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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Exploration, Prediction, and Experimental Verification of Structure and Optoelectronic Properties in I 2 -Eu-IV-X 4 (I = Li, Cu, Ag; IV = Si, Ge, Sn; X = S, Se) Chalcogenide Semiconductors

Recently, there has been extensive research into photovoltaic, thermoelectric, and nonlinear optical applications of chalcogenide semiconductors within the large set of defect-resistant I 2 -II-IV-X4 (I = Li, Cu, Ag; II = Ba, Sr, Eu, Pb; IV = Si, Ge, Sn; X = S, Se) compounds. Five Eu-including compounds have previously been reported within this family, but a comparative study of possible structures and electronic properties of all 18 Eu-based combinations is still absent. Herein, we use hybrid density functional theory to study rare-earth-including I 2 -II-IV-X 4 semiconductors with Eu on the II site, in order to further understand this family and test the geometric tolerance factor approach (reported in our previous work) as a tool for predicting potential stable structures. We investigate how the exchange mixing parameter of the HSE06 density functional, α, affects the energetic positions of electronic levels, especially of the localized f-electron orbitals near the band edges of the extended semiconductor structures, using literature photoemission and band gap data of EuS for comparison. Lowest-energy quaternary structure candidates, energy band structures, and densities of states are computationally predicted for all 18 materials. Based on its predicted photovoltaics-relevant band gap, the previously unknown compound Cu 2 EuSnSe 4 was selected and synthesized. Furthermore, the experimental structure, lattice parameters, and band gap of Cu 2 EuSnSe 4 are consistent with the computational predictions, confirming a 1.55 eV band gap.

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

Molecular-Scale Characterization of Photoinduced Charge Separation in Mixed-Dimensional InSe–Organic van der Waals Heterostructures

Layered indium selenide (InSe) is an emerging two-dimensional semiconductor that has shown significant promise for high-performance transistors and photodetectors. The range of optoelectronic applications for InSe can potentially be broadened by forming mixed-dimensional van der Waals heterostructures with zero-dimensional molecular systems that are widely employed in organic electronics and photovoltaics. Here, we report the spatially resolved investigation of photoinduced charge separation between InSe and two molecules (C 70 and C 8 -BTBT) using scanning tunneling microscopy combined with laser illumination. We experimentally and computationally show that InSe forms type-II and type-I heterojunctions with C 70 and C 8 -BTBT, respectively, due to an interplay of charge transfer and dielectric screening at the interface. Laser-excited scanning tunneling spectroscopy reveals a ~0.25 eV decrease in the energy of the lowest unoccupied molecular orbital of C 70 with optical illumination. Furthermore, photoluminescence spectroscopy and Kelvin probe force microscopy indicate that electron transfer from InSe to C 70 in the type-II heterojunction induces a photovoltage that quantitatively matches the observed downshift in the tunneling spectra. In contrast, no significant changes are observed upon optical illumination in the type-I heterojunction formed between InSe and C 8 -BTBT. Density functional theory calculations further show that, despite the weak coupling between the molecular species and InSe, the band alignment of these mixed-dimensional heterostructures strongly differs from the one suggested by the ionization potential and electronic affinities of the isolated components. Self-energy-corrected density functional theory indicates that these effects are the result of the combination of charge redistribution at the interface and heterogeneous dielectric screening of the electron–electron interactions in the heterostructure. In addition to providing specific insight for mixed-dimensional InSe–organic van der Waals heterostructures, this work establishes a general experimental methodology for studying localized charge transfer at the molecular scale that is applicable to other photoactive nanoscale systems.

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

Hydrogen in disordered titania: connecting local chemistry, structure, and stoichiometry through accelerated exploration

Hydrogen incorporation in native surface oxides of metal alloys often controls the onset of metal hydriding, with implications for materials corrosion and hydrogen storage. A key representative example is titania, which forms as a passivating layer on a variety of titanium alloys for structural and functional applications. These oxides tend to be structurally diverse, featuring polymorphic phases, grain boundaries, and amorphous regions that generate a disparate set of unique local environments for hydrogen. Here, we introduce a workflow that can efficiently and accurately navigate this complexity. First, a machine learning force field, trained on ab initio molecular dynamics simulations, was used to generate amorphous configurations. Density functional theory calculations were then performed on these structures to identify local oxygen environments, which were compared against experimental observations. Second, to classify subtle differences across the disordered configuration space, we employ a graph-based sampling procedure. Finally, local hydrogen binding energies and hopping kinetics are computed using exhaustive density functional theory calculations on representative configurations. Here, we leverage this methodology to show that hydrogen binding energetics are described by local oxygen coordination, which in turn is affected by stoichiometry, and form the basis of hopping kinetics and diffusion. Together these results imply that hydrogen incorporation and transport in TiO x can be tailored through compositional engineering, with implications for improving the performance and durability of titanium-derived alloys in hydrogen environments.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Conventional High-Temperature Superconductivity in Metallic, Covalently Bonded, Binary-Guest C–B Clathrates

Inspired by the synthesis of XB 3 C 3 (X = Sr, La) compounds in the bipartite sodalite clathrate structure, density functional theory (DFT) calculations are performed on members of this family containing up to two different metal atoms. A DFT chemical pressure analysis on systems with X = Mg, Ca, Sr, Ba reveals that the size of the metal cation, which can be tuned to stabilize the B–C framework, is key for their ambient-pressure dynamic stability. High-throughput density functional theory calculations on 105 Pm$\bar{3}$ symmetry XYB 6 C 6 binary-guest compounds (where X, Y are electropositive metal atoms) find 22 that are dynamically stable at 1 atm, expanding the number of potentially synthesizable phases by 19 (18 metals and 1 insulator). Here, the density of states at the Fermi level and superconducting critical temperature, T c , can be tuned by changing the average oxidation state of the metal atoms, with T c being highest for an average valence of +1.5. KPbB 6 C 6 , with an ambient-pressure Eliashberg T c of 88 K, is predicted to possess the highest T c among the studied Pm$\bar{3}$n XB 3 C 3 or Pm$\bar{3}$XYB 6 C 6 phases, and calculations suggest it may be synthesized using high-pressure high-temperature techniques and then quenched to ambient conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

When Do Band Gap Calculations Agree with Experiments in Monolayer-Protected Cu 14 and Au 20 Atomically Precise Nanoclusters? A (TD)-DFT Comparison of HOMO–LUMO, Fundamental, Optical, and Electrochemical Energy Gaps

In view of the tremendous progress in atomically precise metal nanoclusters where electrochemical and optical energetics are routinely supported by computations to establish structure−function correlations, we explore the relationship between different protocols for measuring and computing band gaps of two distinct organic ligand-protected nanoclusters: [Cu 14 H 10 (MBN) 3 (PPh 3 ) 8 ] + and Au 20 (TBBT) 16 . Through UV/visible spectroscopy and differential pulse voltammetry, we measure optical and electrochemical band gaps in those systems. We then compare these experimentally determined gaps to HOMO−LUMO gaps, fundamental gaps, vertical excitation energies, and E o ox − E o red potentials computed using different density functional theory (DFT) or time-dependent DFT (TDDFT) methods. Specifically, in both copper and gold nanoclusters, we test the effect of truncating inert ligands from the model and compare density functionals with varying degrees of Hartree−Fock (HF) exchange from 0 to 50%, range-separated hybrids with a varying long-range tuning parameter, different correlation functionals, basis sets, and (equilibrium and nonequilibrium) continuum solvation models. Despite having different frontier orbital characters (the copper nanocluster has a metal-to-ligand charge transfer character while the gold nanocluster has metal-centered frontier orbitals), both nanoclusters display a similar sensitivity of the HOMO−LUMO gap to the HF exchange that is partially mitigated when computing the fundamental, optical, and electrochemical gaps. Other factors, such as the nature of the correlation functional, basis set, and geometry relaxation, have a considerably smaller effect on computed band gaps in these systems. Overall, this work provides guidelines for factors of varied importance for correlating computed and experimental band gap values.

Chemical calculations↗
DOE OSTI2022

Verification of stability and unraveling the electronic and physical properties of bulk and (001)-surfaces of newly synthesized Ti 2 ZnX (X = C, N) MAX phases

MAX phase family has been extended by the addition of late transition metals at the A-site with the expectation of diverse functional properties. Here, we present our systematic density functional investigation on the thermodynamic and phonon stabilities, elastic properties, including elastic constants, elastic moduli and elastic anisotropy of newly synthesized Ti 2 ZnX (X = C, N) phases in comparison with conventional Ti 2 AlX (X = C, N). Due to the smaller size of N as compared to C, the unit cell dimension is reduced when C atoms are replaced by N atoms at the X-site. Furthermore, the Ti 2 ZnC and Ti 2 ZnN are stable at the equilibrium volume of 110.84 Å 3 and 105.70 Å 3 . The thermodynamic, mechanical and dynamical stabilities are validated by estimating the formation energies, elastic constants and phonon dispersions, respectively. The elastic properties of Ti 2 ZnN are less anisotropic as compared to those of Ti 2 ZnC. To understand the thin-film characteristics in Ti 2 ZnX, the surface properties with (001)-terminated slabs are investigated. Both Ti 2 ZnX bulk and (001)-surfaces exhibit metal-like electronic structures. There is a strong covalent bonding between Ti-X and Ti-Zn atoms confirmed by the charge density map and Mulliken population analysis. Additional states are generated at the Fermi level (EF) due to the unusual d-p states hybridization between Ti and Zn atoms. The anisotropy in chemical bonding is confirmed by the cleavage energy difference between Ti-X and Ti-Zn. Here, Ti(X)-001 and Zn-001 terminations are stable surfaces; however, in terms of chemical potentials, Zn-001 termination is the most favourable in Ti 2 ZnX.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

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

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Improving scalability of electronic structure code for molecular simulations in the presence of environment

A scalable density functional electronic code with Gaussian basis set, called UTEP-NRLMOL, is developed to perform simulations of molecular systems in the presence of the environment with particular attention to the memory requirements. In the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for density functional calculations scale as N*N, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure codes hinder their efficient usage of these platforms. We have introduced new scaling and parallelization paradigms using MPI-3 shared-memory functionality combined with usage of sparse algebra and storage of matrices in sparse format. This extends the range of applicability of the UTEP-NRLMOL code to large systems over 10,000 atoms, or using up to 67,000 basis functions, and making use of HPC architectures using over 6,000 processors utilizing all available cores. We have also interfaced code with effective fragment potential and polarizable continuum model libraries. The code was used in simulations of several applications which are published in reputed scientific journals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Photoluminescence spectra of point defects in semiconductors: Validation of first-principles calculations

Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide information on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first-principles calculations, including the use of the Franck-Condon principle and the displaced harmonic oscillator approximation. We focus on prototypical examples of solid state qubits, the divacancy centers in SiC and the nitrogen-vacancy in diamond, and we report computed photoluminescence spectra as a function of temperature that are in very good agreement with the measured ones. As expected we find that the use of hybrid functionals leads to more accurate results than semilocal functionals. Interestingly our calculations show that constrained density functional theory (CDFT) and time-dependent hybrid DFT perform equally well in describing the excited state potential energy surface of triplet states; our findings indicate that CDFT, a relatively cheap computational approach, is sufficiently accurate for the calculations of photoluminescence spectra of the defects studied here. Finally, we find that only by correcting for finite-size effects and extrapolating to the dilute limit can one obtain a good agreement between theory and experiment. Our results provide a detailed validation protocol of first-principles calculations of photoluminescence spectra, necessary both for the interpretation of experiments and for robust predictions of the electronic properties of point defects in semiconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ab Initio Electron-Phonon Interactions in Correlated Electron Systems

Electron-phonon ( e - ph ) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons, and metal-insulator transitions. First-principles approaches enable accurate calculations of e - ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable e - ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials, and multiferroics. Here we show first-principles calculations of e - ph interactions in CES, using the framework of Hubbard-corrected density functional theory ( DFT + U ) and its linear response extension ( DFPT + U ), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its e - ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged e - ph interactions, DFPT + U is shown to remove the divergences and properly account for the long-range Fröhlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e - ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Local lattice distortions and the structural instabilities in bcc Nb–Ta–Ti–Hf high-entropy alloys: An ab initio computational study

Local lattice distortions (LLD) and structural stability of body-centered cubic (bcc) Nb–Ta–Ti–Hf high-entropy alloys (HEAs) are studied as functions of composition employing ab initio density-functional theory calculations, with specific focus on the role of the relative concentrations of group IV (Ti and Hf) versus group V (Nb and Ta) elements. Calculated results are presented as a function of composition x in Nb x Ta 0.25 Ti (0.75-x)/2 Hf (0.75-x)/2 alloys, for elastic moduli, phonon spectral functions, LLD and structural energy differences for the bcc and competing hexagonal close-packed (hcp) and ω phases. The results highlight the important role of group V elements and LLD in stabilizing the bcc structure. They further reveal how composition x can be tuned to alter both the magnitude of the LLD and structural energy differences. Specifically, the magnitude of the structural energy differences, and elastic and dynamic stability of the bcc phase, are enhanced with increasing x, while the LLD increase in magnitude as this concentration is decreased. The results also show evidence of correlated LLD at lower values of x, reflecting local structural distortions towards the ω phase, but not hcp. The degree of ω-collapse is nevertheless partial i.e., transformation towards this phase is not observed to be complete due to the presence of Ta and Nb. At lower values of x we further find an energy landscape characterized by multiple, nearly degenerate local energy minima for different values of the LLD.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Phase Transformations among TiO2 Polymorphs

Polymorphs widely exist in nature and synthetic systems and are well known to determine material properties. Understanding phase transformation mechanisms among polymorphs enables the design of structures and tuning of phases to tailor material properties. However, current understanding is limited due to the lack of direct observations that track the processes and the structural evolution is not known at atomic scale. Here, integrating (semi) in situ transmission electron microscopy and density functional theory, we report atomic structural evolutions of phase transformation from anatase (A) to rutile (R), brookite (B), R-phase, and TiO. Besides the consistent paths with previous reports, we discover several unreported paths, including a [001] direction and (020) plane of anatase to [100]A and (011)R of rutile, respectively, ( , ) and , . Density functional theory analysis elucidates atomic structural evolution during the processes and over 16% of Ti-O bonds break and reform during the processes with energy barriers of ~0.7-1.0 eV per TiO2 formula unit. Under electron-beam irradiation, anatase particles transform into TiO2-R phase or TiO at high or room temperature, respectively. We also reveal the anisotropic nature of electron-beam effect, which is seldom discussed: dependence of crystallographic orientation with respect to electron-beam irradiation direction. Understanding the atomic structural evolution sheds light on interpreting and controlling TiO2 polymorphs and interface structures for various applications. The revealed electron-beam effects in our work provide guidance for in situ transmission electron microscopy studies.

Song, Miao↗
DOE OSTI2026

Ultrafast One-Dimensional Peierls-Distortion Dynamics in 1⁢T′−Re⁢S 2 Revealed by 4D Electron Microscopy

Rhenium disulfide (ReS 2 ), a prototypical 2D semiconductor with an anisotropic 1⁢T′ structure due to the pronounced Peierls distortion, has demonstrated great potential for polarization-dependent optoelectronics and photonics. Here, we report an ultrafast phase transition occurring within 1 ps, accompanied by a one-dimensional Peierls-distortion relaxation in 1⁢T′−ReS 2 revealed with combined 4D electron microscopy and time-dependent density functional theory calculations. Upon femtosecond laser pulse excitation, the Re-Re dimerization morphology rapidly transforms from a diamond cluster to zigzag chains and persists for several nanoseconds. Here, this ultrafast Peierls-distortion relaxation is further verified by transient changes in optical anisotropy via polarization-dependent transient absorption spectroscopy. Time-dependent density functional theory calculations attribute this novel phase transition to strong correlation between Peierls distortion and impulsive photoexcited carrier doping, predicting a transient band-gap collapse. This Letter opens up an exciting avenue for ultrafast control of Peierls-distortion-induced anisotropy and the metal-insulator transition in 1⁢T′−ReS 2 .

1T’-ReS2↗
NASA NTRS1989

Ginzburg-Landau theory for the solid-liquid interface of bcc elements. II - Application to the classical one-component plasma, the Wigner crystal, and He-4

The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.

Zeng, X. C.↗
DOE OSTI2022

Strongly correlated itinerant magnetism near superconductivity in NiTa 4 Se 8

Metallic ferromagnets with strongly interacting electrons often exhibit remarkable electronic phases such as ferromagnetic superconductivity, complex spin textures, and nontrivial topology. Here, in this report, we discuss the synthesis of a layered magnetic metal NiTa 4 Se 8 (or Ni 1/4 TaSe 2 ) with a Curie temperature of 58 Kelvin. Magnetization data and density functional theory calculations indicate that the nickel atoms host uniaxial ferromagnetic order of about 0.7µ B per atom, while an even smaller moment is generated in the itinerant tantalum conduction electrons. Strong correlations are evident in flat bands near the Fermi level, a high heat capacity coefficient, and a high Kadowaki-Woods ratio. Density functional theory calculations suggest that electron and hole Fermi surfaces in the ferromagnetic phase are associated with opposite spin polarization. When the system is diluted of magnetic ions, the samples become superconducting below about 2 Kelvin. We discuss possible mechanisms for superconductivity in this family.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals

The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as “Thiel’s set.” Literature reference data based on Gaussian-type orbitals are reproduced to about one millielectron-volt precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted “tier2+aug2” is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.

Liu, Chi↗