Efficient algorithm for band connectivity resolution
Abstract
An efficient algorithm for band connectivity (BC) resolution is presented. The method uses only readily available band coefficients and the overlap matrix, and has a low computational cost. The accuracy of the BC resolution is such that the method is practical for meshes of k points typically used in systems with small unit cells (e.g., 16×16×16 mesh for a 3 Å unit cell). We establish that the errors in the linear tetrahedron (LT) method due to the undetected crossings have ∆^{2} dependence with respect to the characteristic spacing between k points. The intrinsic error of the LT method is proportional to ∆^{2}, while for the ``improved'' LT method (iLT) it is proportional to ∆^{4}. Thus, the BC error is in fact the leading error of the iLT method. Our benchmarks demonstrate that the resolution of band connectivity restores the high accuracy of the ``improved'' LT method (∆^{4}) in systems with band crossings near or at the Fermi level.
 Publication:

Physical Review B
 Pub Date:
 May 2002
 DOI:
 10.1103/PhysRevB.65.205117
 Bibcode:
 2002PhRvB..65t5117Y
 Keywords:

 71.20.b;
 71.15.Ap;
 71.15.Mb;
 Electron density of states and band structure of crystalline solids;
 Basis sets and related methodology;
 Density functional theory local density approximation gradient and other corrections