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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Combined Error and Uncertainty Estimates for CFD Problems

Given input sources of uncertainty, non-intrusive uncertainty propagation methods quantify the uncertainty in output quantities of interest (QoI) by performing a nite number of CFD (Computational Fluid Dynamics) instance realizations needed in the calculation of output statistics. It is well known that this introduces multiple sources of error. CFD codes often utilize finite-dimensional approximation (grids, basis functions, etc.) thus incurring CFD numerical errors often approximately reinterpreted as a statistical bias. Uncertainty propagation methods calculate uncertainty statistics for output quantities of interest using a numerical method (e.g. deterministic quadrature, sampling, etc.) thus incurring UQ (Uncertainty Quantification) numerical errors. Importance of quantifying these errors in large scale scientific computing: How accurate is an output statistic?; How should additional computational resources be invested to further reduce the error in a statistic?

Posteriori↗
DOE OSTI2018

Linear response time-dependent density functional theory of the Hubbard dimer

The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. In conclusion, many exact results, limits, and expansions about those limits are given in the Appendices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. Methods that account for temperature dependence, such as Mermin–Kohn–Sham finite-temperature density functional theory and free energy density functional theory, are now employed with more regularity and available in many standard code packages. However, approximations from zero-temperature density functional theory are still often used in temperature-dependent simulations using thermally weighted electronic densities as an input to exchange–correlation functional approximations, a practice known to miss temperature-dependent effects in the exchange–correlation free energy of these systems. Here, in this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange–correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb–Oxford inequality, which provides a lower bound for the ground-state exchange–correlation energy, bounds for the exchange–correlation at finite temperatures are approximated for various degrees of electronic correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

On the mechanism of intermolecular nitrogen-atom transfer from a lattice-isolated diruthenium nitride intermediate

Catalyst confinement within microporous media provides the opportunity to site isolate reactive intermediates, enforce intermolecular functionalization chemistry by co-localizing reactive intermediates and substrates in molecular-scale interstices, and harness non-covalent host–guest interactions to achieve selectivities that are complementary to those accessible in solution. As part of an ongoing program to develop synthetically useful nitrogen-atom transfer (NAT) catalysts, we have demonstrated intermolecular benzylic amination of toluene at a Ru 2 nitride intermediate confined within the interstices of a Ru2-based metal–organic framework (MOF), Ru 3 (btc) 2 X 3 (btc = 1,3,5-benzenetricarboxylate, i.e., Ru-HKUST-1 for X = Cl). Nitride confinement within the extended MOF lattice enabled intermolecular C–H functionalization of benzylic C–H bonds in preference to nitride dimerization, which was encountered with soluble molecular analogues. Detailed study of the kinetic isotope effects (KIEs, i.e., k H /k D ) of C–H amination, assayed both as intramolecular effects using partially labeled toluene and as intermolecular effects using a mixture of per-labeled and unlabeled toluene, provided evidence for restricted substrate mobility on the time scale of interstitial NAT. Analysis of these KIEs as a function of material mesoporosity provided approximate experimental values for functionalization in the absence of mass transport barriers. Here, we disclose a combined experimental and computational investigation of the mechanism of NAT from a Ru 2 nitride to the C–H bond of toluene. Computed kinetic isotope effects for a H-atom abstraction (HAA)/radical rebound (RR) mechanism are in good agreement with experimental data obtained for C–H amination at the rapid diffusion limit. These results provide the first detailed analysis of the mechanism of intermolecular NAT to a C–H bond, bolster the use of KIEs as a probe of confinement effects on NAT within MOF lattices, and provide mechanistic insights unavailable by experiment because rate-determining mass transport obscured the underlying chemical kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low-rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed-point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low-rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed-point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous self-consistent field iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from ~100 to 1100 atoms (~500–20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized d orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20–30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed-point iteration in some cases. Lastly, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4-fold reduction in computational cost for the total ground-state calculation compared to other preconditioners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2010

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Pak, Chan-gi↗
NASA NTRS2010

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Pak, Chan-gi↗
NASA NTRS1993

Average-cost based robust structural control

A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed.

Hagood, Nesbitt W.↗
NASA NTRS1990

Maximum likelihood tuning of a vehicle motion filter

This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.

Trankle, Thomas L.↗
DOE OSTI2023

ORNL_AISD-Ex: Quantum chemical prediction of UV/Vis absorption spectra for over 10 million organic molecules

We performed calculations of electronic excitation energies and associated oscillator strengths based on the time-dependent density-functional tight-binding (TD-DFTB) method [1]. The SMILES (Simplified molecular-input line-entry system) strings of the molecules from the AISD HOMO-LUMO database [2] were converted to a 3D atomistic structure and stored in a PDB file after preliminary geometry optimization using the Merck Molecular Force Field (MMFF94) in RDKit [3,4]. The primary information stored in the PDB file archive consists of Cartesian coordinates for each atom of the molecule in their 3D location in space, along with summary information about the structure, sequence, and experiment. We then performed molecular geometry optimization using the density-functional tight-binding (DFTB) method [5] in the electronic ground state, followed by single-point excited states calculations, as described below. We note that, since RDKit employs a random choice for the generation of molecular conformers, the molecular geometries obtained in this dataset could be different from the ones that were generated when the AISD HOMO-LUMO dataset was generated. The computed excitation energies and associated oscillator strengths can be converted to predict UV/Vis absorption spectra, where excitation energies correspond to absorption peak positions, and oscillator strengths are a good measure of the probability of absorption of visible or UV light in transitions between electronic ground and excited states. The conversion of SMILES strings to 3D Cartesian coordinates of fully DFTB-optimized molecules was successful for 10,502,904 out of 10,502,917 molecules. For these molecules, both geometry optimizations and excited states calculations were successful. The DFTB calculations did not complete for 13 molecules of the original AISD HOMO-LUMO dataset. We still provide information about the geometry of these molecules. The molecules are diverse for chemical compositions (which span 5 non-hydrogen elements: oxygen, carbon, nitrogen, fluorine, sulfur) and molecular size (the smallest molecule contains 5 non-hydrogen atoms, and the largest molecule contains 71 non-hydrogen atoms). The DFTB method [5] is an approximation to density functional theory (DFT), utilizing a minimal basis set in conjunction with a two-center approximation to the electronic Hamiltonian and overlap matrix elements. The DFTB total energy is the sum of an electronic and a repulsive energy contribution, and their calculation requires optimized electronic parameters and diatomic repulsive potential energy functions. All DFTB calculations were performed using the DFTB+ code [6] (version 21.2) and the wrapper for DFTB+ in the Atomic Simulation Environment (ASE) (version 3.22.1) [7], which performed an internal conversion of Cartesian coordinates from PDB to the .gen file format. For the geometry optimizations on the electronic ground state potential energy surface of the molecules, we have chosen the third-order DFTB (DFTB3) method [5c] and employed the matching 3ob set of electronic parameters and repulsive potentials [8]. The empirical γ-damping for hydrogen bond correction, and Grimme's D3 empirical dispersion correction with Becke-Johnson damping (D3(BJ)) [9] dispersion correction was included to improve the description of non-covalent interactions. For excited states single-point energy calculations, we employed the TD-DFTB method in conjunction with the DFTB2 method [5b] and the matching mio [5b,10] and halorg [11] parameter sets. We opted to request the simultaneous calculation of 50 excited states for singlet transition to investigate sufficient number of excited states, based on linear response theory using the Casida equation [Ref: T. A. Niehaus, S. Suhai, F. Della Sala, P Lugli, M. Elstner, G. Seifert, and Th. Frauenheim. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 63:085108, 2001] and the ARPACK diagonalizer [R. B. Lehoucq, D. C. Sorensen, and C. Yang. Arpack users guide: Solution of large-scale eigenvalue problems by implicitly restarted arnoldi methods, 1997. 46, 51]. The dataset contains 1001 tar.gz files. Tar files are named as “ornl_aisd_ex_1.tar.gz†through “ornl_aisd_ex_1000.tar.gzâ€. Additionally, the 13 failed molecules are in “ornl_aisd_ex_unprocessed.tar.gzâ€. Except for the tar files listed below, each tar file contains 10,500 molecules. Tar files numbered 34, 121, 128, 352, 360, 429, 495, 509, 518, 627, 676, 668, and 862 contain 10,499 molecules each. The last tar file numbered 1000 contains 13,417 molecules. The total size of the uncompressed dataset is over 283 Gigabytes. The code for calculating the electronic excitation energies and statistical analysis of the dataset is provided at the following GitLab repository: https://github.com/ORNL/Analysis-of-Large-Scale-Molecular-Datasets-with-Python Calculating the UV spectrum of a molecule requires performing 3 main operations: 1. Converting the smiles string representation of a molecule into a geometric structure where each atom is assigned XYZ coordinates. The geometric structure is written to the file smiles.pdb. 2. Using smiles.pdb to compute the relaxed geometry of the molecule, which corresponds with the position of the atoms at the position of equilibrium at the ground state. This generates the files band.out, detailed.out, and geo_end.gen. 3. Using geo_end.gen to calculate the UV spectrum of the molecule which is written into the file EXC.DAT. Every molecule in the dataset has its own directory. The files contained in each molecule directory are as follows: 1. geo_end.gen 2. detailed.out 3. band.out 4. EXC.DAT 5. smiles.pdb REFERENCES [1] Niehaus, T. A.; Suhai, S.; Della Salla, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, Th. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 2001, 63, 085108/1-9. [2] Blanchard, A.; Gounley, J.; Metha, K.; Yoo, P.; Irle, S. AISD HOMO-LUMO. DOI: 10.13139/ORNLNCCS/1869409 [3] RDKit: Cheminformatics and Machine Learning Software. 2013, [http://www.rdkit.org] [4] Tosco, P.; Stiefl, N. and Landrum, G. Bringing the MMFF force field to the RDKit: implementation and validation. J Cheminform. 2014, 6, 1–4. [5] a) Porezag, D.; Frauenheim, T.; Kohler, T.; Seifert, G.; Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon, R. Phys. Rev. B 1995, 51, 12947-12957; b) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.; Phys. Rev. B 1998, 58, 7260-7268; c) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB), J. Chem. Theory Comput. 2011, 7, 931-948; d) Cui, Q.; Elstner, M. Density functional tight binding: values of semi-empirical methods in an ab initio era, Phys. Chem. Chem. Phys. 2014, 16, 14368-14377. [6] Hourahine, B. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations, J. Chem. Phys. 2020, 152, 124101/1-19. [7] Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Cond. Matter 2017, 29, 273002. [8] Kubillus, M.; Kubar, T.; Gaus, M.; Rezac, J.; Elstner, M. Parameterization of the DFTB3 Method for Br, Ca, Cl, F, I, K, and Na in Organic and Biological Systems, J. Chem. Theory Comput. 2015, 11, 332-342. [9] Brandenburg, J. G.; Grimme, S. Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB), J. Phys. Chem. Lett. 2014, 5, 1785−1789. [10] a) Niehaus, T. A.; Elstner, M.; Frauenheim, Th.; Suhai, S. Application of an approximate density-functional method to sulfur containing compounds. J. Mol. Struct.: THEOCHEM 2001, 541, 185-94; b) Elstner, M.; Hobza, P.; Frauenheim, Th.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. J. Chem. Phys. 2001, 114, 5149-55. [11] Kubar, T.; Bodrog, Z.; Gaus, M.; Köhler, C.; Aradi, B.; Frauenheim, Th.; Elstner, M. Parametrization of the SCC-DFTB Method for Halogens. J. Chem. Theory Comput. 2013, 9, 2939-49.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Composite-particle decay widths by the generator coordinate method

We study the feasibility of applying the Generator Coordinate Method (GCM) of self-consistent mean-field theory to calculate decay widths of composite particles to composite-particle final states. The main question is how well the GCM can approximate continuum wave functions in the decay channels. The analysis is straightforward under the assumption that the GCM wave functions are separable into internal and Gaussian center-of-mass wave functions. Two methods are examined for calculating decay widths. In one method, the density of final states is computed entirely in the GCM framework. In the other method, it is determined by matching the GCM wave function to an asymptotic scattering wave function. Both methods are applied to a numerical example and are found to agree within their determined uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

On Coarse Grid Correction Methods in Krylov Subspaces

Two approaches using coarse grid correction in the course of a certain Krylov iterative process are presented. The aim of the correction is to accelerate the iterations. These approaches are based on an approximation of the function sought for by simple basis functions having finite supports. Additional acceleration can be achieved if the iterative process is restarted and the approximate solution is refined. In this case, the resulting process turns out to be a two-level preconditioned method. The influence of different parameters of the iterative process on its convergence is demonstrated by numerical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Role of electron correlation on the adenine dimer interaction for non-equilibrium geometries: a benchmark Quantum Monte Carlo study

The accurate description of non-covalent interactions is critical for understanding the structure, dynamics, and eventual function of biomolecules. The adenine dimer serves as a benchmark system for computational methods due to its role in nucleic acid structures and its rich conformational landscape. In this study, we employ benchmark diffusion quantum Monte Carlo (DMC) methods to investigate the relative energies and role of electron correlation on a set of adenine dimer conformations generated via a search of the potential energy landscape using the global optimizer algorithm. Relative DMC energies are compared against a wide range of density functional theory (DFT) approximation results. We find that although most of the DFT functionals perform well for low-energy structures, their accuracy varies significantly for higher-energy conformations, including stacked and T-shaped structures. A large fraction of the variation is due to the treatment of the van der Waals interaction. BLYP, B3LYP, and PBE0 significantly improve with added D4 dispersion, while the recent r2SCAN-D4 and ωB97M-V functionals show the least scatter and closest agreement with the DMC. These findings highlight the delicate nature of these interactions in biomolecular systems and provide guidance for simulations of their structure and dynamics and for the development of machine learned interatomic potentials.

Washburn, Laurel [ORNL] (ORCID:0000000324179335)↗
NASA NTRS1977

Symbolic Laplace transforms of special functions

A MACSYMA implementation of the Laplace transform for special functions is described. The generalized hypergeometric functions are used as a basis for the representation of approximately fifty special functions. Only a relatively small number of formulas that generally involve generalized hypergeometric functions are utilized for the integration stage. A sample of actual examples and their timing is provided.

Avgoustis, Y.↗