Automated generation of highly accurate, efficient and transferable pseudopotentials

A multi-objective genetic algorithm (MOGA) was used to automate a search for optimized pseudopotential parameters. Pseudopotentials were generated using the atomPAW program and density functional theory (DFT) simulations were conducted using the pwPAW program. The optimized parameters were the cutoff radius and projector energies for the s and p orbitals. The two objectives were low pseudopotential error and low computational work requirements. The error was determined from (1) the root mean square difference between the all-electron and pseudized-electron log derivative, (2) the calculated lattice constant versus reference data of Holzwarth et al., and (3) the calculated bulk modulus versus reference potentials. The computational work was defined as the number of flops required to perform the DFT simulation. Pseudopotential transferability was encouraged by optimizing each element in different lattices: (1) nitrogen in GaN, AlN, and YN, (2) oxygen in NO, ZnO, and SiO4, and (3) fluorine in LiF, NaF, and KF. The optimal solutions were equivalent in error and required significantly less computational work than the reference data. This proof-of-concept study demonstrates that the combination of MOGA and ab-initio simulations is a powerful tool that can generate a set of transferable potentials with a trade-off between accuracy (error) and computational efficiency (work).