The analytical calculation of our AC-QM/MM gradients requires atomic gradients as well as point charge gradients to be output from the QM program employed. Unfortunately, these are not always available and the contributions are usually too big to simply neglect them. For this reason, numerical gradients can be employed as follows. For each atom A of the "central molecule" a displacement ∆ r of the cartesian coordinates is generated and is applied to all equivalent atoms within the cluster molecules m according to