Isomerization of nitrosomethane to formaldoxime: Energies, geometries, and frequencies from the parametric variational two-electron reduced-density-matrix method

The isomerization of nitrosomethane to trans-formaldoxime is treated with the parametric variational two-electron reduced-density-matrix (2-RDM) method. In the parametric 2-RDM method, the ground-state energy is minimized with respect to a 2-RDM that is parameterized to be both size extensive and nearly $N$-representable. The calculations were performed with an efficient version of the 2-RDM method that we developed as an extension of the PSI3 ab initio package. Details of the implementation, which scales like configuration interaction with single and double excitations, are provided as well as a comparison of two optimization algorithms for minimizing the energy functional. The conversion of nitrosomethane to trans-formaldoxime can occur by one of two pathways: (i) a 1,3-sigmatropic hydrogen shift or (ii) two successive 1,2-sigmatropic hydrogen shifts. The parametric 2-RDM method predicts that the reaction channel involving two sequential 1,2-shifts is about 10 kcal/mol more favorable than the channel with a single 1,3-shift, which is consistent with calculations from other ab initio methods. We computed geometric parameters and harmonic frequencies for each stationary point on the reaction surfaces. Transition-state energies, geometries, and frequencies from the 2-RDM method are often more accurate than those from traditional wave function methods of a similar computational cost. Although electronic-structure methods generally agree that the 1,2-shift is more efficient, the energy ordering of the reactant nitrosomethane and the 1,2-shift intermediate formaldonitrone is unresolved in the literature. With an extrapolation to the complete-basis-set limit the parametric 2-RDM method predicts formaldonitrone to be very slightly more stable than nitrosomethane.