Brillouin zone integration

Monkhorst H J and J D Pack 1976. Special Points for Brillouin-zone Integration. Physical Review B13 5188-5192. 

The pseudopotential density-functional technique is used to calculate total energies, forces on atoms and stress tensors as described in Ref. 13 and implemented in the computer code CASTEP. CASTEP uses a plane-wave basis set to expand wave-functions and a preconditioned conjugate gradient scheme to solve the density-functional theory (DFT) equations iteratively. Brillouin zone integration is carried out via the special points scheme by Monkhorst and Pack. The nonlocal pseudopotentials in Kleynman-Bylander form were optimized in order to achieve the best convergence with respect to the basis set size. 5... 

HJ. Monkhorst and J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 5188... 

Table 1 Time per iteration (in seconds) for the RMM-DIIS and CGa algorithms applied to Fe-ensembles with Natom atoms and using Nkpointa -points for Brillouin-zone integrations. The calculations performed at the T-point only where performed with a version of the code using real wave-functions.

Calculations were done with a full-potential version of the LMTO method with nonoverlapping spheres. The contributions from the interstitial region were accounted for by expanding the products of Hankel functions in a series of atom-ce- -ered Hankels of three different kinetic energies. The corrected tetrahedron method was used for Brillouin zone integration. Electronic exchange and correlation contributions to the total energy were obtained from the local-density functional calculated by Ceperley and Alder " and parametrized by Vosko, Wilk, and Nusair. ... 

AN ADAPTIVE QUADRATURE METHOD FOR BRILLOUIN ZONE INTEGRATION OF KKR FUNCTIONS... 

Brillouin zone integrations, pervasive in any solid-state calculation, are best performed with the Monkhorst-Pack scheme [6]. These integrations are essentially equally demanding in any representation and with any basis set. This satisfies criterion 5. 

In the LDA, Adolph and Bechstedt [157,158] adopted the approach of Aspnes [116] with a plane-wave-pseudopotential method to determine the dynamic x of the usual IB V semiconductors as well as of SiC polytypes. They emphasized (i) the difficulty to obtain converged Brillouin zone integration and (ii) the relatively good quality of the scissors operator for including quasiparticle effects (from a comparison with the GW approximation, which takes into account wave-vector- and band-dependent shifts). Another implementation of the SOS x —2 ffi, ffi) expressions at the independent-particle level was carried out by Raskheev et al. [159] by using the linearized muffin-tin orbital (LMTO) method in the atomic sphere approximation. They considered... 

Periodic conventional DFT was used in this study [47]. The calculations were performed using VASP [55, 56] with GGA [107] and using an energy cutoff of 270 eV (defined Irom plane wave convergence test performed on bulk NiO) and ultrasoft pseudopotenlials [108, 109]. The Brillouin zone integrations have been performed using a Monkhorst-Pack grid... 

All the calculations are performed in momentum space and (unless otherwise stated) plane waves with kinetic energy up to 9.15 Ry are included in the expansions of the wave functions. Only those with kinetic energy S 2.55 Ry are dealt with exact, the remaining ones are treated by Lowdin perturbation theory up to second order. This corresponds to approximately 21 + 125 waves when working with the two-atoms cells, 43 + 240 when working with the doubled (four atoms) ui it cells, 85 + 500 on quadrupled cells, etc. Two to five special k-points are used for Brillouin zone integration (corresponding to (222) in the notation of... 

The suggested modification of Monkhorst-Pack special-points meshes for Brillouin-zone integration is essentially useful for crystals with many atoms in a primitive unit... 

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