Reinvestigation of the reaction of ethylene and singlet oxygen by the approximate spin projection method. Comparison with multireference coupled-cluster calculations.

We quantify a spin contamination error caused by a broken-symmetry (BS) method on the geometry at the stationary points and barrier heights of the [2 + 2] reaction between singlet oxygen and ethylene, which goes through a diradical intermediate. Several hybrid GGA, hybrid meta-GGA, and long-range corrected hybrid functionals, O3LYP, B3LYP, PBE0, MPW1B95, BHandHLYP, and omegaB97X, are examined to elucidate their original nature without the spin contamination error. For that purpose, the geometry of each reaction step for the BS state as well as its total energy is corrected by using an approximate spin projection method. The CCSD and CCSD(T) single-point calculations are also carried out at optimized geometries at the DFT level to confirm the results of the DFT methods. The single-point calculations by means of Mukherjee's multireference coupled cluster with single and double excitations at CASSCF(10e,8o)-optimized geometries are also presented to assess the DFT methods. After the energy and geometry corrections, the barrier height of each functional is consistent with conventional closed-shell-type reactions even in the reaction involving singlet diradical species. We also find that the spin contamination error on the geometric change is not negligible especially at the early stage of the reaction ( approximately 3 kcal/mol), where the triplet state is the ground state.

Multireference character of 1,3-dipolar cycloaddition of ozone with ethylene and acrylonitrile.

In the present study, the concerted and stepwise reaction mechanisms for 1,3-dipole cycloaddition of ozone with ethylene (1) and acrylonitrile (2) are investigated. The stationary points are optimized by using four hybrid R(U)DFT methods. A geometry optimization method based on an approximate spin projection (AP-opt method) is applied to eliminate a spin contamination from the broken-symmetry (BS) solution. The AP-opt method reveals that a diradical intermediate for the stepwise pathway is spurious due to the spin contamination. The revised reaction profile with no diradical intermediate supports the stereospecificity. On the basis of the experimental data, the RCCSD(T) method outperforms AP-UCCSD(T), AP-UBD(T), and MkMRCCSD(4e,4o) for the systems, indicating that the RCCSD(T) method can describe the diradical character of ozone within a framework of single reference wave function. The subsequent single point energy calculations show that the highly synchronous transition state is much more favorable than the asynchronous one for 1. In the case of 2, there is not much difference between two transition states because of its asymmetric structure and charge separations in the transition states.