Orbital Degeneracy Research Articles

Stabilization of orthorhombic distortions in Cu-doped and Co-doped ferrimagnetic Mn3O4

Using synchrotron x-ray diffraction, we investigate how the tetragonal-to-orthorhombic phase transition in the ferrimagnetic $(cga)$ spinel ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ is driven by the ${t}_{2}$ orbital degeneracy of ${\mathrm{Cu}}^{2+}\phantom{\rule{4pt}{0ex}}(3{d}^{9})$ ions doped in its tetrahderal sites. At high temperatures where the orthorhombic phase initially appears, we observe that the local elongations of Cu-doped tetrahedra cause the unit cells to contract along the same direction. The signs of the local and global lattice strains finally agree with each other when the orthorhombic phase transition is completed below ${T}_{\mathrm{N}}=42.5$ K. Using neutron diffraction, we report that ${\mathrm{Co}}^{2+}\phantom{\rule{4pt}{0ex}}(3{d}^{7})$ doping also stabilizes the orthorhombic phase but without enhancing the associated lattice strains. These results are consistent with the scenario that the orthorhombic instability of the undoped ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ is driven by the spin-lattice coupling.

Interference effect in high-order harmonic generation from degenerate current-carrying orbitals of polyatomic molecules

When the molecules with degenerate current-carrying orbitals are exposed to the bichromatic counterrotating circularly polarized (BCCP) laser fields, the destructive interference between high harmonics from these orbitals results in a strong suppression of harmonic emission with the selected helicity. As a result, there are large intensity differences between the high harmonics with opposite helicities in a wide spectral range. This interference effect is related to the noncylindrical symmetry of the molecular current-carrying orbitals and therefore depends on the relative orientation between the molecule and the driving laser fields. Furthermore, our results show that this interference can be controlled by adjusting the relative intensity ratio of the BCCP field. Finally, we show that highly elliptically polarized attosecond pulses can be generated by using this interference and their ellipticities can be tuned by controlling the molecular orientation.

Jahn–Teller Driven Electronic Instability in Thermoelectric Tetrahedrite

AbstractTetrahedrite, Cu12Sb4S13, is an abundant mineral with excellent thermoelectric properties owing to its low thermal conductivity. The electronic and structural origin of the intriguing physical properties of tetrahedrite, including its metal‐to‐semiconductor transition (MST), remains largely unknown. This work presents the first determination of the low‐temperature structure of tetrahedrite that accounts for its unique properties. Contrary to prior conjectures, the results show that the trigonal–planar copper cations remain in planar coordination below the MST. The atomic displacement parameters of the trigonal–planar copper cations, which have been linked to low thermal conductivity, increase by 200% above the MST. The phase transition is a consequence of the orbital degeneracy of the highest occupied 3d cluster orbitals of the copper clusters found in the cubic phase. This study reveals that a Jahn–Teller electronic instability leads to the formation of “molecular‐like” Cu57+ clusters and suppresses copper rattling vibrations due to the strengthening of direct copper–copper interactions. First principles calculations demonstrate that the structural phase transition opens a small band gap in the electronic density of states and eliminates the unstable phonon modes. These results provide insights on the interplay between phonon transport, electronic properties, and crystal structure in mixed‐valence compounds.

The geometry of the Coble cubic and orbital degeneracy loci

The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating trivectors in nine variables. Exploring this relation further, we show how the Hilbert scheme of pairs of points on an abelian surface, and also its Kummer fourfold, a very remarkable hyper-K\"ahler manifold, can very naturally be constructed in this context. Moreover, we explain how this perspective allows us to describe the group law of an abelian surface, in a strikingly similar way to how the group structure of a plane cubic can be defined in terms of its intersection with lines.

D-orbital energy levels in planar [MIIF4]2-, [MII(NH3)4]2+ and [MII(CN)4]2- complexes: the nature of M-L π bonding and the implications for ligand field theory.

Qualitative MO theory predicts degenerate dπ orbitals for planar coordination complexes with formally σ-only ligands and the splitting energy, ΔEπ = E(dxy) - E(dxz,dyz), should be zero. For π-donor ligands, ΔEπ should be positive (dxy > dxz,yz) while for π-acceptors, ΔEπ should be negative (dxy < dxz,yz). However, experimental d-d spectra, ab initio ligand field theory (AI LFT) and crystal field theory for σ-only [M(NH3)4]2+ complexes give pronounced dπ splittings with ΔEπ around +2500 cm-1 for first-row, divalent metal ions. AI LFT further suggests ΔEπ values around +4500 cm-1 for [MF4]2- and +1000 cm-1 for [M(CN)4]2- species. The origins of these dπ orbital splittings can be traced to the effects of the ligand field potential surrounding the metal centre which includes not only the intrinsic metal-ligand π bonding but also substantial contributions from the 'void' regions above and below the molecular plane. The π component of the 'void cell' potentials increases ΔEπ which, if not explicitly taken into account, artificially enhances the apparent π-donor strength of the ligands. With the inclusion of void cell π interactions, even though the AI LFT d orbital sequence always places dxz,yz below dxy, the ligand field analysis provides a chemically-reasonable description of the M-L π interactions with cyanide being a weak π acceptor, ammonia being π-neutral and fluoride being a strong π donor. In the case of [Ni(CN)4]2-, ligand field calculations further show that, contrary to the recent claims of Oppenheim et al. (Inorg. Chem., 2019, 58, 15202) the sequence of the many-electron excited states is not a definitive guide to the underlying order of one-electron d orbital energies and that the observed sequence of nA2g > nEg > nB1g, n = 1 or 3, does not guarantee a d-orbital sequence of dxy < dxz,yz < dz2.

Mechanism analysis of Au, Ru noble metal clusters modified on TiO2 (101) to intensify overall photocatalytic water splitting.

Accelerating the separation and migration of photo-carriers (electron–hole pairs) to improve the photo-quantum utilization efficiency in photocatalytic overall water splitting is highly desirable. Herein, the photo-deposition of Ru or Au noble metal clusters with superior electronic properties as a co-catalyst on the (101) facet of anatase TiO2 and the mechanism of intensifying the photocatalysis have been investigated by calculation based density functional theory (DFT). As a result, the as-synthesized Ru/TiO2 and Au/TiO2 exhibit high hydrogen evolution reaction (HER) activity. Such a greatly enhanced HER is attributed to the interfacial interactivity of the catalysts due to the existence of robust chemical bonds (Ru–O–Ti, Au–O–Ti) as electron-traps that provide the photogenerated electrons. In addition, the formation of new degenerate energy levels due to the existence of Ru-4d and Au-5d electronic impurity states leads to the narrowing of the band gap of the catalysts. In addition, the as-synthesized Au/TiO2 exhibits more faster HER rate than Ru/TiO2, which is attributed to the effects of surface plasmon resonance (SPR) as a synergistic effect of plasmon-induced ‘hot’ electrons that enhance the harvesting of the final built-in electric field and promote the migration and separation of the photo-carriers, which efficiently facilitates hydrogen evolution from the photocatalytic overall water splitting reaction.

Interlayer coupling prolonged the photogenerated carrier lifetime of few layered Bi2OS2 semiconductors.

Layered semiconductors with broad photoabsorption, a long carrier lifetime and high carrier mobility are of crucial importance for high-performance optoelectronic and photovoltaic devices; however it is hard to satisfy these requirements simultaneously in a system due to the opposite dependence on the layer thickness. Herein, by means of ab initio time-domain nonadiabatic molecular dynamic simulations, we find a new mechanism in Bi2OS2 nanosheets inducing an anomalous layer-dependent property of carrier lifetimes, which makes the few layered Bi2OS2 a possible system for fulfilling the above requirements concurrently. It is revealed that the interlayer dipole-dipole interaction in few layered Bi2OS2 effectively breaks the two-fold degenerate orbitals of [BiS2] layers, which not only cuts down the overlap of the electron and hole wave functions, but also accelerates the electron decoherence process. This significantly suppresses the electron-hole recombination and prolongs the photogenerated carrier lifetime of few layered Bi2OS2. The mechanism unveiled here paves a possible way for developing advanced optoelectronic and photovoltaic devices through engineering interlayer dipole-dipole coupling.

Electron-phonon coupling in d -electron solids: A temperature-dependent study of rutile TiO2 by first-principles theory and two-photon photoemission

The authors present experimental and theoretical results on the electron-phonon interaction in TiO2 and SiO2 and show that the different behavior can be attributed to the split of the degeneracy of atomic orbitals induced by the crystal field of the ligand species.

Hidden Supersymmetries of Deformed Supersymmetric Mechanics

We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline d = 1 realizations of the supergroup SU( N/2 |1), where the number of supersymmetries N is arbitrary even number. Constructed models possess the hidden supersymmetry SU( N/2 |2). Degeneracies of energy levels are spanned by representations of the hidden supersymmetry group.

Poor man’s scaling and Lie algebras

We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive general scaling equation for the model, and analyse the connection between its particular forms and the symmetry of interaction. On the basis of this analysis we write down scaling equations for the Hamiltonians which are the direct products of su(3) Lie algebras and have either SU(2) × U(1) or SU(2) symmetry. We also put into a new context anisotropic Coqblin—Schrieffer models proposed by us earlier.

HEAVY-LIGHT MESONS IN THE SYMMETRIES OF EXTENDED NONRELATIVISTIC QUARK MODEL

In present work, the modified Schrödinger equation (MSE) is analytically solved. The Heavy-Light Mesons (HLM) under modified nonrelativistic quark-antiquark potential, are extended to the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The energy a spectrum of HLM has been investigated in the framework of the perturbative quantum chromodynamics (PQCD) extended nonrelativistic quark model. The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. The masses of the scalar, vector, pseudoscalar, and pseudovector for (B, Bs , D and Ds) mesons have been calculated in (NC: 3D-RSP). Moreover, using the perturbation approach, we found that the perturbative solutions of discrete spectrum can be expressed by the parabolic cylinder functions function, Gamma function, the discreet atomic quantum numbers (j, l, s, m) of the ǪǬ state and (the spin independent and spin dependent) parameters (a, b, g, h), in addition to noncommutativity parameters. Furthermore, we have shown that the total complete degeneracy of new energy levels of HLM was changed to become equals to the new value 3n2 instead to the old values n2 in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCQM.

Flux Tube S -Matrix Bootstrap

We bootstrap the S matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S matrices is strongly constrained by the existence of a UV completion. In the context of flux tube (FT) physics, this allows us to constrain several terms in the S matrix low energy expansion or-equivalently-on Wilson coefficients of several irrelevant operators showing up in the FT effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large FTs. We find that the S matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass, and width are precisely those of the world-sheet axion proposed by Athenodorou, Bringoltz, and Teper and Dubovsky, Flauger, and Gorbenko. The general method proposed here should be extendable to massless S matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and, also, in gauge and gravity theories.

Complexation of trivalent lanthanides and actinides with diethylenetriaminepentaacetic acid: Theoretical unraveling of bond covalency

Separation of trivalent actinides (An(III)) and lanthanides (Ln(III)) is a pivotal step with respect to the treatment of nuclear waste based on the partitioning and transmutation (P&T) strategy, which is also extraordinarily challenging due to their similar coordination chemistry. The diethylenetriaminepentaacetate (DTPA) ligand has been demonstrated to possess selective separation ability toward An(III) over Ln(III) in aqueous media. Nevertheless, the extracted complexes of An(III)/Ln(III) with DTPA, and the origin of selectivity for An(III) are still not well deciphered. In this work, from theoretical perspective and at the molecular level, the geometrical structures, bonding nature as well as thermodynamic behaviors of possible complexes of An(III) (An = Am, Cm, Cf) and Ln(III) (Ln = Nd, Eu) with DTPA in the aqueous phase have been systematically studied using scalar relativistic density functional theory (DFT). All bonding analyses indicate that the metal-ligand bonds possess weak but non-negligible covalent interactions, and An(III)-DTPA species demonstrate more covalency compared to Ln(III) analogues. In addition, the covalency of the metal-ligand bonding of An(III)-DTPA increases across the actinide series from Am to Cf, which stems from the increased orbital degeneracy of the 5f orbitals of actinides and the 2p orbitals of the ligands. According to thermodynamic analysis, the anhydrous species [Cf(HDTPA)]− is the most likely species for Cf(III) in acidic solution, whereas [M(HDTPA)(H2O)]− are more favorable for Am(III) and Cm(III), probably due to the different bonding nature of the transplutonium series. This work affords new theoretical insights into the coordination chemistry of An(III)/Ln(III)-DTPA complexes, and paves the way to further design efficient DTPA-based ligands for An(III)/Ln(III) separation. Moreover, the DTPA ligand may also be applied for in-group separation of trivalent actinides, which is quite meaningful for the extraction of Cf(III).

Evolution of Magnetic Anisotropy of an Organometallic Molecule in a Mechanically Controlled Break Junction: The Roles of Connecting Electrodes

The precise control of local spin states in magnetic organometallic molecules by means of a mechanically controlled break junction (MCBJ) is a cutting edge frontier of single molecule science. For instance, a fine-tuning of the magnetic anisotropy of a Co(tpy–SH)2 molecule has been achieved experimentally by sandwiching the molecule between two electrodes and gradually enlarging their separation. However, an accurate simulation of such a process has remained rather challenging, which is largely due to the complex structure of the composite junction as well as the static electron correlation originating from the nearly degenerate d-orbitals of the cobalt atom. In this work, by employing an embedding method which combines the high-level complete active space self-consistent field (CASSCF) method and a density functional theory (DFT) method, we carefully simulate the evolution of magnetic anisotropy of the Au–Co(tpy–S)2–Au junction during the mechanical stretching process. It is found that the presence of th...

Spherical topological insulator nanoparticles: Quantum size effects and optical transitions

We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers $j$ and $m=-j, -j+1, \dots, j$ for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires $j$ to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues $(-1)^{j\mp 1/2}$. The existence of energy eigenstates having the same $j$ but opposite parity enables optical transitions where $j$ is conserved, in addition to those adhering to the familiar selection rule where $j$ changes by $\pm 1$. All optical transitions satisfy the usual selection rule $\Delta m = 0, \pm 1$. We treat intra- and inter-band optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependences of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multi-band models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

Heat flow reversals without reversing the arrow of time: The role of internal quantum coherences and correlations

One of the stunning consequences of quantum correlations in thermodynamics is the reversal of the arrow of time, recently shown experimentally in [K. Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a reversal of the heat flow (from the cold system to the hot one). Here, we show that contrary to what could have been expected, heat flow reversal can happen without reversal of the arrow of time. Moreover, contrasting with previous studies, no initial correlations between system and bath is required. Instead, the heat flow reversal only relies on internal quantum coherences or correlations, which provides practical advantages over previous schemes: one does not need to have access to the bath in order to reverse the heat flow. The underlying mechanism is explained and shown to stem from the collective system-bath coupling and the impact of non-energetic coherences (coherences between degenerate energy levels) on apparent temperatures. The phenomenon is first uncovered in a broad framework valid for diverse quantum systems containing energy degeneracy. By the end of the paper, aiming at experimental realisations, more quantitative results are provided for a pair of two-level systems. Finally, as a curiosity, we mention that our scheme can be adapted as a correlations-to-energy converter, which have the particularity to be able to operate at constant entropy, similarly to ideal work sources.

Impact of Sn4+ Substitution at Cr3+ Sites on Thermoelectric and Electronic Properties of p-Type Delafossite CuCrO2

The effects of Sn4+ substitution at Cr3+ sites on the thermoelectric and electronic properties of p-type delafossite CuCrO2 have been studied. CuCr1−xSnxO2 (x = 0.01, 0.03) samples were prepared via conventional solid-state reaction. The Seebeck coefficient results confirmed that all the samples exhibited p-type conduction. X-ray photoelectron spectroscopy verified the presence of Sn4+ ions and the appearance of mixed-state Cr3+/Cr2+ ions. The experimental results revealed that addition of Sn impacted the electrical conductivity due to the mixed Cu1+/Cu2+ states while the Seebeck coefficient was affected by the mixed Cr3+/Sn4+ states. The electrical conductivity was governed by the polaron hopping mechanism, and the large Seebeck coefficient was controlled by the spin and orbital degeneracy of the mixed Cr3+/Sn4+ ions. The electrical conductivity activation energy values were 0.410 eV and 0.407 eV while the thermal activation energy values were 0.208 eV and 0.160 eV, for x = 0.01 and 0.03, respectively. The results confirm that Sn4+ substitution at Cr3+ sites impacted the Seebeck coefficient and electronic behavior of delafossite CuCrO2 oxide even for low dopant levels of x = 0.01 and 0.03, resulting in p-type conduction and optically conducting materials.

Orbital-Weighted Dual Descriptor for the Study of Local Reactivity of Systems with (Quasi-) Degenerate States.

An alternative response function, based on the dual descriptor in terms of Koopmans' approximation, is hereby proposed for the description of chemical reactivity in systems with (quasi-) degenerate frontier molecular orbitals. This descriptor is constructed from Fukui functions that include contributions from different orbitals, i.e., orbital-weighted Fukui functions. The methodology is applied to three case studies: the first case consists of a series of benchmark organic and inorganic molecules from which the dual descriptor, based only on frontier orbitals, is not appropriate to describe their reactivity. The second case deals with the proper description of chemical reactivity in Diels-Alder reactions between fullerene C60 and cyclopentadiene (CP), revealing the importance of considering secondary orbital interactions for an adequate regioselectivity description. The third, and last case, consists of a series of polycyclic aromatic hydrocarbons (PAHs) possessing molecular orbital degeneracy. By means of analyzing of this descriptor, an alternative approach to the description of aromaticity is proposed. In all cases, the proposed index called "orbital-weighted dual descriptor" has proven to accurately describe the chemical reactivity and aromaticity of the studied systems.

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

We briefly present some of the most modern and outstanding non-conventional density-functional theory (DFT) methods, which have largely broadened the field of applications with respect to more traditional calculations. The results of these ongoing efforts reveal that a DFT-inspired solution always exists even for pathological cases. Among the set of emerging methods, we specifically mention FT-DFT, OO-DFT, RSX-DFT, MC-PDFT, and FLOSIC-DFT, complementing the last generation of existing density functionals, such as local hybrid and double-hybrid expressions.

Slow Magnetic Relaxation, Antiferromagnetic Ordering, and Metamagnetism in MnII (H2 dapsc)-FeIII (CN)6 Chain Complex with Highly Anisotropic Fe-CN-Mn Spin Coupling.

Reactions of [Mn(H2 dapsc)Cl2 ]⋅H2 O (dapsc=2,6- diacetylpyridine bis(semicarbazone)) with K3 [Fe(CN)6 ] and (PPh4 )3 [Fe(CN)6 ] lead to the formation of the chain polymeric complex {[Mn(H2 dapsc)][Fe(CN)6 ][K(H2 O)3.5 ]}n ⋅1.5n H2 O (1) and the discrete pentanuclear complex {[Mn(H2 dapsc)]3 [Fe(CN)6 ]2 (H2 O)2 }⋅4 CH3 OH⋅3.4 H2 O (2), respectively. In the crystal structure of 1 the high-spin [MnII (H2 dapsc)]2+ cations and low-spin hexacyanoferrate(III) anions are assembled into alternating heterometallic cyano-bridged chains. The K+ ions are located between the chains and are coordinated by oxygen atoms of the H2 dapsc ligand and water molecules. The magnetic structure of 1 is built from ferrimagnetic chains, which are antiferromagnetically coupled. The complex exhibits metamagnetism and frequency-dependent ac magnetic susceptibility, indicating single-chain magnetic behavior with a Mydosh-parameter φ=0.12 and an effective energy barrier (Ueff /kB ) of 36.0 K with τ0 =2.34×10-11 s for the spin relaxation. Detailed theoretical analysis showed highly anisotropic intra-chain spin coupling between [FeIII (CN)6 ]3- and [MnII (H2 dapsc)]2+ units resulting from orbital degeneracy and unquenched orbital momentum of [FeIII (CN)6 ]3- complexes. The origin of the metamagnetic transition is discussed in terms of strong magnetic anisotropy and weak AF interchain spin coupling.