CCSD(T) Rotational Constants for Highly Challenging C5H2 Isomers—A Comparison between Theory and Experiment

Abstract

<p>We evaluate the accuracy of CCSD(T) and density functional theory (DFT) methods for the calculation of equilibrium rotational constants (A_e, B_e, and C_e ) for four experimentally detected low-lying C₅H₂ isomers (ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 2-cyclopropen-1-ylidenethenylidene (8)). The calculated rotational constants are compared to semi-experimental rotational constants obtained by converting the vibrationally averaged experimental rotational constants (A₀, B₀, and C₀ ) to equilibrium values by subtracting the vibrational contributions (calculated at the B3LYP/jun-cc-pVTZ level of the theory). The considered isomers are closed-shell carbenes, with cumulene, acetylene, or strained cyclopropene moieties, and are therefore highly challenging from an electronic structure point of view. We consider both frozen-core and all-electron CCSD(T) calculations, as well as a range of DFT methods. We find that calculating the equilibrium rotational constants of these C₅H₂ isomers is a difficult task, even at the CCSD(T) level. For example, at the all-electron CCSD(T)/cc-pwCVTZ level of the theory, we obtain percentage errors ≤ 0.4% (C_e of isomer 3, B_e and C_e of isomer 5, and B_e of isomer 8) and 0.9–1.5% (B_e and C_e of isomer 2, A_e of isomer 5, and C_e of isomer 8), whereas for the A_e rotational constant of isomers 2 and 8 and B_e rotational constant of isomer 3, high percentage errors above 3% are obtained. These results highlight the challenges associated with calculating accurate rotational constants for isomers with highly challenging electronic structures, which is further complicated by the need to convert vibrationally averaged experimental rotational constants to equilibrium values. We use our best CCSD(T) rotational constants (namely, ae-CCSD(T)/cc-pwCVTZ for isomers 2 and 5, and ae-CCSD(T)/cc-pCVQZ for isomers 3 and 8) to evaluate the performance of DFT methods across the rungs of Jacob’s Ladder. We find that the considered pure functionals (BLYP-D3BJ, PBE-D3BJ, and TPSS-D3BJ) perform significantly better than the global and range-separated hybrid functionals. The double-hybrid DSD-PBEP86-D3BJ method shows the best overall performance, with percentage errors below 0.5% in nearly all cases.</p>