Toward Efficient GW Calculations Using Numerical Atomic Orbitals: Benchmarking and Application to Molecular Dynamics Simulations.

The use of atomic orbitals in Hedin's GW approximation provides, in principle, an inexpensive alternative to plane-wave basis sets, especially when modeling large molecules. However, benchmarking of the algorithms and basis sets is essential for a careful balance between cost and accuracy. In this paper, we present an implementation of the GW approximation using numerical atomic orbitals and a pseudopotential treatment of core electrons. The combination of a contour deformation technique with a one-shot extraction of quasiparticle energies provides an efficient scheme for many applications. The performance of the implementation with respect to the basis set convergence and the effect of the use of pseudopotentials has been tested for the 117 closed-shell molecules from the G2/97 test set and 24 larger acceptor molecules from another recently proposed test set. Moreover, to demonstrate the potential of our method, we compute the thermally averaged GW density of states of a large photochromic compound by sampling ab initio molecular dynamics trajectories at different temperatures. The computed thermal line widths indicate approximately twice as large electron-phonon couplings with GW than with standard DFT-GGA calculations. This is further confirmed using frozen-phonon calculations.

X-ray Emission Spectrum of Liquid Ethanol: Origin of Split Peaks.

The X-ray emission spectrum of liquid ethanol was calculated using density functional theory and a semiclassical approximation to the Kramers-Heisenberg formula including core-hole-induced dynamics. Our spectrum agrees well with the experimental spectrum. We found that the intensity ratio between the two peaks at 526 and 527 eV assigned as 10a' and 3a″ depends not only on the hydrogen bonding network around the target molecule but also on the intramolecular conformation. This effect is absent in liquid methanol and demonstrates the high sensitivity of X-ray emission to molecular structure. The dependence of spectral features on hydrogen-bonding as well as on dynamical effects following core excitation are also discussed.

Core level binding energies of functionalized and defective graphene.

X-ray photoelectron spectroscopy (XPS) is a widely used tool for studying the chemical composition of materials and it is a standard technique in surface science and technology. XPS is particularly useful for characterizing nanostructures such as carbon nanomaterials due to their reduced dimensionality. In order to assign the measured binding energies to specific bonding environments, reference energy values need to be known. Experimental measurements of the core level signals of the elements present in novel materials such as graphene have often been compared to values measured for molecules, or calculated for finite clusters. Here we have calculated core level binding energies for variously functionalized or defected graphene by delta Kohn-Sham total energy differences in the real-space grid-based projector-augmented wave density functional theory code (GPAW). To accurately model extended systems, we applied periodic boundary conditions in large unit cells to avoid computational artifacts. In select cases, we compared the results to all-electron calculations using an ab initio molecular simulations (FHI-aims) code. We calculated the carbon and oxygen 1s core level binding energies for oxygen and hydrogen functionalities such as graphane-like hydrogenation, and epoxide, hydroxide and carboxylic functional groups. In all cases, we considered binding energy contributions arising from carbon atoms up to the third nearest neighbor from the functional group, and plotted C 1s line shapes by using experimentally realistic broadenings. Furthermore, we simulated the simplest atomic defects, namely single and double vacancies and the Stone-Thrower-Wales defect. Finally, we studied modifications of a reactive single vacancy with O and H functionalities, and compared the calculated values to data found in the literature.

First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides.

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach-e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.

Temperature-dependent classical phonons from efficient nondynamical simulations.

We present a method to calculate classical lattice-dynamical quantities, such as the temperature-dependent vibrational spectrum, from simulations that do not require an explicit solution of the time evolution. We start from the moment expansion of the relevant time-correlation function for a many-body system and show that it can be conveniently rewritten by using a basis in which the low-order moments are diagonal. This allows us to approximate the main spectral features (i.e., position and width of the phonon peaks) from thermal averages available from any statistical simulation. We illustrate our method with an application to a model system that presents a structural transition and strongly temperature-dependent phonons. Our theory also clarifies the status of previous heuristic schemes to estimate phonon frequencies.

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.

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

We analyze the validity of the commonly used electric-field (E-field) approximation to vibrational OH stretch Raman spectra of dilute HOD in D(2)O by computing the OH stretch frequency of all molecules in several different structure models, each containing around 2000 molecules. The calculations are done at the B3LYP level using clusters containing 32 molecules centered around the molecule for which the frequencies are calculated; the large cluster size is required due to significant nonlocal contributions influencing the computed frequencies. The vibrational frequencies are determined using a six-point potential optimized discrete variable representation. Raman and infrared intensities are furthermore computed to generate the spectra. We find that a quadratic fit of E-field versus frequency gives a reasonable representation of the calculated distribution of frequencies. However, the mapping depends significantly on the structural model and is thus not universal. Anharmonic couplings are calculated for several optimized clusters showing a general trend to compress the computed frequency distributions, which is in agreement with dynamical simulations (motional narrowing).

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.

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.

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.