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.