Electron Correlation Interactions Research Articles

Perturbational Analysis of Magnetic Force Theorem for Magnetic Exchange Interactions in Molecules and Solids

There have been increasing efforts to compute magnetic exchange coupling constants for transition metal complexes and magnetic insulators using the magnetic force theorem and Green’s function-based linear response methods. These were originally conceived for magnetic metals, yet it has not been clear how these methods fare conceptually with the conventional models based on electron-correlation interactions among so-called magnetic orbitals. We present a spinor-based theoretical analysis pertinent to the magnetic force theorem and linear response theory using Brillouin–Wigner perturbation method and Green’s function perturbation method, and we shed light on the conceptual nature of the Lichtenstein formula in its applications for calculations of the total energy and magnetic exchange coupling constants for both molecules and solids. Derivation of the magnetic force theorem in this perturbational analysis identifies the first-order energy correction terms, which are considered as the ferromagnetic component for the magnetic exchange interactions of transition metal compounds but are not included in the Lichtenstein formula. Detailed perturbational analysis of the energy components involved in the magnetic force theorem identifies the energy components that are missing in the Lichtenstein formula but are critical in the Anderson’s model for transition metal complexes and magnetic insulators where magnetic orbitals can overlap.

Reconciliation of Theoretical Lifetimes of the 5s5p Metastable State for 88Sr with Measurement: The Role of the Blackbody-Radiation-Induced Decay

We conducted measurement and calculation to resolve the long-standing large discrepancy in the metastable state lifetime for the 88Sr atom between theoretical and experimental results. The present lifetime s, measured using the magneto-optical trap as a photon amplifier to detect the weak decay events, is approximately 60% larger than the previous experimental value s. By considering the electron correlation effects in the framework of the multiconfiguration Dirac–Hartree–Fock theory, we obtained a theoretical lifetime of 1079(54) s, which lies in the range of measurements with error bars. Furthermore, we considered the higher-order electron correlation and Breit interaction to control the uncertainty of the theoretical calculation. The significant improvement in the agreement between calculations and measurements is attributed to the updated blackbody radiation-induced decay rate.

Magnetism, spin-phonon coupling and Kitaev interaction in Mott insulator La2ZnIrO6 single crystal oxide

Due to the coexistence of spin-orbital coupling (SOC) and electron correlation interactions, double perovskite iridates are considered ideal material to investigate the Mott insulating states and Kitaev interactions. In this work, we studied the spin-orbital coupling (SOC), spin-phonon coupling (SPC), and Kitaev magnetism in antiferromagnetic La2ZnIrO6 single crystal by magnetometer and Raman scattering spectroscopy measurements. Based on the temperature dependence of the magnetization under different magnetic fields, we found that all the initial temperatures of the paramagnetic-ferromagnetic transition were basically concentrated around 8.8 K, while the temperature of ferromagnetic-antiferromagnetic transition continued to decrease from 7 K to 2 K. Anomalous modes of frequency softening at magnetic-order temperature were detected from the polarized Raman scattering spectra, indicating the presence of strong spin-phonon coupling and Kitaev interaction in La2ZnIrO6.

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of HeliumSupported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), and the National Natural Science Foundation of China (Grant Nos. 11774344 and 11474033).

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s 2, 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

Covalent states and spin-orbit coupling in electronic and magnetic properties of Ba6Y2Rh2Ti2O17

In $4d$ and $5d$ transition metal compounds, novel properties usually arise from the interplay of electron correlation and spin-orbit interaction based on isolated single-site physics. However, there are also a large number of compounds where the intersite effect plays an important role. Here, we report the electronic and magnetic properties of a hexagonal perovskite ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$, which is featured with widely spaced ${\mathrm{Rh}}_{2}{\mathrm{O}}_{9}$ spin dimers. Our calculations indicate that ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ is a semiconductor with a small band gap of 0.2 eV, which is consistent with the experimental value of 0.16 eV. In particular, the band gap of ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ is not due to the ${J}_{\mathrm{eff}}=1/2$ state from isolated single site but due to the joint effect of covalent states and spin-orbit coupling formed by Rh's ${t}_{2g}$ orbitals inside the ${\mathrm{Rh}}_{2}{\mathrm{O}}_{9}$ dimers. Furthermore, we find a giant magnetic anisotropy energy (MAE) of about 20 meV/Rh in ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ with the easy axis being the $c$ axis. Model calculations show that the giant MAE is mainly due to first-order perturbation on the doubly degenerate antibonding states of ${e}_{g}^{\ensuremath{\pi}}$ orbitals. Our work not only reveals the interesting electronic and magnetic properties of ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ but also could stimulate more studies on the materials with $4d$ and $5d$ spin dimers.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates.

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Substrate effect on excitonic shift and radiative lifetime of two-dimensional materials

Substrates have strong effects on optoelectronic properties of two-dimensional (2D) materials, which have emerged as promising platforms for exotic physical phenomena and outstanding applications. To reliably interpret experimental results and predict such effects at 2D interfaces, theoretical methods accurately describing electron correlation and electron-hole interaction such as first-principles many-body perturbation theory are necessary. In our previous work (2020 Phys. Rev. B 102 205113), we developed the reciprocal-space linear interpolation method that can take into account the effects of substrate screening for arbitrarily lattice-mismatched interfaces at the GW level of approximation. In this work, we apply this method to examine the substrate effect on excitonic excitation and recombination of 2D materials by solving the Bethe–Salpeter equation. We predict the nonrigid shift of 1s and 2s excitonic peaks due to substrate screening, in excellent agreements with experiments. We then reveal its underlying physical mechanism through 2D hydrogen model and the linear relation between quasiparticle gaps and exciton binding energies when varying the substrate screening. At the end, we calculate the exciton radiative lifetime of monolayer hexagonal boron nitride with various substrates at zero and room temperature, as well as the one of WS2 where we obtain good agreement with experimental lifetime. Our work answers important questions of substrate effects on excitonic properties of 2D interfaces.

A scaled explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol-1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

Radial and Angular Electron Ejection Patterns of Two-Electron Quantum Dots in THz Fields

In this work, we develop and apply an ab-initio method to calculate the joint radial- and- angular electron distributions following the interaction of two-electron spherical quantum dots (QD) with intense terahertz pulses of subpicosecond duration. By applying the method to two QDs of different size, we could investigate two particular ionization mechanisms: the direct and the sequential two-photon double ionization. According to our results, the two ionization mechanisms show some similarity in the angular distribution patterns, whereas the corresponding radial distributions are distinctly different, associated with their joint kinetic energy spectrum. We also discuss the time-evolution of the ionization process in the context of the different nature of the interaction of the QD with the external radiation and the electron–electron correlation interactions.

Establishing best practices to model the electronic structure of CuFeO2 from first principles

The cuprous delafossite, ${\mathrm{CuFeO}}_{2}$, has received significant attention in recent years as a potential photocathode material in photoelectrochemical water-splitting cells. Presented herein is an investigation of the electronic structure of ${\mathrm{CuFeO}}_{2}$ in the framework of density functional theory. We have benchmarked three of the most popular formulations for the treatment of the electron exchange and correlation interactions, highlighting their strengths and weaknesses in predicting electronic structures compatible with the available spectroscopic measurements. Although some features are correctly reproduced by the simplest approach, which is based on the generalized gradient approximation, this fails in describing the fundamental semiconducting character of the material. The introduction of the fully self-consistent Hubbard $U$ correction in the exchange correlation functional accounts explicitly for the on-site Coulomb interaction among localized $d$ electrons, thereby opening a gap in the band structure. However, our results indicate that the $U$ correction disrupts the crystal-field splitting of the ${t}_{2g}$ and ${e}_{g}$ states, resulting in an inaccurate description of the conduction-band edge. We provide a qualitative and quantitative analysis to explain why the ${t}_{2g}$ and ${e}_{g}$ states behave differently when the Hubbard correction is switched on. We find that best practice for accurate, yet computationally viable, simulations of CFO makes use of hybrid functionals, where the fraction of exact exchange is not arbitrarily selected but tuned according to the static dielectric constant of the material. In this case, theoretical predictions are found to be in excellent agreement with experimental results.

Charge Transfer Interactions of p-Azoxyanisole Complexes for Electrooptical Activity

In particular interactions due to organic-inorganic molecules results self assembled structures organize supramolecular structures for molecular, electronic and electrooptical properties. Supramolecular structures originated are complexes with organic (p-azoxyanisole) molecule, synthesized with metal nanoparticles (iron, copper and aluminium.) Spectroscopic studies interpret infrared spectra with wavenumbers of characteristic bands in assigned regions; wavenumbers with reduced intensity in Raman spectra attribute metal-organic framework with charge transfer. Designed frame work with dense participation of carriers interpret electron correlation and exchange interaction specifying molecular, electronic and electrooptical properties with Gaussian package using electron density method. Deterministic procedure attribute vital role of charge transfer interactions responsible in formation of complex with improvement in properties responsible for electrooptical activity.

Energy Levels and Transition Parameters in Ce6+ from MCDHF Model

Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations and subsequent Relativistic Configuration Interaction (RCI) calculations have been performed for the 5s\({}^{2}\)5p\({}^{4}\), 5s\({}^{2}\)5p\({}^{3}\)6s and 5s5p\({}^{5}\) configurations of six times ionized cerium using GRASP2018 package. The electron correlation effects, (BI) interaction and Quantum Electrodynamics (QED) effects have been considered in the calculation. Energy levels, oscillator strength and transition probabilities among the transitions of 5s\({}^{2}\)5p\({}^{4}\), 5s5p\({}^{5}\) and 5s\({}^{2}\)5p\({}^{3}\)6s have been calculated. The calculated energy levels are compared with experimental data available and show good agreement with it.

First-principles calculation study of electronic structures of alkali metals (Li, K, Na and Rb)-incorporated formamidinium lead halide perovskite compounds

Electronic structures of alkali metals (Li, Na, K or Rb)-incorporated formamidinium lead halide perovskite compounds were investigated by first-principles calculation. The conduction band were supplied with electrons from energy levels at 2s, 3s, 4s and 5s orbital of alkali metal to energy levels at 6p orbital of Pb atom in the perovskite crystal. Deviation of charge distribution in the perovskite crystal promoted the photo-induced charge generation, electron correlation and electron-lattice interaction as phonon effectiveness. The chemical shifts of 127I-NMR in the perovskite crystal were originated in a slight perturbation of the coordination structure with nuclear quadruple interaction based on the electric field gradient. The slight incorporation of alkali metal near the ligand structure decreased the enthalpy with the Gibbs free-energy by contribution of the entropy due to the PI stretching vibration.

Novel Molecular Magnetism at Surface Arising from Electron Correlation and Spin-Orbit Interaction

Novel Molecular Magnetism at Surface Arising from Electron Correlation and Spin-Orbit Interaction

Ab initio calculations of spectroscopic properties of Cr5+ using coupled-cluster theory

In this paper, we present ionization potentials, excitation energies, fine-structure splittings, and allowed and forbidden transition amplitudes of five-times-ionized chromium ion as calculated using the relativistic coupled-cluster theory. The wave functions of different single-valence electron configurations are generated using the Dirac–Coulomb–Gaunt Hamiltonian. Effects of electron correlation and Gaunt interaction in the calculations of these properties are studied explicitly. Contributions from different correlation terms associated with the coupled-cluster theory are reported in the calculations of the transition amplitudes. Using these amplitudes and the experimental wavelengths, we calculate astrophysically important transition parameters of several transition lines. Lifetime of the metastable state \(3d^2D_{5/2}\) is found to be 111.66 s.

Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models

We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU(2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin-orbit interaction coexist.

Valence state of manganese and iron ions in La1−xAxMnO3 (A = Ca, Sr) and Bi1−xSrxFeO3 systems from Mn2p, Mn3s, Fe2p and Fe3s X-ray photoelectron spectra. Effect of delocalization on Fe3s spectra splitting

La1−xCaxMnO3 (x = 0.5, 0.7, 0.85, 0.95) ceramic samples are synthesized by solid state reaction method. Mn3s and Mn2p X-ray photoelectron spectra (XPS) of La1−xCaxMnO3, and Fe3s-spectra of Bi1−xSrxFeO3 (0 ≤ x ≤ 1) are measured at room temperature. Both Mn3+ and Mn4+ ions are discovered in La1−xCaxMnO3 similarly to the case of Fe3+ and Fe4+ found earlier in Bi1−xSrxFeO3 ceramics. Relative Mn3+/Mn4+ contents are determined by fitting measured Mn2p spectra with combinations of Mn2p spectra of compounds containing tri- and quadrivalent Mn ions. Relative portion of Mn4+ is shown to increase with the increase of x. Fe3s spectrum splitting in Bi1−xSrxFeO3 increases with x in contrast to the Mn3s-spectrum splitting in La1−xCaxMnO3 and La1−xSrxMnO3. Anomalous behavior of Fe3s splitting is explained in the frame of the model of partly itinerant 3d-electrons by strong effect of 3d electron delocalization on electron correlation interaction in final state of 3s photoabsorption.

Metal–Insulator Transition ofc-Axis-Controlled V2O3Thin Film

We prepared c-axis-controlled V2O3 thin films by RF magnetron sputtering and proved their metal–insulator transition (MIT) in terms of electronic structure. The lattice constant of the c-axis depends on the film thickness and the lattice mismatch of the substrate and V2O3. MIT is observed at a temperature of ∼150 K in the V2O3 thin films with the lattice constants of c = 13.942 and 13.992 A, although the V2O3 thin film with c = 13.915 A exhibits metallic conductivity without MIT. The electron correlation energy, which corresponds to the energy difference between the lower Hubbard band and the upper Hubbard band, increases with increasing lattice constant of the c-axis. Bandwidths also depend on the lattice constant of the c-axis. The intensity of the a1g orbital around the Fermi level decreases with increasing lattice constant of the c-axis. These results suggest that the electron correlation interaction and bandwidths play important roles in the MIT of c-axis-controlled V2O3 thin films.

From Ligand Fields to Molecular Orbitals: Probing the Local Valence Electronic Structure of Ni2+ in Aqueous Solution with Resonant Inelastic X-ray Scattering

Bonding of the Ni(2+)(aq) complex is investigated with an unprecedented combination of resonant inelastic X-ray scattering (RIXS) measurements and ab initio calculations at the Ni L absorption edge. The spectra directly reflect the relative energies of the ligand-field and charge-transfer valence-excited states. They give element-specific access with atomic resolution to the ground-state electronic structure of the complex and allow quantification of ligand-field strength and 3d-3d electron correlation interactions in the Ni(2+)(aq) complex. The experimentally determined ligand-field strength is 10Dq = 1.1 eV. This and the Racah parameters characterizing 3d-3d Coulomb interactions B = 0.13 eV and C = 0.42 eV as readily derived from the measured energies match very well with the results from UV-vis spectroscopy. Our results demonstrate how L-edge RIXS can be used to complement existing spectroscopic tools for the investigation of bonding in 3d transition-metal coordination compounds in solution. The ab initio RASPT2 calculation is successfully used to simulate the L-edge RIXS spectra.

Phenomenon of quantum entanglement in a system composed of two minimal protocells.

The quantum mechanical self-assembly of two separate photoactive supramolecular systems with different photosynthetic centers was investigated by means of density functional theory methods. Quantum entangled energy transitions from one subsystem to the other and the assembly of logically controlled artificial minimal protocells were modeled. The systems studied were based on different photoactive sensitizer molecules covalently bonded to a non-canonical oxo-guanine::cytosine supramolecule with the precursor of a fatty acid (pFA) molecule attached via Van der Waals forces, all surrounded by water molecules. The electron correlation interactions responsible for the weak hydrogen and Van der Waals chemical bonds increased due to the addition of polar water solvent molecules. The distances between the separated sensitizer, nucleotide, pFA, and water molecules are comparable to Van der Waals and hydrogen bonding radii. As a result, the overall system becomes compressed, resulting in photo-excited electron tunneling from the sensitizer (bis(4-diphenylamine-2-phenyl)-squarine or 1,4-bis(N,N-dimethylamino)naphthalene) to the pFA molecules. Absorption spectra as well as electron transfer trajectories associated with the different excited states were calculated using time dependent density functional theory methods. The results allow separation of the quantum entangled photosynthetic transitions within the same minimal protocell and with the neighboring minimal protocell. The transferred electron is used to cleave a "waste" organic molecule resulting in the formation of the desired product. A two variable, quantum entangled AND logic gate was proposed, consisting of two input photoactive sensitizer molecules and one output (pFA molecule). It is proposed that a similar process might be applied for the destruction of tumor cancer cells or to yield building blocks in artificial cells.