A study of the lowest-lying triplet and singlet states of the cyclopentadienyl cation (c-C₅H₅⁺)

Abstract

High-level abinitio studies [up to the CASSCF+MP2 and RCCSD(T) level] are performed on the cyclopentadienyl cation. The ground state is found to be the X̃³A₂^′ state, arising from a ···(a₂^″)²(e₁^″)² electronic configuration, which is of D_5h symmetry. The equilibrium bond lengths are determined to be: r_C–C=(1.425±0.002) Å, and r_C–H=(1.080±0.005) Å. In D_5h symmetry, from the ground state electronic configuration, a ¹E₂^′ state and a ¹A₁^′ state also arise, with the former splitting into two states in C_2v symmetry (¹A₁ and ¹B₂) under the influence of the Jahn–Teller effect. The ¹A₁^′ state (¹A₁ in C_2v symmetry) can then interact with the ¹A₁ state that arises from the ¹E₂^′ state. It is found that these two electronic states, despite having very different geometries, are almost isoenergetic, and it is not possible to decide conclusively which one is the lower, even at the highest levels of theory used. In addition, the C_2v stationary points on the two ¹A₁ surfaces change their character between minimum and saddle point at different levels of theory. The vibration corresponding to the imaginary frequency suggests an in-plane distortion to a C_s minimum, but this was difficult to converge. The ¹B₂ state is found to be a saddle point at the lower levels of theory, but to have a C_2v minimum at the UMP2/6-311G(2d,p) level; however, one of the harmonic frequencies is anomalously large. The lowest singlet–triplet gap (¹A₁–X̃³A₂^′) is calculated to be 6.5 kcal mol^-1 (0.28 eV) at the RCCSD(T)/ cc-pVTZ//QCISD/6-31G** level of theory; the ¹B₂–X̃³A₂^′ separation is calculated to be 13.3 kcal mol^-1 (0.58 eV) at the UQCISD/6-31G** level of theory. c-C₅H₅⁺ is often quoted as being a typical "‘4n’' antiaromatic compound, however it will be argued that on geometric grounds, the X̃state could be thought of as aromatic. The geometry of the two ¹A₁ states indicate antiaromatic behaviour, and that of the ¹B₂ state indicates close to aromatic behaviour, based on the A parameter of Julg and François.

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