Real-space electronic-structure calculations: combination of the finite-difference and conjugate-gradient methods

A.P. Seitsonen, M.J. Puska, R.M. Nieminen

Research output: Contribution to journalArticleScientificpeer-review

113 Citations (Scopus)
242 Downloads (Pure)

Abstract

We present a scheme for a rapid solution of a general three-dimensional Schrödinger equation. The Hamiltonian operator is discretized on a point grid using the finite-difference method. The eigenstates, i.e., the values of the wave functions in the grid points, are searched for as a constrained (due to the orthogonality requirement) optimization problem for the eigenenergies. This search is performed by the conjugate-gradient method. We demonstrate the scheme by solving for the self-consistent electronic structure of the diatomic molecule P2 starting from a given effective electron potential. Moreover, we show the efficiency of the scheme by calculating positron states in low-symmetry solids.
Original languageEnglish
Pages (from-to)14057-14601
Number of pages5
JournalPhysical Review B
Volume51
Issue number20
DOIs
Publication statusPublished - 15 May 1995
MoE publication typeA1 Journal article-refereed

Keywords

  • conjugate-gradient
  • electronic-structure calculations
  • finite-difference

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