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Characterizing phonon dynamics using stochastic sampling

Predicting phonon relaxation time from molecular dynamics (MD) requires a long simulation time to compute the mode energy auto-correlation function. Here, we present an alternative approach to infer the phonon life-time from an approximate form of the energy auto-correlation function. The method requires as an input a set of sampled equilibrium configurations. A stochastic sampling method is used to generate the equilibrium configurations. We consider a truncated Taylor series expansion of the phonon energy auto-correlation function. The different terms in the truncated correlation function are obtained using the stochastic sampling approach. The expansion terms, thus, obtained are in good agreement with the corresponding values obtained using MD. We then use the approximate function to compute the phonon relaxation time. The relaxation time computed using this method is compared with that obtained from the exact correlation function. The two values are in agreement with each other.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗

An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields

Here Tthis work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume fraction field and provide an estimate of the surface normal in all of the interfacial grid cells. Groups of connected grid cells are then identified which all have the same dominant component of the normal vector. This grouping by orientation determines the proper dependent variable to use in the surface reconstruction (e.g. for a 2D curve, this step determines if the surface will be approximated by a function of x or y). A cumulative integral over the surface is constructed and fit using b-splines for two-dimensional problems or tensor-product b-splines for three-dimensional problems. This construction allows for the interface to be recovered through application of the second fundamental theorem of calculus. Fitting the cumulative integral with $\mathscr{N}$ th-order b-splines (or tensor-product b-splines) yields an ($\mathscr{N}$-1) th-order convergence rate of the interface shape. Differentiation of the b-spline interface function(s) allows for the high-order approximation of the normal vector and curvature to be obtained directly anywhere along b-spline. Together, the proposed reconstruction technique can achieve arbitrarily high mesh convergence rates. Validation tests are presented with mesh convergence rates ranging from fourth- to tenth-order.

97 MATHEMATICS AND COMPUTING↗

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons in a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

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↗

Non-additive non-interacting kinetic energy of rare gas dimers

We show approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

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↗

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

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↗

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↗

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↗

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↗

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)↗

Cohesive energy and structural parameters of binary oxides of groups IIA and IIIB from diffusion quantum Monte Carlo

We have applied the diffusion quantum Monte Carlo (DMC) method to calculate the cohesive energy and the structural parameters of the binary oxides CaO, SrO, BaO, Sc{sub 2}O{sub 3}, Y{sub 2}O{sub 3}, and La{sub 2}O{sub 3}. The aim of our calculations is to systematically quantify the accuracy of the DMC method to study this type of metal oxides. The DMC results were compared with local, semi-local, and hybrid Density Functional Theory (DFT) approximations as well as with experimental measurements. The DMC method yields cohesive energies for these oxides with a mean absolute deviation from experimental measurements of 0.18(2) eV, while with local, semi-local, and hybrid DFT approximations, the deviation is 3.06, 0.94, and 1.23 eV, respectively. For lattice constants, the mean absolute deviations in DMC, local, semi-local, and hybrid DFT approximations are 0.017(1), 0.07, 0.05, and 0.04 Å, respectively. DMC is a highly accurate method, outperforming the DFT approximations in describing the cohesive energies and structural parameters of these binary oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modified Steklov Functions and Numerical Differentiation Formulas

We consider an approximation method based on Steklov functions of the first and second order. We obtain estimates for the norms in the space C of continuous periodic functions and clarify how they connect with numerical differentiation formulas.

97 MATHEMATICS AND COMPUTING↗