ALTRUISM: A Higher Calling.

A new robust surface-walking algorithm for locating transition states is presented. By modifying the Trust-Region Image Surface Minimization method to walk to higher-order stationary points, where the Hessian has more than one negative eigenvalue, we have developed an approach that determines transition states from above, by walking downhill on the potential energy surface. We call this algorithm ``ALTRUISM'' -- Alpine Trust-region Image Surface Method. We test the performance of the approach by applying it to a range of systems with several different quantum-chemical methods. Our results demonstrate that ALTRUISM is a systematic, robust, and unbiased method for connecting a reactant and a product via a transition state. The algorithmic combination of walking uphill (to different higher-order stationary points) and downhill to saddle points, enables us to explore qualitatively distinct reaction pathways, and construct a network of elementary reactions on a given potential energy surface.