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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Excited electronic states of O2/-/.

Configuration interaction (CI) variational trial functions (which assure formally correct dissociation) and the single-configuration self-consistent-field approximation are applied to the calculation of the excited electronic states of the negatively charged oxygen molecule. The energy curves and wave functions of these states are analyzed. All the excited states are found to have equilibrium-internuclear separations at least 1 a.u. larger than the ground state. The two lowest energy states are characterized, respectively, as shape and valence Feshbach resonances.

Krauss, M.↗
DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

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

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H 5 O 2 + and Eigen H 9 O 4 + ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure–spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm –1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. In conclusion, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2015

MHD Model Results of Solar Wind Plasma Interaction with Mars and Comparison with MAVEN Observations

The crustal remnant field on Mars rotates constantly with the planet, varying the magnetic field configuration interacting with the solar wind. It has been found that ion loss rates slowly vary with the subsolar longitude, anticorrelating with the intensity of the dayside crustal field source, with some time delay, using a time-dependent multispecies MHD model. In this study, we investigate in detail how plasma properties are influenced locally by the crustal field and its rotation. Model results will be compared in detail with plasma observations from MAVEN.

Crustal↗
DOE OSTI2022

The many-body expansion for metals. I. The alkaline earth metals Be, Mg, and Ca

We examine the many-body expansion (MBE) for alkaline earth metal clusters, Be n , Mg n , Ca n ( n = 4, 5, 6), at the Møller–Plesset second order perturbation theory, coupled-cluster singles and doubles with perturbative triples, multi-reference perturbation theory, and multi-reference configuration interaction levels of theory. The magnitude of each term in the MBE is evaluated for several geometrical configurations. We find that the behavior of the MBE for these clusters depends strongly on the geometrical arrangement and, to a lesser extent, on the level of theory used. Another factor that affects the MBE is the in situ (ground or excited) electronic state of the individual atoms in the cluster. For most geometries, the three-body term is the largest, followed by a steady decrease in absolute energy for subsequent terms. Though these systems exhibit non-negligible multi-reference effects, there was little qualitative difference in the MBE when employing single vs multi-reference methods. Useful insights into the connectivity and stability of these clusters have been drawn from the respective potential energy surfaces and quasi-atomic orbitals for the various dimers, trimers, and tetramers. Through these analyses, we investigate the similarities and differences in the binding energies of different-sized clusters for these metals.

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

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1978

Graphical evaluation of relativistic matrix elements

A graphical representation of angular momentum was used to evaluate relativistic matrix elements between antisymmetrized states of many particle configurations having any number of open shells. The antisymmetrized matrix element was expanded as a sum of semisymmetrized matrix elements. The diagram representing a semisymmetrized matrix element was composed of four diagram blocks; the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials were summarized in ready to use forms. A simple step by step procedure was prescribed generally for calculating antisymmetrized matrix elements of one and two particle operators.

Huang, K. N.↗
DOE OSTI2020

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Recent investigations have emphasized the importance of uncertainty quantification (UQ) in nuclear theory. Here, we carry out UQ for configuration-interaction shell-model calculations in the 1$\textit{s}$–0$\textit{d}$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical uncertainty propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Theoretical study of the nitrogen-atom hyperfine coupling constant. II

The N hyperfine coupling constant has been computed using multireference configuration interaction (MRCI) and averaged coupled pair functional (ACPF) treatments in very large one-particle basis sets. Unlike previous calculations, no selection of configurations has been performed. The calculations again illustrate the difficulty of computing the N hyperfine coupling constant accurately. The best MRCI result of 10.7 MHz is larger than the accurate experimental value of 10.4509 MHz, while the best ACPF result (10.3 MHz) is smaller than experiment. The difference between this work and previous calculations is discussed.

Bauschlicher, Charles W., Jr.↗
DOE OSTI2025

Electromagnetic moments of 215,217 Bi: Probing shell evolution beyond N = 126

The nuclear properties of bismuth isotopes (Z = 83) , with just one valence proton above the closed spherical shell at (Z = 82) , are expected to be governed by a single unpaired proton. However, already in semimagic 209 Bi (Z = 83, N = 126) , , the magnetic moment (μ) strongly deviates from the single-particle Schmidt value. A near linear decrease in μ with the increase of N after the N = 126 magic number was observed up to N = 130 . In order to test whether this trend is kept at N > 130 and to reveal the underlying mechanisms, an investigation of 215,217 Bi (N = 132, 134) has been undertaken. The magnetic dipole and electric quadrupole moments of the I π = 9/2 - nuclear ground states in these isotopes have been measured for the first time using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). It has been shown that the linearly decreasing trend of μ( 209,211,213 Bi g ) is broken in 215,217 Bi with a nearly constant value of μ observed. Experimental data have been compared to calculations in the framework of the configuration-interaction shell model with the monopole-based universal V MU +LS interaction. The peculiarities in the behavior of μ(Bi, 9/2 - ) with increasing neutron number are explained as being due to the shell evolution, change of the neutron orbitals occupancies and strong configuration mixing beyond N = 130 . Also, the difference in the μ trends for bismuth (Z = 83) and astatine (Z = 85) isotopes with N > 126 are reproduced by the shell-model calculations. It is shown that monopole interaction plays noticeable role in the description of the peculiarities of the μ behaviour. Additionally, the extension of the application of the V MU interaction to the μ isotopic trends for heavy nuclei is important for further study of the capabilities of this promising version of the shell-model calculations.

Dipole magnetic moments↗
NASA NTRS1992

Theoretical study of hydrogen and nitrogen interactions - N-H transport cross sections and collision integrals

Potential energy curves have been calculated for the X 3Sigma(-) and 5Sigma(-) states of NH using a complete-active-space self-consistent-field/multireference configuration-interaction procedure and extensive Gaussian basis sets. An accurate dipole moment function is computed for the X 3Sigma(-) state. Transport cross sections have been calculated for the collisions of hydrogen and nitrogen atoms in their ground states. The mean transport cross sections are tabulated for collision energies in the range 0.0001-1 E(h); the mean collision integrals are listed for temperatures between 100 and 100,000 K. The ab initio energies for the 5 Sigma(-) state of NH are found to be consistent with the results of correlation studies and agree well with the prediction from combining relations using the energies of the highest spin states of H2 and N2.

Stallcop, James R.↗
DOE OSTI2021

Quantitative comparison of opacities calculated using the R -matrix and distorted-wave methods: Fe xvii

ABSTRACT We present here a detailed calculation of opacities for Fe xvii at the physical conditions corresponding to the base of the Solar convection zone. Many ingredients are involved in the calculation of opacities. We review the impact of each ingredient on the final monochromatic and mean opacities (Rosseland and Planck). The necessary atomic data were calculated with the R-matrix and the distorted-wave (DW) methods. We study the effect of broadening, of resolution, of the extent of configuration sets and of configuration interaction to understand the differences between several theoretical predictions as well as the existing large disagreement with measurements. New Dirac R-matrix calculations including all configurations up to the n = 4, 5, and 6 complexes have been performed as well as corresponding Breit–Pauli DW calculations. The DW calculations have been extended to include autoionizing initial levels. A quantitative contrast is made between comparable DW and R-matrix models. We have reached self-convergence with n = 6 R-matrix and DW calculations. Populations in autoionizing initial levels contribute significantly to the opacities and should not be neglected. The R-matrix and DW results are consistent under the similar treatment of resonance broadening. The comparison with the experiment shows a persistent difference in the continuum while the filling of the windows shows some improvement. This study defines our path to the next generation of opacities and opacity tables for stellar modelling.

Delahaye, F.↗
DOE OSTI2023

Solving the nuclear pairing model with neural network quantum states

In this work, we present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the groundstate wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗
NASA NTRS1992

H-N2 interaction energies, transport cross sections, and collision integrals

The energies for the interaction of a hydrogen atom with a nitrogen molecule have been calculated for large separation distances using a complete-active-space self-consistent-field/externally contracted configuration interaction method. H-N2 transport cross sections and collision integrals have been calculated using sudden approximations and a semiclassical description of the scattering. The values of these quantities are found to be close to the corresponding values determined from the average (isotropic) potential energy. The collision integrals are applied to determine diffusion and viscosity coefficients; the theoretical diffusion agrees well with the measured data available from experiments at low temperatures.

Stallcop, James R.↗
NASA NTRS2003

Decay Properties of K-Vacancy States in Fe X-Fe XVII

We report extensive calculations of the decay properties of fine-structure K-vacancy levels in Fe X-Fe XVII. A large set of level energies, wavelengths, radiative and Auger rates, and fluorescence yields has been computed using three different standard atomic codes, namely Cowan's HFR, AUTOSTRUCTURE and the Breit-Pauli R-matrix package. This multi-code approach is used to the study the effects of core relaxation, configuration interaction and the Breit interaction, and enables the estimate of statistical accuracy ratings. The Ksigma and KLL Auger widths have been found to be nearly independent of both the outer-electron configuration and electron occupancy keeping a constant ratio of 1.53 +/- 0.06. By comparing with previous theoretical and measured wavelengths, the accuracy of the present set is determined to be within 2 m Angstrom. Also, the good agreement found between the different radiative and Auger data sets that have been computed allow us to propose with confidence an accuracy rating of 20% for the line fluorescence yields greater than 0.01. Emission and absorption spectral features are predicted finding good correlation with measurements in both laboratory and astrophysical plasmas.

Mendoza, C.↗
DOE OSTI2024

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Finally, other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Theoretical study of the X 2Pi and A 2Sigma(+) states of CuO and CuS

Theoretical spectroscopic constants and dipole moments are determined for the X 2Pi and A 2Sigma(+) states of CuO and CuS, using extended Gaussian basis sets and incorporating correlation using both configuration interaction (CI) and coupled pair (CPF) methods. Relativistic corrections (Darwin plus mass velocity), included using first-order perturbation theory, are found to be relatively small. At the CPF level, significant configuration mixing with the 3d(9)4s(1) occupation occurs for both states, resulting in some bond shortening and a significant increase in the dissociation energy. The best spectroscopic parameters are in excellent agreement with experiment for both CuO and CuS. In analogy with CuO, CuS is predicted to have a yet unobserved 2Sigma(+) state near 10,000 per cm.

Langhoff, S. R.↗