Analytic gradient for the adaptive frozen orbital bond detachment in the fragment molecular orbital method

We have developed and implemented the analytic energy gradient for the bond detachment scheme in the fragment molecular orbital method (FMO) suitable to describe solids, and applied it to the geometry optimization of a silicon nanowire at several levels of theory. In addition, we have examined in detail the effects of the particular choice of the fragmentation upon the accuracy and introduced a number of numerical criteria to characterize the errors. The established route is expected to provide guidance for future applications of FMO to surfaces, solids and nanosystems.