Efficient linear scaling geometry optimization and transition-state search for direct wavefunction optimization schemes in density functional theory using a plane-wave basis

Two linear scaling schemes for the search of stationary points on the nuclear potential energy surface have been developed and implemented for density functional theory programs using plane waves: a geometry optimizer based on the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method and a linear scaling method for transition-state search based on the microiterative scheme using the partitioned rational function optimizer (P-RFO) and L-BFGS. These optimizers are written with parallelized execution in mind. It is shown that the electronic wavefunction does not need to be fully optimized in the earlier stages of geometry optimization. The reasons for the robustness and good performance of the proposed schemes are identified. Test calculations are presented that use our implementation in the CPMD code.