Mathias P. Ljungberg

Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

The inhomogeneous structure of water at ambient conditions

Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of ≈1 nm; this is retained with decreasing temperature while the magnitude is enhanced. In contrast, the magnitude of fluctuations in a normal liquid, such as CCl4, exhibits no enhancement with decreasing temperature, as is also the case for water from molecular dynamics simulations under ambient conditions. Based on X-ray emission spectroscopy and X-ray Raman scattering data we propose that the density difference contrast in SAXS is due to fluctuations between tetrahedral-like and hydrogen-bond distorted structures related to, respectively, low and high density water. We combine our experimental observations to propose a model of water as a temperature-dependent, fluctuating equilibrium between the two types of local structures driven by incommensurate requirements for minimizing enthalpy (strong near-tetrahedral hydrogen-bonds) and maximizing entropy (nondirectional H-bonds and disorder). The present results provide experimental evidence that the extreme differences anticipated in the hydrogen-bonding environment in the deeply supercooled regime surprisingly remain in bulk water even at conditions ranging from ambient up to close to the boiling point.

Diffraction and IR/Raman data do not prove tetrahedral water

We use the reverse Monte Carlo modeling technique to fit two extreme structure models for water to available x-ray and neutron diffraction data in q space as well as to the electric field distribution as a representation of the OH stretch Raman spectrum of dilue HOD in D(2)O; the internal geometries were fitted to a quantum distribution. Forcing the fit to maximize the number of hydrogen (H) bonds results in a tetrahedral model with 74% double H-bond donors (DD) and 21% single donors (SD). Maximizing instead the number of SD species gives 81% SD and 18% DD, while still reproducing the experimental data and losing only 0.7-1.8 kJ/mole interaction energy. By decomposing the simulated Raman spectrum we can relate the models to the observed ultrafast frequency shifts in recent pump-probe measurements. Within the tetrahedral DD structure model the assumed connection between spectrum position and H-bonding indicates ultrafast dynamics in terms of breaking and reforming H bonds while in the strongly distorted model the observed frequency shifts do not necessarily imply H-bond changes. Both pictures are equally valid based on present diffraction and vibrational experimental data. There is thus no strict proof of tetrahedral water based on these data. We also note that the tetrahedral structure model must, to fit diffraction data, be less structured than most models obtained from molecular dynamics simulations.

On the Range of Water Structure Models Compatible with X-ray and Neutron Diffraction Data

We use the reverse Monte Carlo (RMC) method to critically evaluate the structural information content of diffraction data on bulk water by fitting simultaneously or separately to X-ray and neutron data; the O-H and H-H, but not the O-O, pair-correlation functions (PCFs) are well-described by the neutron data alone. Enforcing at the same time different H-bonding constraints, we generate four topologically different structure models of liquid water, including a simple mixture model, that all equally well reproduce the diffraction data. Although earlier work [Leetmaa, M.; et al. J. Chem. Phys. 2008, 129, 084502] has focused on tetrahedrality in the H-bond network in liquid water, we show here that, even for the O-O-O three-body correlation, tetrahedrality is not strictly defined by the data. We analyze how well two popular MD models (TIP4P-pol2 and SPC/E) reproduce the neutron data in q-space and find differences in important aspects from the experiment. From the RMC fits, we obtain pair-correlation functions (PCFs) that are in optimal agreement with the diffraction data but still show a surprisingly strong variability both in position and height of the first intermolecular (H-bonding) O-H peak. We conclude that, although diffraction data impose important constraints on the range of possible water structures, additional data are needed to narrow the range of possible structure models.

Are recent water models obtained by fitting diffraction data consistent with infrared/Raman and x-ray absorption spectra?

X-ray absorption (XA) spectra have been computed based on water structures obtained from a recent fit to x-ray and neutron diffraction data using models ranging from symmetrical to asymmetrical local coordination of the water molecules [A. K. Soper, J. Phys.: Condens. Matter 17, S3273 (2005)]. It is found that both the obtained symmetric and asymmetric structural models of water give similar looking XA spectra, which do not match the experiment. The fitted models both contain unphysical structures that are allowed by the diffraction data, where, e.g., hydrogen-hydrogen interactions may occur. A modification to the asymmetric model, in which the non-hydrogen-bonded OH intramolecular distance is allowed to become shorter while the bonded OH distance becomes longer, improves the situation somewhat, but the overall agreement is still unsatisfactory. The electric field (E-field) distributions and infrared (IR) spectra are also calculated using two established theoretical approaches, which, however, show significant discrepancies in their predictions for the asymmetric structural models. Both approaches predict the Raman spectrum of the symmetric model fitted to the diffraction data to be significantly blueshifted compared to experiment. At the moment no water model exists that can equally well describe IR/Raman, x-ray absorption spectroscopy, and diffraction data.

Reply to Soper et al.: Fluctuations in water around a bimodal distribution of local hydrogen-bonded structural motifs

Soper et al. (1) propose that the rise in the structure factor S(Q) at low Q in the small-angle x-ray scattering (SAXS) data reported in ref. 2 is caused by stochastic number fluctuations present in all liquids and that these fluctuations are not qualitatively different for water. Water, however, exhibits enhanced number density fluctuations both at higher and lower temperatures. Clearly, the driving force cannot be the same in both temperature regimes. In ref. 2, we suggest that the balance between minimizing enthalpy (tetrahedral regions) and entropy (disordered regions) provides the driving force dominating at low temperatures and that cooperatively enhanced H bonds associated with lower-density, tetrahedral regions may play an important role.

Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum

We apply the Kramers-Heisenberg formula to a model water dimer to discuss vibrational interference in the x-ray emission spectrum of the donor molecule for which the core-ionized potential energy surface is dissociative but bounded by the accepting molecule. A long core-hole lifetime leads to decay from Zundel-like, fully delocalized vibrational states in the intermediate potential without involvement of a specific dissociated component. Comparison is made to a model with an unbound intermediate state allowing dissociation to infinity which gives a sharp, fully dissociated feature, and a broad molecular peak at long core-hole life time. The implications of the vibrational interference effect on the liquid water spectrum are discussed and it is proposed that this mainly gives rise to an isotope-dependent asymmetrical broadening of the lone pair peak.

Complementarity between high-energy photoelectron and L-edge spectroscopy for probing the electronic structure of 5d transition metal catalysts

We demonstrate the successful use of hard X-ray photoelectron spectroscopy (HAXPES) for selectively probing the platinum partial d-density of states (DOS) in a Pt-Cu nanoparticle catalyst which shows activity superior to pure Pt towards the oxygen-reduction reaction (ORR). The information about occupied Pt d-band states was complemented by Pt L(2)-edge X-ray absorption near-edge spectroscopy (XANES), which probes unoccupied valence states. We found a significant electronic perturbation of the Pt projected d-DOS which was narrowed and shifted to higher binding energy compared to pure platinum. The effect of this electronic structure perturbation on the chemical properties of the nanoparticle surface is discussed in terms of the d-band model. We have thereby demonstrated that the combination of L-edge spectroscopy and HAXPES allows for an experimental derivation of the valence electronic structure in an element-specific way for 5d metal catalysts.

Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems

The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present difficulties for simpler approaches. We present a local basis set formulation of the BSE for molecules where the optical spectrum is computed with the iterative Haydock recursion scheme, leading to a low computational complexity and memory footprint. Using a variant of the algorithm we can go beyond the Tamm-Dancoff approximation (TDA). We rederive the recursion relations for general matrix elements of a resolvent, show how they translate into continued fractions, and study the convergence of the method with the number of recursion coefficients and the role of different terminators. Due to the locality of the basis functions the computational cost of each iteration scales asymptotically as

Assessing the electric-field approximation to IR and Raman spectra of dilute HOD in D2O.

O(N^3)