Where to draw the line: Chasing energy extrapolations, cluster convergence, and molecular trajectories

The adsorption of S on Cu surfaces is studied by density functional theory using both plane-wave and atomic orbital basis sets. Calculations are performed on Cu clusters of increasing sizes, and strong oscillations in the S-Cu binding energy versus cluster size are found. Although expected for small clusters, the oscillations persist even to clusters containing a few hundred atoms. Smearing of the occupancy function in plane-wave DFT, and averaging over clusters of different sizes are presented as possible approaches to approximate bulk results using small to medium sized clusters. Chemically accurate potential energy curves for the lowest lying singlet states of C2 are obtained using the correlation energy extrapolation by intrinsic scaling (CEEIS) method. The potential energies also include complete basis set extrapolation, core-valence correlation, spin-orbit coupling, and scalar relativistic effects. Our calculated ro-vibrational levels show deviations from experiment of between ~10-20 cm-1, demonstrating near spectroscopic accuracy. The correlation energy extrapolation by many-body expansion (CEEMBE) method is presented. Like the CEEIS method, CEEMBE approximates configuration interaction (CI) energies using a linear extrapolation from CI calculations with reduced numbers of virtual orbitals. The method also uses a many-body expansion of the CI energy based on separating the valence orbitals into groups. Tests on ozone and F2 potential energy surfaces show that CI energies can be reproduced to within a few millihartree, and in many cases to within less than 1 millihartree. We also present a hybrid methodology, CEEMBE-h, which adds CEEIS style extrapolations to the CEEMBE procedure. CEEMBE-h reproduces the original CEEMBE energies to within 0.1-0.5 millihartree or less. Nonadiabatic dynamics using spin-flip time-dependent density functional theory (SF-TDDFT) are presented for the penta-2,4-dieniminium cation. We developed an interface between the GAMESS and Newton-X programs for SF-TDDFT dynamics. Time-derivative couplings between SF-TDDFT states are calculated using an approximate wavefunction overlap method. Our comparison with analytical couplings from CASSCF demonstrates that the overlap method for time-derivative couplings is effective for SF-TDDFT. Because of the spin-contamination in SF-TDDFT, the interface includes a state-tracking algorithm to ensure dynamics are propagated on the correct potential energy surface

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Non-intrusive reduced-order modeling of parameterized electromagnetic scattering problems using cubic spline interpolation

International audienceThis paper presents a non-intrusive model order reduction (MOR) for the solution of parameterized electromagnetic scattering problems, which needs to prepare a database offline of full-order solution samples (snapshots) at some different parameter locations. The snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. Because the second dimension of snapshots matrix is large, a two-step or nested proper orthogonal decomposition (POD) method is employed to extract time- and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices (also referred to as the reduced coefficient matrices) of full-order solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed to approximate the dominating time- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the offline and online stages of the proposed RB method, termed as the POD-CSI method, are completely decoupled, which ensures the computational validity of the method. Moreover, a surrogate error model is constructed as an efficient error estimator for the POD-CSI method. Numerical experiments for the scattering of plane wave by a 2-D dielectric cylinder and a multi-layer heterogeneous medium nicely illustrate the performance of POD-CSI method

Research Review, 1983

The Global Modeling and Simulation Branch (GMSB) of the Laboratory for Atmospheric Sciences (GLAS) is engaged in general circulation modeling studies related to global atmospheric and oceanographic research. The research activities discussed are organized into two disciplines: Global Weather/Observing Systems and Climate/Ocean-Air Interactions. The Global Weather activities are grouped in four areas: (1) Analysis and Forecast Studies, (2) Satellite Observing Systems, (3) Analysis and Model Development, (4) Atmospheric Dynamics and Diagnostic Studies. The GLAS Analysis/Forecast/Retrieval System was applied to both FGGE and post FGGE periods. The resulting analyses have already been used in a large number of theoretical studies of atmospheric dynamics, forecast impact studies and development of new or improved algorithms for the utilization of satellite data. Ocean studies have focused on the analysis of long-term global sea surface temperature data, for use in the study of the response of the atmosphere to sea surface temperature anomalies. Climate research has concentrated on the simulation of global cloudiness, and on the sensitivities of the climate to sea surface temperature and ground wetness anomalies

A Computational Study of Material Transformations in Glass Forming Systems

Amorphous solids (glasses) are a class of materials that lack the traditional long-range order found in crystals, and are primarily formed by rapid cooling of a liquid to bypass crystal nucleation. Their lack of crystallinity and associated defects gives them useful electromagnetic and mechanical properties. However, the affinity of a material to vitrification is only loosely understood, and structural detail is difficult to obtain via traditional methods. This thesis firstly investigates the promotion of glass formation via crystal inhibition. Molecular dynamics simulations of binary alloys are used to show crystal frustration via specific interactions of interaction range and particle softness, resulting in a lower enthalpic drive and complex crystal structures. Secondly, a facilitated kinetic Ising model is used to investigate the dynamics of organic glasses in solution. Glass dissolution is shown to have a non-linear dependence on the effective temperature of the solute, switching between a front-like dissolution at low temperatures, and a diffuse interface at higher temperatures. Also shown is a method of preparing an enhanced glass via precipitation from a solution, capable of creating a much lower energy glass than simple bulk cooling

Inferring the equation of state with multi-messenger signals from binary neutron star mergers

The joint detection of the GW170817 and its electromagnetic counterparts was a milestone in multi-messenger astronomy. We investigate the observational constraints on the neutron star equation of state provided by multi-messenger data of binary neutron star mergers, analyzing the gravitational-wave transient GW170817 and its kilonova counterpart AT2017gfo and exploring new scenarios with next-generation gravitational-wave detectors. The LIGO-Virgo data of GW170817 are analyzed using different template models focusing on the implications for neutron star matter properties. We study the systematic tidal errors between current gravitational-wave models finding that waveform systematics dominate over statistical errors at signal-to-noise ratio ≳ 100. We study AT2017gfo using semi-analytical model showing that observational data favor multi-component anisotropic geometries to spherically symmetric profiles. By joining GW170817 and AT2017gfo information with the NICER measurements, we infer the neutron star equation of state constraining the radius of a 1.4M☉ neutron star to 12.39+0.70-0.65 km and the maximum mass MTOV to 2.08+0.16-0.09 M☉ (90% credible level). Finally, we explore future constraints on extreme-matter delivered by postmerger gravitational-waves from binary neutron star merger remnants. These transients can be detected with matched-filtering techniques and numerical-relativity-informed models for signal-to-noise ratios ≳ 7. Postmerger remnants can probe the high-density regimes of the nuclear equation of state, allowing the inference of the maximum neutron star mass MTOV with an accuracy of 12% (90% max credible level). Moreover, postmerger transients can be used to infer the presence of non-nucleonic matter phases through the inference of softening of the equation of state. For particular binary configurations, softening effects of the equation of state can lead to breaking of quasiuniversal properties and earlier collapse into black hole