Analytical Gradients of Hartree–Fock Exchange with Density Fitting Approximations

We extend the local exchange (LK) algorithm [Aquilante, F.; Pedersen, T. B.; Lindh, R. J. Chem. Phys.2007, 126, 194106] to the calculation of analytical gradients with density fitting. We discuss the features of the screening procedure and demonstrate the possible advantages of using this formulation, which is easily interfaced to a standard integral-direct gradient code. With auxiliary basis sets obtained from Cholesky decomposition of atomic or molecular integral blocks with a decomposition threshold of 10–4Eh, typical errors due to the density fitting in bond lengths, bond angles, and dihedral angles are 0.1 pm, 0.1°, and 0.5°, respectively. The overall speedup of geometry optimizations is about 1 order of magnitude for atomic natural-orbital-type basis sets but much less pronounced for correlation-consistent basis sets.