Energy Barriers of Vinylidene Carbene Reactions from the Anti-Hermitian Contracted Schrödinger Equation

Abstract

Computational studies of carbenes must take into account the possibility of multireference correlation because the highest occupied and lowest unoccupied molecular orbitals can be nearly energetically degenerate. We apply the anti-Hermitian contracted Schrodinger equation (ACSE) [Mazziotti, D. A. Phys. Rev. Lett. 2006, 97, 143002] to compute two-electron reduced density matrices (2-RDMs) and their energies for two carbene reactions: (i) the acetylene-vinylidene rearrangement and (ii) the rearrangement of pent-1-en-4-yn-3-one to acryloylvinylidene, which then cyclizes to cyclopenta-2,4-dienone. The ACSE has some unique advantages in the treatment of carbene reactions and more general families of reactions in which the importance of multireference correlation is not known a priori: (i) the ACSE is more reliable than single-reference methods for confirming the presence or absence of multireference correlation and (ii) in the absence of multireference correlation, unlike multireference second-order perturbation theory (MRPT2), the ACSE recovers more single-reference correlation energy than similarly scaling coupled-cluster methods. Because MRPT2 does not recover as much single-reference correlation as the coupled-cluster or ACSE methods, it tends to underestimate reaction barriers within the carbene reactions. For example, in the rearrangement of pent-1-en-4-yn-3-one, the ACSE and CCSD(T) methods produce cyclization barriers of 18.9 and 18.7 kcal/mol with the 6-31G(d) basis set, whereas MRPT2 predicts this barrier to be 12.1 kcal/mol; furthermore, both the ACSE and CCSD(T) determine the energy of the transition state for acryloylvinylidene formation to be 6.6-6.7 kcal/mol above that of the carbene, and yet, MRPT2 does not predict a transition state.