where P µν is the HF density matrix and F KS µν is the Kohn-Sham (KS) Fock matrix constructed from the HF density matrix. Operationally, derivatives ∂P µν /∂x are eliminated in favor of molecular orbital coefficient derivatives, written in Z-vector form for efficiency. This is similar to the procedure used for DFT second derivatives, which require ∂P µν /∂x even when the procedure is variational. DC-DFT and its analytic gradient have been implemented in a locally-modified version of Q-Chem. Validation tests are described in the Supporting Information, including comparisons between analytic and finitedifference gradients (Tables ) and a demonstration that DC-DFT conserves energy in ab initio molecular dynamics simulations (Fig. ). We also reproduced previous results demonstrating that DC-BLYP affords much improved reaction barriers as compared to either selfconsistent BLYP or HF calculations (Table ).