A Distortion Symmetry-based Approach to Minimum Energy Pathways
Venkat Gopalan

Complex systems are most likely to evolve from one state to another along a path of least energy barrier. Without an a-priori knowledge of the energy landscape, the nudged elastic band method (NEB) is a commonly used algorithm to find these minimum energy barrier pathways between the initial and final states of a kinetic process. However, these calculated pathways are critically dependent on the choice of the initial path, thus traditionally requiring multiple calculations with different starting points. Recently, we have introduced the concept of “symmetry of a path” as a whole, that includes all the images along the pathway, and assigning each path a “distortion symmetry group” label.  The complete initial path that is chosen is now perturbed using symmetry-adapted perturbations based on group theory.  Here, numerical implementation of this method within commercial NEB codes is shown to lead to the discovery of previously unknown hidden pathways for the case study of bulk ferroelectric domain switching and wall motion. In contrast to the current methods, the proposed symmetry framework allows for a powerful means to classify the infinite possible pathways into a finite number of symmetry “bins,” and thus explore each bin systematically using rigorous group theoretical methods.  This approach is applicable to a wide variety of physical phenomena ranging from structural, electronic and magnetic distortions, diffusion, and phase transitions in materials.