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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of noninteracting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation, second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Development of Ion Stopping Models for HED Plasmas Using Unified Self-Consistent Field Models and Self-Consistent Electron Distributions

We have implemented several corrections to the electronic stopping power model combining the RPA dielectric response formalism and local density approximation with electronic density distribution calculated in an average atom model. These modifications include strong collision correction, local field correction, electron binding energy correction, and the Barkas effect. The combined results bring the RPA-LDA stopping power in cold targets to closer agreements with experiments for a wide range of materials. The same method is then applied to the stopping of ions in warm dense plasmas. The computational framework developed during this project is publicly available on GitHub (https://github.com/dedx-erpa/dedx). Tabulated data for protons in cold target for common materials are located in the data/ subdirectory of the repository.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Ab initio study on fcc Pr with correlation matrix renormalization theory

Here, we studied fcc praseodymium (Pr) with the ab initio correlation matrix renormalization theory (CMRT) explicitly calculating the Coulomb interactions among basis orbitals and without using any adjustable parameters to work for strongly correlated electron systems. We calculated its total energy in a paramagnetic ground state and studied the role of the correlated 4f electrons in the system. Good agreement was obtained between CMRT and experiments in the pressure volume dependence of the fcc phase. We also compared the CMRT results against other theoretical methods including local density approximation + dynamical mean-field theory and showed consistent results among them. Moreover, we found the normalized local charge fluctuation of the 4f electrons as the function of volume exhibits a clear slope change at the volume collapse region, indicating a switch in their correlation nature there.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

New insights into the electronic structure of α-U and δ-Pu

Here, this work presents the results of a theoretical study of the electronic structure of two actinide metals, α -U and δ -Pu. We compare our ab-initio results obtained with the recently developed self-consistent Vertex corrected GW approach with previously published experimental measurements such as photo-electron spectroscopy, for the occupied density of states, and bremsstralung isochromat spectroscopy (BIS) and inverse photo-electron spectroscopy (IPES), for the unoccupied density of states. Our ab-initio approach includes all important relativistic effects (it is based on Dirac’s equation) and it represents the first application of the Vertex corrected GW approach in the physics of actinides. Overall, our theoretical results are in good agreement with the experimental data, which supports the level of approximations which our theoretical method is based upon. By comparing our vertex corrected GW results with our results obtained with less sophisticated approaches (local density approximation and self-consistent GW) we differentiate the strength of correlation effects in Uranium and Plutonium. Also, our theoretical results allow us to elucidate the subtle differences between the previously published experimental BIS and IPES data on the unoccupied density of states in α -U.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

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

Molecule-surface interaction from van der Waals-corrected semilocal density functionals: The example of thiophene on transition-metal surfaces

Semilocal density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semilocal functionals require an additive nonlocal correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the long-range part. This work reports adsorption energies and the corresponding geometry of aromatic thiophene (C 4 H 4 S) bound to transition-metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well-balanced short- and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy. Here, our methods indicate that the correct interplay is not present in any combination of recent meta-GGA's and rVV10. The simple short-range damping of the vdW correction scheme that is practically successful in the combination of GGA's and vdW approximations is less transferable in SCAN+rVV10 or in the revised version, revSCAN+rVV10. In addition, we present accurate random-phase-approximation-quality adsorption energies from a model based on the one of Zaremba and Kohn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

An investigation of high entropy alloy conductivity using first-principles calculations

The Kubo–Greenwood equation, in combination with the first-principles Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA) can be used to calculate the DC residual resistivity of random alloys at T = 0 K. We implemented this method in a multiple scattering theory based ab initio package, MuST, and applied it to the ab initio study of the residual resistivity of the high entropy alloy Al x CoCrFeNi as a function of x. The calculated resistivities are compared with experimental data. We also predict the residual resistivity of refractory high entropy alloy MoNbTaV x W. Furthermore, the calculated resistivity trends are also explained using theoretical arguments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Exploring the role of electronic structure on photo-catalytic behavior of carbon-nitride polymorphs

A fully self-consistent density-functional theory (DFT) with improved functionals is used herein to provide a comprehensive account of structural, electronic, and optical properties of C 3 N 4 polymorphs. Using our recently developed van Leeuwen-Baerends (vLB) corrected local-density approximation (LDA), we implemented LDA + vLB within full-potential N th -order muffin-tin orbital (FP-NMTO) method and show that it improves structural properties and band gaps compared to semi-local functionals (LDA/GGA). We demonstrate that the LDA + vLB predicts band-structure and work-function for well-studied 2D-graphene and bulk-Si in very good agreement with experiments, and more exact hybrid functional (HSE) calculations as implemented in the Quantum-Espresso (QE) package. The structural and electronic-structure (band gap) properties of C 3 N 4 polymorphs calculated using FP-NMTO-LDA + vLB is compared with more sophisticated hybrid-functional calculations. We also perform detailed investigation of photocatalytic behavior using QE-HSE method of C 3 N 4 polymorphs through work-function, band (valence and conduction) position with respect to water reduction and oxidation potential. Our results show $γ$-C 3 N 4 as the best candidate for photocatalysis among all the C 3 N 4 polymorphs but it is dynamically unstable at ‘zero’ pressure. We show that $γ$-C 3 N 4 can be stabilized under hydrostatic-pressure, which improves its photocatalytic behavior relative to water reduction and oxidation potentials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

Herein we present numerical results of ground-state energies of 9 molecules in the well-established G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy $E_c$. By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with $E_c$ are in general better reproduced, but discrepancies are still observed for some dimers.

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

Accurate Kohn-Sham auxiliary system from the ground-state density of solids

The Kohn-Sham (KS) system is an auxiliary system whose effective potential is unknown in most cases. It is in principle determined by the ground-state density and it has been found numerically for some low-dimensional systems by inverting the KS equations starting from a given accurate density. For solids, only approximate results are available. In this work, we determine accurate exchange-correlation (xc) potentials for Si and NaCl using the ground-state densities obtained from auxiliary field quantum Monte Carlo calculations. We show that these xc potentials can be rationalized as an ensemble of a few local functions of the density, whose form depends on the specific environment and can be well characterized by the gradient of the density and the local kinetic energy density. Further, the KS band structure can be obtained with high accuracy. The true KS band gap turns out to be larger than the prediction of the local density approximation, but significantly smaller than the measurable photoemission gap, which confirms previous estimates. Finally, our findings show that the conjecture that very different xc potentials can lead to very similar densities and other KS observables is true also in solids, which questions the meaning of details of the potentials and, at the same time, confirms the stability of the KS system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Short-range correlation physics at low renormalization group resolution

Recent experiments have succeeded in isolating processes for which short-range correlation (SRC) physics is dominant and well accounted for by SRC phenomenology. But an alternative and compelling picture emerges from renormalization group (RG) evolution to low RG resolution. At high RG resolution, SRCs are identified as components in the nuclear wave function with relative pair momenta greater than the Fermi momentum. Scale separation results in wave-function factorization that can be exploited with phenomenologies such as the generalized contact formalism or the low-order correlation operator approximation. Evolution to lower resolution shifts SRC physics from nuclear structure to the reaction operators without changing the measured observables. We show how the features of SRC phenomenology manifested at high RG resolution are cleanly identified at low RG resolution using simple two-body operators and local-density approximations with uncorrelated wave functions, all of which can be systematically generalized. We verify that the experimental consequences to date follow directly at low resolution from well-established properties of nucleon-nucleon interactions such as the tensor force. Thus the RG reconciles the contrasting pictures of the same experiment and shows how to get correct results using wave functions without SRC components. Finally, our demonstration has implications for the analysis of knockout reactions for which SRC physics is not cleanly isolated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Ab initio calculation of atomic solid hydrogen phases based on Gutzwiller many-body wave functions

We apply two ab initio many-body methods based on Gutzwiller wave functions, i.e., correlation matrix renormalization theory (CMRT) and Gutzwiller conjugate gradient minimization (GCGM), to the study of crystalline phases of atomic hydrogen. Both methods avoid empirical Hubbard U parameters and are free from double-counting issues. CMRT employs a Gutzwiller-type approximation that enables efficient calculations, while GCGM goes beyond this approximation to achieve higher accuracy at higher computational cost. By benchmarking against available quantum Monte Carlo (QMC) results, we demonstrate that while both methods are more accurate than the widely used density-functional theory, GCGM systematically captures additional correlation energy missing in CMRT, leading to significantly improved total energy predictions. We also show that by including the correlation energy Ec from local density approximation in the CMRT calculation, CMRT + E c produces energy in better agreement with the QMC results in these hydrogen lattice systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Re-examining the silicon self-interstitial charge states and defect levels: A density functional theory and bounds analysis study

The self-interstitial atom (SIA) is one of two fundamental point defects in bulk Si. Isolated Si SIAs are extremely difficult to observe experimentally. Even at very low temperatures, they anneal before typical experiments can be performed. Given the challenges associated with experimental characterization, accurate theoretical calculations provide valuable information necessary to elucidate the properties of these defects. Previous studies have applied Kohn–Sham density functional theory (DFT) to the Si SIA, using either the local density approximation or the generalized gradient approximation to the exchange-correlation (XC) energy. The consensus of these studies indicates that a Si SIA may exist in five charge states ranging from -2 to +2 with the defect structure being dependent on the charge state. This study aims to re-examine the existence of these charge states in light of recently derived “approximate bounds” on the defect levels obtained from finite-size supercell calculations and new DFT calculations using both semi-local and hybrid XC approximations. We conclude that only the neutral and +2 charge states are directly supported by DFT as localized charge states of the Si SIA. Within the current accuracy of DFT, our results indicate that the +1 charge state likely consists of an electron in a conduction-band-like state that is coulombically bound to a +2 SIA. Furthermore, the -1 and -2 charge states likely consist of a neutral SIA with one and two additional electrons in the conduction band, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Experimental determination of the valence band offsets of ZnGeN 2 and (ZnGe) 0.94 Ga 0.12 N 2 with GaN

A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN 2 /GaN heterointerface has inspired novel band-engineered III-N/ZnGeN 2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe) 1- x Ga 2 x N 2 , for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN 2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe) 0.94 Ga 0.12 N 2 the value was determined to be 1.29 eV, ~10%–20% lower than that of ZnGeN 2 . The experimental determination of the large band offset between ZnGeN 2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.

Physics↗
DOE OSTI2025

Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals

We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.

coupled cluster theory↗
DOE OSTI2023

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew–Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. Finally, the quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

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

Tetragonal Kondo Insulator EuCd 2 Sb 2 Discovered via High Pressure High Temperature Synthesis

Abstract Magnetic and electronic properties of quantum materials heavily rely on the crystal structure even in the same chemical compositions. In this study, it is demonstrated that a layered tetragonal EuCd 2 Sb 2 structure can be obtained by treating bulk trigonal EuCd 2 Sb 2 under high pressure (6 GPa) and high temperature (600 °C). Magnetization measurements of the newly formed layered tetragonal EuCd 2 Sb 2 confirm an antiferromagnetic ordering with Neel temperature ( T N ) around 16 K, which is significantly higher than that ( T N ≈ 7 K) of trigonal EuCd 2 Sb 2 , consistent with heat capacity measurements. Moreover, bad metal behavior is observed in the temperature dependence of the electrical resistivity and the resistivity shows a dramatic increase around the Neel temperature. Electronic structure calculations with local density approximation dynamic mean–field theory (LDA+DMFT) show that this material is strongly correlated with well‐formed large magnetic moments, due to Hund's coupling, which is known to dramatically suppress the Kondo scale.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗