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.
Physical Review B
- Pub Date:
- May 2002
- 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