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DOE OSTI2023

Accelerating the density-functional tight-binding method using graphical processing units

Acceleration of the density-functional tight-binding (DFTB) method on single and multiple graphical processing units (GPUs) was accomplished using the MAGMA linear algebra library. Herein two major computational bottlenecks of DFTB ground-state calculations were addressed in our implementation: the Hamiltonian matrix diagonalization and the density matrix construction. The code was implemented and benchmarked on two different computer systems: (1) the SUMMIT IBM Power9 supercomputer at the Oak Ridge National Laboratory Leadership Computing Facility with 1–6 NVIDIA Volta V100 GPUs per computer node and (2) an in-house Intel Xeon computer with 1–2 NVIDIA Tesla P100 GPUs. The performance and parallel scalability were measured for three molecular models of 1-, 2-, and 3-dimensional chemical systems, represented by carbon nanotubes, covalent organic frameworks, and water clusters.

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

Surface Studies of β-1,3,5,7-Tetranitro-1,3,5,7-Tetrazoctane and Pentaerythritol Tetranitrate from Density Functional Tight-Binding Calculations and Implications on Crystal Shape

Here, we use density functional tight-binding (DFTB) theory to calculate the surface energies of two energetic crystals: monoclinic β-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (β-HMX) and tetragonal pentaerythritol tetranitrate (PETN). The results are then employed to determine crystal shapes using the Bravais–Friedel–Donnay–Harker, attachment energy, and surface energy models. We find that energy-based models yield predictions in good agreement with experimental observations. Additionally, we propose a simple model that reframes surface energy as a measure of the lost intermolecular interactions during the formation of a surface from the bulk. The model accurately captures the results from the DFTB calculations and enables us to explain and predict surface energies as a function of the local molecular environment.

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

Crystallography of hyperbolic lattices

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. Here we show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.

2-dimensional systems↗
DOE OSTI2021

Predicted Reaction Mechanisms, Product Speciation, Kinetics, and Detonation Properties of the Insensitive Explosive 2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105)

2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105) is a relatively new and promising insensitive high-explosive (IHE) material that remains only partially characterized. IHEs are of interest for a range of applications and from a fundamental science standpoint, as the root causes behind insensitivity are poorly understood. In this work, we adopt a multitheory approach based on reactive molecular dynamic simulations performed with density functional theory, density functional tight-binding, and reactive force fields to characterize the reaction pathways, product speciation, reaction kinetics, and detonation performance of LLM-105. We compare and contrast these predictions to 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a prototypical IHE, and 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX), a more sensitive and higher performance material. The combination of different predictive models allows access to processes operative on progressively longer timescales while providing benchmarks for assessing uncertainties in the predictions. We find that the early reaction pathways of LLM-105 decomposition are extremely similar to TATB; they involve intra- and intermolecular hydrogen transfer. Additionally, the detonation performance of LLM-105 falls between that of TATB and HMX. We find agreement between predictive models for first-step reaction pathways but significant differences in final product formations. Predictions of detonation performance result in a wide range of values, and one-step kinetic parameters show the similar reaction rates at high temperatures for three out of four models considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Emulating 2D Materials with Magnons

Spin waves (magnons) in two-dimensional (2D) materials have received increasing interest due to their unique states and potential for tunability. However, many interesting features of these systems, including Dirac points and topological states, occur at high frequencies, where experimental probes are limited. Here, we study a crystal formed by patterning a hexagonal array of holes in a perpendicularly magnetized thin film. Through simulation, we find that the magnonic band structure imitates that of graphene, but additionally has some kagomelike character and includes a few flat bands. Surprisingly, its nature can be understood using a nine-band tight-binding Hamiltonian. This clear analogy to 2D materials enables band-gap engineering in 2D, topological magnons along 1D phase boundaries, and spectrally isolated modes at 0D point defects. Interestingly, the 1D phase boundaries allow access to the valley degree of freedom through a magnonic analog of the quantum valley Hall insulator. These approaches can be extended to other magnonic systems, but are potentially more general due to the simplicity of the model, which resembles existing results from electron, phonon, photon, and cold-atom systems. This finding brings the physics of spin waves in 2D materials to more experimentally accessible scales, augments it, and outlines a few principles for controlling magnonic states.

Ferrimagnets↗
DOE OSTI2024

Disorder-induced topological phase transition in a driven Majorana chain

Here, we study a periodically driven one-dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or nonexistence of edge modes at zero and π quasienergy. When potential disorder is added, the system parameters get renormalized and the system may exhibit a topological phase transition. When starting from the Majorana π mode (MPM) phase, which hosts only edge Majoranas with quasienergy π, disorder induces a transition into a neighboring phase with both π and zero modes on the edges. We characterize the disordered system using (i) exact diagonalization, (ii) Arnoldi mapping onto an effective tight-binding chain, and (iii) topological entanglement entropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

pH-Dependent Vibrational Dynamics Drives Excited-State Quenching in the Phycobiliprotein Complex PC645

Phycocyanin 645 (PC645) is a closed-form lightharvesting complex found in the lumen of the photosynthetic membrane of cryptophyte algae. These peripheral antenna complexes contain bilin chromophores that absorb sunlight and transfer excitation energy to the core antenna complexes embedded in the thylakoid membrane. The location of cryptophyte antenna complex on the luminal side of the membrane is unusual. During photosynthetic activity, the pH of the lumen drops, by up to two pH units. There is little known about how this pH-change affects the light-harvesting complexes. In this study, we report multiscale simulations using a computationally efficient density functional tight-binding framework to investigate the spectroscopy and excitation energy transfer in the PC645 complex. Complementary experiments were conducted using both steady-state and time-resolved spectroscopic measurements at low, neutral, and high pH values. Our study shows that (de)protonation of specific bilin pigments, namely, the mesobiliverdins (MBVs), modulates the excitation energies, excitonic couplings, and spectral densities. These changes cause excitation transfer rates to increase by up to a factor of two to three, leading to pH-dependent energy transfer pathways in the complex. Using this model, we calculated the pH-dependent fluorescence quantum yield of the system, obtaining quantitative agreement with the experimental results. These computational simulations, supported by experiments, identify MBVs as a more prominent excitation sink than previously realized, and that this role is tuned by pH.

Maity, Sayan [Constructor Univ., Bremen (Germany);↗
DOE OSTI2023

Artificial neural network potentials for mechanics and fracture dynamics of two-dimensional crystals **

Understanding the mechanics and failure of materials at the nanoscale is critical for their engineering and applications. The accurate atomistic modeling of brittle failure with crack propagation in covalent crystals requires a quantum mechanics-based description of individual bond-breaking events. Artificial neural network potentials (NNPs) have emerged to overcome the traditional, physics-based modeling tradeoff between accuracy and accessible time and length scales. Previous studies have shown successful applications of NNPs for describing the structure and dynamics of molecular systems and amorphous or liquid phases of materials. However, their application to deformation and failure processes in materials is still uncommon. In this study, we discuss the apparent limitations of NNPs for the description of deformation and fracture under loadings and propose a way to generate and select training data for their employment in simulations of deformation and fracture simulations of crystals. We applied the proposed approach to 2D crystalline graphene, utilizing the density-functional tight-binding method for more efficient and extensive data generation in place of density functional theory. Then, we explored how the data selection affects the accuracy of the developed artificial NNPs. It revealed that NNP’s reliability should not only be measured based on the total energy and atomic force comparisons for reference structures but also utilize comparisons for physical properties, e.g. stress–strain curves and geometric deformation. In sharp contrast to popular reactive bond order potentials, our optimized NNP predicts straight crack propagation in graphene along both armchair and zigzag (ZZ) lattice directions, as well as higher fracture toughness of ZZ edge direction. Our study provides significant insight into crack propagation mechanisms on atomic scales and highlights strategies for NNP developments of broader materials.

2D materials↗
DOE OSTI2023

Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Here, our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

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

Spin-helical detection in a semiconductor quantum device with ferromagnetic contacts

Spin-helical states, which arise in quasi-one-dimensional (1D) channels with spin-orbital (SO) coupling, underpin efforts to realize topologically protected quantum bits based on Majorana modes in semiconductor nanowires. Detecting helical states is challenging due to non-idealities present in real devices. Past efforts have focused on devices with normal contacts. In contrast, here we show by means of tight-binding calculations that by using ferromagnetic contacts it is possible to detect helical modes with high sensitivity even in the presence of realistic device effects, such as quantum interference. We show that by taking advantage of the spin-selective transmission properties of helical states, new transport signatures become possible. In addition, we show that spin-polarized contacts provide a unique path to investigate the spin-texture and spin-momentum locking properties of helical states. Our results are of interest not only for the ongoing development of Majorana qubits, but also for realizing possible spin-based quantum devices, such as quantum spin modulators and interconnects based on spin-helical channels.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accurate Free Energies for Complex Condensed-Phase Reactions Using an Artificial Neural Network Corrected DFTB/MM Methodology

Semiempirical methods like density functional tight-binding (DFTB) allow extensive phase space sampling, making it possible to generate free energy surfaces of complex reactions in condensed-phase environments. Such a high efficiency often comes at the cost of reduced accuracy, which may be improved by developing a specific reaction parametrization (SRP) for the particular molecular system. Thiol–disulfide exchange is a nucleophilic substitution reaction that occurs in a large class of proteins. Its proper description requires a high-level ab initio method, while DFT-GAA and hybrid functionals were shown to be inadequate, and so is DFTB due to its DFT-GGA descent. We develop an SRP for thiol–disulfide exchange based on an artificial neural network (ANN) implementation in the DFTB+ software and compare its performance to that of a standard SRP approach applied to DFTB. Furthermore, as an application, we use both new DFTB-SRP as components of a QM/MM scheme to investigate thiol–disulfide exchange in two molecular complexes: a solvated model system and a blood protein. Demonstrating the strengths of the methodology, highly accurate free energy surfaces are generated at a low cost, as the augmentation of DFTB with an ANN only adds a small computational overhead.

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

Scaling Ensembles of Data-Intensive Quantum Chemical Calculations for Millions of Molecules

Deep learning models are efficient computational tools that can accelerate the inverse design of molecules with desired functional properties by generating predictions at a fraction of the time required by traditional quantum chemical approaches. To ensure that a model maintains accuracy and transferability across broad regions of the chemical space explored during the inverse design, it must be trained on massively large volumes of simulation data. This requires running large-scale ensemble quantum chemical calculations on high-performance computing (HPC) systems for data collection. However, the efficient execution of such large ensemble calculations and the management of large volumes of output data require tools that can judiciously utilize computational resources and manage metadata overhead on the file system. Therefore, we present a high-performance, scalable, ensemble management framework for performing data-intensive quantum chemical electronic structure calculations for organic molecules. This framework provides abstractions to plug different ab initio, first principles, and first principles-based semi-empirical methods and executes them efficiently at large scale on HPC systems. It dynamically distributes tasks to resources and uses tiered storage for managing large collections of files. We employed this framework to process over ten million organic molecules and generate open-source datasets that provide UV-vis absorption spectra by running time-dependent density-functional tight-binding calculations. It is the largest database containing molecular optical spectra that were simulated with quantum chemical methods in a consistent manner.

Mehta, Kshitij↗
DOE OSTI2023

Enhancing the accuracy of density functional tight binding models through ChIMES many-body interaction potentials

Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of these models can require lengthy effort due to the lack of a systematic approach for their development. In this work, we discuss the use of the Chebyshev Interaction Model for Efficient Simulation (ChIMES) to create rapidly parameterized DFTB models, which exhibit strong transferability due to the inclusion of many-body interactions that might otherwise be inaccurate. We apply our modeling approach to silicon polymorphs and review previous work on titanium hydride. We also review the creation of a general purpose DFTB/ChIMES model for organic molecules and compounds that approaches hybrid functional and coupled cluster accuracy with two orders of magnitude fewer parameters than similar neural network approaches. In all cases, DFTB/ChIMES yields similar accuracy to the underlying quantum method with orders of magnitude improvement in computational cost. In conclusion, our developments provide a way to create computationally efficient and highly accurate simulations over varying extreme thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly, and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.

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

ORNL_AISD_DL-HLgap

This dataset provides supplementary molecular dataset of Deep Learning Workflow for the Inverse Design of Molecules with Specific Optoelectronic Properties. The dataset comprises three main directories such as GDB-9_dataset, Low_HL_Gap_dataset, and High_HL_Gap_dataset which individually has csv files, smiles_txt files, pdb files and xyz files containing information of molecular structures, properties and coordinates generated from deep learning workflow using generative model, surrogate model and DFTB calculation results. GDB-9_dataset contains the molecular data extracted from the original GDB-9 dataset with additional data of DFTB HL gap, surrogate HL gap and molecular property analysis. (the number of atoms, aromaticity and double bond equivalent) Low_HL_Gap_dataset and High_HL_Gap_dataset contains series of dataset for different generations with further split to train and test dataset that were obtained from the iterative workflow described in the manuscript. Additional directory Chemiscope_visualization in Low_HL_Gap_dataset directory contains compressed json files to visualize molecules using chemiscope.org page or application to help readers examine generated molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Investigating 3,4-bis(3-nitrofurazan-4-yl)furoxan detonation with a rapidly tuned density functional tight binding model

In this work, we describe a machine learning approach to rapidly tune density functional tight binding models for the description of detonation chemistry in organic molecular materials. Resulting models enable simulations on the several 10s of ps scales characteristic to these processes, with “quantum-accuracy.” We use this approach to investigate early shock chemistry in 3,4-bis(3-nitrofurazan-4-yl)furoxan, a hydrogen-free energetic material known to form onion-like nanocarbon particulates following detonation. We find that the ensuing chemistry is significantly characterized by the formation of large C x N y O z species, which are likely precursors to the experimentally observed carbon condensates. Beyond utility as a means of investigating detonation chemistry, the present approach can be used to generate quantum-based reference data for the development of full machine-learned interatomic potentials capable of simulation on even greater time and length scales, i.e., for applications where characteristic time scales exceed the reach of methods including Kohn–Sham density functional theory, which are commonly used for reference data generation.

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

Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study

Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗