Kinetic energy cutoff

As a simple example of a QM/MM Car-Parinello study, we present here results from a mixed simulation of the zwitterionic form of Gly-Ala dipeptide in aqueous solution [12]. In this case, the dipeptide itself was described at the DFT (BLYP [88, 89 a]) level in a classical solvent of SPC water molecules [89b]. The quantum solute was placed in a periodically repeated simple cubic box of edge 21 au and the one-particle wavefunctions were expanded in plane waves up to a kinetic energy cutoff of 70 Ry. After initial equilibration, a simulation at 300 K was performed for 10 ps. 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

In order to calculate the band structure and the density of states (DOS) of periodic unit cells of a-rhombohedral boron (Fig. la) and of boron nanotubes (Fig. 3a), we applied the VASP package [27], an ab initio density functional code, using plane-waves basis sets and ultrasoft pseudopotentials. The electron-electron interaction was treated within the local density approximation (LDA) with the Geperley-Alder exchange-correlation functional [28]. The kinetic-energy cutoff used for the plane-wave expansion of... 

Plane-wave GGA density-functional calculations [58] and similar computational conditions as used in the study by Koudriachova et al. [136], in the present work a kinetic energy cutoff of 380 eV and a k-point spacing of 0.06 A-1. c From ref. [137], where a modification of the 6-31G basis set was used. d For studies of pure anatase employing local density approximation (LDA) DFT calculations, see e.g. ref. [138]. 

Table 1 Comparison between cohesive energies per atom of Pbn clusters (in eV) calculated with kinetic energy cutoffs of 8 Ryd. and 16 Ryd.

Use of the plane wave based electronic structure methods introduces two basic parameters the kinetic energy cutoff value, controlling the basis set quality, and the periodic unit-cell (supercell) size, present due to periodic nature of these approaches. Both of these parameters should be large enough to guarantee the convergence in the total energy and in all the physical quantities that are supposed to be determined from the simulation. 

Apart from an expected dependence of the number of plane waves Npw on the kinetic energy cutoff, we find that it also depends on the volume of the simulation cell 17. These are important considerations when assessing the time and memory requirements of a simulation. 

The electronic structure for the MgO crystal was calculated in [608] both in the LCAO approximation and in the PW basis. In both cases the calculations were done by the density-functional theory (DFT) method in the local density approximation (LD A). The Monkhorst Pack set of special points of BZ, which allows a convergence to be obtained (relating to extended special-points sets) in the calculations of electronic structure, was used in both cases. For the LCAO calculations the Durand Barthelat pseudopotential [484] was used. In the case of the PW calculations the normconserving pseudopotential and a PW kinetic energy cutoff of 300 eV were used. 

The unit cell size was [BaTi409]2, and the number of occupied orbitals was 112. The kinetic energy cutoff was 260 eV for the both systems. 

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