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

Abstract

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 new definition of the finite differences method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B \textbf{64}, 193101 (2001)] satisfies one of the two properties of variational behaviour at the cost of larger errors than the conventional finite differences method. On the other hand, a technique which represents functions in a number of plane-waves which is independent of system size, follows closely the plane-wave method and therefore also the criteria for variational behaviour. Its application is only limited by the requirement of having functions strictly localised in regions of real-space but this is a characteristic of most modern real-space methods as they are designed to have a computational cost that scales linearly with system size.

9 pages, 3 figures

References in corpus (4)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Accurate kinetic energy evaluation in electronic structure calculations with localised functions on real space grids
• Variational finite-difference representation of the kinetic energy operator

Cited by in corpus (5)

• O(N) methods in electronic structure calculations
• Real-space electronic-structure calculations with timesaving double-grid technique
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• Using ONETEP for accurate and efficient O(N) density functional calculations
• Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects