Matthias Krack

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach

Abstract We present the Gaussian and plane waves (GPW) method and its implementation in Quickstep which is part of the freely available program package CP2K. The GPW method allows for accurate density functional calculations in gas and condensed phases and can be effectively used for molecular dynamics simulations. We show how derivatives of the GPW energy functional, namely ionic forces and the Kohn–Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn–Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calculations for single molecules and plane wave based calculations in the condensed phase is excellent. Wave function optimisation with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born–Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the density matrix. We illustrate these findings with calculations using commodity PCs as well as supercomputers.

The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the temperature range of 280-380 K. We find a pronounced influence of temperature on the pair correlation functions and on the diffusion constant including nonergodic behavior on the time scale of the simulation in the lower temperature range (which includes ambient temperature). These observations were taken into account in a consistent comparison of a series of density functionals (BLYP, PBE, TPSS, OLYP, HCTH120, HCTH407). All simulations were carried out using an ab initio molecular dynamics approach in which wave functions are represented using Gaussians and the density is expanded in an auxiliary basis of plane waves. Whereas the first three functionals show similar behavior, it is found that the latter three functionals yield more diffusive dynamics and less structure.

Coexistence of tetrahedral-and octahedral-like sites in amorphous phase change materials

Chalcogenide alloys are materials of interest for optical recording and nonvolatile memories. We perform ab initio molecular dynamics simulations aiming at shading light onto the structure of amorphous Ge2Sb2Te5 (GST), the prototypical material in this class. First principles simulations show that amorphous GST obtained by quenching from the liquid phase displays two types of short range order. One third of Ge atoms are in a tetrahedral environment while the remaining Ge, Sb, and Te atoms display a defective octahedral environment, reminiscent of cubic crystalline GST.

Efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics.

We present a new method which combines Car-Parrinello and Born-Oppenheimer molecular dynamics in order to accelerate density functional theory based ab initio simulations. Depending on the system a gain in efficiency of 1 to 2 orders of magnitude has been observed, which allows ab initio molecular dynamics of much larger time and length scales than previously thought feasible. It will be demonstrated that the dynamics is correctly reproduced and that high accuracy can be maintained throughout for systems ranging from insulators to semiconductors and even to metals in condensed phases. This development considerably extends the scope of ab initio simulations.

Static and Dynamical Properties of Liquid Water from First Principles by a Novel Car−Parrinello-like Approach

Using the recently developed Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics ( Kühne, T. D. ; et al. Phys. Rev. Lett. 2007 , 98 , 066401. ), we assess the accuracy of ab initio molecular dynamics at the semilocal density functional level of theory to describe structural and dynamic properties of liquid water at ambient conditions. We have performed a series of large-scale simulations using a number of parameter-free exchange and correlation functionals, to minimize and investigate the influence of finite size effects as well as statistical errors. We find that finite size effects in structural properties are rather small and, given an extensive sampling, reproducible. On the other hand, the influence of finite size effects on dynamical properties are much larger than generally appreciated. So much so that the infinite size limit is practically out of reach. However, using a finite size scaling procedure, thanks to the greater effectiveness of our new method we can estimate both the thermodynamic value of the diffusion coefficient and the shear viscosity. The hydrogen bond network structure and its kinetics are consistent with the conventional view of tetrahedrally coordinated water.

An adaptive numerical integrator for molecular integrals

We present a new numerical integrator for molecular integrals that generates automatically an adaptive molecular grid. The tolerance of the numerical integration is the only input parameter of the integrator besides the atomic coordinates and the atomic numbers. The adaptive numerical integrator was successfully implemented in our new density-functional theory method (DFT method) ALLCHEM using the self consistent field (SCF) procedure. The accuracy of the numerical integration is superior to pruned fixed grids for a given number of grid points. The adaptive grid generator allows a very efficient optimization of the grid for an individual molecular system. It is shown that the grid accuracy increases monotonically, if the given tolerance of the numerical integration is decreased. In this way it is possible to obtain results of high numerical precision. For a given tolerance of the numerical integration the adaptive grid generator automatically adjusts the grid to the basis set and the molecular structure. ...

First-principles study of crystalline and amorphous Ge2Sb2Te5 and the effects of stoichiometric defects

Based on ab initio molecular dynamics simulations, we investigated the structural, electronic and vibrational properties of cubic and amorphous Ge(2)Sb(2)Te(5) (GST) phase change material, focusing in particular on the effects of defects in stoichiometry on the electronic properties. It turned out Ge/Sb deficiencies (excess) in the cubic phase induce a shift of the Fermi level inside the valence (conduction) bands. In contrast, the amorphous network is flexible enough to accommodate defects in stoichiometry, keeping the Fermi level pinned at the center of the bandgap (at zero temperature). Changes in the structural and electronic properties induced by the use of hybrid functionals (HSE03, PBE0) instead of gradient corrected functionals (PBE) are addressed as well. Analysis of vibrational spectra and Debye-Waller factors of cubic and amorphous GST is also presented.

Interfacial water: A first principles molecular dynamics study of a nanoscale water film on salt

Density functional theory (DFT) molecular dynamics simulations of a thin (approximately 15 A) water film on NaCl(001) have been performed, with the aim of understanding the structural and dynamic properties of this important interfacial water system. The interaction of the water film with the surface orders the water molecules in the immediate vicinity of the interface. This is reflected by oscillations in the planar-averaged water density distribution along the surface normal that extend to about 8 A from the surface. The interaction with the substrate leaves many of the water molecules in the immediate vicinity with broken hydrogen bonds and as a consequence considerably reduced dipole moments. Indeed a clear correlation between the number of hydrogen bonds which a water molecule is involved in and its dipole moment for both water on NaCl and bulk water is observed. How the DFT results obtained here compare to those obtained with various empirical potentials is briefly discussed.

Density oscillations in a nanoscale water film on salt: Insight from ab initio molecular dynamics

The salt-water interface is one of the most important and common on earth, playing a prominent role in disciplines such as atmospheric science and biology. Despite the apparent simplicity of such interfaces, arguably the most fundamental question of what the nature and structure of the liquid water/salt interface is under ambient conditions remains unclear. Here we address this issue with an ab initio molecular dynamics simulation of a nanoscale liquid water film on NaCl. A pronounced layering is observed in the film, with the density exhibiting a damped oscillatory behavior in the direction of the surface normal. In addition, water molecules in the contact layer are preferentially adsorbed at specific adsorption sites, involved in about 20% fewer hydrogen bonds with each other, and carry considerably reduced dipole moments compared to bulk liquid water.

Probing the Mechanical Properties of Hybrid Inorganic–Organic Frameworks: A Computational and Experimental Study

Hybrid framework materials are modular compounds consisting of metal ions and organic linkers, variation of which has given rise to a myriad of structures with technologically relevant properties. To date, extensive experimental and theoretical studies have been carried out to understand key factors that affect processes such as gas adsorption, gas separation and heterogeneous catalysis in nanoporous metal-organic frameworks (MOFs). [1] Dense hybrid frameworks are also of growing interest on account of their unique physical properties, such as multiferroics, electronic conductivity and photoluminescence, among others. [2] For all viable applications, the robustness of the materials and, in particular, a detailed understanding of their mechanical properties, are necessary for successful utilization. This field, however, remains largely unexplored. Recent experimental studies [3] have demonstrated that the elastic properties, especially the bulk modulus (B) [4] and the Young’s modulus (E) [5] of nanoporous and dense hybrid frameworks, can be correlated to their density, dimensionality and their underlying chemical structures. In addition, recent computational studies have reported that the bulk moduli of a family of isoreticular metal-organic frameworks (IRMOFs) depend on the size of the aromatic organic linkers (which determines the density). [6] Herein, we employed a combination of computational and experimental approaches to probe the elastic properties of a dense and anisotropic hybrid framework material: zinc phosphate phosphonoacetate hydrate, Zn3(PO4)(O2CCH2PO3)(H2O), 1. [7] We propose an efficient computational scheme for the approximate analysis of the Young’s modulus and the Poisson’s ratio (n) along the principal directions of an anisotropic crystal. Notably, this approach circumvents the intricacies involved in computing the full elastic stiffness tensor. [8] The validity of our theoretical calculations was addition, theoretical studies were performed by subjecting the anisotropic framework to hydrostatic compression to reveal the role of the basic building blocks. Studies to date indicate that both the local density approximation (LDA) and the general gradient approximation (GGA) levels of density functional theory (DFT) have over-predicted the bulk modulus (B) of MOF materials. By way of an example, the B value of the lightweight MOF-5 (density of 0.59 gcm ! 3 ) was calculated to be in the range of 16‐20 GPa, [6] which is notably higher than measurements obtained from other related MOF-type structures of considerably higher densities. Specifically, high pressure experiments have determined B values at only 6.5 GPa (0.93 gcm ! 3 ) and 14 GPa (1.54 gcm ! 3 )f or MOF materials with zeolitic imidazolate framework (ZIF) structures. [3c,9] Likewise, a large discrepancy exists in terms of the Young’s modulus (E). Theoretical studies on cubic crystals of MOF-5 have reported E values in the range of 14.8‐