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Results for “functional approximation”
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Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method
Fermi orbital descriptors (FODs) play a key role in Fermi-Löwdin orbital self-interaction correction (FLOSIC) calculations used to remove self-interaction from approximate density functionals. Optimal FODs are obtained by minimizing the self-interaction-corrected total energy, and, in this process, identifying initial sets of FODs becomes crucial. Here we propose, implement and test a novel method for automatically initializing FODs, quick-FOD, based on the minimization of an empirical energy expression that involves a Coulomb-like FOD-electron density attraction, an FOD-FOD short-range repulsion, and an exchange-like FOD-density repulsion. Quick-FOD successfully reproduces FOD arrangements in qualitatively good agreement with Lewis theory and with full-fledged FLOSIC calculations.
Gradient-based optimization for regression in the functional tensor-train format
Predictive analysis of complex computational models, such as uncertainty quantification (UQ), must often rely on using an existing database of simulation runs. In this paper we consider the task of performing low-multilinear-rank regression on such a database. Specifically we develop and analyze an efficient gradient computation that enables gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT). We compare our algorithms with 22 other nonparametric and parametric regression methods on 10 real-world data sets and show that for many physical systems, exploiting low-rank structure facilitates efficient construction of surrogate models. Here, we use a number of synthetic functions to build insight into behavior of our algorithms, including the rank adaptation and group-sparsity regularization procedures that we developed to reduce overfitting. Finally we conclude the paper by building a surrogate of a physical model of a propulsion plant on a naval vessel.
Norm-Conserving Pseudopotentials and Basis Sets to Explore Actinide Chemistry in Complex Environments
We constructed and tested a new set of norm-conserving pseudopotentials, as well as companion Gaussian basis sets, for the actinide series (Ac–Lr) using the Goedecker, Teter and Hutter (GTH) formalism within the generalized gradient approximation (GGA) functional for exchange-correlation of Perdew, Burke and Ernzerhof (PBE). This fills a critical void in the literature for studying the chemistry of 5f–block elements in condensed phase. The accuracy and reliability of the newly parameterized An–GTH pseudopotentials and basis sets, a variety of tests on actinide-containing molecules were carried out and compared to all-electron and available experimental results. The new pseudopotentials include both medium ( [Xe]4f 14 ) and large core ( [Xe]4f 14 5d 10 ) options that successfully reproduced structure and energetics, particularly redox processes. The medium core size set, in particular, reproduced all electron calculations over multiple oxidation states from 0 to VII, whereas the large core set was suitable only for the early series elements and low oxidation states.
Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme
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Pareto Optimization of Oligomer Polarizability and Dipole Moment Using a Genetic Algorithm
High-performance electronic components are highly sought after in order to produce increasingly smaller and cheaper electronic devices. Drawing inspiration from inorganic dielectric materials, in which both polarizability and polarization contribute, organic materials can also maximize both. For a large set of small molecules drawn from PubChem, a Pareto-like front appears between the polarizability and dipole moment, indicating the presence of an apparent trade-off between these two properties. We tested this balance in π-conjugated materials by searching for novel conjugated hexamers with simultaneously large polar- izabilities and dipole moments with potential use for dielectric materials. Using a genetic algorithm (GA) screening technique in conjunction with an approximate density functional tight-binding method for property calculations, we were able to efficiently search chemical space for optimal hexamers. Given the scope of chemical space, using the GA technique saves considerable time and resources by speeding up molecular searches compared to a systematic search. Here, we also explored the underlying structure–function relationships, including sequence and monomer properties, that characterize large polarizability and dipole moment regimes.
Libration of hydroxyl groups in layered aluminum (oxy)hydroxides and other material analogs: insights from inelastic neutron scattering and theory
We analyzed the hydroxyl librational signatures of five structurally related aluminum (oxy)hydroxides, using inelastic neutron scattering (INS) and plane-wave lattice dynamics simulations. A clear trend across these aluminum-containing phases illustrates the relationship between hydrogen bonding, local atomic structure, and the spectral location and profile of the librational bands. The INS spectra have been compared to previous optical spectroscopy and computational studies, highlighting the complementary nature of the INS technique. Taking into account other structurally or chemically related material analogs, we have identified a correlation between a blueshift (to higher energy) of the upper librational band edge and the geometry of the hydrogen bond interactions, mirroring (with opposite correlation) the well-known redshift in the intramolecular O–H stretching energy with increasing hydrogen bond strength. For hydroxyl groups that do not participate in hydrogen bonding effectively, the bending librations occur at lower energies and hybridize with metal–oxygen lattice modes. Standard density functional theory approximations, including dispersion corrections, struggle to correctly predict vibrational frequencies of motions dominated by H but perform well for metal–oxygen modes, allowing us to make detailed mode assignments in several cases, including a demonstration of how layer-to-layer disorder in boehmite hydrogen bond orientations is reflected in the sharp but minor low energy peaks (at ∼70–80 meV) of the INS spectrum.
Towards quantifying the role of exact exchange in predictions of transition metal complex properties
We estimate the prediction sensitivity with respect to Hartree-Fock exchange in approximate density functionals for representative Fe(II) and Fe(III) octahedral complexes. Based on the observation that the range of parameters spanned by the most widely employed functionals is relatively narrow, we compute electronic structure property and spin-state orderings across a relatively broad range of Hartree-Fock exchange (0%-50%) ratios. For the entire range considered, we consistently observe linear relationships between spin-state ordering that differ only based on the element of the direct ligand and thus may be broadly employed as measures of functional sensitivity in predictions of organometallic compounds. The role Hartree-Fock exchange in hybrid functionals is often assumed to play is to correct self-interaction error-driven electron delocalization (e.g., from transition metal centers to neighboring ligands). Surprisingly, we instead observe that increasing Hartree-Fock exchange reduces charge on iron centers, corresponding to effective delocalization of charge to ligands, thus challenging notions of the role of Hartree-Fock exchange in shifting predictions of spin-state ordering.
The electronic structure, mechanical and thermodynamic properties of Mo{sub 2}XB{sub 2} and MoX{sub 2}B{sub 4} (X = Fe, Co, Ni) ternary borides
The mechanical properties, electronic structure and thermodynamic properties of the Mo{sub 2}XB{sub 2} and MoX{sub 2}B{sub 4} (X = Fe, Co, Ni) ternary borides were calculated by first-principles methods. The elastic constants show that these ternary borides are mechanically stable. Formation enthalpy of Mo{sub 2}XB{sub 2} and MoX{sub 2}B{sub 4} (X = Fe, Co, Ni) ternary borides are at the range of −118.09 kJ/mol to −40.14 kJ/mol. The electronic structures and chemical bonding characteristics are analyzed by the density of states. Mo{sub 2}FeB{sub 2} has the largest shear and Young's modulus because of its strong chemical bonding, and the values are 204.3 GPa and 500.3 GPa, respectively. MoCo{sub 2}B{sub 4} shows the lowest degree of anisotropy due to the lack of strong direction in the bonding. The Debye temperature of MoFe{sub 2}B{sub 4} is the largest among the six phases, which means that MoFe{sub 2}B{sub 4} possesses the best thermal conductivity. Enthalpy shows an approximately linear function of the temperature above 300 K. The entropy of these compounds increase rapidly when the temperature is below 450 K. The Gibbs free energy decreases with the increase in temperature. MoCo{sub 2}B{sub 4} has the lowest Gibbs free energy, which indicates the strongest formation ability in Mo{sub 2}XB{sub 2} and MoX{sub 2}B{sub 4} (X = Fe, Co, Ni) ternary borides.
On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics
Well-defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé-resummed master equations with numerically exact results in the context of the spin–boson model demonstrates that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.
Communication: Fitting potential energy surfaces with fundamental invariant neural network
A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH{sub 3} and CH{sub 4} were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.
A near X-point charge exchange neutral spectroscopy (CENS) system for DIII-D
A 16 channel spectroscopy system has been installed on DIII-D to provide information about the energy distribution of the atomic neutrals using the Doppler shift and broadening of passive Balmer-α emission. Here, the lines of sight are dominantly in the toroidal direction, with tangencies near the lowest point on closed magnetic flux surfaces moving from the lower divertor upward into the confined plasma. This allows the system to provide details of the neutrals as they undergo various atomic physics processes while traveling upward from the lower divertor. The spectrally resolved measurements provide several advantages that complement typical optical filter based measurements of hydrogenic spectral lines. These include more direct measurements of the neutrals that fuel deeper in the plasma and capturing neutral velocity distribution information via the Doppler broadened and shifted line. In addition, the spectral separation of higher energy “thermal” neutrals and bright cold emission from the scrape-off layer allows for a more straightforward calculation of the underlying neutral densities based on the emission because of the dependence of the thermal emission on confined plasma properties that are approximately flux functions and well measured.
Mott vs Kondo: Influence of various density functional based methods on the Ce isostructural phase transition mechanism
The cerium iso-structural phase transition (γ–α) is dominated by f-electron localization changes that results in a magnetic ordering change and a volume collapse. Generally, these physics are difficult to capture with ab initio and first principles methods. However, previous works have shown various methods to be successful in predicting at least some of the physics of the γ to α phase transition. Therefore, here, we perform a broad survey of density functional based methods across three levels of theory and types of functions [GGA (generalized gradient approximation), MetaGGA, and hybrid functionals] and compare the results, focusing on hydrostatic compression across the phase boundary at zero kelvin. For the methods that best reproduce experimental results, we directly probe the predicted mechanisms and frame the results in the Mott/Kondo debate, assessing how the underlying methods and assumptions of different functionals can assess the physical drivers in the phase transition, providing insight into the governing processes of this unique phase transition.
Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions
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A near-infrared census of the multicomponent stellar structure of early-type dwarf galaxies in the Virgo cluster
The fraction of star-forming to quiescent dwarf galaxies varies from almost infinity in the field to zero in the centers of rich galaxy clusters. What is causing this pronounced morphology-density relation? What do quiescent dwarf galaxies look like when studied in detail, and what conclusions can be drawn about their formation mechanism? Here we study a nearly magnitude-complete sample (–19 < M{sub r} < –16 mag) of 121 Virgo cluster early types with deep near-infrared images from the SMAKCED project. We fit two-dimensional models with optional inner and outer components, as well as bar and lens components (in ∼15% of the galaxies), to the galaxy images. While a single Sérsic function may approximate the overall galaxy structure, it does not entirely capture the light distribution of two-thirds of our galaxies, for which multicomponent models provide a better fit. This fraction of complex galaxies shows a strong dependence on luminosity, being larger for brighter objects. We analyze the global and component-specific photometric scaling relations of early-type dwarf galaxies and discuss similarities with bright early and late types. The dwarfs' global galaxy parameters show scaling relations that are similar to those of bright disk galaxies. The inner components are mostly fitted with Sérsic n values close to 1. At a given magnitude, they are systematically larger than the bulges of spirals, suggesting that they are not ordinary bulges. We argue that the multicomponent structures in early-type dwarfs are mostly a phenomenon inherent to the disks and may indeed stem from environmental processing.
Linear response to long wavelength fluctuations using curvature simulations
We study the local response to long wavelength fluctuations in cosmological N -body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naïve derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.
Spatiotemporal forecasting of the edge localized modes in tokamak plasmas using neural networks
Artificial intelligence techniques have been increasingly adopted by the plasma and fusion science to address problems like plasma reconstruction, surrogate modeling, and tokamak/stellarator optimization. A key focus in sustained fusion research is the prediction and mitigation of edge-localized-modes (ELMs), instabilities that occur in short, periodic bursts and can cause erosion to the tokamak vessel wall. Recent research has demonstrated the power of neural networks in approximating continuous functions. In this work, we build spatiotemporal forecasting models that can predict the onset of ELMs and their evolution at early stages. We leverage recent advances in generative modeling, sequence-to-sequence modeling, and Fourier neural operators to propose architectures and training strategies that can learn to forecast short to long term dynamics of the noisy signals due to ELMs. We benchmark the developed model against a state-of-the-art foundation model using the beam emission spectroscopy (BES) data that captures the plasma fluctuations due to ELMs over a 8 x 8 spatial grid. Our models demonstrate high accuracy, outperforming the baselines, in predicting the evolution of BES signals during ELM events. Furthermore, the developed models exhibit high accuracy in predicting the rapid rise and relaxation of the signals due to ELMs within 30–80 µs.
Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities
Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.