In 1959 Charles Coulson popularized the idea of computing a molecule's ground-state energy as a functional of the two-electron reduced density matrix (2-RDM) without the many-electron wave function. For 50 years, however, a practical, direct calculation of the 2-RDM was not achieved because the 2-RDM must be constrained by N-representability conditions to represent an N-electron system. Recently, two general approaches to the direct calculation of the 2-RDM have emerged including the solution of the anti-Hermitian contracted Schrodinger equation (ACSE) [Mazziotti, Phys. Rev. Lett., 2006, 97, 143002]. In this article, after further extending the theoretical development of the ACSE method for multireference correlation, we apply the ACSE to studying an unresolved question regarding the opening of bicyclobutane to gauche-1,3-butadiene by conrotatory and disrotatory pathways. Previous theoretical values for the disrotatory energy barrier reveal a disagreement between correlation methods on the order of 10 kcal/mol. By capturing significantly more correlation energy than traditional multireference methods, the ACSE provides new insight into this discrepancy. The ACSE energy for the conrotatory energy barrier agrees with the 40.6 +/- 2.5 kcal/mol experimental value.