Real-space electronic-structure calculations: Combination of the finite-difference and conjugate-gradient methods
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© 1995 American Physical Society (APS). This is the accepted version of the following article: Seitsonen, Ari P. & Puska, M. J. & Nieminen, Risto M. 1995. Real-space electronic-structure calculations: Combination of the finite-difference and conjugate-gradient methods. Physical Review B. Volume 51, Issue 20. 14057-14061. ISSN 1550-235X (electronic). DOI: 10.1103/physrevb.51.14057, which has been published in final form at http://journals.aps.org/prb/abstract/10.1103/PhysRevB.51.14057.
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Date
1995
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Degree programme
Language
en
Pages
14057-14061
Series
Physical Review B, Volume 51, Issue 20
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.Description
Keywords
Schrödinger equation, electronic-structure calculations, finite-difference, conjugate-gradient methods
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Citation
Seitsonen, Ari P. & Puska, M. J. & Nieminen, Risto M. 1995. Real-space electronic-structure calculations: Combination of the finite-difference and conjugate-gradient methods. Physical Review B. Volume 51, Issue 20. 14057-14061. ISSN 1550-235X (electronic). DOI: 10.1103/physrevb.51.14057.