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Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET
The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
First-principles molten salt phase diagrams through thermodynamic integration
Precise prediction of phase diagrams in molecular dynamics simulations is challenging due to the simultaneous need for long time and large length scales and accurate interatomic potentials. Here, we show that thermodynamic integration from low-cost force fields to neural network potentials trained using density-functional theory (DFT) enables rapid first-principles prediction of the solid–liquid phase boundary in the model salt NaCl. We use this technique to compare the accuracy of several DFT exchange–correlation functionals for predicting the NaCl phase boundary and find that the inclusion of dispersion interactions is critical to obtain good agreement with experiment. Importantly, our approach introduces a method to predict solid–liquid phase boundaries for any material at an ab initio level of accuracy, with the majority of the computational cost at the level of classical potentials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Symmetry-correct bonding in density functional theory calculations for delta phase Pu
The long-held conclusion that magnetic order in delta phase Pu makes the structure mechanically unstable in density functional theory calculations is incorrect if the magnetic order is allowed to be non-collinear. The non-collinear 3Q spin structure is intrinsically cubic and makes all structurally equivalent bonds equivalent in their bonding character. Applied to density functional theory calculations on delta phase Pu, the 3Q spin structure results in elastic constants and phonons with the correct symmetry. Finally, the calculated phonon dispersion agrees better with experiment than previous calculations, and the calculated thermal expansion shows the unique behavior seen experimentally: it is negative.
36 MATERIALS SCIENCE↗
Spatial correlation functions of paracrystals with radial symmetry
Here, we develop a phenomenological model to describe the structure of radially symmetric paracrystals whose long-range order are destroyed by propagation of particle fluctuations. General expressions are derived for the spatial correlation functions in one-, two-, and three-dimensional spaces. And the spatial correlation in paracrystals in reciprocal space is further discussed and clarified. The developed method can be used to quantitatively analyze the microstructure of paracrystalline materials in both real and reciprocal spaces via scattering experiments and computer simulations.
36 MATERIALS SCIENCE↗
Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory
Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn–Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. Here, as in other contexts, correct asymptotic behavior can be enforced via “optimal tuning” based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with “extended” (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.
74 ATOMIC AND MOLECULAR PHYSICS↗
Equilibrium Dynamics of Infinite-Range Quantum Spin Glasses in a Field
We determine the low-energy spectrum and Parisi replica-symmetry-breaking function for the spin-glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ( h ) fields. We show that, for all h , the spin-glass state has full replica symmetry breaking and the local spin spectrum is gapless, with a spectral density that vanishes linearly with frequency. These results are obtained using an action functional—argued to yield exact results at low frequencies—that expands in powers of a spin-glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p -rotor model at nonzero h : here, the spin-glass state has one-step replica symmetry breaking and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted. Published by the American Physical Society 2024
Tikhanovskaya, Maria↗
Gauge dependence of the quark gap equation: An exploratory study
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Universal approximation of symmetric and anti-symmetric functions
In this work, we consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ. While the approximation still suffers from the curse of dimensionality, to the best of our knowledge, these are the first results in the literature with explicit error bounds for functions with symmetry or anti-symmetry constraints
97 MATHEMATICS AND COMPUTING↗
Classical symmetries and the Quantum Approximate Optimization Algorithm
Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.
97 MATHEMATICS AND COMPUTING↗
Hyperstealth dark matter and long-lived particles
A new dark matter candidate is proposed that arises as the lightest baryon from a confining 𝑆𝑈(𝑁) gauge theory which equilibrates with the Standard Model only through electroweak interactions. Surprisingly, this candidate can be as light as a few GeV. The lower bound arises from the intersection of two competing requirements: (i) the equilibration sector of the model must be sufficiently heavy, at least several TeV, to avoid bounds from colliders, and (ii) the lightest dark meson (that may be the dark 𝜂′, 𝜎, or the lightest glueball) has suppressed interactions with the SM and must decay before big bang nucleosynthesis. The low-energy dark sector consists of one flavor that is electrically neutral and an almost electroweak singlet. The dark matter candidate is the lightest baryon consisting of 𝑁 of these light flavors leading to a highly suppressed elastic scattering rate with the Standard Model (SM). The equilibration sector consists of vectorlike dark quarks that transform under the electroweak group, ensuring that the dark sector can reach thermal equilibrium with the SM in the early Universe. The lightest dark meson lifetimes vary between 10 −3 ≲ 𝑐𝜏 ≲ 10 7 m, providing an outstanding target for LHC production and experimental detection. We delineate the interplay between the lifetime of the light mesons, the suppressed direct detection cross section of the lightest baryon, and the scale of equilibration sector that can be probed at the LHC.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics
We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.
97 MATHEMATICS AND COMPUTING↗
Wave functions of multiquark hadrons from representations of the symmetry groups S n
Construction of the wave functions of multiquark hadrons by a traditional method based on the tensor products of colors, flavors, spins (and orbital) parts becomes quite complex when quark numbers grow n = 5 , 6 … 12 , as it gets difficult to satisfy the requirements of Fermi statistics. Our novel approach is focused directly on representations of the permutation symmetry generators. After showing how C 3 is manifested in the wave functions of (excited) baryons, we use it to construct the wave functions for a set of pentaquarks and hexaquarks ( n = 5 , 6 ). We also have some partial results for larger systems, with n = 9 and 12, and even beyond that as far as n = 24 . Published by the American Physical Society 2024
Miesch, Nicholas (ORCID:0000000205937535)↗
Geometry, spin coupling, and dielectric control of redox potentials in [4Fe–4S] Clusters
Iron–sulfur (Fe–S) clusters are common biological cofactors that facilitate vital redox reactions. Despite extensive research, the molecular basis of redox potential tuning in ferredoxin-like proteins remains an active area of debate. In this study, we combine statistical analysis of over one thousand [4Fe–4S]-containing protein structures from the Protein Data Bank (PDB) with broken-symmetry and extended broken-symmetry density functional theory to examine how cysteine ligand orientations and environmental screening affect redox properties of the clusters. We identified five main ligand configurations, three of which are predominant in natural structures. Among these, the adiabatic electron affinity differs by less than 0.1 V, indicating that, while geometry plays a secondary role, it allows localized fine-tuning of redox properties. In contrast, electrostatic and solvation effects primarily determine the overall potential range.
Computational Chemistry↗
Shape polarization in the tin isotopes near N = 60 from precision g-factor measurements on short-lived 11/2 - isomers
The g factors of 11/2 - isomers in semimagic 109 Sn and 111 Sn (isomeric lifetimes $\tau$ = 2.9(3) ns and $\tau$ = 14.4(7) ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses LaBr3 detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, g(11/2 - ; 109 Sn) = -0.186(8) and g(11/2 - ; 111 Sn) = -0.214(4), are significantly lower in magnitude than those of the 11/2 - isomers in the heavier isotopes and depart from the value expected for a near pure neutron h 11/2 configuration. Broken-symmetry density functional theory calculations applied to the sequence of 11/2 - states reproduce the magnitude and location of this deviation. The g(11/2 - ) values are affected by shape core polarization; the odd Oh 11/2 neutron couples to J π = 2 + , 4 + , 6 + ... configurations in the weakly-deformed effective core, causing a decrease in the g-factor magnitudes.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Origin of Ferromagnetic Exchange Coupling in Donor–Acceptor Biradical Analogues of Charge-Separated Excited States
A new donor–acceptor biradical complex, Tp Cum,Me Zn(SQ-VD) (Tp Cum,Me Zn + = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. Here, the magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with $J_{SQ-VD}$ = +77 cm –1 (H = -2$J_{SQ-VD}\bar{S}_{SQ}·\bar{S}_{VD}$) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in Tp Cum,Me Zn(SQ-VD) can be compared with that of the related donor–acceptor biradical complex Tp Cum,Me Zn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where $J_{SQ-NN}$ ≅ +550 cm –1 . This represents a dramatic reduction in the biradical exchange by a factor of ~7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between Tp Cum,Me Zn(SQ-VD) and Tp Cum,Me Zn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQ SOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in Tp Cum,Me Zn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VD LUMO and NN LUMO ) with the SOMO of the SQ radical (SQ SOMO ) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between Tp Cum,Me Zn(SQ-VD) and Tp Cum,Me Zn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the Tp Cum,Me Zn(SQ-VD) ground state, and the intrinsically weaker mixing between the VD LUMO and the SQ SOMO compared to that observed for Tp Cum,Me Zn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet–triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces
Here, this paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C 5 H 5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree–Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Magnetic Blocking in Fluoflavine Radical-Bridged Dilanthanide Complexes
Magnetic exchange coupling is difficult to foster in polynuclear lanthanide (Ln) complexes and poorly understood. While coupling Ln ions through closed-shell ligands is inherently weak due to the contracted 4f orbitals, placing open-shell ligands instead has proven to promote orders of magnitude stronger coupling, giving rise to single-molecule magnets (SMMs) innate to real magnetic memory effect in the case of the anisotropic Ln ions. Notably, the impact of radical bridges with differing oxidation states on magnetic blocking remains unexplored due to lack of Ln SMMs with radicals in two distinct charge states. Herein, the first dilanthanide complexes (Ln = Gd, Dy) containing fluoflavine (flv) bridges, [(Cp* 2 Ln) 2 (μ-flv z )]X, (where X = [Al(OC{CF 3 } 3 ) 4 ] − (z = 1−•), 1-Ln; X = 0 (z = 2−), 2-Ln; X =[K(crypt-222)] + (z = 3−•), 3-Ln) are reported. 1-Ln and 3-Ln, comprising the flv 1−• and flv 3−• radical bridges, were investigated via single-crystal X-ray diffraction (SCXRD), ultraviolet−visible (UV−vis) spectroscopy, Superconducting Quantum Interference Device (SQUID) magnetometry, high-field electron paramagnetic resonance (HF-EPR) spectroscopy and broken-symmetry density functional theory (BS-DFT) calculations. 1-Dy and 3-Dy constitute the first SMMs innate to radicals in two differing oxidation states. 1-Dy exhibits a spin-reversal barrier U eff of 28.36 cm −1 and open magnetic hysteresis loops below 3 K. By contrast, 3-Dy displays a much higher U eff of 143(2) cm −1 and open hysteresis loops until 9.5 K, representing a record for dilanthanide SMMs containing an organic radical bridge. The boost in SMM properties in 3-Dy is attributed to spin-phonon coupling and improved frontier orbital structure. This study paves the way for advanced design strategies of polynuclear Ln SMMs.
Benner, Florian [Michigan State Univ., East Lansin↗