Compact representation of one-particle wavefunctions and scalar fields obtained from electronic-structure calculations

We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the representation insures minimization of digital storage requirements for the computational data, while the code-independence makes the data ready for "big data" analytics. Our approach allows to minimize differences between original and the new representation, and is in principle information-lossless. The procedure for obtaining the wavefunction representation is closely related to construction of natural atomic orbitals, and benefits from the localization of Wannier functions. Thus, our approach fits perfectly any infrastructure providing a code-independent tool set for electronic-structure data analysis

Towards a Common Format for Computational Material Science Data

Preprint arXiv:1607.04738Information and data exchange is an important aspect of scientific progress. In computational materials science, a prerequisite for smooth data exchange is standardization, which means using agreed conventions for, e.g., units, zero base lines, and file formats. There are two main strategies to achieve this goal. One accepts the heterogeneous nature of the community which comprises scientists from physics, chemistry, bio-physics, and materials science, by complying with the diverse ecosystem of computer codes and thus develops “converters” for the input and output files of all important codes. These converters then translate the data of all important codes into a standardized, code-independent format. The other strategy is to provide standardized open libraries that code developers can adopt for shaping their inputs, outputs, and restart files, directly into the same code-independent format. We like to emphasize in this paper that these two strategies can and should be regarded as complementary, if not even synergetic. The main concepts and software developments of both strategies are very much identical, and, obviously, both approaches should give the same final result. In this paper, we present the appropriate format and conventions that were agreed upon by two teams, the Electronic Structure Library (ESL) of CECAM and the NOMAD (NOvel MAterials Discovery) Laboratory, a European Centre of Excellence (CoE). This discussion includes also the definition of hierarchical metadata describing state-of-the-art electronic-structure calculations.This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 676580, The NOMAD Laboratory, a European Center of Excellence, and the BBDC (contract 01IS14013E). We thank James Kermode and Saulius Gražulis for their contribution to the discussion on the metadata, and Pasquale Pavone for precious suggestions on the metadata structure and names. We thank Patrick Rinke for carefully reading the manuscript. We thank Claudia Draxl and Kristian Thygesen for their contribution to the discussions on the necessary information to be stored for excited-state calculations and on the error bars and uncertainties. We gratefully acknowledge Damien Caliste, Fabiano Corsetti, Hubert Ebert, Jan Minar, Yann Pouillon, Thomas Ruh, David Strubbe, and Marc Torrent for their contributions to the ESCDF specifications. We acknowledge inspiring discussions with Georg Kresse, Peter Blaha, Xavier Gonze, Bernard Delley, and Jörg Hutter on the energy-zero definition and scalar-field representation. We thank Ole Andersen, Evert Jan Baerends, Peter Blaha, Lambert Colin, Bernard Delley, Thierry Deutsch, Claudia Draxl, John Kay Dewhurst, Roberto Dovesi, Paolo Giannozzi, Mike Gillan, Xavier Gonze, Michael Frisch, Martin Head-Gordon, Juerg Hutter, Klaus Koepernik, Georg Kresse, Roland Lindh, Hans Lischka, Andrea Marini, Todd Martinez, Jens Jørgen Mortensen, Frank Neese, Richard Needs, Taisuke Ozaki, Mike Payne, Angel Rubio, Trond Saue, Chris Skylaris, Jose Soler, John Stanton, James Stewart, Marat Valiev for checking the information provided in Table 1 and for useful suggestions.Preprin

Quantum Spin Liquids

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.Comment: 60 pages, 8 figures, 1 tabl

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.

The Skyrme Interaction in finite nuclei and nuclear matter

Self-consistent mean-field models are a powerful tool in the investigation of nuclear structure and low-energy dynamics. They are based on effective energy-density functionals, often formulated in terms of effective density-dependent nucleon-nucleon interactions. The free parameters of the functional are adjusted to empirical data. A proper choice of these parameters requires a comprehensive set of constraints covering experimental data on finite nuclei, concerning static as well as dynamical properties, empirical characteristics of nuclear matter, and observational information on nucleosynthesis, neutron stars and supernovae. This work aims at a comprehensive survey of the performance of one of the most successful non-relativistic self-consistent method, the Skyrme-Hartree-Fock model (SHF), with respect to these constraints. A full description of the Skyrme functional is given and its relation to other effective interactions is discussed. The validity of the application of SHF far from stability and in dense environments beyond the nuclear saturation density is critically assessed. The use of SHF in models extended beyond the mean field approximation by including some correlations is discussed. Finally, future prospects for further development of SHF towards a more consistent application of the existing and promisingly newly developing constraints are outlined.Comment: 71 pages, 22 figures. Accepted for publication in Prog.Part.Nucl.Phy

Machine Learning static RPA response properties for accelerating GW calculations

In this thesis, I explore the possibility of constructing machine-learning models of the interacting density-density response function (DDRF) and quantities derived from it. Accurate models of the DDRF are a crucial ingredient to enabling GW quasiparticle calculations of more complex systems. Model DDRFs bypass the expensive calculation and inversion of the dielectric matrix, which is the origin of the poor scaling of the GW method with the number of atoms. The thesis is organized as follows: • Chapter 2 systematically reviews common descriptors used for machine-learning physical quantities. The key ideas behind the construction of such descriptors are discussed. First, I introduce several descriptors that systematically incorporate symmetry transformations that leave the target quantity invariant. These descriptors can be used for learning quantities such as the ground-state energy, atomization energies and scalar polarizabilities. Next, I discuss several descriptors and models that are equivariant under transformations of the molecular structure. These descriptors are ideal for learning quantities which transform in a defined way under the action of a transformation, such as vectors, tensors and functions, including the DDRF. • In Chapter 3, I introduce the key electronic structure methods employed throughout the thesis. I start by introducing density functional theory, followed by a detailed introduction to the GW method and the DDRF. • In Chapter 4, I develop a machine-learning model of an invariant quantity derived from the random phase approximation (RPA) DDRF: the scalar polarizability. In this chapter, I calculate the DDRF of 110 hydrogenated silicon clusters. The results of these calculations are then used to train a model of the scalar polarizability based on the SOAP descriptor [16]. The resulting model is then used to predict the scalar polarizability of clusters with up to 3000 silicon atoms while converging to the correct silicon scalar polarizability bulk limit. The findings of this chapter indicate that the scalar polarizability - even though derived from the non-local DDRF - can be accurately predicted from structural descriptors that only encode the local environment of each atom. These results indicate that the response of a non-metallic system to an external potential described by the DDRF may also be approximated as a sum of localized atomic contributions, which forms the motivation for the following two chapters. • In Chapter 5, I develop an approximation to the DDRF of the silicon clusters based on a projection onto atom-centred auxiliary density-fitting basis sets. The results of this chapter indicate that the plane-wave DDRF can be efficiently represented by a small localized basis, thus significantly reducing the size of the DDRF. At the end of this section, I develop a simple neural-network model of the DDRF in this localized basis, highlighting the necessity for using an equivariant descriptor and motivating the next chapter’s developments. • In Chapter 6, I develop a new approximation to the DDRF, which allows a decomposition into atomic contributions. I further introduce the neighbourhood density matrix (NDM), a non-local extension of the SOAP descriptor, which transforms under rotations in the same way as the atomic contributions to the DDRF. The developed method is then applied to the silicon clusters from the previous chapters. Using the NDM, I develop a neural-network model capable of accurately predicting the atomic contributions to the DDRF. These atomic contributions are transformed into a plane-wave basis and summed to obtain the DDRF of a silicon cluster. The predicted DDRFs are then used in GW calculations, which show that the model DDRFs accurately reproduce the quasiparticle energy corrections from GW calculations, as obtained within the atomic decomposition of the DDRF. This methodology can be used to construct arbitrarily complex model DDRFs based on purely structural properties of clusters and nanoparticles, paving the way towards GW calculations of complex systems, such as disordered materials, liquids, interfaces and nanoparticles.Open Acces