Orbital Degeneracy Research Articles

Effect of Specific Heavy Doping of Silver Atoms into the Icosahedral Au13 on Electronic Structure and Catalytic Performance.

The exploration of specific heavy doping of silver atoms into icosahedral Au13 clusters and their electronic structures and properties has been somewhat limited. Herein, we report two heavily Ag doped nanoclusters, [Au7Ag6(C7H4NOS)4(Dppf)3Cl]0 and [Au7Ag6(C7H4NOS)3(Dppf)3Cl](SbF6) (Au7Ag6-0 and Au7Ag6-1, respectively) [C7H4NOSH = 2-mercaptobenzoxazole, and Dppf = 1,1'-bis(diphenylphosphino)ferrocene]. The electronic structures and superatomic orbitals of nanoclusters were determined by density functional theory (DFT) calculations, and the energy degeneracy of the superatomic orbitals of Au7Ag6-1 is higher than that of Au7Ag6-0. Transient absorption spectroscopy was performed, revealing that Au7Ag6-0 significantly extends the excited-state lifetime. Both nanoclusters were supported on activated carbon for the oxygen reduction reaction. DFT calculations confirm that the catalytic activities mainly stem from the carbon atom of ferrocene rather than the iron atom. This study not only sheds light on the preparation of icosahedral alloy clusters but also provides insights into the regulation of icosahedral superatomic structure and electrocatalytic properties.

Synthesis and Characterization of Ionic Li+ @C70 Endohedral Fullerene.

Ion-endohedral-fullerene has attracted growing interest due to the unique electronic and structural characteristics arising from its distinctive ionic nature. Although there has been only one reported ion-encapsulated fullerene, Li+ @C60 , a significant number of fundamental and applied studies have been conducted, making a substantial impact not only in chemistry and physics but also across various interdisciplinary research fields. Nevertheless, studies on ion-endohedral fullerenes are still in their infancy due to the limitations in variety, and hence, it remains an open question how the size and symmetry of fullerene, as well as the motion and position of the encapsulated ion, affect their physical/chemical properties. Herein, we report the synthesis of lithium-ion-endohedral [70]fullerene (Li+ @C70 X- , X=PF6 - and TFSI- ), a novel ionic endohedral fullerene. X-ray crystallography confirmed the encapsulation of Li+ by C70 cage as well as its ion-pair structure stabilized by external TFSI- counter anion. The encapsulated Li+ drastically lowered the orbital energy of the C70 cage by Coulomb interactions but did not affect the orbital energy gap and degeneracy. DFT studies were also performed, which supported the experimentally observed electronic effects caused by the encapsulated Li+ .

Frontier Orbital Degeneracy: A New Concept for Tailoring the Magnetic State in Organic Semiconductor Adsorbates

Frontier Orbital Degeneracy: A New Concept for Tailoring the Magnetic State in Organic Semiconductor Adsorbates

Tuning Confined States and Valley G‐Factors by Quantum Dot Design in Bilayer Graphene

Electrostatically confined quantum dots in bilayer graphene have shown potential as building blocks for quantum technologies. To operate the dots, e.g., as qubits, a precise understanding and control of the confined states and their properties is required. Herein, a large‐scale numerical characterization of confined quantum states in bilayer graphene dots is performed over an extensive range of gate‐tunable parameters such as the dot size, depth, shape, and the bilayer graphene gap. The dot states’ orbital degeneracy, wave function distribution, and valley g‐factor are established and the parametric dependencies to achieve different regimes are provided. It is found that the dot states are highly susceptible to gate‐dependent confinement and material parameters, enabling efficient tuning of confined states and valley g‐factor modulation by quantum dot design.

Two-step phase manipulation by tailoring chemical bonds results in high-performance GeSe thermoelectrics

In thermoelectrics, phase engineering serves a crucial function in determining the power factor by affecting the band degeneracy. However, for low-symmetry compounds, the mainstream one-step phase manipulation strategy, depending solely on the valley or orbital degeneracy, is inadequate to attain a high density-of-states effective mass and exceptional zT. Here, we employ a distinctive two-step phase manipulation strategy through stepwise tailoring chemical bonds in GeSe. Initially, we amplify the valley degeneracy via CdTe alloying, which elevates the crystal symmetry from a covalently bonded orthorhombic to a metavalently bonded rhombohedral phase by significantly suppressing the Peierls distortion. Subsequently, we incorporate Pb to trigger the convergence of multivalence bands and further enhance the density-of-states effective mass by moderately restraining the Peierls distortion. Additionally, the atypical metavalent bonding in rhombohedral GeSe enables a high Ge vacancy concentration and a small band effective mass, leading to increased carrier concentration and mobility. This weak chemical bond along with strong lattice anharmonicity also reduces lattice thermal conductivity. Consequently, this unique property ensemble contributes to an outstanding zT of 0.9 at 773 K for Ge0.80Pb0.20Se(CdTe)0.25. This work underscores the pivotal role of the two-step phase manipulation by stepwise tailoring of chemical bonds in improving the thermoelectric performance of p-bonded chalcogenides.

Multiorbital exchange Hamiltonians: Derivation and examples

We present a detailed derivation of the effective Hamiltonian for a strongly correlated electron system involving both orbital and spin degrees of freedom. This problem is relevant to a wide class of materials containing ions with the orbitally degenerate ground state (Jahn–Teller ions). We treat in detail the case of double degenerate orbitals, obtain the Kugel–Khomskii model, and then pass to a more general multiorbital case. Based on the derived Hamiltonians, we analyze possible spin and orbital configurations, which can be rather nontrivial, especially in the multiorbital case. A special emphasis is put on to a specific example of the square lattice of Jahn–Teller ions typical of layered perovskites.

Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation.

First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform abinitio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.

Current-Density Calculations on Zn-Porphyrin40 Nanorings.

Two porphyrinoid nanorings have been studied computationally. They were built by linking 40 Zn-porphyrin units with butadiyne bridges. The molecular structures belonging to the D40h point group were fully optimized with the Turbomole program at the density functional theory (DFT) level using the B3LYP functional and the def2-SVP basis sets. The aromatic character was studied at the DFT level by calculating the magnetically induced current-density (MICD) susceptibility using the GIMIC program. The neutral molecules are globally non-aromatic with aromatic Zn-porphyrin units. Charged nanorings could not be studied because almost degenerate frontier orbitals led to vanishing optical gaps for the cations. Since DFT calculations of the MICD are computationally expensive, we also calculated the MICD using three pseudo-π models. Appropriate pseudo-π models were constructed by removing the outer hydrogen atoms and replacing all carbon and nitrogen atoms with hydrogen atoms. The central Zn atom was either replaced with a beryllium atom or with two inner hydrogen atoms. Calculations with the computationally inexpensive pseudo-π models yielded qualitatively the same magnetic response as obtained in the all-electron calculations.

Impact of Cr–O hybridization in ACrO3 (A = La, Y): A theoretical investigation

Electronic properties of spin polarized antiferromagnetic ACrO3 (A = La, Y) are explored with Hubbard model using density functional theory (DFT). These two isostructural systems are investigated using the different Hubbard energy and analyzed the hybridization of chromium 3d orbitals and oxygen 2p orbitals and the change in energy bandgaps against the Hubbard energy. The bond length and bond angle affect significantly the orbital contributions of Cr-3d and O-2p electrons for both the system. We noticed that the Cr–O hybridization affects the orbital degeneracy and is substantiated with partial density of states. These results emphasize the contribution of Hubbard energy in correlated electron systems.

Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for jeff = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM4X8 chalcogenides, and clarifies the basic multiorbital correlations on M4 tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V4+V3+V3+V3+ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital jeff = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems.

Quantum Harmonic Oscillators in One and Two Dimensions

The Schrödinger equation is a significant achievement on the development of quantum mechanics. By solving the Schrödinger equation, the fundamental behaviors and properties of a microscopic particle can be found in one- to three-dimensions. The article focuses on the derivations of quantum harmonic oscillators in one dimension by solving second order-differential equation. The wave functions, probability densities under different energy levels are presented. The results can be used to estimate different forms of continuous potential experienced by an oscillator. By calculating the uncertainty relation of the oscillator under one specific excited state, the general relation can be confirmed. Based on the output, by splitting the variables, the two-dimensional harmonic oscillator can also be derived. The degenerate energy levels are presented as . Numerical simulations are made to visualize those results and suggests the relation of energy levels and number of maxima of the probability densities.

Three-dimensional wormhole with cosmic string effects on eigenvalue solution of non-relativistic quantum particles

In this paper, we explore the quantum system of non-relativistic particles in a unique scenario: a circularly symmetric and static three-dimensional wormhole space-time accompanied by cosmic strings. We focus on a specific case where the redshift function varPhi (r) to be zero and defining the shape function as A(r)=frac{b}{r^2}. After establishing this background space-time, we investigate the behavior of a harmonic oscillator within the same wormhole context. By doing so, we observe the effects of the cosmic string and wormhole throat radius on the eigenvalue solution of the oscillator’s eigenvalue problem. The primary finding is that these cosmic features lead to modifications in the energy spectrum and wave functions of the system, breaking the degeneracy of energy levels that would typically be present in a more conventional setting. As a particular case, we present the specific energy level E_{1,ell } and the corresponding wave function psi _{1,ell }, which are associated with the ground state of the quantum system. These results highlight the fascinating and unique properties of the harmonic oscillator in the background of a circularly symmetric, static wormhole space-time with cosmic strings.

High optical spin-filtering in antiferromagnetic stanene nanoribbons induced by band bending and uniaxial strain

Non-equilibrium spin-polarized transport properties of antiferromagnetic stanene nanoribbons are theoretically studied under the combining effect of a normal electric field and linearly polarized irradiation based on the tight-binding model at room temperature. Due to the existence of spin-orbit coupling in stanene lattice, applying normal electric field leads to splitting of band degeneracy of spin-resolved energy levels in conduction and valence bands. Furthermore, unequivalent absorption of the polarized photons at two valleys which is attributed to an antiferromagnetic exchange field results in unequal spin-polarized photocurrent for spin-up and spin-down components. Interestingly, in the presence of band bending which has been induced by edge potentials, an allowable quantum efficiency occurs over a wider wavelength region of the incident light. It is especially important that the variation of an exchange magnetic field generates spin semi-conducting behavior in the bended band structure. Moreover, it is shown that optical spin-filtering effect is obtained under the simultaneous effect of uniaxial strain and narrow edge potential.

Excitons states and linear absorption spectra of carbon nanotubes with Stone–Wales defects

The exciton states in the single-walled carbon nanotubes (SWNTs) with Stone–Wales (SW) defects are theoretically studied in the tight-binding model. It is found that for the semiconducting zigzag tubes (10, 0) with different concentration of SW defect, the exciton energies move to low energy region with increasing the concentration of SW defect, and the symmetry broken by the SW defects leads to splitting of the degenerate exciton energy levels, which can be seen clearly from the linear absorption spectra of defected SWNTs. As detected from the linear absorption spectra, we can give some information on the concentration of the SW defect existing in the SWNTs.

Multiorbital Nature of Doped Sr_{2}IrO_{4}.

The low-energy j_{eff}=1/2 band of Sr_{2}IrO_{4} bears stark resemblances with the x^{2}-y^{2} band of La_{2}CuO_{4}, and yet no superconductivity has been found so far by doping Sr_{2}IrO_{4}. Behind such a behavior could be inherent failures of the j_{eff}=1/2 picture, in particular when electrons or holes are introduced in the IrO_{2} planes. In view of this, here we reanalyze the j_{eff}=1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective j_{eff}=1/2 state is surprisingly stable upon doping. This supports the j_{eff}=1/2 picture. We show that, nevertheless, Sr_{2}IrO_{4} remains in essence a multiorbital system: The hybridization with the j_{eff}=3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the j_{eff}=3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the j_{eff}=3/2 states contribute both to the Drude peak and to relatively low-energy features.

Photoelectron Photoion Coincidence Spectroscopy of Biradicals.

The electronic structure of biradicals is characterized by the presence of two unpaired electrons in degenerate or near-degenerate molecular orbitals. In particular, some of the most relevant species are highly reactive, difficult to generate cleanly and can only be studied in the gas phase or in matrices. Unveiling their electronic structure is, however, of paramount interest to understand their chemistry. Photoelectron photoion coincidence (PEPICO) spectroscopy is an excellent approach to explore the electronic states of biradicals, because it enables a direct correlation between the detected ions and electrons. This permits to extract unique vibrationally resolved photoion mass-selected threshold photoelectron spectra (ms-TPES) to obtain insight in the electronic structure of both the neutral and the cation. In this review we highlight most recent advances on the spectroscopy of biradicals and biradicaloids, utilizing PEPICO spectroscopy and vacuum ultraviolet (VUV) synchrotron radiation.

Tuning orbital-selective phase transitions in a two-dimensional Hund’s correlated system

Hund’s rule coupling (J) has attracted much attention recently for its role in the description of the novel quantum phases of multi-orbital materials. Depending on the orbital occupancy, J can lead to various intriguing phases. However, experimental confirmation of the orbital occupancy dependency has been difficult as controlling the orbital degrees of freedom normally accompanies chemical inhomogeneities. Here, we demonstrate a method to investigate the role of orbital occupancy in J related phenomena without inducing inhomogeneities. By growing SrRuO3 monolayers on various substrates with symmetry-preserving interlayers, we gradually tune the crystal field splitting and thus the orbital degeneracy of the Ru t2g orbitals. It effectively varies the orbital occupancies of two-dimensional (2D) ruthenates. Via in-situ angle-resolved photoemission spectroscopy, we observe a progressive metal-insulator transition (MIT). It is found that the MIT occurs with orbital differentiation: concurrent opening of a band insulating gap in the dxy band and a Mott gap in the dxz/yz bands. Our study provides an effective experimental method for investigation of orbital-selective phenomena in multi-orbital materials.

Role of excitation in the electron rotational asymmetry in circularly polarized laser fields

We comparatively study electron rotational asymmetries in photoionization of excited hydrogen atoms and photodetachment of the fluorine anions in single circularly polarized laser fields by numerically solving the three-dimensional time-dependent Schrödinger equation. We first show that single-photon ionization (or detachment) is more favorable as the electron initially corotates with respect to the direction of the laser field. More interestingly, we systematically demonstrate that the electron rotational asymmetry of the excited hydrogen atom is completely contrary to that of the fluorine anion in the multiphoton ionization (or detachment) regime, which can be attributed to the role played by excited bound states by analyzing the total excitation probability in the excited hydrogen atom. Furthermore, we also confirm that the electron rotational asymmetry of and degenerate orbitals in the excited hydrogen atom changes when the ionization mechanism switches from three-photon to over-the-barrier.

Bandwidth Control and Symmetry Breaking in a Mott‐Hubbard Correlated Metal

AbstractIn Mott materials strong electron correlation yields a spectrum of complex electronic structures. Recent synthesis advancements open realistic opportunities for harnessing Mott physics to design transformative devices. However, a major bottleneck in realizing such devices remains the lack of control over the electron correlation strength. This stems from the complexity of the electronic structure, which often veils the basic mechanisms underlying the correlation strength. This study presents control of the correlation strength by tuning the degree of orbital overlap using picometer‐scale lattice engineering. This study illustrates how bandwidth control and concurrent symmetry breaking can govern the electronic structure of a correlated SrVO3 model system. This study shows how tensile and compressive biaxial strain oppositely affect the SrVO3 in‐plane and out‐of‐plane orbital occupancy, resulting in the partial alleviation of the orbital degeneracy. The spectral weight redistribution under strain is derived and explained, which illustrates how high tensile strain drives the system toward a Mott insulating state. Implementation of such concepts can push correlated electron phenomena closer toward new solid‐state devices and circuits. These findings therefore pave the way for understanding and controlling electron correlation in a broad range of functional materials, driving this powerful resource for novel electronics closer toward practical realization.

Frontier Orbital Views of Stacked Aromaticity.

Recent studies have theoretically and experimentally demonstrated that antiaromatic molecules with 4n π electrons exhibit stacked aromaticity according to π-π stacking when arranged in a face-to-face manner. However, the mechanism of its occurrence has not been clearly studied. In this study, we investigated the mechanism of stacked aromaticity using cyclobutadiene. When the antiaromatic molecules are stacked in a face-to-face manner, the orbital interactions between the degenerate singly occupied molecular orbitals (SOMOs) of the monomer unit cause a larger energy gap between the degenerate highest-occupied molecular orbitals (HOMOs) and the lowest-unoccupied molecular orbitals (LUMOs) of the dimer. However, the antiaromatic molecules are more stable in less symmetric conformations, mainly because of pseudo-Jahn-Teller distortions. In the case of cyclobutadiene, the two SOMOs of the monomer unit split into HOMO and LUMO because of the bond alternation. When the molecules are stacked in a face-to-face manner, the HOMO-LUMO gap of the dimer is smaller than that of the monomer due to the interactions between the HOMOs and LUMOs of the two monomer units. When the monomer units are within a specific distance of each other, the HOMO and LUMO of the dimer, which correspond to antibonding and bonding between the units, respectively, are interchanged. This alternation of molecular orbitals may result in an increase in the bond strength between the monomer units, exhibiting stacked aromaticity. We demonstrated that it is possible to control the distance exhibited by stacked aromaticity by engineering the HOMO-LUMO gap of the monomer units.