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Finding the order in complexity: The electronic structure of 14-1-11 zintl compounds

Yb 14 MnSb 11 and Yb 14 MgSb 11 have rapidly risen to prominence as high-performing p-type thermoelectric materials. However, the fairly complex crystal structure of A 14 MX 11 Zintl compounds renders the interpretation of the electronic band structure obscure, making it difficult to chemically guide band engineering and optimization efforts. In this work, we delineate the valence-balanced Zintl chemistry of A 14 MX 11 compounds using the molecular orbital theory. By analyzing the electronic band structures of Yb 14 MgSb 11 and Yb 14 AlSb 11 , we show that the conduction band minimum is composed of either an antibonding molecular orbital originating from the (Sb 3 ) 7– trimer or a mix of atomic orbitals of A, M, and X. The singly degenerate valence band is comprised of non-bonding Sb pz orbitals primarily from the Sb atoms in the (MSb 4 ) m– tetrahedra and of isolated Sb atoms distributed throughout the unit cell. Such a chemical understanding of the electronic structure enables strategies to engineer electronic properties (e.g., the bandgap) of A 14 MX 11 compounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic structure, dimer physics, orbital-selective behavior, and magnetic tendencies in the bilayer nickelate superconductor $\mathrm{La_3Ni_2O_7}$under pressure

Motivated by the recently reported high-temperature superconductivity in the bilayer La 3 Ni 2 O 7 (LNO) under pressure, we comprehensively study this system using ab initio techniques. The Ni 3d orbitals have a large bandwidth at ambient pressure, increasing by ~22% at 29.5 GPa. Without electronic interactions, the Ni d 3z 2 -r 2 orbitals form a bonding-antibonding molecular orbital state via the O p z inducing a “dimer” lattice in the LNO bilayers. The Fermi surface consists of two-electron sheets with mixed e g orbitals and a hole pocket defined by the d 3z 2 -r 2 orbital, suggesting a Ni two-orbital minimum model. Different from the infinite-layer nickelate, we obtained a large interorbital hopping between d 3z 2 -r 2 and d x 2 -y 2 states in LNO, caused by the ligand “bridge” of in-plane O p x or p y orbitals connecting those two orbitals, inducing d-p σ-bonding characteristics. The competition between the intraorbital and interorbital hoppings leads to an interesting dominant spin stripe (π,0) order because of bond ferromagnetic tendencies via the recently discussed “half-empty” mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Molecular-orbital model for metal-sapphire interfacial strength

Self-consistent-field X-Alpha scattered-wave cluster molecular-orbital models have been constructed for transition and noble metals (Fe, Ni, Cu, and Ag) in contact with a sapphire (Al2O3) surface. It is found that a chemical bond is established between the metal d-orbital electrons and the nonbonding 2p-orbital electrons of the oxygen anions on the Al2O3 surface. An increasing number of occupied metal-sapphire antibonding molecular orbitals explains qualitatively the observed decrease of contact shear strength through the series Fe, Ni, Cu, and Ag.

Johnson, K. H.↗

NEXAFS spectroscopy of alkylated benzothienobenzothiophene thin films at the carbon and sulfur K-edges

Alkylated benzothienobenzothiophenes are an important class of organic semiconductors that exhibit high performance in solution-processed organic field-effect transistors. In this work, we study the near-edge x-ray absorption fine-structure (NEXAFS) spectra of 2,7-didecyl[1]benzothieno[3,2-b][1]benzothiophene (C 10 -BTBT) at both the carbon and sulfur K-edges. Angle-resolved experiments of thin films are performed to characterize the dichroism associated with molecular orientation. First-principles calculations using the density functional theory-based many-body x-ray absorption spectroscopy (MBXAS) method are also performed to correlate the peaks observed and their dichroism with transitions to specific antibonding molecular orbitals. Interestingly, the dichroism of the dominant, lowest energy peak is opposite at the carbon and sulfur K-edges. While the low-energy peak at the carbon K-edge is assigned to carbon 1s → π* transitions with transition dipole moment (TDM) perpendicular to the planar BTBT core, the dominant low energy peak at the sulfur K-edge is assigned to sulfur 1s → σ* transitions with TDM oriented along the long axis of the BTBT core. These differences at the sulfur and carbon K-edges are understood through the MBAXS simulations that find a reordering of the energy of the lowest energy π* and σ* transitions at the sulfur K-edge due to the strong localization of the σ* orbital over the sulfur atom. This work highlights differences in the NEXAFS spectra of organic semiconductors at carbon and sulfur K-edges and provides new insights into peak assignment and x-ray dichroism relevant for studying the molecular orientation of organic semiconductor films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The electronic structure and deexcitation pathways of an isolated metalloporphyrin ion resolved by metal L-edge spectroscopy

The local electronic structure of the metal-active site and the deexcitation pathways of metalloporphyrins are crucial for numerous applications but difficult to access by commonly employed techniques. Here, we applied near-edge X-ray absorption mass spectrometry and quantum-mechanical restricted active space calculations to investigate the electronic structure of the metal-active site of the isolated cobalt(III) protoporphyrin IX cation (CoPPIX+) and its deexcitation pathways upon resonant absorption at the cobalt L-edge. The experiments were carried out in the gas phase, thus allowing for control over the chemical state and molecular environment of the metalloporphyrin. The obtained mass spectra reveal that resonant excitations of CoPPIX+ at the cobalt L3-edge lead predominantly to the formation of the intact radical dication and doubly charged fragments through losses of charged and neutral side chains from the macrocycle. The comparison between experiment and theory shows that CoPPIX + is in a 3 A 2g triplet ground state and that competing excitations to metal-centred non-bonding and antibonding σ* molecular orbitals lead to distinct deexcitation pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distinguishing homolytic vs heterolytic bond dissociation of phenylsulfonium cations with localized active space methods

Modeling chemical reactions with quantum chemical methods is challenging when the electronic structure varies significantly throughout the reaction and when electronic excited states are involved. Multireference methods, such as complete active space self-consistent field (CASSCF), can handle these multiconfigurational situations. However, even if the size of the needed active space is affordable, in many cases, the active space does not change consistently from reactant to product, causing discontinuities in the potential energy surface. The localized active space SCF (LASSCF) is a cheaper alternative to CASSCF for strongly correlated systems with weakly correlated fragments. The method is used for the first time to study a chemical reaction, namely the bond dissociation of a mono-, di-, and triphenylsulfonium cation. LASSCF calculations generate smooth potential energy scans more easily than the corresponding, more computationally expensive CASSCF calculations while predicting similar bond dissociation energies. Furthermore, our calculations suggest a homolytic bond cleavage for di- and triphenylsulfonium and a heterolytic pathway for monophenylsulfonium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Oxygen magnetic polarization, nodes in spin density, and zigzag spin order in oxides

Recent studies on Ba 2 CoO 4 (BCO) and SrRuO 3 (SRO) have unveiled a variety of intriguing phenomena, such as magnetic polarization on oxygens, unexpected nodes in the spin density profile along bonds, and unusual zigzag spin patterns in triangular lattices. Here, using simple model calculations supplemented by density functional theory we explain the presence of nodes based on the antibonding character of the dominant singly occupied molecular orbitals along the transition metal (TM) to oxygen bonds. Our simple model also allows us to explain the net polarization on oxygen as originated from the hybridization between atoms and mobility of the electrons with spins opposite to those of the closest TM atoms. Overall, our results are not limited to BCO and SRO, but they are generic and qualitatively predict the net polarization expected on any ligands, according to the spin order of the closest TM atoms and the number of intermediate ligand atoms. Finally, we propose that a robust easy-axis anisotropy would suppress the competing 120° antiferromagnetic order to stabilize the zigzag pattern order as ground state in a triangular lattice. Our generic predictions should be applicable to any other compound with characteristics similar to those of BCO and SRO.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Molecular orbital symmetry-driven trimer formation in Kagome correlated electron materials

Correlated electron materials with molecular orbital states extending over transition metal clusters can host multiferroicity, spin frustration, and unconventional insulating phases. However, the fundamental criteria that govern cluster formation and stability remain unclear. Here, we identify a symmetry, correlation, and electron-filling-driven criteria that stabilize triangular metal trimers in materials displaying transition metal Kagome patterns. Using density functional theory and chemical bonding analysis, we show that trimer formation emerges when 6–8 electrons occupy molecular orbitals derived from transition metal d-states, achieving near-complete filling of bonding states while avoiding antibonding occupation, and correlations are of intermediate strength. This principle explains the stability of Nb 3 X 8 (X = Cl, Br, I), and more broadly, our findings offer a general design rule to obtain quantum materials with quantum states extended across transition metal clusters.

Kumari, Varsha [Indiana Univ., Bloomington, IN (Un↗

π-Orbital Yin–Yang Kagome bands in anilato-based metal–organic frameworks

π-Orbital bonding plays an important role not only in traditional molecular science and solid-state chemistry but also in modern quantum physics and materials, such as the relativistic Dirac states formed by bonding and antibonding π-bands in graphene. In this work, we disclose an interesting manifestation of π-orbitals in forming the Yin–Yang Kagome bands, which host potentially a range of exotic quantum phenomena. Based on first-principles calculations and tight-binding orbital analyses, we show that the frontier π 2 - and π 3 -orbitals in anilato-based metal–organic frameworks form concurrently a conduction and valence set of Kagome bands, respectively, but with opposite signs of lattice hopping to constitute a pair of enantiomorphic Yin and Yang Kagome bands, as recently proposed in a diatomic Kagome lattice. The twisted configuration of neighboring benzene-derived organic ligands bridged by an octahedrally O-coordinated metal ion is found to play a critical role in creating the opposite sign of lattice hopping for the π 2 - versus π 3 -orbitals. Our finding affords a new material platform to study π-orbital originated quantum chemistry and physics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Orbital-selective Peierls phase in the metallic dimerized chain MoOCl 2

Using ab initio density functional theory, here we systematically study the monolayer MoOCl 2 with a 4 d 2 electronic configuration. Our main result is that an orbital-selective Peierls phase (OSPP) develops in MoOCl 2 , resulting in the dimerization of the Mo chain along the b axis. Specifically, the Mo- d x y orbitals form robust molecular-orbital states inducing localized d x y singlet dimers, while the Mo- d x z / y z orbitals remain delocalized and itinerant. Our study shows that MoOCl 2 is globally metallic, with the Mo- d x y orbital bonding-antibonding splittings opening a gap and the Mo- d x z / y z orbitals contributing to the metallic conductivity. Overall, the results resemble the recently much discussed orbital-selective Mott phase but with the localized band induced by a Peierls distortion instead of Hubbard interactions. Finally, we also qualitatively discuss the possibility of OSPP in the 3 d 2 configuration, as in CrOCl 2 .

1-dimensional systems↗

Why CO bonds side-on at low coverage and both side-on and upright at high coverage on the Cr(110) surface

An atom superposition and electron delocalization molecular orbital study of CO adsorption on the Cr(110) surface shows a high coordinate lying down orientation is favored. This is a result of the large number of empty d-band energy levels in chromium, which allows the antibonding counterparts to sigma and pi donation bonds to the surface to be empty. When lying down, backbonding to CO pi sup * orbitals is enhanced. Repulsive interactions cause additional CO to stand upright at 1/4 monolyer coverage. The results confirm the recent experimental study of Shinn and Madey.

Mehandru, S. P.↗

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗

Methane Adsorption on Heteroatom-Modified Maquettes of Porous Carbon Surfaces

Experimental and theoretical studies disagree on the energetics of methane adsorption on carbon materials. However, this information is critical for the rational design and optimization of the structure and composition of adsorbents for natural gas storage. The delicate nature of dispersion interactions, polarization of both the adsorbent and the adsorbate, interplay between H-bonding and tetrel bonding, and induced dipole/Coulomb interactions inherent to methane physisorption require computational treatment at the highest possible level of theory. In this study, we employed the smallest reasonable computational model, a maquette of porous carbon surfaces with a central site for substitution and methane binding. The most accurate predictions of methane adsorption energetics were achieved by electron-correlated molecular orbital theory CCSD(T) and hybrid density functional theory MN15 calculations employing a saturated, all-electron basis set. Here, the characteristic geometry of methane adsorption on a carbon surface (“lander approach”) arises due to bonding interactions of the adsorbent π-system with the proximal H–C bonds of methane, in addition to tetrel bonding between the antibonding orbital of the distal C–H bond and the central atom of the maquette (C, B, or N). The polarization of the electron density, structural deformations, and the comprehensive energetic analysis clearly indicate a ∼3 kJ mol –1 preference for methane binding on the N-substituted maquette. The B-substituted maquette showed a comparable or lower binding energy than the unsubstituted, pure C model, depending on the level of theory employed. The calculated thermodynamic results indicate a strategy for incorporating electron-enriched substitutions (e.g., N) into carbon materials as a way to increase methane storage capacity over electron-deficient (e.g., B) modifications. The thermochemical analysis was revised for establishing a conceptual agreement between the experimental isosteric heat of adsorption and the binding enthalpies from statistical thermodynamics principles.

03 NATURAL GAS↗

Electron donation of non-oxide supports boosts O 2 activation on nano-platinum catalysts

Activation of O 2 is a critical step in heterogeneous catalytic oxidation. Here, the concept of increased electron donors induced by nitrogen vacancy is adopted to propose an efficient strategy to develop highly active and stable catalysts for molecular O 2 activation. Carbon nitride with nitrogen vacancies is prepared to serve as a support as well as electron sink to construct a synergistic catalyst with Pt nanoparticles. Extensive characterizations combined with the first-principles calculations reveal that nitrogen vacancies with excess electrons could effectively stabilize metallic Pt nanoparticles by strong p-d coupling. The Pt atoms and the dangling carbon atoms surround the vacancy can synergistically donate electrons to the antibonding orbital of the adsorbed O 2 . This synergistic catalyst shows great enhancement of catalytic performance and durability in toluene oxidation. The introduction of electron-rich non-oxide substrate is an innovative strategy to develop active Pt-based oxidation catalysts, which could be conceivably extended to a variety of metal-based catalysts for catalytic oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ternary Complexes of BiI 3 /CuI and SbI 3 /CuI with Tetrahydrothiophene

Reactions of BiI 3 /CuI mixtures with tetrahydrothiophene (THT) in toluene produce 2-D sheet networks BiCu 3 I 6 (THT) n (n = 2, 3, or 4), depending on reaction conditions. All three structures are based on BiI 6 octahedra, which share pairs of (μ 2 -I) 2 with Cu 3 (THT) n units. BiCu 3 I 6 (THT) 2 features Cu 2 (μ 2 -I) 2 rhombs with close Cu···Cu interactions and is accompanied by formation of the very complex HBi 3 Cu 12 I 22 (THT) 8 . Reactions of SbI 3 /CuI with THT in toluene produced a SbCu 3 I 6 (THT) 2 network shows Cu 3 (μ 2 -THT) 2 units, like its Bi congener, but Cu 6 (μ 2 -I) 6 barrels rather than rhombs. Isolated SbI 3 units are stacked above the Cu 6 I 6 barrels. A molecular compound, Sb 3 Cu 3 I 12 (THT) 6 consists of a face-sharing Sb 3 I 12 stack, in which the Cu-THT units are bonded in asymmetric fashion about the central SbI 6 . Metal-halide bonds were investigated via QTAIM and NLMO analyses, demonstrating that these bonds are largely ionic and occur between the Bi/Sb and I p orbitals. Hirshfeld analysis shows significant H···H and H···I interactions. Diffuse reflectance spectroscopy (DRS) reveals band edges for the Bi species of 1.71–1.82 eV, while those for the neutral Sb complexes are in the range of 1.94–2.06 eV. Mapping of the electronic structure via density of state calculations indicates population of antibonding Bi/Sb–I orbitals in the excited state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of the effects of cobalt ions on epoxy properties

The effects of Co(acac)sub x complexes on MY-720 epoxy properties have been investigated. It appears that Co2(+) ions form antibonding or nonbonding orbitals which increase the free volume and also reduce the cohesiveness of the host epoxy. The effects of Co2(+) ions, on the other hand, seem to result in increased Cohesiveness of the epoxy. The experimental values of magnetic moments of both types of ions in MY-720 suggest that the orbital momentum contributions of the (3d) electrons are partially conserved, though the effect is more pronounced for Co2(+) ions. The coordination environment of the cobalt ions in the host epoxy does not appear to be uniquely defined. These results indicate that the effects of metal ions on resin properties cannot be easily predicted on the basis of ligand field theory argument alone. Complex interactions between metal ions and host epoxy molecular structure suggest the desirability of parallel experimental investigations of electronic, magnetic, and mechanical properties of metal ion-containing epoxy samples for comparison with theory.

Singh, J. J.↗