LENGTH-SCALE ILL CONDITIONING IN LINEAR-SCALING DFT

We discuss the problem of searching for the electronic ground state in linear-scaling DFT techniques, with particular attention to the pseud opotential scheme embodied in the CONQUEST code. An important source o f difficulty in the groundstate search is ill conditioning associated with the different dependence of the total energy on wavefunction vari ations at different length scales. We recall how this 'length-scale il l conditioning' is handled by preconditioning in conventional plane-wa ve methods, and we show that analogous preconditioning schemes can be derived in the linear-scaling framework. We present the results of pra ctical tests which show that the proposed preconditioning gives a subs tantial speed-up in convergence to the ground state. (C) 1998 Elsevier Science B.V.