Curvature correction for microiterative optimizations with QM/MM electronic embedding

One of the most common methods to treat the electrostatic effect of the environment in QM/MM calculations is to include the MM atoms as point charges in the QM Hamiltonian. In this case, a microiterative geometry optimization ignoring the QM contributions to the forces in the relaxation of the environment cannot yield exact stationary points. One solution that has been suggested in the literature is based on using a constant additive correction to the MM gradient during the microiterations, determined in the preceding macroiteration. Here, we analyze the convergence properties of the gradient correction method and point out that a smooth relaxation is not ensured if the curvature of the approximate, MM-based description of the potential energy surface of the environment is too small in comparison with the exact one. We suggest a computationally cheap second-order correction that uses an estimated Hessian from the Davidon-Fletcher-Powell method to tackle the problems caused by the too small curvature. Test calculations on four metalloenzymatic systems (∼100 QM atoms, ∼2000 relaxed MM atoms, ∼20,000 atoms in total) show that our approach efficiently restores the convergence where gradient correction alone would lead to oscillations.