Scalar relativistic all-electron density functional calculations on periodic systems

Scalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the third-order Douglas-Kroll-Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic all-electron density functional calculations using the traditional local spin-density and generalized gradient approximations (GGA), as well as meta-GGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gap semiconductors AgF and AgCl.     

Accurate density functional calculations on large systems

The theoretical underpinnings of the linear combination of Gaussian-type orbitals (LCGTO ) calculations of the density functional (DF ) energy of molecules and clusters are described. The generating function for three-center integrals of arbitrary angular momenta is given in the solid-spherical-harmonic basis. Variational fitting is described and its accuracy tested. The LCGTO-DF method is used to address questions related to the problem of how it is that the methods of cluster science, i.e., high-energy beams or currents, can be used to make C₆₀ in bulk quantities. In particular, it is shown that C₆₀ is neither especially stable nor is it the only large, stable, perfectly round, approximately sp² carbon molecule. © 1996 John Wiley & Sons, Inc.     

Fractional occupation numbers and spin density functional calculations of degenerate systems

We implemented ab initio self‐consistent field (SCF) fractional occupation numbers (FON) calculation with Dunlap's interpolation scheme for the twisted ethylene, which is a prototype molecule of a σ–π biradical system. The calculational results are compared with those of complete‐active‐space (CAS) SCF and spin‐unrestricted Kohn–Sham (UKS) calculations on potential surfaces, occupation numbers of natural orbitals, and correlation entropies. It was found that the UKS methods gave similar results to CASSCF, while the FON solutions appeared in only the nearly complete degenerate region. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 317–323, 2003     

Doping of polyaniline by acid-base chemistry: density functional calculations with periodic boundary conditions

Calculations with Gaussian orbitals and periodic boundary conditions using several density functionals are carried out to study the proton-doping of polyaniline. We explore previously proposed mechanisms to explain the spectacular increase of the electrical conductivity of polyaniline upon protonation. The structural and spectroscopic theoretical predictions for both polaron and bipolaron lattices agree quite well with the experimental data, and we find that the bipolaron structure is lower in energy.     

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). © 2012 Wiley Periodicals, Inc.     

Application of semiempirical long-range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from M?ller-Plesset second-order perturbation theory with basis set extrapolation.     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Lithium adsorption on graphite from density functional theory calculations

The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.     

Transition metal atoms on oxide supports density functional calculations

The adsorption properties of Cu, Ag, Ni, and Pd atoms on O^2?, F, and F⁺ sites of MgO, CaO, SrO, and BaO (001) surfaces have been studied by means of density functional calculations. The examined clusters were embedded in the simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces. The adsorption properties have been analyzed with reference to the basicity and energy gap of the oxide support in addition to orbital interactions. While the free Ni d⁹s¹ triplet ground state is preserved on adsorption on the O^2? sites of MgO, CaO, and SrO surfaces, it is no longer preserved on the O^2? site of BaO. For all adsorbates considered, adsorption is found to be stronger on F⁺ sites compared with regular O^2? sites. While on the O^2? site, Pd and Ni form the most stable complexes, on the F site, Pd and Cu form the most stable counterparts. On the F⁺ site, the single valence electron of Cu and Ag atoms couples with the unpaired electron of the vacancy forming a covalent bond. As a result, the adsorption energies of these atoms on the F⁺ site are stronger than those on the F and O^2? sites. The adsorption properties correlate linearly with the basicity and energy gap of the oxide support in addition to orbital interactions. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Atomic multiplet energies from density functional calculations

Atomic multiplet term energies for dⁿ configurations have been estimated within density functional theory (DFT) exploiting symmetry to the largest possible extent. The electrostatic two-electron integrals, as well as term energies, are expressed in function of only three non-redundant single determinants (NRSDs), each of them being obtained from density functional calculations. The influence of correlation effects described with a gradient-corrected functional (GGA) is examined and discussed. Comparison with experimental data shows the reliability of this symmetry-based density functional approach.     

Structure and magnetic properties of nitroxide molecular crystals by density functional calculations employing periodic boundary conditions.

The structure and magnetic properties of one-dimensional chains of representative nitroxides have been studied by a density functional model employing periodic boundary conditions. The optimized geometries are in better agreement with experiments than those obtained from optimizations of model dimeric systems. The spin populations and isotropic hyperfine couplings compare well with the values measured by polarized neutron and electron spin resonance experiments. Magnetic couplings computed by the broken symmetry approach reproduce the ferro- or antiferromagnetic behavior of different nitroxides derived from experiments. These results point out the reliability of the computational model and the significant tuning of all the magnetic properties by intermolecular hydrogen bridges.     

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.     

Conjugate-gradient optimization method for orbital-free density functional calculations

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient.     

Performance of parallel TURBOMOLE for density functional calculations

The parallelization of density functional treatments of molecular electronic energy and first-order gradients is described, and the performance is documented. The quadrature required for exchange correlation terms and the treatment of exact Coulomb interaction scales virtually linearly up to 100 nodes. The RI-J technique to approximate Coulomb interactions (by means of an auxiliary basis set approximation for the electron density) even shows superlinear speedup on distributed memory architectures. The bottleneck is then linear algebra. Demonstrative application examples include molecules with up to 300 atoms and 3000 basis functions that can now be treated in a few hours per geometry optimization cycle in C₁ symmetry. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1746–1757, 1998     

A rotationally invariant procedure for density functional calculations

A simple method which is rigorously invariant under molecular rotations is presented for evaluation of the density functional exchange—correlation energy by numerical quadrature. The corresponding expressions for the first and second derivatives of the energy with respect to nuclear displacement are presented. In particular, such a scheme is necessary to remove the difficulties previously encountered in calculating Kohn—Sham harmonic vibrational frequencies for low-lying modes.     

Benchmark density functional theory calculations for nanoscale conductance

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k|| points in the surface plane. For all systems we find that the SIESTA transmission functions converge toward the plane-wave result as the SIESTA basis is enlarged. Overall, we find that an atomic basis with double zeta and polarization is sufficient (and in some cases, even necessary) to ensure quantitative agreement with the plane-wave calculation. We observe a systematic downshift of the SIESTA transmission functions relative to the plane-wave results. The effect diminishes as the atomic orbital basis is enlarged; however, the convergence can be rather slow.     

H2S splitting on Cu(110): Insight from combined periodic density functional theory calculations and microkinetic simulation

Practical copper (Cu)‐based catalysts for the water–gas shift (WGS) reaction was long believed to expose a large proportion of Cu(110) planes. In this work, as an important first step toward addressing sulfur poisoning of these catalysts, the detailed mechanism for the splitting of hydrogen sulfide (H₂S) on the open Cu(110) facet has been investigated in the framework of periodic, self‐consistent density functional theory (DFT‐GGA). The microkinetic model based on the first‐principles calculations has also been developed to quantitatively evaluate the two considered decomposition routes for yielding surface atomic sulfur (S*): (1) H₂S → H₂S* → SH* → S* and (2) 2H₂S → 2H₂S* → 2SH* → S* + H₂S* → S* + H₂S. The first pathway proceeding through unimolecular SH* dissociation was identified to be feasible, whereas the second pathway involving bimolecular SH* disproportionation made no contribution to S* formation. The molecular adsorption of H₂S is the slowest elementary step of its full decomposition, being related with the large entropy term of the gas‐phase reactant under realistic reaction conditions. A comparison of thermodynamic and kinetic reactivity between the substrate and the close‐packed Cu(111) surface further shows that a loosely packed facet can promote the S* formation from H₂S on Cu, thus revealing that the reaction process is structure sensitive. The present DFT and microkinetic modeling results provide a reasonably complete picture for the chemistry of H₂S on the Cu(110) surface, which is a necessary basis for the design of new sulfur‐tolerant WGS catalysts. © 2013 Wiley Periodicals, Inc.