Variational finite-difference representation of the kinetic energy operator

Details Variational finite-difference representation of the kinetic energy operator Variational finite-difference representation of the kinetic energy operator

2001-08-13

arxiv.org/abs/cond-mat/0108196v1

Physics

Condensed Matter

Materials Science

3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution for the 10th anniversary of the eprint server

Scientific paper

10.1103/PhysRevB.64.193101

A potential disadvantage of real-space-grid electronic structure methods is the lack of a variational principle and the concomitant increase of total energy with grid refinement. We show that the origin of this feature is the systematic underestimation of the kinetic energy by the finite difference representation of the Laplacian operator. We present an alternative representation that provides a rigorous upper bound estimate of the true kinetic energy and we illustrate its properties with a harmonic oscillator potential. For a more realistic application, we study the convergence of the total energy of bulk silicon using a real-space-grid density-functional code and employing both the conventional and the alternative representations of the kinetic energy operator.

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