Length-scale ill conditioning in linear-scaling DFT Original Research Article

We discuss the problem of searching for the electronic ground state in linear-scaling DFT techniques, with particular attention to the pseudopotential scheme embodied in the CONQUEST code. An important source of difficulty in the ground-state search is ill conditioning associated with the different dependence of the total energy on wavefunction variations at different length scales. We recall how this ‘length-scale ill conditioning’ is handled by preconditioning in conventional plane-wave methods, and we show that analogous preconditioning schemes can be derived in the linear-scaling framework. We present the results of practical tests which show that the proposed preconditioning gives a substantial speed-up in convergence to the ground state.