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DOE OSTI2023

Realizing the potentials of density functional theory (DFT) and of the materials genome initiative (MGI)

Abstract From 1964 and 1965 to present, the wide spread utilization of an incomplete density functional theory (DFT) has led to mixed results: The second theorem of the theory asserts that the energy functional reaches its minimum if the calculation employs the ground state charge density—without providing a mechanism for finding this density. Calculations purporting to employ DFT have mostly assumed that results obtained with a judiciously selected basis set, following self-consistent iterations, are those of the ground state. The state obtained with a single basis set is a stationary one, among an infinite number of such states, with no proven relation to the actual ground state of the material. Most failures or limitations of the incomplete DFT can be traced to this error. We present results from calculations using the completed DFT. They are in excellent agreement with experiment and portend the realization of the Materials Genome Initiative.

Bagayoko, Diola↗

DOE OSTI2020

New, low-energy excitations in 107 Mo and 109 Mo

New ground-state level with spin-parity 1/2 + is established in 109 Mo, 69.8 keV below the previously reported 5/2(+) ground state in this nucleus, based on precise spectroscopy measurements of gamma radiation following spontaneous fission of 248 Cm performed using the Eurogam2 array of anti-Compton spectrometers. Analogous measurement of gamma radiation following spontaneous fission of 252 Cf, performed using the Gammasphere array, confirms the new 1/2 + ground state of 107 Mo, proposed recently and establishes the isomeric character of the 5/2 + first excited state in 107 Mo. Two beta-decaying isomers are suggested in 111 Mo nucleus based on regular energy systematics, supporting previous predictions. Low-energy excitations in Mo isotopes are interpreted and compared to calculations reported in the literature. The results suggest shape transition from prolate to oblate deformation at N >= 67.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Cross sections of 147–149 Sm( 6 Li,x) reactions for the production of 149 Tb for targeted alpha therapy

Terbium-149g (t 1/2 = 4.12 h) is of particular interest for targeted alpha therapy cancer treatment due to its ability to decay via both alpha and positron emission, making it a potential theranostic nuclide. Due to many challenges facing its production, there are limited facilities worldwide that have demonstrated the ability to produce this nuclide in quantities sufficient for medical research. Since the Cyclotron Institute at Texas A&M University is a specialized accelerator facility capable of accelerating a wide variety of ions, we are investigating production pathway options. One of the major challenges facing its production is the known co-production of the excited isomeric state, 149m Tb (t 1/2 = 4.1 min). However, this state does not decay to the ground state of 149g Tb, negating any potential contribution to its yield. Due to its short-half life, the cross section for the population of this state has never been measured. After calculating several potential reaction yields using predictive models, the reactions of 147–149 Sm( 6 Li,xn) 149 Tb were identified as candidates. Lithium-6 beams of varied energies between 45-65 MeV were impinged on enriched 147 Sm, 148 Sm, and 149 Sm targets at the Cyclotron Institute at Texas A&M University, and the reaction products were measured immediately following irradiation using high-purity germanium detectors, enabling detection of both 149m Tb and 149g Tb. Cross sections for all nuclides produced in sufficient activity in these reactions were also measured and reported here. We conclude that the population of 149m Tb is much preferred over population of the ground state for these 6 Li-induced reactions, and it is necessary to explore other options for 149g Tb production.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗

DOE OSTI2022

Electronic Configuration Assignments for UO from Electric Dipole Moment Measurements

Diatomic UO has more than 48 bound states within 10000 cm -1 of the ground state. This electronic state congestion has been attributed to interleaved states from the electronic configurations U 2+ ($5f^37s$)O 2- and U 2+ ($5f^27s^2$)O 2- , respectively. Ligand field theory predicts that each electronic configuration will exhibit states with distinguishable, characteristic vibrational and rotational constants. However, vibronic state mixing modifies the observed vibration–rotation constants, leading to uncertainty in the configurational assignments. The permanent electric dipole moment ($μ_e$) of an electronic state should also manifest a value that is characteristic of the parent electronic configuration. $μ_e$ and other electrostatic and magnetostatic properties should be less influenced by the vibronic state mixing, providing more robust indicators for configurational assignments. In the present study, we have measured the $μ_e$ values for four electronic states of UO. Here, the results clearly demonstrate that the ground state (X(1)4) and the first electronically excited state ((2)4) are derived from the U 2+ ($5f^37s$)O 2– and U 2+ ($5f^27s^2$)O 2– configurations, respectively.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Size-Dependent Lattice Symmetry Breaking Determines the Exciton Fine Structure of Perovskite Nanocrystals

The order of bright and dark excitonic states in lead-halide perovskite nanocrystals is debated. It has been proposed that the Rashba effect, driven by lattice-induced symmetry breaking, causes a bright excitonic ground state. Direct measurements of excitonic spectra, however, show the signatures of a dark ground state, bringing the role of the Rashba effect into question. We use an atomistic theory to model the exciton fine structure of perovskite nanocrystals, accounting for realistic lattice distortions. We calculate optical gaps and excitonic features that compare favorably with experimental works. The exciton fine structure splittings show a nonmonotonic size dependence due to a structural transition between cubic and orthorhombic phases. Additionally, the excitonic ground state is found to be dark with spin triplet character, exhibiting a small Rashba coupling. Here we additionally explore the effects of nanocrystal shape on the fine structure, clarifying observations on polydisperse nanocrystals.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Mapping the Electronic Structure of the Uranium(VI) Dinitride Molecule, UN 2

A combined anion photoelectron spectroscopic and relativistic electronic-structure computational study of the electronic structure of the UN 2 molecule is reported. Since the photoelectron spectrum of uranium dinitride’s negative ion, UN 2 - , (UN 2 plus an additional electron) directly reflects the electronic structure of neutral UN 2 , we have measured and relied upon the photoelectron spectrum of the UN 2 – anion as a means of mapping the electronic structure of neutral UN 2 . In addition to the electron affinity of the UN 2 ground state (the energy released when attaching an electron to UN 2 molecule), energy levels of the UN 2 excited states (electronic states with higher energies than the ground state) were well characterized by the close interplay between experiment and high-level theory. We found that both electron attachment and electronic excitation significantly bend the UN 2 molecule and elongate its U≡N bond. Implications for the activation of UN 2 are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Initial Fulcher band observations from high resolution spectroscopy in the MAST-U divertor

High resolution D$^*_2$ Fulcher band spectroscopy was used in the MAST-U divertors during Super-X and (shorter-legged) elongated divertor density ramps with D 2 fuelling from the mid-plane high-field side. In the Super-X case, the upper divertor showed ground state rotational temperatures of the D 2 molecules increasing from ~6000 K, starting at the detachment onset, to ~9000 K during deepening detachment. This was correlated with the movement of the Fulcher emission region towards the X-point, which is in turn correlated with the movement of the ionisation source. The increase in rotational temperature occurred throughout the divertor except near the divertor entrance, where ionisation was still the dominant process. Qualitative agreement was obtained between the lower and upper divertor. Similar rotational temperatures were obtained in the elongated divertor before the detachment onset, although the increase in rotational temperature during detachment was less clearly observed as less deep detachment was obtained. The measured vibrational distribution of the upper Fulcher state does not agree with a ground state Boltzmann distribution but shows a characteristically elevated population in the ν = 2 and ν = 3 bands in particular; which is strongly correlated to the rotational temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Electronic structures and pseudogap nature of the strongly correlated Kondo semimetals and insulators CeNiSn and CeRhX(X=As, Sb)

Employing temperature (T)-dependent angle-resolved photoemission spectroscopy (ARPES) near the Ce 4d absorption edge, we have investigated the electronic structures of the strongly correlated Kondo insulators (KIs) and/or Kondo semimetals of CeNiSn and CeRhX (X=As, Sb), which also belong to potential topological KIs (TKIs). Good agreement is found between the Fermi surfaces (FSs) measured at the Ce 4d→4f on resonance and those calculated and unfolded into the Ce-only Brillouin zone, supporting the crucial Ce 4f contribution to the Fermi-edge states in them. While the FSs of CeRhSb and CeNiSn are similar to each other, they are quite different from those of CeRhAs, which is understood to originate from the semimetallic Kondo ground states of CeNiSn and CeRhSb in contrast to the insulating Kondo ground state of CeRhAs. T-dependent ARPES demonstrates the existence of the Kondo resonance above the Fermi level (EF) and its T-driven decoherence in CeNiSn and CeRhSb, and the existence of the Ce 4f Kondo-like peak well below EF with a pseudogap in CeRhAs. With increasing T, the tail of the Kondo resonance in CeNiSn and CeRhSb loses its coherence, whereas the Ce 4f Kondo-like peak in CeRhAs persists up to T≥200 K. The Kondo temperatures (TKs) are estimated via the analysis of T-dependent ARPES, yielding TK≈80 K (CeNiSn), TK≈180 K (CeRhSb), and TK≫200 K (CeRhAs). High-resolution, low-T ARPES confirms the Kondo resonance just above EF in CeNiSn and CeRhSb Kondo semimetals and the KI ground state of CeRhAs with a pseudogap of Δ≈30 meV, demonstrating the importance of the coherent Kondo states in determining their potential topological properties. The differences in the T-dependent ARPES of CeNiSn and CeRhSb suggest the weaker f-c hybridization in CeNiSn than in CeRhSb (c: conduction electron), which is likely due to the more localized Ni 3d orbitals than the delocalized Rh 4d orbitals. The differences between the T-dependent ARPES of CeNiSn/CeRhSb Kondo semimetals and those of CeRhAs Kondo insulator are likely due to the smaller volume of CeRhAs than those of CeNiSn/CeRhSb.

Kang, J-S↗

DOE OSTI2024

Magnetism and finite-temperature effects in UZr 2 : A density functional theory analysis

The structure and the thermophysical properties of d-UZr 2 are investigated using 0 K density functional theory and ab initio molecular dynamics (AIMD). Modeling the true paramagnetic state of this intermetallic compound has been challenging using first-principles calculations. For the first time, we find that the generalized gradient approximation method without applying an on-site Coulomb interaction term (Hubbard U) can result in a ground state that is antiferromagnetic (AFM). We believe that this weak AFM ground state is the closest to the real paramagnetic state. We found that structure optimization at finite temperatures using AIMD is necessary to achieve this ground state instead of the non-magnetic and ferromagnetic states previously reported in the literature. Our findings indicate that applying the Hubbard U on uranium f-orbitals in this metallic system is unnecessary and not recommended, as it leads to a large overestimation of the volume and introduces an unphysical strong spin polarization. Finally, our approach results in atomic volume, thermal expansion, and heat capacities that have strong agreement with experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Potential neutron-induced γ-ray background on natural tellurium relevant to 130 Te 0 ν ββ decay searches at the CUORE and SNO+ detectors

Gamma-ray production cross-section data have been obtained for the inelastic neutron scattering reactions 126,128,130 Te(n,n'γ) at five neutron energies between 3.6 and 10 MeV. We report data for the γ-ray energy region relevant to 0ν ββ decay of 130 Te with a Q ββ value of 2527.515 keV, assuming natural-abundance tellurium, as used at CUORE and SNO+. The natural abundance of 130 Te, 128 Te, and 126 Te is 34%, 32%, and 19%, respectively. For CUORE the γ-ray cascades from the excited state in 130 Te at 2527.06 keV and in 126 Te at 2533.85 keV are of concern. For SNO+, accounting for its inferior energy resolution, an additional four levels are important in 130 Te, an additional nine levels in 128 Te, and an additional eight levels in 126 Te. Of these, we report neutron-induced γ-ray production cross sections for the strongest transitions: the 2581.15 keV level in 130 Te, the 2494.20, 2508.06, and 2630.14 keV levels in 128 Te, and the 2496.83 and 2585.46 keV level in 126 Te. Here, the largest cross-section values were found for cascade γ-ray transitions to the ground state, while direct transitions to the ground state are very weak and were not observed in the present work. Both the CUORE and SNO+ detectors, however, may not be able to distinguish between cascade transitions and direct transitions to the ground state, making the neutron-induced excitation of the 2527.06 keV state of 130 Te in particular a potential problem for 0νββ decay searches of 130Te, because it matches its Q ββ value.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Stability, electronic quantum states, and magnetic interactions of Er 3+ ions in Ga 2 ⁢O 3

Here, we report an ab initio study of phase stability, defect formation, electronic structure, and multiple magnetic, Dzyaloshinskii-Moriya, optical, hyperfine, and crystal field interactions in erbium (Er)-doped wide band gap 𝛼- and 𝛽-gallium oxides (Ga 2 ⁢O 3 ), critically important to make a foundation for both optoelectronic and quantum information applications. The chemical, structural, mechanical, and dynamical stabilities of the pristine phases are confirmed from respective negative formation energies, negative cohesive energies, favorable elastic constants, and positive phonon frequencies. The phonon dispersions indicate that the Ga-O bonds are uniform in the 𝛼-phase, while they vary in the 𝛽-phase due to the anisotropic polyhedral movement. The defect formation energy analysis confirms that both Er-doped 𝛼- and 𝛽−Ga 2 ⁢O 3 prefer Er 3+ (neutral) state. The underestimated band gaps of the pristine phases from standard density functional theory (DFT) calculations as compared to experimental values are corrected by employing the hybrid functional calculations, resulting in the indirect band gaps of 5.21 eV in 𝛼−Ga 2 ⁢O 3 and 4.94 eV in 𝛽−Ga 2 ⁢O 3 . The site preference energy analysis indicates partial occupation of Er in the octahedral site of Ga. The anisotropic nature of hyperfine tensor coefficients of Er is similar in both phases, which may be due to the occupation of Er in the same octahedral Ga site. On the other hand, the calculated magnetic exchange interaction between two Er dopants is negative for 𝛼 and positive for 𝛽, indicating an antiferromagnetic (AFM) ground state in the former and a ferromagnetic (FM) ground state in the latter. Large values of Dzyaloshinskii-Moriya interactions (DMIs) are obtained along the 𝑥 direction in the 𝛼 and along the 𝑦 direction in the 𝛽. The large DMI may support exotic magnetic textures, a promising direction for spintronic applications. The analysis of dielectric constants and refractive indices of both pristine and Er-doped phases shows a good agreement with available experimental values. The calculated optical anisotropy is slightly higher in 𝛽 than those in 𝛼, which is due to the involvement of lower symmetry in 𝛽. The crystal field coefficients (CFCs) calculated from DFT are used to analyze 4⁢𝑓 multiplets and 4⁢𝑓 −4⁢𝑓 transitions. Thus calculated lowest energy level of the first excited state to the lowest energy level of the ground state is about 1.53 µ⁢m, which is in a good agreement with available experiments, and it falls within the quantum telecommunication wavelength range.

3-dimensional systems↗

DOE OSTI2021

Ground electronic state description of thiourea coordination in homoleptic Zn 2+ , Ni 2+ and Co 2+ complexes using sulfur K -edge X-ray absorption spectroscopy

Sulfur K-edge X-ray absorption spectroscopy (XAS) was employed to experimentally characterize the coordinative bond between the thiourea (TU) or thiocarbamide ligand and transition metal (TM) ions Zn 2+ , Co 2+ and Ni 2+ in distorted tetrahedral and octahedral homoleptic coordination environments. Comparisons of XAS spectra of the free TU ligand and [Zn(TU) 4 ] 2+ , [Co(TU) 4 ] 2+ and [Ni(TU) 6 ] 2+ complexes clearly identify spectral features unique to TM 2+ –S(TU) bonding. Quantitative analysis of pre-edge intensities describes the covalency of Ni 2+ —S(TU) and Co 2+ —S(TU) bonding to be at most 21% and 9% as expressed by the S 3p contributions per TM 3d electron hole. Using relevant Ni 2+ complexes with dithiocarbamate and thioether ligands, we evaluated the empirical S 1s → 3p transition dipole integrals developed for S-donor ligands and their dependence on heteroatom substitutions. With the aid of density functional theory-based ground electronic state calculations, we found evidence for the need of using a transition dipole that is dependent on the presence of conjugated heteroatom (N) substitution in these S-donor ligands.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2025

Short-range spin freezing in the double trillium lattice spin-liquid candidate KSrFe 2 ⁢(PO 4 ) 3 revealed via 31 P NMR

A comprehensive 31 P nuclear magnetic resonance (NMR) study, combined with thermodynamic measurements and first-principles band-structure calculations, has been conducted to explore the ground state of the 𝑆=5/2 double trillium lattice antiferromagnet KSrFe 2 ⁢(PO 4 ) 3 . Our experimental results indicate that the magnetic ground state is neither a conventional three-dimensional (3D) long-range order (LRO) nor a pure gapless spin-liquid state, as conjectured previously [Boya et al., APL Mater. 10, 101103 (2022)]. Specifically, the observation of a nearly field-independent NMR linewidth below 𝑇* = (3.5 ± 0.4)⁢ K, and a significant enhancement of spin-spin relaxation rate 1/𝑇 2 below 2⁢𝑇* (where 𝑇* is the characteristic temperature identified from the magnetic susceptibility), indicate a complex magnetic ground state where spin freezing coexists with persistent dynamics. Furthermore, we argue that the lack of magnetic LRO and the persistence of strong magnetic fluctuations in KSrFe 2 ⁢(PO 4 ) 3 are unlikely to originate from intersite K/Sr disorder, rather they arise due to intrinsic magnetic frustration. In conclusion, our findings position KSrFe 2 ⁢(PO 4 ) 3 into a broader family of geometrically frustrated magnets characterized by coexisting spin freezing and pronounced antiferromagnetic fluctuations, marking it as a promising platform for investigating exotic phenomena in 3D frustrated magnets.

Exotic phases of matter↗

DOE OSTI2023

Spectroscopic quadrupole moments in 124 $\mathrm{Xe}$

The Xe isotopic chain with four valence protons above the Z=50 shell closure is an ideal laboratory for the study of the evolution of nuclear deformation. At the N=82 shell closure, 136 Xe presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to N=50, the α-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of 100 Sn. Additionally, the Xe isotopes present higher order symmetries in the nuclear deformation such as the octupole degree of freedom near N=60 and N=90 or O(6) symmetry in stable isotopes. The relevance of the O(6) symmetry has been investigated by measuring the spectroscopic quadrupole moment of the first excited states in 124 Xe. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null. A stable 124 Xe beam with energies of 4.03A MeV and 4.11 A MeV was used to bombard a nat W target at the GANIL facility. Excited states were populated via the safe Coulomb excitation reaction. The collision of the heavy ions with a large Z at low energy make this reaction sensitive to the diagonal E2 matrix element of the excited states. The recoils were detected in the VAMOS++ magnetic spectrometer and the γ rays in the AGATA tracking array. The least squares fitting code gosia was used for the analysis to extract both E2 and M1 transitional and E2 diagonal matrix elements. The rotational ground state band was populated up to the 8$^{+}_{1}$ state as well as the 2$^{+}_{2}$ and 4$^{+}_{2}$ states. Using high precision spectroscopic data to constrain the gosia fit, the spectroscopic quadrupole moments of the 2$^{+}_{1}$, 4$^{+}_{1}$, and 6$^{+}_{1}$ states were determined for the first time. The spectroscopic quadrupole moments were found to be negative, large, and constant in the ground state band underlining the prolate axially deformed ground state band of 124 Xe. Here, the present experimental data confirm that the O(6) symmetry is substantially broken in 124 Xe .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

𝛽−decay of neutron-rich 45 Cl located at the magic number 𝑁 = 28

Results from the β-decay study of 45 Cl, produced in the fragmentation of a 140-MeV/u 48 Ca beam, are presented. The half-life of 45 Cl is measured to be 513(36) ms. β – and β – 1n decay populate excited states in 45 Ar and 44 Ar, respectively, and decay schemes for both daughter nuclei are established based on γ-ray singles and γ-γ coincidence data. Comparison with shell-model calculations using the FSU interaction shows that the low-lying negative-parity states in 45 Ar are well described by single-neutron configurations near the Fermi surface, whereas positive-parity states require neutron excitations across the N = 20 shell gap, consistent with allowed Gamow–Teller decay from 45 Cl. The strong β-feeding to the 5/2 + state in 45 Ar supports a 3/2 + ground-state assignment for 45 Cl over 1/2 + . Furthermore, the high Q β – value enables population of 1p1h states above the neutron separation energy in 45 Ar, leading to positive-parity states in 44 Ar through neutron emission. Tentative spin-parity assignments for excited levels in 44 Ar are made for the first time based on comparison with shell-model predictions, and the 2978-keV level is identified as an excited 0 + state with a configuration distinct from the ground state.

39 ≤ A ≤ 58↗

DOE OSTI2025

Ultrafast optical modulation of vibrational strong coupling in ReCl(CO) 3 (2,2-bipyridine)

Polaritons – hybrid light-matter states formed from the strong coupling of a bright molecular transition with a confined photonic mode – may offer new opportunities for optical control of molecular behavior. Vibrational strong coupling (VSC) has been reported to impact ground-state chemical reactivity, but its influence on electronic excited-state dynamics remains unexplored. Here, we take a first step towards excited-state VSC by demonstrating optical modulation of the ReCl(CO) 3 (bpy), (bpy = 2,2-bipyridine) complex under VSC using femtosecond ultraviolet (UV)-pump/infrared (IR)-probe spectroscopy. We establish ground-state VSC of ReCl(CO) 3 (bpy) in a microfluidic Fabry-Pérot cavity equipped with indium tin oxide (ITO)-coated mirrors. ITO is effectively dichroic as it is reflective in the IR and transmissive in the UV-visible and therefore minimizes optical interference. Excitation with UV pump light drives ReCl(CO) 3 (bpy) into a manifold of electronic excited states that subsequently undergo non-radiative relaxation dynamics. We probe the transient response of the strongly-coupled system in the mid-IR, observing both Rabi contraction and cavity-filtered excited-state absorption signatures. We reconstruct the intrinsic response of intracavity molecules from the transient cavity transmission spectra to enable quantitative comparison with extracavity control experiments. We report no changes in the excited-state dynamics of ReCl(CO) 3 (bpy) under ground-state VSC. However, we do observe significant amplification of transient vibrational signals due to classical cavity-enhanced optical effects. This effort lays the groundwork to pursue direct excited-state VSC aimed at modulating photochemical reactivity.

cavity-enhanced spectroscopy↗

DOE OSTI2020

Dual-cone variational calculation of the two-electron reduced density matrix

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $\textit{N}$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. Further, we apply the method to computing the energies and properties of strongly correlated electrons—including atomic charges, electron densities, dipole moments, and orbital occupations—in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗