Journal ArticleDOI
New Method for Calculating Wave Functions in Crystals and Molecules
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TLDR
In this article, it is shown that advantage of crystal symmetry can be taken to construct wave functions which are best described as the smooth part of symmetrized Bloch functions.Abstract:
For metals and semiconductors the calculation of crystal wave functions is simplest in a plane wave representation. However, in order to obtain rapid convergence it is necessary that the valence electron wave functions be made orthogonal to the core wave functions. Herring satisfied this requirement by choosing as basis functions "orthogonalized plane waves." It is here shown that advantage can be taken of crystal symmetry to construct wave functions ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ which are best described as the smooth part of symmetrized Bloch functions. The wave equation satisfied by ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ contains an additional term of simple character which corresponds to the usual complicated orthogonalization terms and has a simple physical interpretation as an effective repulsive potential. Qualitative estimates of this potential in analytic form are presented. Several examples are worked out which display the cancellation between attractive and repulsive potentials in the core region which is responsible for rapid convergence of orthogonalized plane wave calculations for $s$ states; the slower convergence of $p$ states is also explained. The formalism developed here can also be regarded as a rigorous formulation of the "empirical potential" approach within the one-electron framework; the present results are compared with previous approaches. The method can be applied equally well to the calculation of wave functions in molecules.read more
Citations
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Journal ArticleDOI
On the success of pseudopotential methods
TL;DR: In this article, the reasons that the concept of pseudopotential can be successfully applied are discussed in the light of some alternative augmented plane wave calculations, and a graphic illustration of the basic observations which originally suggested the concept is provided.
Book ChapterDOI
Band Structure of Relaxed Silicon
TL;DR: In this paper, the authors show that the band gap E g =112eV at 300K separates the maximum of the last filled band called valence band from the minimum of the first empty band called conduction band.
Journal ArticleDOI
Orthonormalized and complete basis for the description of electronic states in solids
Y. Soulet,R. Fleckinger,A. Gomes +2 more
TL;DR: In this article, an orthonormalized and complete O.P.W. basis based on Girardeau's idea is proposed to determine the electronic states in solids, in particular in some pseudopotential methods.
Journal ArticleDOI
Chirp-wave expansion of the electron wavefunctions in atoms
E. Torres,Rafael Torres +1 more
TL;DR: The method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case, and it is shown that chirP basis sets substantially improve the convergence in the description of the electron density.