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At least 217 records · Page 12

Engineering infinite-range SU($\textit{n}$) interactions with spin-orbit-coupled fermions in an optical lattice

Here, we study multilevel fermions in an optical lattice described by the Hubbard model with on-site SU($\textit{n}$) -symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all SU($\textit{n}$)-symmetric couplings. Raman pulses that address internal spin states modify the atomic dispersion relation and induce spin-orbit coupling, which can act as a synthetic inhomogeneous magnetic field that competes with the SU($\textit{n}$) exchange interactions. We investigate the mean-field dynamical phase diagram of the resulting model as a function of $\textit{n}$ and different initial configurations that are accessible with Raman pulses. Consistent with previous studies for $\textit{n}$ = 2 , we find that for some initial states the spin model exhibits two distinct dynamical phases that obey simple scaling relations with $\textit{n}$. Moreover, for $\textit{n}$ > 2 we find that dynamical behavior can be highly sensitive to initial intraspin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth-metal(-like) atoms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Exploring Spin‐Orbit Effects in a [Cu 6 Tl] + Nanocluster Featuring an Uncommon Tl−H Interaction

Reaction of [CuH(PPh 3 )] 6 with 1 equiv. of Tl(OTf) results in formation of [Cu 6 TlH 6 (PPh 3 ) 6 ][OTf] ([1]OTf]), which can be isolated in good yields. Variable-temperature 1 H NMR spectroscopy, in combination with density functional theory (DFT) calculations, confirms the presence of a rare Tl−H orbital interaction. According to DFT, the 1 H chemical shift of the Tl-adjacent hydride ligands of [1] + includes 7.7 ppm of deshielding due to spin-orbit effects from the heavy Tl atom. In conclusion, this study provides valuable new insights into a rare class of metal hydrides, given that [1][OTf] is only the third isolable species reported to contain a Tl−H interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ghost states and surface structures of the charge density wave kagome metal ScV 6 Sn 6

In this work, we investigate the high-temperature phase of the kagome metal ScV 6 Sn 6 using scanning tunneling microscopy/spectroscopy (STM/S) and density functional theory calculations. STM topographic images of the cleaved sample reveal two distinct surface terminations: flat islands with Sn termination and trenches terminated by kagome layers with Sn as the outermost atomic layer. STS measurements on the Sn-terminated and kagome-terminated surfaces show significant differences, in particular the presence of large density of states near the Fermi level in the former case. Our first-principles calculations reveal that the charge density on the kagome-terminated surface gives rise to “ghost states” which show intensity away from surface atoms, arising due to hybridization of orbitals above the surface. These states can obscure the intrinsic properties of the surface, potentially leading to misattribution of the surface termination. This underscores the need for careful interpretation in STM studies, especially when discerning surface states of localized states. Understanding the surface structure of this versatile quantum material provides essential information for interpreting surface-sensitive experiments, tailoring material properties, engineering interfaces, and controlling stability and reactivity. This knowledge paves the way for further exploration and potential applications of kagome lattice materials in various fields, including quantum computing, topological physics, and advanced electronic devices.

36 MATERIALS SCIENCE↗

Selective carboxylation of alkenes with CO 2 to form unsaturated carboxylic acid on Sc-exchanged MFI zeolite

Utilization of CO 2 in chemical synthesis as C1 carbon feedstock to introduce a carboxylic group into alkene is valuable for producing unsaturated carboxylic acids. Selective carboxylation of alkenes at targeted positions can be used to regulate the production of such specific unsaturated carboxylic acids or functionalize hydrocarbon plastics that possess residual C=C double bonds. In this study, we investigated the carboxylation of 1-butene and 2-butene (as representative alkene) with CO 2 on Sc-exchanged MFI zeolites using density functional theory calculations. Here, we find that similar to ethylene, the carboxylation of butene is also rate-limited by the β–H transfer. We examined carboxylation at the C1 and C2 positions of 1-butene and cis and trans isomers for 2-butene. Based on activation barriers of the β–H transfer, our results demonstrate that Sc-MFI zeolite preferably carboxylates at the terminal position of butene. In the case of 2-butene, carboxylation of the trans isomer is more favorable than the cis isomer. Furthermore, We show that the energy of degenerate orbitals of C, O and H atoms (involved in the β–H transfer) in the metallalactone ring regulates the activation energy of the β–H transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mapping valence electron distributions with multipole density formalism using 4D-STEM

Recent advancement in aberration correction and detector technology opened a door to various applications using 4D-STEM, which yields a diffraction pattern for each scanning position within a crystal unit-cell in scanning transmission electron microscopy (STEM) and generates incredible amounts of data in momentum space. Currently 4D-STEM analysis relies on the center-of-mass of the diffraction patterns in electric field and charge density mapping. It only derives the total projected charge density and is limited to phase objects, e.g. extremely thin samples. Here, we propose a new analytical method to accurately map aspherical valence electron distributions with atom-centered multipolar functions formalism using the whole 4D-STEM dataset. We demonstrate that, with the full dynamical calculations for various sample thicknesses, the method is sensitive not only to the miniscule charge transfer, but also to the atomic site symmetry and aspherical electron orbitals. The process of the refinement is much more robust and reliable than quantitative convergent beam electron diffraction.

4D-STEM↗

Linear versus Bent Uranium(II) Metallocenes—A Local Vibrational Mode Study

Uranium metallocenes have recently attracted attention driven by their use as catalysts in organometallic synthesis. In addition to bent U(IV) and U(III), an U(II) metallocene [(η 5 -C 5 i Pr 5 ) 2 U] was synthesized with an unusual linear Cp–U–Cp angle. Here, in this work, we investigated 22 U(II) metallocenes, (i) assessing the intrinsic strength of the U-ring interactions in these complexes with a novel bond strength measure based on our local vibrational mode analysis and (ii) systematically exploring what makes these U(II) metallocenes bent. We included relativistic effects through the NESCau Hamiltonian and complemented the local mode analysis with natural bonding orbital (NBO) and quantum theory of atoms in molecules (QTAIM) data. Our study led to the following results: (i) reduction of bulky U-ring ligand substituents does not lead to bent complexes for alkyl substituents ( i Pr and i Bu) in contrast to SiMe 3 ring substituents, which are all bent. (ii) The most bent complexes are [(η 5 -C 5 H 4 SiMe 3 ) 2 U] (130°) and [η 5 -P 5 H 5 ) 2 U] (143°). (iii) Linear complexes showed one hybridized NBO with s/d character, while bent structures were characterized by s/d/f mixing. (iv) We did not observe a correlation between the strength of the U-ring interaction and the amount of the ring-U-ring bend; the strongest interaction was found for [η 5 -Cp) 2 U] and the weakest for [η 5 -P 5 H 5 ) 2 U]. In conclusion, our results provide a foundation for the design of U(II) metallocenes with specific physicochemical properties and increased reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidation of an Unusually Long Pu–N Bond in a Plutonium(III)-Tetrazolate Complex

Four trivalent, f-element tetrazolate hydrate complexes [M(H 2 O) 9 ](Hdtb) 3 ·nH 2 O (Nd1, n = 7 and Pu1, n = 9; dtb 2– = 1,3-di(tetrazolate-5-yl)benzene) and [M(Hdtb)(H 2 O) 8 ](dtb)·11H 2 O (Nd2 and Pu2) were prepared using metathesis reactions. These complexes contain hydrated M(III) cations, but in the latter complexes, Nd2 and Pu2, one of the water molecules has been displaced by a long interaction between the M(III) cation and a Hdtb – anion. Notably, the Pu(III)–N bond in Pu2, representing the longest IX Pu(III)–N ( IX = nine coordinate) bond reported has a length of 2.8338(15) Å and is slightly shorter than the Nd(III)–N bond length of 2.8425(13) Å in Nd2. Analysis of bond lengths, Wiberg bond indices (WBI), natural localized molecular orbitals (NLMOs), and quantum theory of atoms in molecules (QTAIM) reveals that the metal contribution to the Pu(III)–N bond is marginally greater than that of the Pu(III)–OH 2 bonds in Pu2 and the Nd(III)–N bond in Nd2. Thus, this rather long M–N interaction provides an example where the expectation that An(III) compounds exhibit greater covalency with soft donor ligands compared to harder ligands fails. Furthermore, the absorption spectra of Pu1 and Pu2 further support this observation, highlighting a surprising degree of similarity in their electronic structures.

Covalent bonding↗

Dynamically tunable multicolor emissions from zero-dimensional Cs 3 LnCl 6 (Ln: europium and terbium) nanocrystals with wide color gamut

This study demonstrates dynamically tunable multicolor emissions from a single component, zero-dimensional (0-D) cesium europium chloride (Cs 3 EuCl 6 ) and cesium terbium chloride (Cs 3 TbCl 6 ) nanocrystals (NCs). Highly uniform colloidal Cs 3 EuCl 6 and Cs 3 TbCl 6 NCs are synthesized via the heating-up method. Excitation-wavelength-dependent multicolor emissions from Cs 3 EuCl 6 and Cs 3 TbCl 6 NCs are observed. Under excitation of 330–400 nm, both NCs exhibit blue photoluminescence (PL). Under wavelengths shorter than 330 nm, characteristic red and green emissions are observed from Cs 3 EuCl 6 and Cs 3 TbCl 6 , respectively, owing to the atomic emissions from the f-orbitals in trivalent europium (Eu 3+ ) and terbium (Tb 3+ ) ions. Cs 3 EuCl 6 and Cs 3 TbCl 6 NCs exhibit broadband excitation spectra and enhanced absorption properties. Particularly, Cs 3 EuCl 6 NCs exhibit a very narrow full-width at half-maximum in both blue and red PL and no overlap between the two spectra. Further, the photophysical properties of these NCs are further investigated to understand the multicolor PL origins by time-resolved and temperature-dependent PL measurements. Finally, the potential applications of Cs 3 EuCl 6 and Cs 3 TbCl 6 NCs as anti-counterfeiting inks for high-level security are demonstrated. Given their broadband excitation with enhanced absorption properties and dynamically tunable colors with a wide color gamut, Cs 3 EuCl 6 and Cs 3 TbCl 6 NCs have great potential as novel multicolor NC emitters for many emerging applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Unveiling the ambipolar carrier transport property of SnO 2–X for multiple-functional interlayers in perovskite solar cells

Tin oxides are the most promising electron transport layers in perovskite solar cells. An ambipolar carrier transport property has been recently demonstrated which enables a simple interconnection structure for all-perovskite tandem solar cells. However, the underlying mechanism for its ambipolar behavior is unclear which cannot be explained by the intrinsic defects in SnO 2-x . Here by using density functional theory calculations, we unveil the origin of the ambipolar carrier transport of non-stoichiometry SnO 2-x with a structure of SnO embedded in SnO 2 matrix. The hybridization of O 2p and Sn 5s orbitals of SnO introduces mid-gap states in the bandgap of SnO 2 , enabling hole transport property for SnO 2-x when x is > 0.2. Increasing the percentage of SnO in SnO 2-x significantly enhances the hole transport capability of SnO 2-x due to the enlarged Sn-O-Sn angles that increases orbital overlapping between O and Sn atoms, thus providing strategies for the further tuning of the carrier transport properties of SnO 2-x by compositional and structural designs.

14 SOLAR ENERGY↗

Photoionization branching ratios of spin-orbit doublets far above thresholds: Interchannel and relativistic effects in the noble gases

Photoionization branching ratios of all of the spin-orbit doublets in the noble gas atoms Ne, Ar, Kr, and Xe have been investigated theoretically at energies well above the thresholds. The results confirm in all cases that the general behavior of the branching ratios is to decrease monotonically below their statistical value with increasing photon energy. Here, this effect gets more pronounced with increasing Z. In addition, the branching ratios can be strongly affected by interchannel coupling with inner shell photoionization channels. Although these effects are strongest in the neighborhood of the inner shell thresholds, they can persist over a broad range of energies,

74 ATOMIC AND MOLECULAR PHYSICS↗

Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides (Final Report)

The overarching goal of this research program, as originally delineated in the proposal “Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides” was to develop a predictive, chemistry-driven understanding of the impact of the phonon behavior on thermal properties of bulk layered materials. At finite temperatures, atomic vibrations (phonons) strongly impact the thermodynamics, thermal and electrical transport, and phase-switching properties of functional materials. In particular, soft phonon modes and strongly anharmonic potentials can have spectacular consequences, including structural phase transitions (for example in ferroelectrics and phase-change memory materials), metal-insulator transitions, and extreme thermal resistance preventing heat propagation. Bulk materials with highly-anisotropic bonding may provide unique strategies to induce soft-phonon modes and lattice instabilities. Recently, increasingly detailed investigations of the lattice dynamics in layered materials have been made possible by the advent of first-principles phonon calculations and advanced characterization techniques based on neutron and X-ray scattering. However, due to the lack of studies in which composition and bonding character are systematically varied, there are still fundamental questions regarding the impacts of anisotropic bonding and anharmonicity on lattice stability and thermal transport. One of the major goals of this research program is therefore to address this gap by coherently tuning bonding anisotropy and anharmonicity across families of related compounds. Such approaches have revealed new strategies for exploiting structural anisotropy in quasi-1D and 2D bulk materials to obtain tailored functional properties. This project systematically explored the lattice dynamics, phase stability, and transport properties in bulk layered materials by using both composition and applied pressure to tune the degree of bonding anisotropy and anharmonicity. To accomplish this work, we combined i) single-crystal growth of key material systems with tunable anisotropy, ii) in-situ high-temperature/high-pressure characterization of structure and phonons to probe bonding anisotropy and anharmonicity, including state-of-the-art inelastic X-ray scattering (IXS) and inelastic neutron scattering (INS), and iii) first-principles simulations leveraging large-scale computing to identify the fundamental origins of the observed effects, by relating atomic structure and dynamics to electronic orbital interactions. Finally, we modeled and verified the impact of the phonon behavior on thermal transport to identify new strategies for a-priori design of thermal conductivity. Our integrated collaborative approach helped to systematically unravel the effects of anisotropy and bonding anharmonicity on phonon transport, thermodynamics, and thermal properties of complex anisotropic materials.

30 DIRECT ENERGY CONVERSION↗

Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides. Final Report

The overarching goal of this research program, as originally delineated in the proposal “Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides” was to develop a predictive, chemistry-driven understanding of the impact of the phonon behavior on thermal properties of bulk layered materials. At finite temperatures, atomic vibrations (phonons) strongly impact the thermodynamics, thermal and electrical transport, and phase-switching properties of functional materials. In particular, soft phonon modes and strongly anharmonic potentials can have spectacular consequences, including structural phase transitions (for example in ferroelectrics and phase-change memory materials), metal-insulator transitions, and extreme thermal resistance preventing heat propagation. Bulk materials with highly-anisotropic bonding may provide unique strategies to induce soft-phonon modes and lattice instabilities. Recently, increasingly detailed investigations of the lattice dynamics in layered materials have been made possible by the advent of first-principles phonon calculations and advanced characterization techniques based on neutron and X-ray scattering. However, due to the lack of studies in which composition and bonding character are systematically varied, there are still fundamental questions regarding the impacts of anisotropic bonding and anharmonicity on lattice stability and thermal transport. One of the major goals of this research program is therefore to address this gap by coherently tuning bonding anisotropy and anharmonicity across families of related compounds. Such approaches have revealed new strategies for exploiting structural anisotropy in quasi-1D and 2D bulk materials to obtain tailored functional properties. This project systematically explored the lattice dynamics, phase stability, and transport properties in bulk layered materials by using both composition and applied pressure to tune the degree of bonding anisotropy and anharmonicity. To accomplish this work, we combined i) single-crystal growth of key material systems with tunable anisotropy, ii) in-situ high-temperature/high-pressure characterization of structure and phonons to probe bonding anisotropy and anharmonicity, including state-of-the-art inelastic X-ray scattering (IXS) and inelastic neutron scattering (INS), and iii) first-principles simulations leveraging large-scale computing to identify the fundamental origins of the observed effects, by relating atomic structure and dynamics to electronic orbital interactions. Finally, we modeled and verified the impact of the phonon behavior on thermal transport to identify new strategies for a-priori design of thermal conductivity. Our integrated collaborative approach helped to systematically unravel the effects of anisotropy and bonding anharmonicity on phonon transport, thermodynamics, and thermal properties of complex anisotropic materials.

36 MATERIALS SCIENCE↗

Accelerating Biomimetic Solar - Energy Harvesting: Mapping the Interaction Landscape of Plasmonic-Excitonic Hybrid Nanosystems (Final Report)

In general, excitonic and plasmonic nanoscale materials in close proximity show high potential for significant breakthroughs in energy related materials research. The interactions between these two kinds of materials result in coupled optical transitions (plexcitons), distinct from those of both the individual exciton and plasmon as well as from those of the sum of their constituents (synergistic effects). By linking together materials-research and physical-research approaches, this project contributes to a concerted approach on nanomaterials energy research. The project’s overall goal is to accelerate the development of well-defined plexcitonic model systems consisting of carefully engineered plasmonic and excitonic nanomaterial— essential for both gaining a fundamental understanding of plexcitonic nanomaterials and the development of novel design principles for biomimetic solar energy harvesting. During the 3-year project period and the terminal renewal with limited support for a 12-month period, we successfully synthesized and characterized (1) a robust excitonic nanomaterial and (2) a library of plasmonic nanoparticles as well as developed (3) a microfluidic platform for homogenous nanosynthesis as summarized below: (1) Robust Excitonic Nanomaterial. Supramolecular assemblies are Nature’s most successful material system for solar energy harvesting. However, photovoltaic devices based on artificial supramolecular assemblies continue to be stymied by disappointing efficiencies and poor stability. The conceptual failure may lie in current solar cell architectures, which rely on solidifying supramolecular assemblies as an ensemble into a solid matrix, neglecting the intrinsic fragility of the assemblies’ internal structure, thus disrupting or even destroying their delicate optoelectronic properties, that is, delicate Frenkel excitonic properties. Supramolecular assemblies may finally serve as usable light harvesting material systems for solar energy conversion technologies, only if they meet the following criteria: (a) Stability, that is, the fragile structure including its delicate Frenkel excitonic character needs to be stable, (b) Robustness, that is, resistant against elevated and fluctuating temperatures, and (c) Viability for device integration, that is, capable of being immobilized onto solid substrates. Here, by developing a nanocomposite via a tunable, cage-like scaffold design, we successfully provided stable supramolecular nanocomposites, that inhabit robust Frenkel excitons despite harming environmental conditions such as extreme heat stress. (2) Library of Plasmonic Nanoparticles. Naturally, current models describing plasmonic hybrid quantum states—plasmonic hybridizations—parallel those developed for molecular orbitals, equating individual plasmonic nanostructures with “atoms” and the plasmonic nanoassemblies with “molecules.” In analogy to organic synthesis, a suitably robust fabrication method would allow for “atom-like” manipulation of “molecule-like” plasmonic nanoassemblies; of high value for next-generation energy nanotechnologies. Despite this frequent comparison, current plasmonic nanoassembly fabrication methods favor top-down templating over wet-chemical synthesis, however, achieving precise control over nanostructure’s geometry and surface characteristics remain an art and a scientific challenge. The conceptual failure may lie in the current wet-chemical synthesis paradigm, as it relies on the accessibility of a multi-dimensional synthesis parameter space through limited, rather one-dimensional synthesis procedures by employing step-by-step approaches. Solution-based nanoarchitectonics for rational design of precisely built plasmonic nanoassemblies via solution-based fabrication may finally be possible only if multi-dimensional syntheses approaches are available that allow for comprehensive control over the plasmonic nanomaterials’ (a) Structural Properties and (b) Surface Properties. Here, by developing an innovative multidimensional 1,3-propanediol based polyol synthesis, we successfully provided control over the plasmonic building-block’s geometry (size and shape) together with its surface characteristics. Our results present a critical step toward the vision of a “periodic table-like” system for plasmonic materials based on straightforward wet-chemical syntheses for energy nanotechnologies. Developing deliberate modifications on this synthesis, we generated a library of plasmonic nanostructures covering the vast parameter space—opening the door for fundamental investigation of plexcitonic model systems. (3) Microfluidic Platform for Homogenous Nanosynthesis. Control over structural properties of plexcitonic nanocomposites remains a challenge due to current limitations in nanosynthesis techniques. Slight variations in nanostructure’s geometry impact their optoelectronic properties, demanding precise synthesis beyond the capabilities of solution-based (batch) synthesis processes. In contrast, the small, confined liquid volumes used in microfluidics—a reaction technique where the manipulation of fluids takes place in channels with dimensions of tens of micrometers—allows for homogenous synthesis conditions, providing excellent control of the reaction and, as a result, of the materials’ geopmetry and composition. However, thus far, the majority of plexcitonic systems has been developed via batch synthesis. Here, by successfully developing a two-channel microreactor, our microfluidic-supported synthesis approach combines the advantages of both microfluidics and batch platforms, allowing for precise spatio-temporal control over all synthesis parameters opening the possibility for homogenous nanosythnesis of well-defined plexcitonic model systems.

14 SOLAR ENERGY↗

Strongly anisotropic electronic and magnetic structures in oxide dichlorides RuOCl 2 and OsOCl 2

The van der Waals oxide dichlorides MOX 2 (M=V, Ta, Nb, Ru, and Os; X=halogen element), with different electronic densities, are attracting considerable attention. Ferroelectricity, spin-singlet formation, and orbital-selective Peierls phases were reported in this family with d 1 or d 2 electronic configurations, all believed to be caused by the strongly anisotropic electronic orbital degree of freedom. Here, using density functional theory and density matrix renormalization group methods, we investigate the electronic and magnetic properties of RuOCl 2 and OsOCl 2 with d 4 electronic configurations. Different from a previous study using VOI 2 with d 1 configuration, these systems with 4d4 or 5d4 do not exhibit a ferroelectric instability along the a axis. Due to the fully occupied dxy orbital in RuOCl 2 and OsOCl 2 , the Peierls instability distortion disappears along the b axis, leading to an undistorted Immm phase (No. 71). Furthermore, we observe strongly anisotropic electronic and magnetic structures along the a axis. For this reason, the materials of our focus can be regarded as “effective one-dimensional” systems even when they apparently have a dominant two-dimensional lattice geometry. The large crystal-field splitting energy (between dxz/yz and dxy orbitals) and large hopping between nearest-neighbor Ru and Os atoms suppresses the J = 0 singlet state in MOCl 2 (M=Ru or Os) with electronic density n = 4, resulting in a spin-1 system. Moreover, we find staggered antiferromagnetic order with π wave vector along the M-O chain direction (a axis) while the magnetic coupling along the b axis is weak. Based on Wannier functions from first-principles calculations, we calculated the relevant hopping amplitudes and crystal-field splitting energies of the t 2g orbitals for the Os atoms to construct a multiorbital Hubbard model for the M-O chains. Staggered AFM with ↑|-|↓-↑|-|↓ spin structure dominates in our density matrix renormalization group calculations, in agreement with density functional theory calculations. Our results for RuOCl 2 and OsOCl 2 provide guidance to experimentalists and theorists working on this interesting family of oxide dichlorides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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↗

Electron Configurations and Basic Chemical Bonding

The goal of this lecture is to cover the basics of atomic electrons: Definitions of shells, subshells, and orbitals; Max number of electrons per subshell; Order of filling shells; The Periodic Table and electron configuration; and Covalent and Ionic Bonding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relativistic Douglas–Kroll–Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas–Kroll–Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin–orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin–orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Chemistry↗

Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System

The local structure of NaTiSi 2 O 6 is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that, on warming, the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning ~ 6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗