ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Most band structure calculations approximate the integral over the Brillouin zone of momentum (i.e., wave vector) dependent properties with an appropriately weighted sum over a discrete set of points in the Brillouin zone. The best choice for such a set of points has long been a point of discussion in crystalline band structure calculations. For one-dimensionally periodic systems, however, the usual choice of points has been evenly spaced points in the one-dimensional Brillouin zone with equal weights. We have analyzed the exact error for the integral over the π band of a tight-binding model of trans-polyacetylene as a function of bond alternation. We find that the error in π band energy decreases in magnitude as q-2, where q is the total number of points treated in the Brillouin zone, for the metallic polyacetylene system with equal bond lengths. As bond alternation increases, however, we find that the error in π band energy decreases in magnitude roughly exponentially as a function of bond alternation for any given value of q. We find that this systematic change in error as a function of bond alternation can lead to either apparent overestimation or underestimation of the equilibrium dimerization and stabilization energy of Peierls distorted systems using first-principles total energy calculations.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560320716
