Implementation of empirical dispersion corrections to density functional theory for periodic systems.

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT-D3) is implemented in the plane-wave program package VASP. The DFT-D3 implementation is compared with an implementation of the earlier DFT-D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT-D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three-center terms as implemented in the original molecular DFT-D3 version is investigated. The empirical parameters are taken from the original DFT-D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid-state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT-D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106).

A MinMax self-consistent-field approach for auxiliary density functional theory.

A MinMax self-consistent-field (SCF) approach is derived in the framework of auxiliary density functional theory. It is shown that the SCF convergence can be guided by the fitting coefficients that arise from the variational fitting of the Coulomb potential. An in-core direct inversion of the iterative subspace (DIIS) algorithm is presented. Due to its reduced memory demand this new in-core DIIS method can be applied without overhead to very large systems with tens of thousands of basis and auxiliary functions. Due to the new DIIS error definition systems with fractional occupation numbers can be treated, too.

Boron-doped diamond: Investigation of the stability of surface-doping versus bulk-doping using cyclic cluster model calculations.

Boron-doped bulk diamond and the boron-doped hydrogen terminated (001) surface of diamond were investigated using the cyclic cluster model. Structure and stability of the hydrogen-terminated (001) surface were calculated and compared with experimental and other theoretical results from the literature. Boron-doping was modeled by substitution of a carbon atom by a boron atom in different positions with increasing distance from the surface up to boron-doped bulk diamond. In agreement with experiments on nanoclusters, boron is most stable in the first surface layers. (c) 2008 Wiley Periodicals, Inc. J Comput Chem, 2008.

Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods.

The development of the cyclic cluster model (CCM) formalism for Kohn-Sham auxiliary density functional theory (KS-ADFT) methods is presented. The CCM is a direct space approach for the calculation of perfect and defective systems under periodic boundary conditions. Translational symmetry is introduced in the CCM by integral weighting. A consistent weighting scheme for all two-center and three-center interactions appearing in the KS-ADFT method is presented. For the first time, an approach for the numerical integration of the exchange-correlation potential within the cyclic cluster formalism is derived. The presented KS-ADFT CCM implementation was applied to covalent periodic systems. The results of cyclic and molecular cluster model (MCM) calculations for trans-polyacetylene, graphene, and diamond are discussed as examples for systems periodic in one, two, and three dimensions, respectively. All structures were optimized. It is shown that the CCM results represent the results of MCM calculations in the limit of infinite molecular clusters. By analyzing the electronic structure, we demonstrate that the symmetry of the corresponding periodic systems is retained in CCM calculations. The obtained geometric and electronic structures are compared with available data from the literature.

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems.

Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.

Parallelization of the deMon2k code.

The parallelization of the LCGTO-KS-DFT code deMon2k is presented. The parallelization of the three-center electron repulsion integrals, the numerical integration using a direct grid algorithm and the matrix multiplication and diagonalization are described. The efficiency of the parallelization is analyzed by selected benchmark calculations. It is shown that geometry optimizations of systems with more than 8,000 basis functions are feasible on cluster architectures.