A Gaussian Process Based Saddle-Point Search Method for Temperature-Dependent Energy Surfaces

In this work, we present a unique saddle-point search method based on a Gaussian process regression of the temperature-dependent energy surface to simultaneously sample the temperature-dependent energy surface and converge to the saddle point. We showcase the use of this method for solid-state diffusion in bcc phases of titanium and zirconium. These phases are chosen because they exhibit harmonic phonon instabilities, implying that the thermodynamic equilibrium state does not correspond to a local minimum on their Born-Oppenheimer energy surface. Therefore, saddle point search schemes cannot locate the diffusion transition state according to forces drawn from the Born-Oppenheimer energy surface [1]. Instead, forces drawn from an effective temperature-dependent energy surface are necessary to correctly guide the search scheme towards the transition state. In our method, a Gaussian process is used to estimate the temperature-dependent effective energy surface based on stochastically sampled atomic configurations along the transition path. We utilize the dimer and nudged-elastic band algorithms for the saddle point search on the temperature-dependent effective energy surface. Our method provides a useful alternative to methods such as molecular dynamics, which directly simulate diffusive hops.<br/><br/>References<br/><br/>[1] Fattahpour, Seyyedfaridoddin and Davariashtiyani, Ali and Kadkhodaei, Sara. Understanding the role of anharmonic phonons in diffusion of bcc metals. Phys. Rev. Materials, 10.1103/PhysRevMaterials.6.023803