Orbital Correlation Research Articles

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra.

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

Spatial and orbital planes of the Milky Way satellites: unusual but consistent with ΛCDM

ABSTRACT We examine the spatial distribution and orbital pole correlations of satellites in a suite of zoom-in high-resolution dissipationless simulations of Milky Way (MW)-sized haloes. We use the measured distribution to estimate the incidence of satellite configurations as flattened and as correlated in their orbital pole distribution as the satellite system of the MW. We confirm that this incidence is sensitive to the radial distribution of subhaloes and thereby to the processes that affect it, such as artificial disruption due to numerical effects and disruption due to the central disc. Controlling for the resolution effects and bracketing the effects of the disc, we find that the MW satellite system is somewhat unusual (at the ≈2–3σ level) but is statistically consistent with the Lambda cold dark matter model, in general agreement with results and conclusions of other recent studies.

Discerning element and site-specific fluctuations of the charge-orbital order in Fe3O4 below the Verwey transition

Despite countless experimental probes into magnetite's electronic structure across the Verwey transition ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$, the exact origin of this archetypical metal-insulator transition remains a puzzle. Advanced x-ray diffraction techniques have mostly resolved the monoclinic structure of the insulating phase, including interatomic bond lengths, but the complexity of the charge-orbitally ordered state is difficult to disentangle. We combined resonant elastic x-ray scattering and x-ray photon correlation spectroscopy to probe charge-orbital fluctuations in the insulating state of magnetite. By accessing the Bragg forbidden ${(00\frac{1}{2})}_{\mathrm{c}}$ peak at the oxygen $K$-edge, we complement our previous study on the iron ${L}_{\mathit{3}}\ensuremath{-}\mathrm{edge}$ to reveal the dynamics of the iron $3d$ and oxygen $2p$ orbital domains. Our new results reveal a decoupling of the orbital correlation lengths between the oxygen $2p$ states and site-specific iron $3d$ states, and we further show charge-orbital domain fluctuations at the iron ${t}_{2g}$ orbital sites of trimeron chains. These results also demonstrate an experimental method capable of distinguishing electronic dynamics between the oxygen ligands and the transition metal that underpins emergent behaviors in complex oxides.

Orbital correlations in ultrathin films of late transition metals

We develop a two-orbital Hubbard model of electron correlations in ultrathin (111)-oriented fcc films of late transition metals such as Co and Ni. Our model indicates that the Mott-Hund's interaction results in ferromagnetic nearest-neighbor orbital correlations. Frustration associated with the mismatch between orbital and crystal symmetries prevents orbital ordering, resulting in the orbital liquid state. This state can be manifested in phenomena involving spin-orbit coupling, such as magnetic anisotropy.

Static embedding with pair coupled cluster doubles based methods.

Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.

The relationship between structure and excited-state properties in polyanilines from geminal-based methods.

We employ state-of-the-art quantum chemistry methods to study the structure-to-property relationship in polyanilines (PANIs) of different lengths and oxidation states. Specifically, we focus on leucoemeraldine, emeraldine, and pernigraniline in their tetramer and octamer forms. We scrutinize their structural properties, HOMO and LUMO energies, HOMO-LUMO gaps, and vibrational and electronic spectroscopy using various Density Functional Approximations (DFAs). Furthermore, the accuracy of DFAs is assessed by comparing them to experimental and wavefunction-based reference data. We perform large-scale orbital-optimized pair-Coupled Cluster Doubles (oo-pCCD) calculations for ground and electronically excited states and conventional Configuration Interaction Singles (CIS) calculations for electronically excited states in all investigated systems. The EOM-pCCD+S approach with pCCD-optimized orbitals allows us to unambiguously identify charge transfer and local transitions across the investigated PANI systems-an analysis not possible within a delocalized canonical molecular orbital basis obtained, for instance, by DFAs. We show that the low-lying part of the emeraldine and pernigraniline spectrum is dominated by charge transfer excitations and that polymer elongation changes the character of the leading transitions. Furthermore, we augment our study with a quantum informational analysis of orbital correlations in various forms of PANIs.

Understanding ground and excited-state molecular structure in strong magnetic fields using the maximum overlap method

ABSTRACT The maximum overlap method (MOM) provides a simple but powerful approach for performing calculations on excited states by targeting solutions with non-Aufbau occupations from a reference set of molecular orbitals. In this work, the MOM is used to access excited states of H 3 + and H 3 in strong magnetic fields. The lowest 1 A 1 ′ , 1 E ′ and 3 E ′ states of H 3 + in the absence of a field are compared with the corresponding states in strong magnetic fields. The changes in molecular structure in the presence of the field are examined by performing excited state geometry optimisations using the MOM. The 3 E ′ state is significantly stabilised by the field, becoming the ground state in strong fields with a preferred orientation perpendicular to the applied field. Its potential energy surface evolves from being repulsive to bound, with an equilateral equilibrium geometry. In contrast, the 1 A 1 ′ state is destabilised and its structure distorts to an isosceles form with the longest H−H bond parallel to the applied field. Comparisons are made with the 4 A 2 ′ state of H3, which also becomes bound with an equilateral geometry at high fields. The structures of the high-spin ground states are rationalised by orbital correlation diagrams constructed using constrained geometry optimisations.

Spin-orbital liquids and insulator-metal transitions on the pyrochlore lattice

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin-glass metal and then to a spin-glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure and establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The electrons see an effective disorder, due to orbital frustration, already in the ferromagnetic phase. The disorder is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. As a result, increasing AF coupling shifts the metal-insulator transition to lower Hubbard interaction and gives it an additional ``Anderson'' character. We provide detailed results on the magnetic and orbital correlations, the density of states, and the optical conductivity.

Core spectroscopy of oxazole.

We have measured, analyzed, and simulated the ground state valence photoelectron spectrum, x-ray absorption (XA) spectrum, x-ray photoelectron (XP) spectrum as well as normal and resonant Auger-Meitner electron (AE) spectrum of oxazole at the carbon, oxygen, and nitrogen K-edge in order to understand its electronic structure. Experimental data are compared to theoretical calculations performed at the coupled cluster, restricted active space perturbation theory to second-order and time-dependent density functional levels of theory. We demonstrate (1) that both N and O K-edge XA spectra are sensitive to the amount of dynamical electron correlation included in the theoretical description and (2) that for a complete description of XP spectra, additional orbital correlation and orbital relaxation effects need to be considered. The normal AE spectra are dominated by a singlet excitation channel and well described by theory. The resonant AE spectra, however, are more complicated. While the participator decay channels, dominating at higher kinetic energies, are well described by coupled cluster theory, spectator channels can only be described satisfactorily using a method that combines restricted active space perturbation theory to second order for the bound part and a one-center approximation for the continuum.

Classical and quantum orbital correlations in molecular electronic states

The quantum superposition principle has been extensively utilized in the quantum mechanical description of bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of near-exact electronic wavefunctions. On the other hand, its existence in composite systems may give rise to nonclassical correlations that are regarded as a resource in quantum technologies. Here, we approach the electronic ground states of three prototypical molecules in the light of the framework set by fermionic information theory. By introducing the notion of orbital discord, we additively decompose the pairwise orbital correlations into their classical and quantum parts in the presence of superselection rules. We observe that quantum orbital correlations can be stronger than classical orbital correlations though not often. Moreover, quantum orbital correlations can survive even in the absence of orbital entanglement depending on the symmetries of the constituent orbitals. Finally, we demonstrate that orbital entanglement would be underestimated if the orbital density matrices were treated as qubit states.

Influence of Multi‐Orbitals and Hund's Coupling Induced Pseudogap on Specific Heat Jump in Iron‐Pnictide High T c Superconductors

A three-orbital per site theoretical model study is attempted to analyze nature of specific heat in iron-based superconductors. Based on recent experimental data in these systems, it is found that Fe five 3d orbitals, Hund’s coupling and intra- and inter-electron orbital correlations play significant role in electronic properties of these systems. Thus, in present work, we employed model Hamiltonian, containing hopping between orbitals, Hund’s coupling and intra- and inter- orbital Coulomb interactions for iron pnictide. Employing Green’s function technique within BCS mean field approximation, expressions of superconducting energy gap parameter and quasiparticle energies are obtained. Considering these parameters, we calculated specific heat and analyzed its variation with temperature and other parameters of model Hamiltonian. Also, a pseudogap (PG) parameter, arising out of multi-orbitals’ Hund’s coupling, as supported by ARPES and STM experiments, is introduced. The expression of specific heat is numerically analyzed to pinpoint its variation below and above transition temperature (T c ). A self-consistent numerical analysis of the specific heat jump as a function of multi-orbital hopping, electron interactions and Hund’s coupling in terms of PG parameter is shown in detail. Finally, we compared outcomes with recent theoretical and experimental data available on specific heat variations in iron superconductors like LaOFeAs system. This article is protected by copyright. All rights reserved.

Anatomical investigation on the craniofacial and ocular morphometrics of the male Western Cattle egret (Bubulcus ibis)

The heron species, Cattle egret (Bubulcus ibis) can be found all over the world. In the South-Western region of Nigeria, they are colonial, white in colour, and are seen in open lands and around water bodies. Morphometric data are important parameter in the assessment of functional morphology, hence we here present for the first time, data on the craniofacial indices of cattle egret. The cranium, nasal, orbital and beak morphometric indices and correlation data of the cattle egret were investigated on the fresh specimen and macerated skull of the male cattle egrets, using the GraphPad Prism. The height of the cranium was 33.92±0.970 cm, while the cranium length and breadth were 52.92±1.800 and 34.48±1.714, respectively. The right eye socket length, 36.17±5.636 and breadth, 31.67±2.160 were slightly greater than the left eye socket length, 35.92±4.128 and breadth, 31.00±2.757. There was a strong positive correlation between the right eye socket breadth and the left eye socket breadth (r=0.940), and also, a very strong positive correlation was found between the right and the left eye socket length (r=0.981). Results showed the foramen magnum length and breadth to be 19.17±0.753 and 18.83±0.753, respectively, however, a low positive correlation was recorded between the foramen magnum length and breadth (r=0.059). A strong positive correlation was observed between the upper beak length and the lower beak length (r=0.901), while similar values were recorded for the nasal breadth and length, respectively. Data generated from this study will prove useful in comparative, regional and clinical anatomy and could also help in identifying archaeological remains of the cattle egrets.

Revealing the Orbital Angular Momentum Spectrum and Correlation Phase of Optical Vortices With Wander Perturbations and Spiral Offsets

Controlling the orbital angular momentum (OAM) spectrum, as well as the modulus and phase of the first-order correlation function of a vortex beam produced by a dynamic wander source, is critical for the use of OAM photons in turbulent environments. Based on a derived analytical formula for the first-order correlation function of the light field, a theoretical model and an experimental approach are proposed for synthesizing and detecting complex wander vortex beams in the laboratory. Wander perturbations and spiral phase offsets are considered. The correlation phase and OAM spectrum of complex wander vortex beams are measured with a single spatial light modulator (SLM). The experimental results agree with the theoretical simulations and show that, given a limited region of interest, wander perturbations broaden the OAM spectrum asymmetrically with respect to the initial input mode, with a higher proportion of lower ordered non-signal modes than higher ordered modes. For a large spiral phase offset, the main peak of the OAM spectrum shifts away from the signal mode and toward a lower ordered side mode. Generation and measurement strategies have significant potential for free-space communication and remote sensing in turbulent environments.

Quasiparticle multiplets and 5f electronic correlation in prototypical plutonium borides

In this paper, we investigate the electronic structures of plutonium borides (PuB x , x = 1, 2, 6, 12) to uncover the fascinating bonding behavior and orbital dependent correlations of 5f valence electrons by using the density functional theory combined with single-site dynamical mean-field method. We not only reproduce the correlated topological insulator of PuB6, but also predict the metallicity in PuB x (x = 1, 2, 12). It is found that the band structure, density of states, hybridization functions all indicate partially itinerant 5f states in PuB x (x = 1, 2, 6, 12). Especially, quasiparticle multiplets induced noteworthy valence state fluctuations implying the mixed-valence behavior of plutonium borides. Moreover, the itinerant degree of freedom for 5f electrons in PuB x (x = 1, 2, 12) is tuned by hybridization strength between 5f states and conduction bands, which is affected by atomic distance in plutonium borides. Lastly, 5f electronic correlations encoded in the electron self-energy functions demonstrate moderate 5f electronic correlations in PuB6 and orbital selective 5f electronic correlations in PuB x (x = 1, 2, 12). Consequently, the understanding of electronic structure and related crystal structure stability shall shed light on exploring novel 5f electrons states and ongoing experiment study.

Lattice and magnetic dynamics in the YVO3 Mott insulator studied by neutron scattering and first-principles calculations

The Mott insulator YVO$_{3}$ with $T_{N}$ = 118 K is revisited to explore the role of spin, lattice and orbital correlations across the multiple structural and magnetic transitions observed as a function of temperature. Upon cooling, the crystal structure changes from orthorhombic to monoclinic at 200 K, and back to orthorhombic at 77 K, followed by magnetic transitions. From the paramagnetic high temperature phase, C-type ordering is first observed at 118 K, followed by a G-type spin re-orientation transition at 77 K. The dynamics of the transitions were investigated via inelastic neutron scattering and first principles calculations. An overall good agreement between the neutron data and calculated spectra was observed. From the magnon density of states, the magnetic exchange constants were deduced to be $J_{ab}$ = $J_{c}$ = -5.8 meV in the G-type spin phase, and $J_{ab}$ = -3.8 meV, $J_{c}$ = 7.6 meV at 80 K and $J_{ab}$ = -3.0 meV, $J_{c}$ = 6.0 meV at 100 K in the C-type spin phase. Paramagnetic scattering was observed in the spin ordered phases, well below the C-type transition temperature, that continuously increased above the transition. Fluctuations in the temperature dependence of the phonon density of states were observed between 50 and 80 K as well, coinciding with the G-type to C-type transition. These fluctuations are attributed to optical oxygen modes above 40 meV, from first principles calculations. In contrast, little change in the phonon spectra is observed across $T_{N}$.

Correlation-assisted Peierls gap in divalent metal ion (Zn+2, Cd+2, Mg+2, Ca+2, Sr+2 and Ba+2) doped M1-VO2: First principle analysis

This work investigates energetic, electronic structures and optical properties of (M+2 = Zn, Cd, Mg, Ca, Sr, and Ba) doped M1-VO2 systems using density functional theory (DFT) with DFT + U extension to describe the strong V d-d orbital correlations. The results show that M+2 doping ions increase the internal stress, which weakens the stability of insulating states. The calculated formation energies indicate that this incorporation is possible at high concentrations and more favorites under O-rich growth conditions. In addition, analysis of the electronic structure reveals that the decrease of Eg1 values at 12.5% of Zn+2 doping is not only due to the excess electrons generating by oxygen vacancies as reported by experimental results. Multiple degrees of freedom contribute to the gap change in both case of AEMs or TM doping, where the strength of the covalent bonds reflects which; electronic correlation, structural distortion and orbital filling are the dominants factors. Furthermore, the energy upshift of the π∗ band due to the decrease of V–O apical bond lengths leads to the gap widening between O2p and V3dπ* orbitals and the weakly reduction of transition energy.

Properties of spinel-type Ti-Li-M composite oxides (M = Li, Na, Cu, and Ag) predicted by density functional theory.

Spinel-type titanate is an important material already being used as a stable anode for Li-ion batteries. In addition, spinel titanate shows superconducting properties upon tuning the amount of Li+-doping; hence, research on magnetic and superconducting materials has been conducted. However, it is believed that only the tiny Li+ monocation can occupy the 8a sites due to its small voids and the charge valence with Ti cations. In recent years, new spinel-type titanium oxides have been discovered, in which 8a sites are occupied by Na+ or Ag+. Although the application of these new compounds to catalyst and electrode materials has been attempted, the effect of 8a site monocations on the physical properties of spinel-type titanium oxide is unclear. In this study, to systematise the effects of 8a-site monocations on the Ti-O framework, theoretical calculations based on density functional theory (DFT), such as GGA, GGA+U, and hybrid-DFT, were performed for the electronic structures and geometric stabilities of four spinel-titanium oxides: LTO (8a sites occupied by Li+), NTO (8a sites occupied by Na+), CTO (8a sites occupied by Cu+), and ATO (8a sites occupied by Ag+). Furthermore, to verify the effect of the partial substitution, Li+, Na+, Cu+, and Ag+ doping of LTO, NTO, CTO, and ATO was also investigated. Throughout these calculations, the performance of spinel-type titanates can be categorised by (1) the magnitude of O-displacement and (2) the orbital correlation between the Ti-O framework and the 8a site cations. By appropriately selecting cations, the spinel titanates can be applied to battery materials, catalysts, optical materials, photocatalysts, and precursors to these materials.

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach.

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.

Tuning the Quantum Chemical Properties of Flavins via Modification at C8.

Flavins are central to countless enzymes but display different reactivities depending on their environments. This is understood to reflect modulation of the flavin electronic structure. To understand changes in orbital natures, energies, and correlation over the ring system, we begin by comparing seven flavin variants differing at C8, exploiting their different electronic spectra to validate quantum chemical calculations. Ground state calculations replicate a Hammett trend and reveal the significance of the flavin π-system. Comparison of higher-level theories establishes CC2 and ACD(2) as methods of choice for characterization of electronic transitions. Charge transfer character and electron correlation prove responsive to the identity of the substituent at C8. Indeed, bond length alternation analysis demonstrates extensive conjugation and delocalization from the C8 position throughout the ring system. Moreover, we succeed in replicating a particularly challenging UV/Vis spectrum by implementing hybrid QM/MM in explicit solvents. Our calculations reveal that the presence of nonbonding lone pairs correlates with the change in the UV/Vis spectrum observed when the 8-methyl is replaced by NH2, OH, or SH. Thus, our computations offer routes to understanding the spectra of flavins with different modifications. This is a first step toward understanding how the same is accomplished by different binding environments.

Tuning the Quantum Chemical Properties of Flavins via Modification at C8.

Flavins are central to countless enzymes but display different reactivities depending on their environments. This is understood to reflect modulation of the flavin electronic structure. To understand changes in orbital natures, energies, and correlation over the ring system, we begin by comparing seven flavin variants differing at C8, exploiting their different electronic spectra to validate quantum chemical calculations. Ground state calculations replicate a Hammett trend and reveal the significance of the flavin π-system. Comparison of higher-level theories establishes CC2 and ACD(2) as methods of choice for characterization of electronic transitions. Charge transfer character and electron correlation prove responsive to the identity of the substituent at C8. Indeed, bond length alternation analysis demonstrates extensive conjugation and delocalization from the C8 position throughout the ring system. Moreover, we succeed in replicating a particularly challenging UV/Vis spectrum by implementing hybrid QM/MM in explicit solvents. Our calculations reveal that the presence of nonbonding lone pairs correlates with the change in the UV/Vis spectrum observed when the 8-methyl is replaced by NH2, OH, or SH. Thus, our computations offer routes to understanding the spectra of flavins with different modifications. This is a first step toward understanding how the same is accomplished by different binding environments.