Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.