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Spectral Point Schemes for Evaluating the Expansion Coefficients of State Densities into Orthogonal Functions
Author(s) -
Pisani C.,
Ugliengo P.
Publication year - 1982
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221120129
Subject(s) - legendre polynomials , mathematics , position (finance) , trigonometric functions , sampling (signal processing) , brillouin zone , orthogonal polynomials , mathematical analysis , interval (graph theory) , point (geometry) , symmetry (geometry) , geometry , quantum mechanics , combinatorics , physics , finance , economics , detector , optics
An expansion technique for calculating densities of states (DOS) of crystalline systems previously presented is here tested by evaluating numerically the expansion coefficients. To this purpose, existing special point schemes for Brillouin zone integrations are critically compared. It is shown that schemes where the sampling points are arranged according to a commensurate net are of unpaired efficiency for cubic systems. Very efficient sets of sampling points are also easily generated owing a closed diophantine technique, which can become competitive when lower‐symmetry crystals are considered. The DOS of one of the d‐bands of tight‐binding cubic systems is chosen to test the quality of the results obtained using Legendre polynomials and trigonometric functions as orthogonal sets. 220 sampling points are used to evaluate 16 expansion coefficients; the reconstructed curves are affected by an average relative error of about 4% over the whole band interval. As few as six expansion terms provide an estimate of the position of the Fermi level with an error within 1% of the band interval.