János G. Ángyán

Screened hybrid density functionals applied to solids

Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections

The implementation of technique for full structural optimizations of complex periodic systems in the DFT-PAW package VASP, including the volume and shape of the unit cell and the internal coordinates of the atoms, together with a correction that allows an appropriate modeling of London dispersion forces, as given by the DFT-D2 approach of Grimme [Grimme, S. J. Comp. Chem. 2006, 27, 1787], is reported. Dispersion corrections are calculated not only for the forces acting on the atoms, but also for the stresses on the unit cell. This permits a simultaneous optimization of all degrees of freedom. Benchmark results on a series of prototype systems are presented and compared to results obtained by other methods and experimental data. It is demonstrated that the computationally inexpensive DFT-D2 scheme yields reasonable predictions for the structure, bulk moduli, and cohesive energies of weakly bonded materials.

Assessing the performance of recent density functionals for bulk solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and nonmetals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation PBEsol GGA, the second-order GGA SOGGA, and the Armiento-Mattsson 2005 AM05 GGA. For completeness, we also test more standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties lattice constant and bulk modulus. For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zeropoint phonon and finite-temperature effects ignored by many workers. We show how GAUSSIAN basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline-earth metal, and alkali halide crystals where the maximum value of the reduced density gradient is about 2, but perform very similarly for most of the other solids where it is often about 1. Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.

Polymorphism in silica studied in the local density and generalized-gradient approximations

The crystal structures of a large number of silica polytypes (- and -quartz, - and -cristobalite, -tridymite, keatite, coesite and stishovite) have been studied using density functional theory, both in the local density approximation and including generalized-gradient corrections to the exchange-correlation functional. All crystal structures have been optimized by minimizing the total energy with respect to all lattice parameters and to the atomic coordinates within the unit cell (up to 40 structural parameters in the case of coesite). The transitions in quartz and cristobalite have been studied in detail, including different variants proposed for the structure of -cristobalite. The tetragonal (I2d) and simple cubic (P213) structures are found to be energetically almost degenerate near the equilibrium volume. On volume expansion both structures converge towards the idealized highly symmetric Fd3m structure. A similar continuous transition from a more compact orthorhombic (C2221) to a highly symmetric hexagonal (P63/mmc) variant is also proposed for -tridymite. For coesite two monoclinic variants (with C2/c and P21/c space-group symmetries, respectively) have been examined and found to be energetically degenerate to within 1 meV per SiO2 unit. It is shown that within the local density approximation (LDA) the equilibrium atomic volume of all polytypes is predicted with an accuracy better than one per cent. The LDA also leads to excellent structural predictions and to accurate values of the bulk modulus. Corrections in the framework of the generalized-gradient approximation (GGA) lead to substantially larger equilibrium volumes, although at fixed volume the LDA and GGA lead to identical crystal structures. The increased volume also leads to less accurate structural parameters. However, we find that gradient corrections are essential for achieving accurate structural energy differences between the tetrahedrally coordinated phases found at larger atomic volumes (all polytypes except stishovite) and the octahedrally coordinated high-pressure polymorphs (stishovite and post-stishovite phases).

Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density-functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be2 and Ne2.

Distributed polarizabilities using the topological theory of atoms in molecules

Distributed atom-atom multipolar polarizabilities have been calcd. at the coupled perturbed Hartree-Fock level, using Baders topol. theory to partition the mol. charge d. into at. domains. The proposed scheme applies without difficulty to mols. of arbitrary shape and symmetry and maintains a remarkable stability of the individual at. polarizability components with respect to basis set extension, exemplified by the mols. CO, H2O, NH3 and BF3.

Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions

Range-separated methods combining a short-range density functional with long-range random phase approximations (RPAs) with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx, which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5-0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7%-9% depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order Moller-Plesset (MP2) perturbation theory (RSH+MP2).

Reaction field factors for a multipole distribution in a cavity surrounded by a continuum

Abstract The reaction field factors appear in the generalization of the Kirkwood model of solvation for a molecule imbedded in a cavity surrounded by a dielectric continuum. A general algorithm is proposed to compute these factors for a distributed multipole analysis of the charge distribution of the solute.

Correlation Energy Expressions from the Adiabatic-Connection Fluctuation-Dissipation Theorem Approach.

We explore several random phase approximation (RPA) correlation energy variants within the adiabatic-connection fluctuation-dissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these variants, named dRPA-II, is original to this work and closely resembles the second-order screened exchange (SOSEX) method. We discuss and clarify the connections among different RPA formulations. We derive the spin-adapted forms of all the variants for closed-shell systems and test them on a few atomic and molecular systems with and without range separation of the electron-electron interaction.

THE ORIGIN OF THE PROBLEMS WITH THE PM3 CORE REPULSION FUNCTION

Abstract We investigate the cause of failures of PM3 for H⋯H, O⋯H and N⋯H interactions. We show that the actual choice of parameters for the Gaussian correction functions leads to spurious oscillations in the interatomic core repulsion functions and in the potential energy surfaces. The positions of the minima of the Gaussian correction functions considerably influence the positions of the minima on the potential energy hypersurface of weak interactions. The PM3 potential energy curve of water dimer as a function of the O⋯H distance clearly illustrates the problem. The minimum at 1.8 A and the wide shoulder at 2.1 A correspond to a minimum and a maximum of the O⋯H Gaussian correction function, respectively.