Efficient and accurate determination of lattice-vacancy diffusion coefficients via non equilibrium ab initio molecular dynamics

We revisit the color-diffusion algorithm [P. C. Aeberhard et al., Phys. Rev. Lett. 108, 095901 (2012)] in nonequilibrium ab initio molecular dynamics (NE-AIMD), and propose a simple efficient approach for the estimation of monovacancy jump rates in crystalline solids at temperatures well below melting. Color-diffusion applied to monovacancy migration entails that one lattice atom (colored-atom) is accelerated toward the neighboring defect-site by an external constant force F. Considering bcc molybdenum between 1000 and 2800 K as a model system, NE-AIMD results show that the colored-atom jump rate k_{NE} increases exponentially with the force intensity F, up to F values far beyond the linear-fitting regime employed previously. Using a simple model, we derive an analytical expression which reproduces the observed k_{NE}(F) dependence on F. Equilibrium rates extrapolated by NE-AIMD results are in excellent agreement with those of unconstrained dynamics. The gain in computational efficiency achieved with our approach increases rapidly with decreasing temperatures, and reaches a factor of four orders of magnitude at the lowest temperature considered in the present study.