LYP, CAM-B3LYP, and RCCSD(T) calculations focusing on the ground-state geometries, as well as with the CASSCF calculation for the structural optimizations of the ground and first excited states. The present studies reveal that these cation radicals possess stable structures with the ground state of X²Î u when n is even or X²Î g when n is odd, featuring some sort of cumulenic character for the middle carbon chains. Consistent with the previous studies of HCnSi+ clusters, the odd-numbered HCnH⁺ chains are less stable than the even-numbered ones. The vertical excitation energies for the dipole-allowed 1²Î _g/u←X²Î _u/g transitions of HC_2n+1H⁺ (n = 2–7), obtained by the CASPT2/cc-pVTZ level, are 2.59, 2.11, 1.87, 1.65, 1.49, and 1.35 eV, respectively, which mutually agree with the available experimental data of 2.48, 2.07, 1.78, 1.57, 1.42, and 1.29 eV. Particularly the corresponding absorption wavelengths are predicted to have the remarkably linear size dependence, as experimentally observed. In addition, the higher excited electronic transitions of HC_2n+1H⁺ (n = 2–7) are also calculated, indicating that the absorption wavelengths for the 3²Î _g/u←X²Î _u/g transitions also exhibit similar linear relationship and the largest oscillator strengths make them accessible more easily in the further experiments.