Spin-orbit Coupling Calculations Research Articles

Implementation of Nonadiabatic Molecular Dynamics for Intersystem Crossing Based on a Time-Dependent Density-Functional Tight-Binding Method.

Intersystem crossing (ISC) and internal conversion (IC) are types of nonadiabatic transitions that play important roles in a wide range of fields, including photochemistry, photophysics, and photobiology. The nonadiabatic molecular dynamics (NA-MD) method is a powerful tool for computational simulations of dynamic phenomena involving nonadiabatic transitions. In this study, we implemented the NA-MD method, which treats ISC and IC on an equal footing, where the electronic structure is treated at the level of the time-dependent (TD) density-functional tight-binding (DFTB) method, a low-cost semiempirical analog of TD density functional theory (DFT). In particular, the spin-orbit coupling calculation algorithm was implemented in the TD-DFTB framework, and the results showed trends similar to those obtained using TD-DFT. In addition, the NA-MD method successfully reproduced ultrafast ISC of 2-nitronaphthalene.

Hund’s three rules in actinide-containing superatoms with spin-orbit coupling calculations

The intriguing and challenge issue in magnetic superatoms is searching for the suitable candidates to validate the Hund’s rules. Here, early actinide elements (An: Ac, Th, Pa, U, Np, Pu, Am) whose 5f electrons may crossover the localization and delocalization characteristics have been chosen to alloy with Al atoms in designing magnetic An@Al12 superatoms. By doing the global minimum structure search and the spin-orbital coupling density functional theory calculations, we provide an original idea to give theoretical argument that Hund’s three rules are still applicable in superatoms, which can be related to the fillings of highly localized An-5f orbitals into large exchange-splitting 2 F superatom orbitals. Specifically, selective 5f sub-orbitals of several An dopants can exhibit a dual nature in superatomic bonding, i.e. partial 5f electrons of Pa, U and Pu are reactive whereas all 5f electrons of Np and Am are highly localized. The molecular orbital analyses, combined with the qualitative interpretation of the phenomenological superatom sub-shell model, address the intricate interplays between the structure symmetry, electronic structure, spin and orbital magnetic moments. These findings have important implications for understanding the bonding and magnetic behaviors of An-containing superatoms and pave the way for designing novel magnetic superatoms.

A Multiconfigurational Wave Function Theoretical Study on Electronic Structure and Magnetic Susceptibility of Dilanthanide Single Molecule Magnet.

Single molecule magnets (SMMs) have been a promising material for next-generation high-density information storage and molecular spintronics. N23--bridged dilanthanide complexes, {[(Me3Si)2N]2Ln(THF)(μ-η2:η2-N2)(THF)Ln[(Me3Si)2N]2}1-, exhibit high blocking temperatures and have been one of the promising candidates for future application. Rational understanding should be established between the magnetic properties and electronic structure. However, the theoretical study is still challenging due to the complexities in their electronic structures. Here, we theoretically studied the magnetic susceptibility of dilanthanide SMMs based on the state-of-the-art multistate-complete active space self-consistent field and perturbation theory at the second order and restricted active space state interaction with spin-orbit coupling calculations. Temperature dependence of the magnetic susceptibility (χmT-T curve) was quantitatively reproduced by the theoretical calculations. The complexities in the electronic states of these dilanthanide complexes originate from significantly strong static electron correlations in the lanthanide 4f and N2 π* orbitals and the SOC effect. The temperature dependence of the magnetic susceptibility results from the energy levels and magnetic properties of the low-lying excited state. The χmT values below 50 K are dominated by the ground state, while thermal distribution in the low-lying excited state affects the χmT values over 50 K. Saturation magnetization at low temperatures was also evaluated, and the result agrees with the experimental observation.

Spin-to-charge conversion origin in graphene on ferromagnetic substrate revealed: Rashba effects at Dirac point

Spin-to-charge current conversion (SCC) by inverse Rashba Edelstein effect (IREE) has been recently observed by spin-pumping experiment in single layer graphene (SLG) placed on ferromagnetic substrate composed mostly of Ni. However, a prior angle-resolved photoemission spectroscopy (ARPES) shows a negligible Rashba splitting at Γ−M, unsupportive of SCC by IREE. In this work, using density functional theory with spin-orbit coupling (DFT + SOC) calculations, we obtained the Rashba-type spin-resolved bandstructure on relevant symmetric k-points of SLG on Ni(111). We found no Rashba splitting at Γ−M confirming ARPES, however, we discovered considerable Rashba splittings in the dispersions along M−K−M, that is, involving the Dirac point, paving the way for SCC by IREE. Thus, for the first time, this work has reconciled the above seemingly contradicting spin-pumping and ARPES experiments, revealed the physical and magnetic origin of SCC by IREE and proposed means to increase the SCC coefficient without the use of heavy precious metals.

Comparison of state-interaction and spinor-representation calculations of spin-orbit coupling within exact two-component coupled-cluster theories

A benchmark study of state-interaction and spinor-representation calculations of spin-orbit coupling using the exact two-component Hamiltonians with atomic mean-field integrals (the X2CAMF schemes) at the equation-of-motion coupled-cluster singles and doubles level is reported. We adopt a version of the X2CAMF scheme with spin-orbit integrals correct to first order for the state-interaction calculations and a version correct to infinite order for the spinor-representation calculations. The differences between the state-interaction calculations with minimum active spaces to account for (quasi-)degeneracy and the spinor-representation calculations thus correspond to higher-order spin-orbit contributions. This state-interaction approach with scalar-relativistic effects accurately included in the reference functions and in the spin-orbit integrals is shown to exhibit robust performance for elements across the periodic table. On the other hand, the more rigorous spinor representation shows more rapid convergence with respect to the number of correlated electrons and is the preferred choice for accurate calculations for heavy elements.

Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling.

In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.

Mechanical Stability and Energy Gap Evolution in Cs-Based Ag, Bi Halide Double Perovskites under High Pressure: A Theoretical DFT Approach.

Due to their intrinsic stability and reduced toxicity, lead-free halide double perovskite semiconductors have become potential alternatives to lead-based perovskites. In the present study, we used density functional theory simulations to investigate the mechanical stability and band gap evolution of double perovskites Cs2AgBiX6 (X = Cl and Br) under an applied pressure. To investigate the pressure-dependent properties, the hydrostatic pressure induced was in the range of 0-100 GPa. The mechanical behaviors indicated that the materials under study are both ductile and mechanically stable and that the induced pressure enhances the ductility. As a result of the induced pressure, the covalent bonds transformed into metallic bonds with a reduction in bond lengths. Electronic properties, energy bands, and electronic density of states were obtained with the hybrid HSE06 functional, including spin-orbit coupling (HSE06 + SOC) calculations. The electronic structure study revealed that Cs2AgBiX6 samples behave as X-Γ indirect gap semiconductors, and the gap reduces with the applied pressure. The pressure-driven samples ultimately transform from the semiconductor to a metallic phase at the given pressure range. Also, the calculations demonstrated that the applied pressure and spin-orbit coupling of the states pushed VBM and CBM toward the Fermi level which caused the evolution of the band gap. The relationship between the structure and band gap demonstrates the potential for designing lead-free inorganic perovskites for optoelectronic applications, including solar cells as well as X-ray detectors.

Spin-orbit coupling corrections for the GFN-xTB method.

Spin-orbit coupling (SOC) is crucial for correct electronic structure analysis in molecules and materials, for example, in large molecular systems such as superatoms, for understanding the role of transition metals in enzymes, and when investigating the energy transfer processes in metal-organic frameworks. We extend the GFN-xTB method, popular to treat extended systems, by including SOC into the hamiltonian operator. We followed the same approach as previously reported for the density-functional tight-binding method and provide and validate the necessary parameters for all elements throughout the Periodic Table. The parameters have been obtained consistently from atomic SOC calculations using the density-functional theory. We tested them for reference structures where SOC is decisive, as in the transition metal containing heme moiety, chromophores in metal-organic frameworks, and in superatoms. Our parameterization paves the path for incorporation of SOC in the GFN-xTB based electronic structure calculations of computationally expensive molecular systems.

First principles calculations to investigate structural, electronic, mechanical, thermoelectric and optical properties of Bi- and Se-doped SnTe

Lead-based thermoelectric materials have a maximum figure of merit but are hazardous to humans and the environment. For this reason, we can replace tin-based lead-free materials and achieve the same figure of merit as lead-based thermoelectric materials. In this paper, we calculate the structural, electronic, mechanical, thermoelectric and optical properties of SnTe by co-doping it with Bi and Se using first principles calculation within the Generalized Gradient Approximation (GGA) through the Perdew-Burke-Ernzerhof(PBE) correlation scheme. Cohesive energies were calculated for each co-doping material and found to be maximum for Sn0.875Bi0.125Te0.875Se0.125. Computed elastic constants of all the cubic materials were obtained using the Thomas Charpin method integrated with the World of Interacting Electron and Nuclei due-2 Walter Kohn (WIEN2k) package. We found several mechanical properties of each material based on these constant values. We have observed an improvement in ductility and good stability for the Sn0.125Bi0.875Te0.125Se0.875 material as confirmed by various mechanical properties. Boltzmann semi-classical approach as implemented in the BoltzTraP package with and without the calculation of spin-orbit coupling. Here the figure of merit is calculated without the contribution of phonons and SOC calculations were included with the ambient conditions. From the results, we achieve maximum power factor and ZT values using SOC and non-SOC calculations. We identified that the Sn0.875Bi0.125Te0.875Se0.125 material shows a maximum ZT of 0.55, which is very much higher than the undoped SnTe and Sn0.125Bi0.875Te0.125Se0.875 material shows a ZT of 0.49 using SOC calculations. The optical properties of each material were studied at ambient conditions and Sn0.875Bi0.125Te0.875Se0.125 is consistent in the visible, IR and UV regions and it is adorable for IR detectors, solar cells and optoelectronic applications.

Accurate Spin-Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT.

Relativistic mixed-reference spin-flip (MRSF)-TDDFT is developed considering the spin-orbit coupling (SOC) within the mean-field approximation. The resulting SOC-MRSF faithfully reproduces the experiments with very high accuracy, which is also consistent with the values by four-component (4c) relativistic CASSCF and 4c-CASPT2 in the spin-orbit-energy splitting calculations of the C, Si, and Ge atoms. Even for the fifth-row element Sn, the SOC-MRSF yielded accurate splittings (∼ 3 % error). In the SOC calculations of the molecular 4-thiothymine with a third-row element, SOC-MRSF values are in excellent agreement with those of the SO-GMC-QDPT2 level, regardless of geometries and exchange-correlation functionals. The same SOC-MRSF predicted the anticipated chance of S1 (nπ*) → T1 (ππ*) intersystem crossing, even in thymine with only second-row elements. With its accuracy and practicality, thus, SOC-MRSF is a promising electronic structure protocol in challenging situations such as nonadiabatic molecular dynamics (NAMD) incorporating both internal conversions and intersystem crossings in large systems.

Photolysis of fungicide triadimefon: A combined experimental and theoretical investigation on homolytic C[sbnd]O and C[sbnd]N bonds dissociation mechanisms

Among the most frequently used fungicides, triazole has been widely applied in agriculture on many crops. Extensive usage and low effective utilization result in the widespread occurrence of this kind of chemicals in the environment. Known as an important decomposition pathway in aquatic environment, photochemical transformation is believed to significantly affect the fate of organic contaminants. Herein, we reported the detailed photodegradation mechanism of a typical triazole, triadimefon (TDF), based on a combined experimental and theoretical strategy. Our results reveled that TDF could undergo a relative fast photodegradation with a pseudo-first-order rate constant of 0.14 h−1. Photoproducts identification using high-resolution mass spectrometry (HRMS) analyses indicated two different photolysis pathways of TDF, namely, the homolytic CO and CN bonds dissociation processes. Density functional theory (DFT) and time-dependent DFT (TDDFT) methods were employed to explore these two processes. Theoretical results showed that the CO bond dissociation could occur in either the S1 or T1 state, with the energy barrier being 9.0 and 10.7 kcal/mol, respectively, while the CN bond dissociation was only possible to occur in the T1 state, with a higher energy barrier of 24.3 kcal/mol. In addition, spin-orbit coupling calculations indicated that the triplet state could be effectively populated through S1 → T3 intersystem crossing. The present study highlighted the potential application of DFT and TDDFT methods as stable methods in photochemical study.

Janus Type Monolayers of S-MoSiN2 Family and Van Der Waals Heterostructures with Graphene: DFT-Based Study.

Novel representative 2D materials of the Janus type family X-M-ZN2 are studied. These materials are hybrids of a transition metal dichalcogenide and a material from the MoSi2N4 family, and they were constructed and optimized from the MoSi2N4 monolayer by the substitution of SiN2 group on one side by chalcogen atoms (sulfur, selenium, or tellurium), and possibly replacing molybdenum (Mo) to tungsten (W) and/or silicon (Si) to germanium (Ge). The stability of novel materials is evaluated by calculating phonon spectra and binding energies. Mechanical, electronic, and optical characteristics are calculated by methods based on the density functional theory. All considered 2D materials are semiconductors with a substantial bandgap (>1 eV). The mirror symmetry breaking is the cause of a significant built-in electric field and intrinsic dipole moment. The spin-orbit coupling (SOC) is estimated by calculations of SOC polarized bandstructures for four most stable X-M-ZN2 structures. The possible van der Waals heterostructures of considered Janus type monolayers with graphene are constructed and optimized. It is demonstrated that monolayers can serve as outer plates in conducting layers (with graphene) for shielding a constant external electric field.

Magnetic ground state of plutonium dioxide: DFT+U calculations

The magnetic states of the strongly correlated system plutonium dioxide (PuO2) are studied based on the density functional theory (DFT) plus Hubbard U (DFT+U) method with spin–orbit coupling (SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO2 and a longitudinal 3k antiferromagnetic (AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT+U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT+U approaches to this system is made.

Triplet state harvesting and search for forbidden transition intensity in the nitrogen molecule.

Triplet excited states of the N2 molecule play an important role in electric discharges through air or liquid nitrogen accompanied by various afterglows. In the rarefied upper atmosphere, they produce aurora borealis and participate in other energy-transfer processes connected with atmospheric photochemistry and nightglow. In this work, we present spin-orbit coupling calculations of the intensity of various forbidden transitions, including the prediction of the electric dipole transition moment of the new band, which is strongly prohibited by the (+|-) selection rule, the new spin-induced magnetic transition, magnetic and electric quadrupole transitions for the B3Πg Wilkinson band, and the Lyman-Birge-Hopfield a1Πg ← X1Σg transition. Also, two other far-UV singlet-singlet quadrupole transitions are calculated for the first time, namely, the Dressler-Lutz a"1Σg +-X1Σg + and the less studied z1Δg-X1Σg + weak transitions.

High Curie temperature and large perpendicular magnetic anisotropy in two-dimensional half metallic OsI3 monolayer with quantum anomalous Hall effect

The 5d transition heavy elements with large spin-orbit coupling (SOC) effect can induce a large magnetic anisotropy energy (MAE) in magnetic materials. Meanwhile, the asymmetric occupation of 5d orbital electrons in transition metal trihalides can also trigger interesting orbital ordering. Here, the electronic structure and magnetic properties of two-dimensional (2D) OsI3 monolayer were investigated by first-principles calculations. The OsI3 monolayer has two orbital orderings with low spin states, where the half-metallic state is an Ising ferromagnet with a Curie temperature (TC) of 208 K and a perpendicular magnetic anisotropy (PMA) of −45.8 meV, but the Mott insulator state has an in-plane magnetic anisotropy (IMA) of 13.7 meV. The half-metallic state included non-self-consistent SOC calculations opens a band gap of 118.3 meV, showing a quantum anomalous Hall effect (QAHE) with a Chern number (C) of −1. A topologically trivial band gap opened in self-consistent SOC calculations, where QAHE of C = −2 can be realized by shifting Fermi surface. The in-plane biaxial strain can significantly tailor the MAE of the half-metallic state, yielding a PMA of −33.0 and −50.7 meV at a compressive strain of 6% and −2%. Meanwhile, TC rises to 275 K at a tensile strain of 6%. The transition between Mott insulator and half-metallic states can also be regulated by strain. These findings suggest that OsI3 monolayer is promising for 2D magnetism and spintronics.

Spin-Orbit Coupling Calculation Combined with the Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution.

Studying the radiative and non-radiative decay processes of molecules in a solution is an important issue in the design of organic and functional molecules. Theoretical approaches have great potential for revealing this decay process through computation of various parameters, such as the energy surfaces at the excited state and spin-orbit coupling (SOC). The development of quantum chemical programs has enabled the calculation of SOC values to become popular for the gas phase. However, SOC calculations in solution have some difficulties that need to be overcome. In the present study, the authors combined the SOC calculations with the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution. To validate the reliability of our method, the decay process of dimethylaminobenzonitrile in cyclohexane and acetonitrile was studied. By computing the SOC values in both solution systems, the authors were able to investigate the decay process at the atomistic level. Furthermore, a natural transition orbital analysis and the measurement of the decomposed SOC values were found to provide a clear understanding of intersystem crossing.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets.

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

First-principles calculations on novel Co-based Equiatomic Quaternary Heusler Alloys for Spintronics

The structural, mechanical, electronic, and magnetic properties of the new series of Co-based Equiatomic Quaternary Heusler Alloys (EQHAs) XX'YZ (X = Co; X' = Zr, Ru; Y = Ti, V; Z = Sn, Al, Ga, Si, Ge) have been calculated using first-principles calculations. The Full Potential-Linearized Augmented Plane Wave (FP-LAPW) approach was used in association with Density Functional Theory (DFT). We treated the exchange-correlation (XC) energy functional using a Generalized Gradient Approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) scheme. We included the TB-mBJ potential (GGA-mBJ) and the Hubbard correction (GGA + U) to improve the precision of the band gap values. Spin-orbit coupling (GGA-SOC) calculations are required due to the existence of heavier elements such as Zr and Ru. We have included the GGA-SOC calculations to estimate the total and partial magnetic moment and their impact on the electronic structure of Co-based EQHAs. The ground state parameters of proposed Co-based EQHAs were determined, including the lattice parameter, total energy, bulk modulus, and its derivative. The electronic structure of these materials revealed the presence of half-metallic ferromagnetism and spin-gapless semiconductor behavior. In addition, the origin of the band gap in spin channels was also investigated. In addition, we employed the mean-field approximation (MFA) method based on the Heisenberg model to determine the Curie temperature (TC). This theoretical analysis adds a new level of sophistication to the application of Co-based EQHAs in spintronic applications.

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.

Folding-Induced Spin-Orbit Coupling Enhancement for Efficient Pure Organic Room-Temperature Phosphorescence.

For the direct luminescence of triplet excitons, different mechanisms have been proposed for realizing pure organic room-temperature phosphorescence (RTP). To further verify the mechanism of folding-induced spin-orbit coupling (SOC) enhancement, two analogues of thianthrene (TA) were introduced by gradually replacing the sulfur atom with an oxygen atom for a systematical comparison, corresponding to phenoxathiine (PX) and dioxins (DX) molecules with increasing folding dihedral angles (or decreasing degrees of folding). Photophysical measurements show an obviously enhanced RTP efficiency from DX and PX to TA, which is consistent with their greatly enhanced SOC with a decrease in folding dihedral angle. The folding angle-dependent SOC calculations for each molecule reveal that this enhanced RTP is dominated by folding-induced SOC enhancement, in contrast with the negligible heavy-atom effect from oxygen to sulfur. This work further validates the rationality of the folding-induced SOC enhancement mechanism, which provides an innovative molecular design strategy for developing efficient pure organic RTP materials using folding structures.