Corrected penalty-functional method for linear-scaling calculations within density-functional theory

We present a method for the calculation of ground-state total energies within density-functional theory, based upon the single-particle density-matrix formulation, which requires a computational effort which scales only linearly with system size. The difficult idempotency constraint is imposed approximately using a penalty functional constructed to allow efficient minimization. The resulting error in the total energy due to the violation of idempotency is removed by an analytic correction. The results for a system comprising 216 atoms of crystalline silicon are compared with those from a standard plane-wave code. Linear scaling to 512 atoms is also demonstrated on a workstation. [S0163-1829(99)10519-8].