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This paper is a collaboration between SNL and the Israel Atomic Energy Commission (IAEC) - sponsored by NA211, Office of International Nuclear Security. The paper was accepted for publication by the International Atomic Energy Agency's (IAEA) International Conference on Nuclear Security (ICONS 2024).
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.
Here, empirical, highly accurate non-relativistic electronic total atomization energies (eTAEs) are established by combining experimental or computationally converged treatments of the nuclear motion and relativistic contributions with the total atomization energies of HF, CO, N 2 , and H 2 O obtained from the Active Thermochemical Tables. These eTAEs, which have estimated (2σ) uncertainties of less than 10 cm -1 (0.12 kJ mol -1 ), form the basis for an analysis of high-level ab initio quantum chemical calculations that aim at reproducing these eTAEs for the title molecules. The results are then employed to analyze the performance of the high-accuracy extrapolated ab initio thermochemistry, or High-Accuracy Extrapolated Ab Initio Thermochemistry (HEAT), family of theoretical methods. The method known as HEAT-345(Q), in particular, is found to benefit from fortuitous error cancellation between its treatment of the zero-point energy, extrapolation errors in the Hartree-Fock and coupled cluster contributions, neglect of post-(T) core-correlation, and the basis-set error involved in higher-level correlation corrections. In addition to shedding light on a longstanding curiosity of the HEAT protocol—where the cheapest HEAT-345(Q) performs comparably to the theoretically more complete HEAT-456QP procedure—this study lays the foundation for extended HEAT variants that offer substantial improvements in accuracy relative to the established approaches.
The objective of the international collaboration between United States Department of Energy (U.S.-DOE) and Generation IV International Forum (GIF) is the development of the next generation of nuclear energy systems. The current GIF Project Arrangement (PA) on Materials (2018-2022) was revised in 2019 and extended for another 10 years (2020-2030). The Work Package 1 (“Graphite”) of the extended Project Plan (PP) on Materials specifies technical tasks and High Level Deliverables for research and development (R&D) activities related to using graphite in fuel elements, reflectors, and support structures of Very High Temperature Reactors (VHTR). The graphite tasks include specification and acquisition, qualification and development of new grades, characterization of properties, and development of behavior models. Specifically, Task 1.4 (“Graphite Oxidation Behavior”) outlines planned activities related to acute oxidation by air and chronic oxidation by impurities in the helium coolant. A final report on experimental data regarding graphite oxidation behavior is scheduled for 2022 (deliverable 3.1.1.4.a). In preparation of this deliverable, this document summarizes the R&D activities funded by U.S.-DOE from 2006 (the inception of the VHTR system arrangement) through present (2021). This report is being submitted to the GIF Graphite Working Group (GWG) to serve as input for the GWG high-level deliverable to the Project Management Board (PMB) of PA on Materials. Besides U.S.-DOE, other organizations participating to Task 1.4 of the current PA on Materials are: European Commission’s Joint Research Center (JRC), Korea Atomic Energy Research Institute (KAERI), and Japan Atomic Energy Agency (JAEA). U.S.-DOE is the main contributor on graphite oxidation R&D, with 85 % commitment of total funding during 2018-2022.
In compliance with their Comprehensive Safeguards Agreements, based on INFCIRC/153 (corrected) (International Atomic Energy Agency, 1972), States Party to the Treaty on the NonProliferation of Nuclear Weapons (NPT) are obligated to declare to the International Atomic Energy Agency (IAEA) all changes in their nuclear material inventory as well as movement of the material across boundaries of IAEA recognized material balance areas (MBA), inventories and nuclear material balances. This project addresses capabilities to detect irregularities in State reports, thus ensuring their accuracy and completeness, and in the broader context, States’ compliance with safeguards obligations of the NPT. A recent study (Henzl et al., 2022) (lead by this project’s PI) demonstrated how analysis of dynamic correlations in nuclear material movement within the entire fuel cycle of a State (viewed as a single system) can reveal variances consistent with and indicative of “irregular” activities. Expanding on this concept, novel ways to analyze State declarations themselves—again, for the State as a whole entity—will help the IAEA draw accurate safeguards conclusions and trust the validity and authenticity of Stategenerated declaration reports. Introducing new declaration analyses capabilities explored in this project will help to provide credible assurance of both the non-diversion of nuclear material from declared activities and of the absence of undeclared nuclear material and activities in the State in general.
This report presents pertinent aspects of the ~50-year United States experience in siting a mined geologic disposal repository for spent nuclear fuel (SNF), transuranic (TRU) waste, and high-level radioactive waste (HLW) as related to site selection and the staged process for site investigations as specified in the Nuclear Waste Policy Act of 1982 and generic and site-specific regulations of the US Department of Energy (DOE), US Environmental Protection Agency (EPA), and US Nuclear Regulatory Commission (NRC). The roles of the Environmental Impact Statement and guidance in international consensus standards by the International Atomic Energy Agency are also mentioned. The focus is on siting and developing the Waste Isolation Pilot Plant, an operating repository for TRU waste from atomic energy defense activities, and the proposed Yucca Mountain repository for commercial SNF and HLW. In the social dimension, the role of institutional stakeholders is described. Past national surveys related to waste management options for storage and disposal provide insight on public preferences of other stakeholders. The descriptions are intended to help other countries more fully understand the stages adopted for siting and developing repositories in the United States.
Helium is one of the dominant gases of the lunar atmosphere. Its presence is easily identified in data from the mass spectrometer at the Apollo 17 landing site. The major part of these data was obtained in lunar nighttime, where helium concentration reaches the maximum of its diurnal cyclic variation. The large night to day concentration ratio agrees with the basic theory of exospheric lateral transport reported by Hodges and Johnson (1968). A reasonable fraction of atmospheric helium atoms has a velocity in excess of the gravitational escape velocity. The result is a short average lifetime and a tenuous helium atmosphere. A description is presented of an investigation which shows that the atmosphere of the moon has two distinct components including low energy atoms, which are gravitationally bound in trajectories that intersect the lunar surface, and higher energy atoms, which are trapped in satellite orbits. The total helium abundance in the lunar corona is shown to be about 1.3 times 10 to the 30th power atoms.
The contribution of the Lamb shift to the atomization energies of some prototype molecules, BF3, AlF3, and GaF3, is estimated by a perturbation procedure. It is found to be in the range of 3-5% of the one-electron scalar relativistic contribution to the atomization energy. The maximum absolute value is 0.2 kcal/mol for GaF3. These sample calculations indicate that the Lamb shift is probably small enough to be neglected for energetics of molecules containing light atoms if the target accuracy is 1 kcal/mol, but for higher accuracy calculations and for molecules containing heavy elements it must be considered.
Energy transfer during atomic recombination on solid surfaces
The G2 atomization energies of fluorine and oxygen containing Ga compounds are greatly in error. This arises from an inversion of the Ga 3d core orbital and the F 2s or O 2s valence orbitals. Adding the Ga 3d orbital to the correlation treatment or removing the F 2s orbitals from the correlation treatment are shown to eliminate the problem. Removing the O 2s orbital from the correlation treatment reduces the error, but it can still be more than 6 kcal/mol. It is concluded that the experimental atomization energy of GaF2 is too large.
By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of mu = 0.5 bohr(-1) provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.
The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C 2 singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B 2 , C 2 , O 2 , and F 2 in the local spin density approximation (LSDA), the Perdew–Burke–Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C 2 . Here, this work shows that spin symmetry breaking in singlet C 2 , which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.
Correlation-consistent basis sets are compared with Pople-type basis sets for the calculation of atomization energies using the G2(B3LYP/MP2/CC) approach. Without a higher-level correction, the smallest errors are found for the augmented- correlation-consistent polarized valence triple zeta plus tight d basis sets. However, after inclusion of a higher-level correction, the combination of the 6-311G** basis set for the high-level correlation treatment and 6-311+G(3df,2p) for the MP2 step yields the best results. At the spin-unrestricted CCSD(T) level and for the basis set considered in this work, the G2(B3LYP/MP2/CC) approach works better than the PCIX approach for the atomization energies of the 55 G2 molecules.
Machine learning force field (ML-FF) has emerged as a potential promising approach to simulate various material phenomena for large systems with ab initio accuracy. However, most ML-FFs have been used to study the phenomena relatively close to the equilibrium ground states. In this work, we have studied a far from equilibrium system of liquid to crystal Si growth using ML-FF. Here, we found that our ML-FF based on ab initio decomposed atomic energy can reproduce all the aspects of ab initio simulated growth, from local energy fluctuations to transition temperatures, to diffusion constant, and growth rates. We have also compared the growth simulation with the Stillinger-Weber classical force field and found significant differences. A procedure is also provided to correct a systematic fitting bias in the ML-FF training process, which exists in all training models, otherwise critical results like transition temperature will be wrong.
Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.
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