Search NASA⌕ Search

SEARCH · Search NASA

Results for “Basis function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Toward an Understanding of Linear Scaling Relations through Energy Decomposition Analysis

The discovery of linear scaling relations has fundamentally changed the field of heterogeneous catalysis. The scaling relations have been rationalized based on the d-band theory, specifically a separation of sp and d electron contributions to adsorption energies. Within the framework of energy decomposition analysis, a full understanding of such a separation would require one to further break down the adsorption energy into distinct energy components such as electrostatics, polarization, charge transfer, and van der Waals interactions, and to examine the sp and d contributions to each of them. As a step in this direction, we analyzed the interaction energy between CH x (x = 1–4) adsorbates and fcc(100) transition metal surfaces (M = Cu, Ag, Au, Rh, and Pt), with the surfaces represented both as slabs in plane-wave density functional theory (pw-DFT) calculations and as atomic clusters in atomic-orbital basis density functional theory (ao-DFT) calculations. Through an absolutely localized molecular orbital (ALMO) based energy decomposition analysis of the ao-DFT adsorption energy, each of the interaction energy components (electrostatics, polarization, van der Waals, and charge transfer) was found to follow its own scaling relations, with an intricate interplay among these energy components yielding the overall scaling relations for the total adsorption energies. Using the recently introduced ALMO-based polarization and charge-transfer analysis schemes, we further dissected polarization into metal surface and adsorbate contributions, and charge transfer into metal → adsorbate and adsorbate → metal contributions. The contributions from the sp and d electrons of the metal to these terms were further quantified, and the dominant role of the metal d electrons was reaffirmed. These results shed light on how CHx adsorbates interact with metal surfaces and further reveal the physical origin of the scaling relations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory

With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions—noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms—with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen’s pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Molecular basis for the distinct cellular functions of the Lsm1–7 and Lsm2–8 complexes

Eukaryotes possess eight highly conserved Lsm (like Sm) proteins that assemble into circular, heteroheptameric complexes, bind RNA, and direct a diverse range of biological processes. Among the many essential functions of Lsm proteins, the cytoplasmic Lsm1–7 complex initiates mRNA decay, while the nuclear Lsm2–8 complex acts as a chaperone for U6 spliceosomal RNA. It has been unclear how these complexes perform their distinct functions while differing by only one out of seven subunits. Here, we elucidate the molecular basis for Lsm-RNA recognition and present four high-resolution structures of Lsm complexes bound to RNAs. The structures of Lsm2–8 bound to RNA identify the unique 2',3' cyclic phosphate end of U6 as a prime determinant of specificity. In contrast, the Lsm1–7 complex strongly discriminates against cyclic phosphates and tightly binds to oligouridylate tracts with terminal purines. Lsm5 uniquely recognizes purine bases, explaining its divergent sequence relative to other Lsm subunits. Lsm1–7 loads onto RNA from the 3' end and removal of the Lsm1 carboxy-terminal region allows Lsm1–7 to scan along RNA, suggesting a gated mechanism for accessing internal binding sites. These data reveal the molecular basis for RNA binding by Lsm proteins, a fundamental step in the formation of molecular assemblies that are central to eukaryotic mRNA metabolism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2012

Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion plus Selected Inversion

We describe how to apply the recently developed pole expansion plus selected inversion (PEpSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating charge density, total energy, Helmholtz free energy and atomic forces without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEpSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEpSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEpSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEpSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes on a single processor. We also show that the use of PEpSI does not lead to loss of accuracy required in a practical DFT calculation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Enrichment of root-associated Streptomyces strains in response to drought is driven by diverse functional traits and does not predict beneficial effects on plant growth

The genus Streptomyces has consistently been found enriched in drought-stressed plant root microbiomes, yet the ecological basis and functional variation underlying this enrichment at the strain and isolate level remain unclear. Using two 16S rRNA sequencing methods with different levels of taxonomic resolution, we confirmed drought-associated enrichment (DE) of Streptomyces in field-grown sorghum roots and identified five closely related but distinct amplicon sequence variants (ASVs) belonging to the genus with variable drought enrichment patterns. From a culture collection of sorghum root endophytes, we selected 12 Streptomyces isolates representing these ASVs for phenotypic and genomic characterization. Whole-genome sequencing revealed substantial variation in gene content, even among closely related isolates, and exometabolomic profiling showed distinct metabolic responses to media supplemented with drought- versus well-watered root tissue. Traits linked to drought survival, including osmotic stress tolerance, siderophore production, and carbon utilization, varied widely among isolates and were not phylogenetically conserved. Using a broader panel of 48 Streptomyces, we demonstrate that DE scores, determined through mono-association experiments in gnotobiotic sorghum systems, showed high variability and lacked correlation with plant growth promotion. Pangenome-wide association identified orthogroups involved in osmolyte transport (e.g., proP) and membrane biosynthesis (e.g., fabG) as positively associated with DE, though most associations lacked phylogenetic signal. Collectively, these results demonstrate that Streptomyces DE is not a conserved genus-level trait but is instead strain-specific and functionally heterogeneous. Furthermore, DE in the root microbiome was shown not to predict beneficial effects on plant growth. This work underscores the need to resolve functional traits at the strain level and highlights the complexity of microbe-host-environment interactions under abiotic stress.

Fonseca-Garcia, Citlali↗
DOE OSTI2013

Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies

For a set of eight equilibrium intermolecular complexes, it is discovered in this paper that the basis set limit (BSL) cannot be reached by aug-cc-pV5Z for three of the Minnesota density functionals: M06-L, M06-HF, and M11-L. In addition, the M06 and M11 functionals exhibit substantial, but less severe, difficulties in reaching the BSL. By using successively finer grids, it is demonstrated that this issue is not related to the numerical integration of the exchange-correlation functional. In addition, it is shown that the difficulty in reaching the BSL is not a direct consequence of the structure of the augmented functions in Dunning’s basis sets, since modified augmentation yields similar results. By using a very large custom basis set, the BSL appears to be reached for the HF dimer for all of the functionals. As a result, it is concluded that the difficulties faced by several of the Minnesota density functionals are related to an interplay between the form of these functionals and the structure of standard basis sets. It is speculated that the difficulty in reaching the basis set limit is related to the magnitude of the inhomogeneity correction factor (ICF) of the exchange functional. A simple modification of the M06-L exchange functional that systematically reduces the basis set superposition error (BSSE) for the HF dimer in the aug-cc-pVQZ basis set is presented, further supporting the speculation that the difficulty in reaching the BSL is caused by the magnitude of the exchange functional ICF. In conclusion, the BSSE is plotted with respect to the internuclear distance of the neon dimer for two of the examined functionals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Applications of the modified Hulthén-Kohn method for bound and scattering states

We adapt the Hulthén–Kohn method suggested by Efros [Phys. Rev. C 99, 034620 (2019)] for calculating various observables in the continuum and discrete spectrum using two-body interactions in single- and coupled channel systems. We explore the convergence of phase shifts and wave functions as well as the location of S-matrix poles which enables obtaining both resonance and bound state parameters. We find that employing a harmonic oscillator basis, together with an interaction smoothing scheme introduced by Gyarmati et al. [Nucl. Phys. A 326, 119 (1979)], and adopting approximate bound-state solutions for the short-range components of basis wave functions lead to good convergence even with restricted oscillator quanta accessible for modern no-core shell model codes. The adapted Efros method will facilitate ab initio many-body nuclear structure applications.

Nuclear reactions↗
DOE OSTI2018

Crossover-Induced Spin Fluctuation and Electron Pairing in Strongly Correlated Electrons

We investigate the two-dimensional (2D) Hubbard model and d-p model as a model for cuprate high-temperature superconductors, by employing an optimized variational Monte Carlo method. We improved the many-body wave function starting from the simple Gutzwiller function. On the basis of optimized variational wave functions, we show that there is a superconducting phase in the ground state of the 2D Hubbard model. The on-site repulsive Coulomb interaction U can bring about high-temperature superconductivity because its characteristic energy is of the order of eV. The attractive interaction between electrons is induced by the crossover from weakly to strongly correlated regions. High-temperature superconductivity is possible in the strongly correlated region, where U is greater than the bandwidth.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys. 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Identification of genes that regulate phosphate acquisition and plant performance during arbuscular my corrhizal symbiosis in medicago truncatula and brachypodium distachyon

Most vascular flowering plants have the ability to form symbiotic associations with arbuscular mycorrhizal (AM) fungi. The symbiosis develops in the roots and can have a profound effect on plant productivity, largely through improvements in plant mineral nutrition. Within the root cortical cells, the plant and fungus create novel interfaces specialized for nutrient transfer, while the fungus also develops a network of hyphae in the rhizosphere. Through this hyphal network, the fungus acquires and delivers phosphate and nitrogen to the root. In return, the plant provides the fungus with carbon. In addition, to enhancing plant mineral nutrition, the AM symbiosis has an important role in the carbon cycle, and positive effects on soil health. Here we identified and characterized plant genes involved in the regulation and functioning of the AM symbiosis in Medicago truncatula and Brachypodium distachyon. This included the identification and and characterization of a M. truncatula transcription factors that are required for symbiosis. Additionally, we investigated the molecular basis of functional diversity among AM symbioses in B. distachyon and analysed the transcriptome of Brachypodium distachyon during symbiosis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Lysosomal integral membrane protein-2 as a phospholipid receptor revealed by biophysical and cellular studies

Lysosomal integral membrane protein-2 (LIMP-2/SCARB2) contributes to endosomal and lysosomal function. LIMP-2 deficiency is associated with neurological abnormalities and kidney failure and, as an acid glucocerebrosidase receptor, impacts Gaucher and Parkinson’s diseases. Here we report a crystal structure of a LIMP-2 luminal domain dimer with bound cholesterol and phosphatidylcholine. Binding of these lipids alters LIMP-2 from functioning as a glucocerebrosidase-binding monomer toward a dimeric state that preferentially binds anionic phosphatidylserine over neutral phosphatidylcholine. In cellular uptake experiments, LIMP-2 facilitates transport of phospholipids into murine fibroblasts, with a strong substrate preference for phosphatidylserine. Taken together, these biophysical and cellular studies define the structural basis and functional importance of a form of LIMP-2 for lipid trafficking. We propose a model whereby switching between monomeric and dimeric forms allows LIMP-2 to engage distinct binding partners, a mechanism that may be shared by SR-BI and CD36, scavenger receptor proteins highly homologous to LIMP-2.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater- Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value of an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗
DOE OSTI2014

Harmonics in the dark-matter sky: directional detection in the Fourier-Bessel basis

Details about the velocity distribution of weakly interacting massive particle (WIMP) dark matter in our galaxy may be revealed by nuclear-recoil detectors with directional sensitivity. Previous studies have assumed that the velocity distribution takes a simple functional form characterized by a small number of parameters. More recent work has shown that basis-function expansions may allow for more general parameterization; such an approach has been considered for both the one-dimensional speed and momentum distributions, and also for three-dimensional velocity distributions obeying certain equilibrium conditions. In this work, I extend this basis-function approach to allow for arbitrary velocity distributions by working in the Fourier-Bessel basis, deriving an analytic expression for the directional recoil spectrum. Such an approach is completely general, and may be useful if the velocity distribution is too complex to be characterized by simple functional forms or is not completely virialized. Results concerning the three-dimensional Radon transform of the Fourier-Bessel basis functions may be of general interest for tomographic applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Multisliced gausslet basis sets for electronic structure

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced waveletlike smooth orthogonal functions. We adapt the gausslets to particular systems using one-dimensional (1D) coordinate transformations, putting more basis functions near the nuclei, while maintaining orthogonality. Furthermore, three-dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate these bases with both Hartree-Fock and density matrix renormalization group calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Understanding, inhibiting, and engineering membrane transporters with high-throughput mutational screens

Promiscuous membrane transporters play vital roles across domains of life, mediating the uptake and efflux of structurally and chemically diverse substrates. Although many transporter structures have been solved, the fundamental rules of polyspecific transport remain inscrutable. In recent years, high-throughput genetic screens have solidified as powerful tools for comprehensive, unbiased measurements of variant function and hypothesis generation, but have had infrequent application and limited impact in the transporter field. In this primer, we describe the principles of high-throughput screening methods available for studying polyspecific transporters and comment on the necessity and potential of high-throughput methods for deciphering these transporters in particular. We present several screening approaches which could provide a fundamental understanding of the molecular basis of function and promiscuity in transporters. Here, we further posit how this knowledge can be leveraged to design inhibitors that combat multidrug resistance and engineer transporters as needed tools for synthetic biology and biotechnology applications.

EPIs↗