where D pq and d pqrs are the CASSCF one-and two-body reduced density matrices. If the active space is chosen inconsistently between two geometries, one will obtain an unphysical "active space inconsistency error" (ASIE) resulting from the inconsistent treatment of correlation in the density matrices of equation 2. This error generally remains present even when addressing the remaining dynamic correlation perturbatively with methods such as CASPT2 or NEVPT2. The most common approach for reducing ASIE involves interpolating the active space orbitals between geometries, providing a continuous set of orbitals along the reaction coordinate. However, this approach is quite cumbersome: active orbitals often rotate in and out of the active space randomly during this procedure, and the active space may change size along a reaction coordinate, such as when moving from a fairly uncorrelated reactant to a correlated transition state. Furthermore, this interpolation scheme dramatically increases the cost of the calculation relative to approaches such as DFT, as CASSCF calculations are necessary along several points between the reactant and product, whereas KS-DFT only requires calculations at the individual end points.