Physical Review B 66, 035119 (2002)

Comparison of variational real-space representations of the kinetic energy operator

Chris-Kriton Skylaris, Oswaldo Diéguez, Peter D. Haynes and Mike C. Payne

Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, U.K.

We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a real-space method that is not variational) and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-difference method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B 64, 193101 (2001)] satisfies one of the two properties of variational behavior at the cost of larger errors than the conventional finite-difference method. On the other hand, a technique which represents functions in a number of plane waves which is independent of system size closely follows the plane-wave method and therefore also the criteria for variational behavior. Its application is only limited by the requirement of having functions strictly localized in regions of real space, but this is a characteristic of an increasing number of modern real-space methods, as they are designed to have a computational cost that scales linearly with system size.

PACS numbers: 31.15.Fx, 71.15.Nc, 71.15.Ap

Last updated: 29 August 2002
Peter Haynes