Importance Of Spin-orbit Coupling Research Articles

Analytical energy gradients for ionized states using equation-of-motion coupled-cluster theory with spin-orbit coupling.

Spin-orbit coupling (SOC) may have a significant effect on the structure and harmonic frequencies of particularly heavy p-block element compounds. However, reports on analytical energy gradients with SOC are scarce, especially for excited states. In this work, we implemented analytical energy gradients for ionized states using the equation-of-motion coupled-cluster (CC) theory at the CC singles and doubles level (EOM-IP-CCSD) with SOC. Effects of SOC on structure and harmonic frequencies as well as properties for both the ground and some excited states of open-shell compounds with one unpaired electron can be investigated efficiently with the present implementation. A closed-shell reference is required in the calculations, and SOC is included in post-Hartree-Fock treatment. Relativistic effective core potentials are employed in dealing with both scalar relativistic effects and SOC, and we treat perturbations that are even under time reversal in this work. Both time-reversal symmetry and double point group symmetry for D2h * and its subgroups are exploited in the implementation. The method is applicable to states which can be reached by removing one electron from a closed-shell reference state. The results of some open-shell cations indicate the importance of SOC on structures and harmonic frequencies of heavy element compounds.

Tuning the thermoelectric properties of YNiBi half-Heusler alloy

A detail comparison between the results obtained for the electronic and transport properties of YNiBi half-Heusler alloy by local density approximation (LDA) and generalized gradient approximation (GGA) functionals with and without spin–orbit coupling (SOC) is presented. In the presence of SOC both functionals provide ∼30% smaller band gap. The transport coefficients computed without SOC confirm that YNiBi is a promising p-type thermoelectric material. However, with SOC at higher temperature, Seebeck coefficient was found to be negative because of the bipolar effects. Without SOC the computed power factor (PF) is found to be closer to the experimental value, while in the presence of SOC we have obtained comparatively smaller PF. No importance of SOC has been observed in the calculations of transport properties of the compound. The appropriate Ti doping in place of Y is predicted to significantly enhance the thermoelectric properties of YNiBi compound.

Covalency and spin-orbit coupling driven magnetism in the double-perovskite iridates Sr2MIrO6 ( M=Ca , Mg)

We have investigated the effect of spin-orbit coupling (SOC) and strong covalency on the magnetism of double-perovskite iridates (${\mathrm{Sr}}_{2}{M\mathrm{IrO}}_{6}$, $M=\mathrm{Ca}$, Mg) using first principles as well as model Hamiltonian calculations. Our calculation shows that strong Ir-$d$ and O-$p$ covalency in these double-perovskite iridates results in the deviation from the expected $6+$ charge state of Ir, leading to an unquenched orbital moment in the presence of SOC. We have studied in detail the nature of magnetism and our calculations of isotropic exchange interactions for these double-perovskite iridates suggest the systems to be frustrated. We argue that the SOC driven easy plane anisotropy possibly promotes long range magnetic order suggested for these systems indicating the importance of SOC in both these systems. Further, our model calculation considering ideal ${d}^{3}$ electronic configuration for Ir emphasizes the role of SOC, noncubic crystal field and Ir-Ir hopping in the reduction of the spin moment.

Importance of spin-orbit coupling in layered organic salts

We investigate the spin-orbit coupling (SOC) effects in $\ensuremath{\alpha}$- and $\ensuremath{\kappa}$-phase BEDT-TTF and BEDT-TSF organic salts. Contrary to the assumption that SOC in organics is negligible due to light C, S, and H atoms, we show the relevance of such an interaction in a few representative cases. In the weakly correlated regime, SOC manifests primarily in the opening of energy gaps at degenerate band touching points. This effect becomes especially important for Dirac semimetals such as $\ensuremath{\alpha}\ensuremath{-}{(\mathrm{ET})}_{2}{\mathrm{I}}_{3}$. Furthermore, in the magnetic insulating phase, SOC results in additional anisotropic exchange interactions, which provide a compelling explanation for the puzzling field-induced behavior of the quantum spin-liquid candidate $\ensuremath{\kappa}\ensuremath{-}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}$. We conclude by discussing the importance of SOC for the description of low-energy properties in organics.

Spin-orbit coupling induced band structure change and orbital character of epitaxialIrO2films

We investigated the electronic structure of $\mathrm{Ir}{\mathrm{O}}_{2}$ to address the controversy regarding spin-orbit coupling (SOC) effects in metallic $5d$ transition-metal oxides. Two issues have come to the forefront: (1) SOC effects on electronic structure and physical properties of $\mathrm{Ir}{\mathrm{O}}_{2}$ and (2) the possible formation of a novel ground state in this material, the ${J}_{\mathrm{eff}}=1/2$ state. To better understand the SOC mechanism, we grew epitaxial $\mathrm{Ir}{\mathrm{O}}_{2}$ films whose $dc$ resistivity values were comparable with those of a single crystal. We obtained polarization-dependent optical and x-ray absorption spectra (XAS) and compared these results with those acquired using the generalized gradient approximation (GGA) and $\mathrm{GGA}+\mathrm{SOC}$ calculations. From the optical spectra, peak structures were identified at 0.4 and 2.0 eV, which could only be explained using the $\mathrm{GGA}+\mathrm{SOC}$ calculation. This suggests that SOC plays an important role in the electronic structure of $\mathrm{Ir}{\mathrm{O}}_{2}$. From the polarization-dependent $\mathrm{O}\phantom{\rule{0.16em}{0ex}}1s$ XAS spectra, we observed that the empty state near the Fermi level lacks involvement of an Ir ${d}_{xy}$ orbital. Despite the importance of SOC in $\mathrm{Ir}{\mathrm{O}}_{2}$, the ${J}_{\mathrm{eff}}=1/2$ state does not form in metallic $\mathrm{Ir}{\mathrm{O}}_{2}$.

Spin-state transition inLaCoO3by variational cluster approximation

The variational cluster approximation is applied to the calculation of thermodynamical quantities and single-particle spectra of LaCoO3. Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of a CoO6 cluster. The VCA correctly predicts LaCoO3 as a paramagnetic insulator and a gradual and relatively smooth increase of the occupation of high-spin Co3+ ions causes the temperature dependence of entropy and magnetic susceptibility. The single particle spectral function agrees well with experiment, the experimentally observed temperature dependence of photoelectron spectra is reproduced satisfactorily. Remaining discrepancies with experiment highlight the importance of spin orbit coupling and local lattice relaxation.

Observation of relativistic E⊗e vibronic coupling in Rb3 and K3 quartet states on helium droplets

Spectroscopy of alkali-metal complexes on helium droplets (He(N), N=1000-10 000) provides the unique opportunity to observe high-spin species, which exhibit prominent spin-orbit (SO) effects. In this work we present laser-induced-fluorescence and magnetic-circular-dichroism (MCD) spectra of the (2)(4)E(')<--(1)(4)A(2) (') band of Rb(3) and K(3) on He(N). For Rb(3) we find a progression of four SO split bands, weakly perturbed by linear vibronic [Jahn-Teller (JT)] coupling. The K(3) transition was previously observed and interpreted in terms of linear and quadratic JT effects in the (2)(4)E(') state [J. H. Reho et al., J. Chem. Phys. 115, 10265 (2001)]. The structure of the MCD spectrum, however, clearly reveals the importance of SO coupling also for the K(3) transition and suggests a different assignment with weak linear JT and nonsignificant quadratic JT coupling. The observed strong C-type MCD spectra arise from different populations of the ground-state Zeeman sublevels. Thus a quantitative analysis allows a determination of the spin temperature, and since alkali-metal complexes are situated on the surface of the helium droplet this corresponds to a determination of the surface temperature. Our results from the trimer spectra are consistent with the value of approximately 0.4 K, which is found in the interior of a droplet and which we already confirmed for the surface from the spectra of triplet-state alkali-metal dimers in a previous work.

The importance of spin-orbit coupling and electron correlation in the rationalization of the ground state of the CUO molecule.

We present calculations at the relativistic coupled cluster theory that predict the (1)Sigma(0) (+) ground state of CUO to lie 58.2 kJ/mol below the first excited state, (3)Phi(2). This can be contrasted with the outcome of earlier density functional theory and complete active space second order perturbation theory (CASPT2) calculations that both predicted a (3)Phi(2) ground state upon inclusion of spin-orbit coupling in the calculations. Our result gives further justification to the interpretation of the measured frequency shifts of this species in various noble gas matrices as being caused by significant interaction between the uranium and the heavier noble gas atoms.

Protonation-induced paramagnetism. Structures and stabilities of six- and seven-coordinate complexes of Os(II) in singlet and triplet states: a density functional study.

Li, Yeh, and Taube in 1993 (J. Am. Chem. Soc. 1993, 115, 10384) synthesized a number of complexes which can be formally regarded as protonated Os(II) species. Some of these were paramagnetic, in contrast to the diamagnetism of the closed shell 5d(6) Os(II) ions. This intriguing phenomenon is investigated theoretically using density functional theory. The geometries, stabilities, and electronic structures of a series of six- and seven-coordinate osmium complexes were studied in gas phase and aqueous solution using the B3P86 functional, in conjunction with the isodensity-polarized continuum model of solvation. The general formula for these complexes is [Os(NH(3))(4)H(L(1)(x)())(m)()(L(2)(y)())(n)()](()(x)()(+)(y)()(+3)+), where L(1) and L(2) = H(2)O, NH(3), CH(3)OH, CH(3)CN, Cl(-), and CN(-), which could be regarded as protonated Os(II) species or hydrides of Os(IV), although according to this work the osmium-hydrogen interaction is best described as a covalent Os(III)-H bond, in which the hydrogen is near-neutral. The ground states are generally found to be singlets, with low-lying triplet excited states. Solvation tends to favor the singlet states by as much as approximately 18 kcal mol(-)(1) in the 3+ ions, an effect which is proportional to the corresponding difference in molecular volumes. To have realistic estimates of the importance of spin-orbit coupling in these systems, the spin-orbit energy corrections were computed for triplet [Os(NH(3))(4)](2+), [Os(NH(3))(4)H](3+), and [Os(NH(3))(4)H(H(2)O)](3+), along with gas-phase Os and its ions as well as [Os(H(2)O)(6)](3+). The seven-coordinate triplet-state complex [Os(NH(3))(5)H(CH(3)OH)](3+), which had been successfully isolated by Li, Yeh, and Taube, is predicted to be a stable six-coordinate complex which strongly binds to a methanol molecule in the second coordination shell. The calculations further suggest that the singlet-triplet splitting would be very small, a few kilocalories per mole at most. The geometries and the electronic structures of the complexes are interpreted and rationalized in terms of Pauling's hybridization model in conjunction with conventional ligand field theory that effectively precludes the existence of true seven-coordinate triplet-state complexes of the above formula.

Electronic and structural properties of extended-chain compounds and polymers

Results of density functional calculations on infinite, periodic chains are reported. The method that is applied is based on linearized muffin-tin orbitals as basis functions, although the full potential and not only its muffin-tin part is included in the calculations. Special emphasis is put on analyzing the interatomic interactions by means of crystal-orbital overlap or Hamilton populations (COOP and COHP, respectively). As examples of conjugated polymers, trans-polyacetylene and polycarbonitrile are studied. Here, in particular, the existence of a bond length alternation is discussed. Subsequently, PtS{sub 2} (both without and with K counterions) and NbSe{sub 3} chains are considered. For the former, the single-chain calculations are supplemented with calculations on the crystalline compounds, and it is shown how single-chain effects are responsible for the structural properties whereas interchain effects have to be included in order to account for all the electronic properties. Parts of the results are explained through an analysis of the COOP and COHP. For NbSe{sub 3} the three different structures occurring in the crystalline material are considered, and the implications of the results for the existence of charge density waves as well as the importance of spin-orbit couplings are discussed. Finally, HF as an example of an extendedmore » hydrogen-bonded system is examined, and it is demonstrated how the electronic interactions change when the covalent and hydrogen bonds are interchanged as it occurs in charge transport via solitons.« less

Interpretation of 13C NMR chemical shifts in halomethyl cations. On the importance of spin-orbit coupling and electron correlation

The first explicit study of both spin-orbit and electron correlation effects on NMR chemical shifts has been carried out. It is shown by spin-orbit corrected DFT-IGLO calculations on the halomethyl cations CX 3 + (X  F, Cl, Br, I) that the experimentally observed decrease in the 13C chemical shifts with increasing atomic number of X is due to spin-orbit coupling. Previous explanations for this example of a ‘normal halogen dependence’ via electronegativity arguments were based on fortuitious empirical correlations. Comparison between DFT-IGLO, HF-GIAO and MP2-GIAO results for these systems also demonstrates an increasing importance of electron correlation along the same series.

Electron impact excitation of the lowest-lying excited states of krypton

Excitation of the 4p5(2P32/)5s3P1 and 4p5(2P12/)5s 1P1 states of krypton by electron impact has been studied using the electron-photon angular correlation technique. Measurements are reported at an incident electron energy of 60 eV for electron scattering angles theta e up to 30 degrees . The serious disagreement between two previous measurements at theta e=20 degrees is discussed. The difficulty of obtaining a quantitative measure of the importance of spin-orbit coupling through the parameter epsilon using this technique is demonstrated.

The importance of spin-orbit coupling in the magnetised hydrogen problem

On the basis of the authors' previously determined highly accurate numerical wavefunctions they investigate, in quantitative terms, the effect of spin-orbit coupling on low-lying states of the hydrogen atom in magnetic fields of arbitrary strength. They stress the point that, in spite of the expected minute corrections of Coulomb binding energies, spin-orbit coupling produces narrow anticrossings of levels having identical parity and projection mj of the total angular momentum. In this way they find the correlation diagram (between the low- and high-field quantum numbers) of the physically 'real' hydrogen atom to be quite different from that derived by Simola and Virtamo (1978) for the idealised non-relativistic hydrogen problem with infinite proton mass.

Relativistic corrections to the atomic volumes of the actinide metals

The effect of spin-orbit coupling upon the energy band structure of the light actinide metals has been examined. A measure of the importance of spin-orbit coupling is the ratio of the number of f electrons in the j=5/2 and j=7/2 bands, which approaches 6/8 when spin-orbit coupling is small. The computed ratio from ab initio self-consistent relativistic calculations for the metals Ac-Am varies from 0.75 for Ac to 2.4 for Am. The change in atomic volume due to the preferential occupation of the j=5/2 band has also been computed. It is small for the elements Ac-U but the volumes of Np-Am increase progressively. There is a corresponding decrease in the change of volume for the expected phase transition in americium under pressure.

Dynamic Properties of the Phosphorescent Triplet State of 9H-Thioxanthen-9-one (Thioxanthone) from Optically Detected Magnetic Resonance Spectroscopy

Abstract A variety of optically detected magnetic resonance (ODMR) experiments have been performed on the lowest excited triplet state of 9H-thioxanthen-9-one at 1.4 K. The absorption and phosphorescence excitation spectra were also measured to supplement the ODMR studies. The results were analyzed to determine the mechanisms responsible for the radiative decay and intersystem crossing processes. The z sublevel has large activity in vibronic bands due to non-totally symmetric vibrations. The intensity mainly comes from mechanisms involving vibronic coupling between 1n,π* and 1π,π* states. The y sublevel is selectively affected by the introduction of the sulfur atom, because of the increased importance of spin orbit coupling with 1σ′,π* state which is largely localized on the thioether group.

Optical properties of 3(nπ*) benzophenones in 4, 4′-dibromodiphenylether host crystals

A variety of optical and zero-field optically-detected magnetic resonance (zf ODMR) experiments have been performed on the lowest (nπ*) triplet states of benzophenone (BP-h 10), perdeuterobenzophenone (BP-d 10), and 4,4′-dibromobenzophenone (4,4′-DBBP) in single crystals of 4,4′-dibromodiphenylether (DDE) at temperatures of 1·4 K and above. The data obtained include high resolution phosphorescence, phosphorescence excitation, zf ODMR, amplitude-modulated zf ODMR phosphorescence excitation, and single-sublevel phosphorescence spectra as well as the guest sublevel phosphorescence lifetimes, relative radiative and non-radiative decay constants, intersystem crossing rates, and steady-state populations. At short wavelengths, the guest triplets are also populated via two energy transfer routes (S 0 H → T 1 H ↝ T 1 G and S 0 H → S 1 H ↝ T 1 H ↝ T 1 G); hence, the relative radiative rate constants and intersystem crossing rates of the host 3(ππ*) state sublevels have also been measured. The results are analysed to determine the principal spin-orbit (SO) and spin-orbit plus vibronic (SOV) mechanisms responsible for the population and depopulation of the spin sublevels of the parent molecule and its derivatives. A localized model suffices for triplet BP-h 10 in which the z sublevel is most active. The S 1 ↝ T 1 intersystem crossing process is governed primarily by SOV terms involving 3(ππ*) [and possibly 1(ππ*)] states and vibrations of a 2 symmetry, the T 1 → S 0 radiative process by SO coupling with 1(ππ*) states, and the T 1 ↝ S 0 non-radiative process by SO coupling with the ground state. Deuterium substitution has only a small effect on the radiative and non-radiative properties of 3(nπ*) BP. In contrast, bromine substitution has a large (and selective) effect; this is a consequence of n and π spin delocalization. All ISC rates and decay constants of 4,4′-DBBP are larger than those of the parent molecule. This is attributed to the increased importance of SO coupling with 1(σπ*) and 1(nσ*) states having significant heavy-atom character. The reasons for the preferential enhancement of Kx and Ky, kx r, and ky nr and kz nr are discussed. New vibronic coupling routes influencing the radiative decay are also introduced by the substitution of bromine atoms; these involve totally symmetric vibrations, affect only the Tx and Ty sublevels, and produce a decrease in the relative intensity of the carbonyl-stretching bands in the emission spectra of these sublevels. Finally, it is shown that correlations exist between the optical and magnetic properties of 3(nπ*) benzophenone and between the changes in these properties which are produced by heavy-atom substitution.

Effect of Spin-Orbit Coupling on the Energy Levels in the6dBand for Actinide Metals

The importance of spin-orbit coupling in modifying the energy levels in the $6d$ band for the actinide metals is discussed. The energy matrix, ${H}_{0}$, used in this paper, neglecting spin-orbit effects, is derived from Kohn's variational principle by expanding the wave function in terms of the five atomic $d$ orbitals having cubic symmetry. A single disposable parameter, ${E}_{d}$, occurs in this model such that $2{E}_{d}$ is the width of the $d$ band. The spin-orbit energy matrix, ${H}_{\mathrm{so}}$, contains the spin-orbit splitting parameter, ${E}_{\mathrm{so}}$, which is equal to the ${d}_{\frac{3}{2}}\ensuremath{-}{d}_{\frac{5}{2}}$ level separation. The complete 10\ifmmode\times\else\texttimes\fi{}10 energy matrix has been diagonalized analytically along a fourfold symmetry axis and numerically at 150 points in the Brillouin zone for the case $\frac{{E}_{\mathrm{so}}}{{E}_{d}}=0.2$ appropriate to face-centered cubic thorium with ${E}_{\mathrm{so}}=0.4$ ev and ${E}_{d}=2$ ev. Plots of the energy variation along the two, three, and fourfold axes in the Brillouin zone are presented. Calculations based upon this model are also presented which show that the usual Pauli spin paramagnetism of the conduction electrons can be modified quite significantly by spin-orbit coupling.