Frozen-Core Analytical Gradients within the Adiabatic Connection Random-Phase Approximation from an Extended Lagrangian.

The implementation of the frozen-core option in combination with the analytic gradient of the random-phase approximation (RPA) is reported based on a density functional theory reference determinant using resolution-of-the-identity techniques and an extended Lagrangian. The frozen-core option reduces the dimensionality of the matrices required for the RPA analytic gradient, thereby yielding a reduction in computational cost. A frozen core also reduces the size of the numerical frequency grid required for accurate treatment of the correlation contributions using Curtis-Clenshaw quadratures, leading to an additional speedup. Optimized geometries for closed-shell, main-group, and transition metal compounds, as well as open-shell transition metal complexes, show that the frozen-core method on average elongates bonds by at most a few picometers and changes bond angles by a few degrees. Vibrational frequencies and dipole moments also show modest shifts from the all-electron results, reinforcing the broad usefulness of the frozen-core method. Timings for linear alkanes, a novel extended metal atom chain and a palladacyclic complex show a speedup of 35-55% using a reduced grid size and the frozen-core option. Overall, our results demonstrate the utility of combining the frozen-core option with RPA to obtain accurate molecular properties, thereby further extending the range of application of the RPA method.