Photoexcited conversion of gauche-1,3-butadiene to bicyclobutane via a conical intersection: Energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

Abstract

The photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection is analyzed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions to the anti-Hermitian contracted Schrödinger equation (ACSE). The study utilizes the recent generalization of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)]. We computed absolute energies of the critical points as well as various intermediate points along the ground-and excited-state potential energy surface of gauche-1,3-butadiene and bicyclobutane. To treat multi-reference correlation, we seeded the ACSE with an initial 2-RDM from a multi-configuration self-consistent field (MCSCF) calculation. The ACSE, MCSCF, and second-order multi-reference many-body perturbation theory (MRPT2) all demonstrate that there exists a family of pathways from gauche-1,3-butadiene to bicyclobutane via a conical intersection that are monotonically decreasing in energy, confirming a conjecture by Sicilia et al. [J. Phys. Chem. A 111, 2182 (2007)]. The ACSE recovers more single-reference correlation energy than MRPT2 and more multi-reference correlation energy than comparable single-reference wave function methods. The 2-RDMs from the ACSE nearly satisfy all necessary N-representability conditions.