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At least 217 records · Page 12

Collective rotation from ab initio theory

Through ab initio approaches in nuclear theory, we may now seek to quantitatively understand the wealth of nuclear collective phenomena starting from the underlying internucleon interactions. No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, as evidenced by rotational patterns for excitation energies, electromagnetic moments and electromagnetic transitions. In this review, NCCI calculations of 7–9 Be are used to illustrate and explore ab initio rotational structure, and the resulting predictions for rotational band properties are compared with experiment. We highlight the robustness of ab initio rotational predictions across different choices for the internucleon interaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The many-body electronic interactions of Fe(II)–porphyrin

Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. Furthermore, this technique is used to parse the numerous interactions of two low-lying triplet states ( 3 A 2 g and 3 E g ) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3 A 2 g state. d–π interactions, on the other hand, preferentially stabilize the 3 E g state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be{sub 2} is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be{sub 2} from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be{sub 2}, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm{sup −1}, only slightly below the 935 cm{sup −1} value derived from experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Edge counts for the auxiliary pair graph within the graphical unitary group approach

Closed-form expressions are presented for the numbers of edges in the auxiliary pair graphs (APGs) associated with non spin-orbit and spin-orbit Shavitt graphs for full configuration interaction expansions. A Shavitt graph is a visual representation of a configuration state function expansion space constructed via the graphical unitary group approach (GUGA). An APG is an organisational aid and a programmatic tool generated from a Shavitt graph. The number of edges in an APG determines bounds on the computational scaling as a function of the total numbers of electrons, orbitals, and spin multiplicities. The edge counts extend a suite of Shavitt graph statistics based on these functional parameters. The derivation and the presentation of the formulas for the edge counts has been assisted by the bra-ket interchange symmetry and the particle-hole interchange symmetry in the GUGA formalism. Furthermore, these symmetry operators produce one-to-one correspondences between various sets of edges, and this yields identities among some edge count formulas. There are 208 possible edge types. Of these, some do not contribute to two-electron operators, some are related by bra-ket interchange symmetry, and some are related by particle-hole interchange symmetry. For the remaining unique edge types, explicit expressions are derived for the numbers of edges.

74 ATOMIC AND MOLECULAR PHYSICS↗

Large-scale calculations of atomic level and transition properties in the aluminum isoelectronic sequence from Ti X through Kr XXIV, Xe XLII, and W LXII

Large-scale self-consistent multiconfiguration Dirac–Hartree–Fock subsequent relativistic configuration interaction (RCI) calculations are reported for 360 states belonging to the 30 configurations 3s{sup 2}{3l,4l,5l}, 3p{sup 2}{3d,4l}, 3s{3p"2,3d"2}, 3s{3p3d,3p4l,3p5s,3d4l"′}, 3p3d{sup 2}, 3p{sup 3} and 3d{sup 3} with l=0,1,…,n−1 and l{sup ′}=0,1,2 in 17 systems of the aluminum-like isoelectronic sequence: Ti X through Kr XXIV, Xe XLII, and W LXII. Effects from electron correlation are taken into account by means of large expansions in terms of a basis of configuration state functions (CSF) and calculated energy levels are compared with existing theoretical calculations and the NIST Atomic Spectra database. Radiative E1, E2, M1 and M2 transition rates and associated lifetimes of energy levels are presented in online tables. The uncertainties of the calculated energies are very small, on average between 0.02% and 0.05%, which aid new line identifications in laboratory and astronomical spectra and also make it possible to find and rule out misidentifications. The uncertainties of the E1 transition probabilities, based on the agreement between values in the length and velocity gauges, are estimated to be of the order 0.5% for the strong transitions and 25% for the weaker intercombination transitions. The M1 transition values are not sensitive to electron correlation and are believed to be accurate to well within 1%.

74 ATOMIC AND MOLECULAR PHYSICS↗

Spectroscopic and theoretical studies of the low-lying states of BaO{sup +}

The BaO{sup +} cation is of interest from the perspectives of electronic structure and the potential for cooling to ultra-cold temperatures. Spectroscopic data for the ion have been obtained using a two-color photoionization technique. The ionization energy for BaO was found to be 6.8123(3) eV. The ground state of BaO{sup +} was identified as X{sup 2}Σ{sup +}, and both vibrational and rotational constants were determined. Vibrationally resolved spectra were recorded for A{sup 2}Π, the first electronically excited state. These data yielded the term energy, vibrational frequency, and the spin-orbit interaction constant. Relativistic electronic structure calculations were carried out using multi-reference configuration interaction (MRCI), coupled cluster and density functional theory methods. Transition moments for the pure vibrational and A{sup 2}Π-X{sup 2}Σ{sup +} transitions were predicted using the MRCI method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ACES: Infrastructure As Code. Model Optimization and Performance Capability

Infrastructure as Code (IaC) refers to managing infrastructure (networks, physical/virtual machines, storage, and connection topology) in a descriptive model/language, rather than configuring it manually or using interactive configuration tools. Just like source code can be compiled to generate the same binary code, IaC enables generating the same environment every time it is applied. IaC is a key DevOps practice and is generally used in conjunction with continuous integration (CI) and continuous delivery (CD). In CI, all code changes are merged into a mainline branch and validated multiple times a day as developers check in their changes to the source code. In CD on the other hand, code changes are automatically packaged for a new release-to-production on a regular basis. This typically enables teams to deliver software changes much more quickly and often. Developing and managing the ACES platform using (IaC) is vital for the robust deployment and continued sustainment of this foundational computing capability. IaC and DevOps practices will help us solve many of the common challenges often encountered in developing and maintaining compute infrastructure. First, it will make the provisioning, deployment, and maintenance of the compute infrastructure across multiple environments much more efficient. Second, these processes help make the overall system much more stable by continuously testing new changes as they are introduced to the system. Third, it allows us to be much more confident of the security controls in place since they can be tested as part of the CI process and all new changes can be audited and tracked. Finally, IaC enables the ACES Platform to be adaptable to the emerging technologies due to its ability to spin up different test beds to evaluate and incorporate these technologies. This document addresses common infrastructure-management challenges, describes what happens if they are not addressed, and highlights the value of utilizing IaC to tackle them. Finally, we will provide a high-level overview of the IaC and DevOps practices being utilized by the ACES Platform team.

97 MATHEMATICS AND COMPUTING↗

Energy levels, weighted oscillator strengths, transition rates, lifetimes, hyperfine structures and isotope shifts of He-like-Sn deduced from the relativistic multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory calculations

We disclose relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for SnXLIX. Energy levels, weighted oscillator strengths, isotope shifts, hyperfine structure and Landé g{sub J} factors are calculated for 127 odd- and even-parity states as well as lifetimes and transition rates between these states. To scrutinize the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Second-Order Many-Body Perturbation Theory (MBPT) method. Additionally, the Breit interaction and leading quantum electrodynamic effects (QED) are included as perturbations in extensive relativistic configuration interaction (RCI) calculations. We signal that, our calculations for SnXLIX are made for the first time and they provide to date the most accurate and complete atomic data related to this ion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Symmetry and Shape Coexistence in 10 Be

Within the low-lying spectrum of 10 Be, multiple rotational bands are found, with strikingly different moments of inertia. A proposed interpretation has been that these bands variously represent triaxial rotation and prolate axially-deformed rotation. The bands are well-reproduced in ab initio no-core configuration interaction (NCCI) calculations. Here, we use the calculated wave functions to elucidate the nuclear shapes underlying these bands, by examining the Elliott SU(3) symmetry content of these wave functions. The ab initio results support an interpretation in which the ground-state band, along with an accompanying K = 2 side band, represent a triaxial rotor, arising from an SU(3) irreducible representation in the 0hw space. Then, the lowest excited K = 0 band represents a prolate rotor, arising from an SU(3) irreducible representation in the 2hw space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ab initio rotation in 10 Be

Ab initio theory describes nuclei from a fully microscopic formulation, with no presupposition of collective degrees of freedom, yet signatures of clustering and rotation nonetheless arise. We can therefore look to ab initio theory for an understanding of the nature of these emergent phenomena. To probe the nature of rotation in 10 Be, here we observe the predicted rotational spectroscopy from no-core configuration interaction (NCCI) calculations with the Daejeon16 internucleon interaction, and further find spectra suggestive of coexisting rotational structures having qualitatively different intrinsic deformations: one triaxial and the other with large axial deformation arising primarily from the neutrons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Molecular electric moments calculated by using natural orbital functional theory

The molecular electric dipole, quadrupole, and octupole moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-ζ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 electric moments agree satisfactorily with the corresponding experimental data and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles and multi-reference single and double excitation configuration interaction methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Role of momentum in the generator-coordinate method applied to barrier penetration

Nuclear fission at barrier-top energies is conventionally modeled by a one-dimensional Schrödinger equation applied to internal fission channels, but that treatment is hard to justify in the configuration-interaction approach to nuclear Hamiltonians. Here we show that inclusion of states of finite momentum by the generator coordinate method (GCM) considerably extends the range of energies at which GCM-based Hamiltonians could reproduce the Schrödinger treatment. Furthermore, the transmission probabilities for crossing the barrier are calculated by a discrete version of Kohn's variational method, which may also be useful for other systems of interacting fermions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Energy levels and radiative transition rates for Ba XLVIII

Highlights: • Lowest 431 levels of Ba XLVIII are calculated. • Radiative data for E1, E2, M1 and M2 transitions from the lowest 3 levels to 431 levels are presented. • Lifetimes for lowest 431 fine structure levels are provided. Energy levels and radiative rates are reported for transitions in F-like Ba XLVIII. Configuration interaction has been included among 27 configurations (generating 431 levels) over a wide energy range up to 618 Rydbergs, and the fully relativistic multi-configurational Dirac–Fock method adopted for the calculations. To assess the accuracy, calculations have also been performed with the flexible atomic code, FAC. Radiative rates, oscillator strengths and line strengths are reported for all electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions from the lowest 3 levels, although calculations have been performed for a much larger number of levels. We have made comparisons of our results with existing available results and a good agreement has been achieved. Additionally, lifetimes for all 431 levels are listed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

Abstract For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S 0 S 1 ) and the multiexcitonic state ( 1 TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc‐pV n Z series of basis sets, that both the aug‐cc‐pVDZ and 6–311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Radiative rates for E1, E2, M1, and M2 transitions in F-like ions with 55≤Z≤73

Energy levels, radiative rates and lifetimes are reported for 19 F-like ions with 55≤Z≤73, among 113 levels of the 2s{sup 2}2p{sup 5}, 2s2p{sup 6}, 2s{sup 2}2p{sup 4}3ℓ, 2s2p{sup 5}3ℓ, and 2p{sup 6}3ℓ configurations. The general-purpose relativistic atomic structure package (grasp) has been adopted for the calculations, and radiative rates (and other associated parameters, such as oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are made with earlier available theoretical and experimental energies, especially for Ba XLVIII. Nevertheless, calculations have also been performed with the flexible atomic code (fac), and with a much larger configuration interaction with up to 38 089 levels, for further accuracy assessments, particularly for energy levels.

74 ATOMIC AND MOLECULAR PHYSICS↗

Pair extended coupled cluster doubles

The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreover, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Energy decomposition analysis for exciplexes using absolutely localized molecular orbitals

An energy decomposition analysis (EDA) scheme is developed for understanding the intermolecular interaction involving molecules in their excited states. The EDA utilizes absolutely localized molecular orbitals to define intermediate states and is compatible with excited state methods based on linear response theory such as configuration interaction singles and time-dependent density functional theory. The shift in excitation energy when an excited molecule interacts with the environment is decomposed into frozen, polarization, and charge transfer contributions, and the frozen term can be further separated into Pauli repulsion and electrostatics. These terms can then be added to their counterparts obtained from the ground state EDA to form a decomposition of the total interaction energy. The EDA scheme is applied to study a variety of systems, including some model systems to demonstrate the correct behavior of all the proposed energy components as well as more realistic systems such as hydrogen-bonding complexes (e.g., formamide-water, pyridine/pyrimidine-water) and halide (F - ,Cl - )-water clusters that involve charge-transfer-to-solvent excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗