Automated search of minimum-energy conical intersections with projected metadynamics

We present a new method for the automated search of minimum-energy conical intersections (MECIs) based on metadynamics. In this method, two independent forces are constructed and projected into the minimization subspace and the constraint subspace, respectively. One force is directed toward the minimum-energy point, while the other is directed toward the conical intersection seam. The root-mean-square deviation based bias potential is added to the potential energy surface to force the structure escape from the already explored regions. The additional constraint function is used to enable the structure reach different intersection seams. This method can be used for systematically and automatically searching MECIs or exploring conical intersection seams. Compared to the penalty function-based metadynamics method, this new method is more effective and stable in searching MECIs. Furthermore, this method can be combined with any kind of constraint, whether geometric or non-geometric, making it a generalized tool for the automated search of constrained minimum.