On the Numerical Calculation of the Density of States and Related Properties

Abstract

A method is given for the numerical calculation of energy surface integrals within the Brillouin zone like density of states, conductivity, susceptibility, dielectric function etc. The Brillouin zone is divided into tetrahedrons in which the integrand is interpolated linearly. I n this way the integration can be done analytically avoiding the histogram method. Several similar methods are discussed with regard to the quotient of accuracy and effort.Es wird eine Methode zur numerischen Berechnung von Integralen iiber Energieflachen in der Brillouin-Zone wie Zustandsdichte, Leitfihigkeit, Suszeptibilitat, dielektrische Funktion u. a. angegeben. Die Brillouin-Zone wird in Tetraeder eingeteilt, in denen der Integrand linear interpoliert wird. Dadurch kann die Integration unter Vermeidung der Histogramm-Methode analytisch durchgefuhrt werden. Mehrere ahnliche Methoden werden hinsichtlich des Verhaltnisses von Genauigkeit und Aufwand diskutiert.

First principle electronic, structural, elastic, and optical properties of strontium titanate

“…A total of 152 weighted k points, chosen along the high symmetry lines in the IBZ of SrTiO 3 , are used to solve for the energy eigenvalues from which the electron density of states (DOS) are calculated using the linear analytical tetrahedron method. 73 The partial density of states (pDOS) and the effective charge at each atomic sites are evaluated using the Mulliken charge analysis procedure. 74 We also calculated, the equilibrium lattice constant a o , the bulk modulus (B o ), the associated total energy and the electron and hole effective masses in different directions.…”

Self-trapped exciton defects in a charge density wave: Electronic excitations ofBaBiO3

“…This was evaluated numerically using a tetrahedron code [8,9], and is shown as the dashed line in Fig.6. The behavior of ǫ 2 is dominated by the divergence of the joint-density of states at photon energyhω = 2∆, corresponding to transitions from states at the top of the lower Peierls band into those at the bottom of the upper band.…”

Structural and electronic properties of the martensitic alloys TiNi, TiPd, and TiPt

“…4, calculated with the lineartetrahedron method. 22 In addition to the B2 and B19Ј structure, we also show for comparison the DOS of the other structures we have calculated. The DOS is expressed in number of states per atom per energy interval.…”