Spin-orbit Configuration Research Articles

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction.

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

A spin–orbit configuration interaction study of the low-lying electronic states of the diatomic lithium antimonide cation

High-level ab initio calculations were performed to determine the structural features, electronic characteristics and transitional properties of LiSb+, which is a hitherto experimentally unknown diatomic cation. We acquired and evaluated the potential energy curves, spectroscopic constants and vibrational energy levels for low-lying Λ-S electronic states and their related Ω states. The spin–orbit coupling effect has a slight impact on these states. Transitional properties, such as transition dipole moments, Einstein coefficients, Franck–Condon factors and vibrational branching ratios, as well as the radiative lifetimes of transitions from excited Ω states to the ground state, have been identified and discussed. We anticipate that these prognostic results will act as guidelines for future research.

Environmental considerations in ab initio calculations of electronic states of PtCl4 -2 complexes.

Many quantum chemical methods used for large complexes are based on a limited treatment of electrons due to the computational demand dictated by the number of electrons that must be explicitly considered, especially when considering the chemical environment. Such treatments can fail to correlate accurately with electronic spectra. Ab initio electronic structure theory using the spin-orbit configuration interaction method is applied in a study of spectral transitions in PtCl4 2- including counter-ion environmental effects. In this method, electronic wave functions are eigenfunctions of the total angular momentum operator belonging to one of the symmetry types of the molecular double group. PtCl4 2- is investigated as a charged gas phase complex, a point-charge-neutralized complex, and a pseudopotential-neutralized complex. Results indicate that the use of a whole-atom relativistic effective core potential for the potassium cation provides a more accurate representation of the environment than a point charge and accurately represents electronic states without increasing the complexity of the calculation and, therefore, its computational demand.

Excited states of polonium(IV): electron correlation and spin-orbit coupling in the Po4+ free ion and in the bare and solvated [PoCl5]- and [PoCl6]2- complexes.

Polonium (Po, Z = 84) is a main-block element with poorly known physico-chemical properties. Not much information has been firmly acquired since its discovery by Marie and Pierre Curie in 1898, especially regarding its speciation in aqueous solution and spectroscopy. In this work, we revisit the absorption properties of two complexes, [PoCl5]- and [PoCl6]2-, using quantum mechanical calculations. These complexes have the potential to exhibit a maximum absorption at 418 nm in HCl medium (for concentrations of 0.5 mol L-1 and above). Initially, we examine the electronic spectra of the Po4+ free ion and of its isoelectronic analogue, Bi3+, in the spin-orbit configuration interaction (SOCI) framework. Our findings demonstrate that the SOCI matrix should be dressed with correlated electronic energies and that the quality of the spectra is largely improved by decontracting the reference states at the complete active space plus singles (CAS + S) level. Subsequently, we investigate the absorption properties of the [PoCl5]- and [PoCl6]2- complexes in two stages. Firstly, we perform methodological tests at the MP2/def2-TZVP gas phase geometries, indicating that the decontraction of the reference states can be skipped without compromising the accuracy significantly. Secondly, we study the solution absorption properties by means of single-point calculations performed at the solvated geometries, obtained by an implicit solvation treatment or a combination of implicit and explicit solvation. Our results highlight the importance of saturating the first coordination sphere of the PoIV ion to obtain a qualitatively correct picture. Finally, we conclude that the known-for-decades 418 nm peak could be attributed to a mixture of both the [PoCl5(H2O)]- and [PoCl6]2- complexes. This finding not only aligns with the behaviour of the analogous BiIII ion under similar conditions but also potentially provides an explanation for previous discrepancies in the literature.

Theoretical dissociation, ionization, and spin-orbit energetics of the diatomic platinum hydrides PtH, PtH+, and PtH.

Spin-orbit configuration interaction (SO-CI) and coupled-cluster [CCSDT(Q)] theoretical methods are combined to evaluate zero-temperature thermochemical properties of PtH, PtH+, and PtH-. We obtain vibrational zero-point energies and spin-orbit stabilization energies, which lead to predictions for observable quantities: ionization energy IE(PtH) = (9.44 ± 0.07) eV; electron affinity EA(PtH) = (1.65 ± 0.04) eV; and dissociation energies D0(Pt-H) = (329.6 ± 3.9) kJ mol-1, D0(Pt+-H) = (279.3 ± 5.7) kJ mol-1, and D0(Pt--H) = (285.0 ± 2.4) kJ mol-1 (uncertainty coverage factor = 2). Compared with available experiments, our value of D0(Pt+-H) is higher by (8 ± 8) kJ mol-1, EA(PtH) is higher by 0.15eV, and D0(Pt-H) is lower than the upper bound by (2 ± 4) kJ mol-1.

Spin–orbit configuration interaction study of spectral properties of PbO

Relativistic calculations of the structural and spectral properties of the PbO molecule can provide fundamental information about the importance of a proper treatment of angular momentum coupling among electrons in order to achieve accurate computational results for spectral properties. Specifically, the nature of these couplings in PbO is expected to be intermediate between the LS- and jj-coupling limits because of its light/heavy element composition. This article reports potential energy curves, transition energies, electric dipole transition moments, permanent dipole moments and spectroscopic constants of PbO calculated using a multireference single plus double excitations spin–orbit configuration interaction approach in the context of relativistic effective core potentials and their concomitant spin–orbit coupling operators. The calculated results are in general agreement with both available experimental results as well as earlier calculations. New values for properties of excited states are also reported. It is noteworthy that certain properties show larger deviations from previous calculations. These deviations are attributed to direct and indirect relativistic effects resulting from diatomic electron–electron angular momentum coupling effects, which are included consistently in the calculations reported herein.

The Effect of Post-Newtonian Spin Precessions on the Evolution of Exomoons’ Obliquity

Abstract Putative natural massive satellites (exomoons) have gained increasing attention when they orbit Jupiter-like planets within the habitable zone of their host main-sequence star S. An exomoon s is expected to move within the equatorial plane of its host planet p, with its spin S s aligned with its orbital angular momentum L , which, in turn, is parallel to the planetary spin S p. If, in particular, the common tilt ε of such angular momenta to the plane of the satellite–planet motion about the star, assumed fixed, has certain values, the stellar latitudinal irradiation experienced on the exomoon may allow it to sustain life as we know it, at least for certain orbital configurations. An Earth analog (similar in mass, radius, oblateness, and obliquity) is considered, which orbits within 5–10 planetary radii R p from its Jupiter-like host planet. The de Sitter and Lense–Thirring spin precessions due to the general relativistic post-Newtonian (pN) field of the host planet have an impact on an exomoon’s habitability for a variety of different initial spin–orbit configurations. Here I show it by identifying long-term variations in the satellite’s obliquity ε s, where variations can be ≲10°–100°, depending on the initial spin–orbit configuration, with a timescale of ≃0.1–1 million years. Also the satellite’s quadrupole mass moment J 2 s induces obliquity variations that are faster than the pN ones but do not cancel them. Tidal dissipations, which may potentially have a relevant impact on the outlined pattern, are not included in the present analysis.

Cover Feature: Development and Application of a Complete Active Space Spin‐Orbit Configuration Interaction Program Designed for Single Molecule Magnets (ChemPhysChem 1/2022)

The Cover Feature illustrates how magnetic data of powder samples of oligonuclear transition metal complexes can be simulated and analysed from ab initio energy levels and wave functions obtained by spin orbit configuration interaction. More information can be found in the Article by Bodenstein, Heimermann, Fink, and van Wüllen.

Reliable modeling of weak antilocalization for accurate spin-lifetime extraction

We examine models for the quantum-interference correction to the magnetoconductivity in two-dimensional electron gases (2DEGs) with both Rashba and Dresselhaus spin-orbit coupling for their applicability to experimental data fitting. In particular, we compare the Landau-quantized Cooperon approach, which is mostly only numerically treatable, and the quasiclassical approximation that was recently employed to obtain an explicit solution for arbitrary Rashba and Dresselhaus spin-orbit couplings [Marinescu et al., Phys. Rev. Lett. 112, 156601 (2019)]. It is found that the quasiclassical approximation yields significantly different results even to the lowest order in the magnetic field and appears unsuitable for reliable parameter fitting. The discrepancy emerges when a sum over Landau levels is replaced by an integral over wave vectors. Substantial improvement is achieved by supplementing the quasiclassical model with the first two corrections given by the Euler-MacLaurin formula for approximating a sum by an integral. Corresponding modifications are, however, only feasible in special spin-orbit parameter configurations where the mixing of Landau bands is negligible and a closed-form solution that accounts for Landau quantization is also available. Such a scenario appears in a parameter regime where a persistent spin helix emerges and a transition between weak localization and weak antilocalization takes place. Combining recent findings, we derive a generalized closed-form expression for the magnetoconductivity correction applicable to generic 2DEGs that are grown along a crystal direction with at least two growth-direction Miller indices equal in modulus. The result is a function of spin lifetimes of the long-lived spin textures and valid close to the persistent-spin-helix regime. The accuracy of the derived formula is validated by comparing with results from numerical diagonalization of the multiband Cooperon as well as a recently established Monte Carlo-based real-space simulation in exemplary (001)-, (113)-, and (110)-2DEGs.

Development and Application of a Complete Active Space Spin-Orbit Configuration Interaction Program Designed for Single Molecule Magnets.

We present a spin‐orbit configuration interaction program which has been tailored for the description of the magnetic properties of polynuclear metal complexes with partially filled d‐ and f‐shells. The spin‐orbit operators are directly included in the configuration interaction program based on Slater‐determinants. The lowest states are obtained by a Block‐Davidson‐type diagonalisation. The usage of localised active orbitals enables the construction of start vectors from tensor products of single‐center wave functions that already include spin‐orbit interaction. This allows for an analysis of the role and the interplay of the different metal centres. Furthermore, in case of weak coupling of the metal centres these tensor products are already close to the final wave functions ensuring fast convergence. In combination with a two‐layer hybrid parallelisation, this makes the program highly efficient. Based on the spin‐orbit coupled wave functions, magnetic D‐tensors, g‐tensors and temperature‐dependent susceptibilities can be calculated. The applicability and performance of the program is shown exemplarily on a trinuclear transition metal (CoIIVIICoII) complex.

On the Accuracy of Mean-Field Spin-Orbit Operators for 3d Transition-Metal Systems.

We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Polarizability of atomic Pt, Pt+, and Pt.

Electrostatic properties are important for understanding and modeling many phenomena, such as the adsorption of a catalytic metal upon an oxide support. The charge transfer between the metal and the support can lead to positive or negative charges on the metal. Here, the static dipole polarizability is computed for atomic platinum in charge states 0, +1, and -1 in several low-lying electronic terms and levels. Core pseudopotentials are used along with coupled-cluster theory. The best results are estimates for the coupled-cluster CCSDTQ/q-aug-cc-pwCV∞Z-PP values for atomic terms, combined with compositional data from spin-orbit configuration interaction. The polarizability of the anion Pt- is especially challenging for the theory with wildly varying results from different coupled-cluster perturbative approximations such as CCSD(T). For atomic mercury (Hg), selected as a nearby experimental value, our polarizability volume is larger than experiment by 0.8 bohrs3 (or 0.12 × 10-30 m3). For the ground level of neutral platinum, Pt(3D3), we find α0 = (41.2 ± 1.1) bohrs3 or (6.10 ± 0.16) × 10-30 m3. A handful of density functional theory methods are tested and found generally within 10% of our best values.

Effects of Spin-Orbit Resonances and Tidal Heating on the Inner Edge of the Habitable Zone

Much attention has been given to the climate dynamics and habitable boundaries of synchronously rotating planets around low mass stars. However, other rotational states are possible, particularly when higher eccentricity orbits can be maintained in a system, including spin-orbit resonant configurations. Additionally, the oscillating strain as a planet moves from periastron to apoastron results in friction and tidal heating, which can be an important energy source. Here, we simulate the climate of ocean-covered planets near the inner edge of the habitable zone around M to solar stars with ROCKE-3D, and leverage the planetary evolution software package, VPLanet, to calculate tidal heating rates for Earth-sized planets orbiting 2600 K and 3000 K stars. This study is the first to use a 3-D General Circulation Model that implements tidal heating to investigate habitability for multiple resonant states. We find that in the absence of tidal heating, the resonant state has little impact on the inner edge, because for a given stellar flux, higher-order states tend to be warmer than synchronous rotators, but for a given temperature, have drier upper atmospheres. However, when strong tidal heating is present, the rotational component implies a strong dependence of habitable conditions on the system evolution and rotational state. Since tidal and stellar heating both decrease with orbital distance, this results in a compact orbital width separating temperate and uninhabitable climates. We summarize these results and also compare ROCKE-3D to previously published simulations of the inner edge that used a modified version of the NCAR CAM4 model.

Quantum chemical topology at the spin-orbit configuration interaction level: Application to astatine compounds.

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI- , BrAtBr- , and IAtBr- ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin-orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2.

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

Disentangling orbital and spin textures of surface-derived states in non-symmorphic semimetal HfSiS

We have investigated the spin polarization and orbital configuration of the spin-split surface states in a non-symmorphic semimetal HfSiS by spin- and angle-resolved photoelectron spectroscopy using polarized tunable photons combined with detailed theoretical calculations. We have found that the surface states surrounding the $\overline{X}$ point with ${C}_{2v}$ symmetry exhibit an exotic unidirectional spin texture coupled with ${d}_{yz}$ orbital. The observed unidirectional spin texture is well reproduced by the theoretical calculations. Our work clarifies the significance of orbital symmetry in the manipulation of spin orientations, providing an approach to realize the persistent spin texture for the prolonged spin-coherence time in spintronic applications.

Evolution of structure and magnetism across the metal-insulator transition in the pyrochlore iridate (Nd1−xCax)2Ir2O7

We report on the evolution of the thermal metal-insulator transition in polycrystalline samples of Nd$_2$Ir$_2$O$_7$ upon hole-doping via substitution of Ca$^{2+}$ for Nd$^{3+}$. Ca substitution mediates a filling-controlled Mott-like transition with minimal resolvable structural changes and without altering site symmetry. Local structure confirms that Ca substitution does not result in local chemical phase separation, and absorption spectroscopy establishes that Ir cations maintain a spin-orbit entangled electronic configuration. The metal-insulator transition coincides with antiferromagnetic ordering on the Ir sublattice for all measured samples, and both decrease in onset temperature with Ca content. Weak low-temperature upturns in susceptibility and resistivity for samples with high Ca content suggest that Nd sublattice antiferromagnetism continues to couple to carriers in the metallic regime.

UV-Vis Absorption Spectroscopy of Polonium(IV) Chloride Complexes: An Electronic Structure Theory Study.

More than a hundred years after its discovery, the chemistry of the polonium radioelement is still largely unknown. However, it is quite clear that the properties of this heavy element ( Z = 84) may be affected by relativistic effects, in particular scalar relativistic effects and the so-called spin-orbit coupling (SOC). In this Article, we revisit the interpretation of UV-vis absorption spectra of polonium(IV) complexes in HCl medium, reported decades ago. From the data, two complexes were hypothesized, complex I with a maximum of absorption at 344 nm (at low HCl concentration) and complex II with a maximum at 418 nm (the only visible peak for HCl concentrations above 0.5 M). By monitoring the absorbance at 344 and 418 nm as a function of both the HCl concentration and the pH, complex I was formulated as [Po(OH)Cl x]3- x while complex II was formulated as [PoCl2+ x]2- x. In this work, we study the ground-state geometries of the [Po(OH)Cl x]3- x and [PoCl2+ x]2- x complexes for x = 4-2, i.e. for the most probable complexes, with density functional theory (DFT), demonstrating that solvation can remarkably change the geometries of such systems. The electronic excitation energies are then computed with time-dependent DFT (TD-DFT), second-order N-electron valence state perturbation theory (NEVPT2), and contracted spin-orbit configuration interaction (c-SOCI), showing (i) that the SOC must be at play to obtain excitation energies in the right energy domain and (ii) that the quantum chemical calculations point toward x = 4, i.e., toward the [Po(OH)Cl4]- and [PoCl6]2- complexes.

Electronic structure of Fe and magnetism in the 3d/5d double perovskites Ca2FeReO6 and Ba2FeReO6

The Fe electronic structure and magnetism in (i) monoclinic ${\mathrm{Ca}}_{2}{\mathrm{FeReO}}_{6}$ with a metal-insulator transition at ${T}_{MI}\ensuremath{\sim}140\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and (ii) quasicubic half-metallic ${\mathrm{Ba}}_{2}{\mathrm{FeReO}}_{6}$ ceramic double perovskites are probed by soft x-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD). These materials show distinct Fe ${L}_{2,3}$ XAS and XMCD spectra, which are primarily associated with their different average Fe oxidation states (close to ${\mathrm{Fe}}^{3+}$ for ${\mathrm{Ca}}_{2}{\mathrm{FeReO}}_{6}$ and intermediate between ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ for ${\mathrm{Ba}}_{2}{\mathrm{FeReO}}_{6}$) despite being related by an isoelectronic (${\mathrm{Ca}}^{2+}/{\mathrm{Ba}}^{2+}$) substitution. For ${\mathrm{Ca}}_{2}{\mathrm{FeReO}}_{6}$, the powder-averaged Fe spin moment along the field direction ($B=5\phantom{\rule{0.28em}{0ex}}\mathrm{T}$), as probed by the XMCD experiment, is strongly reduced in comparison with the spontaneous Fe moment previously obtained by neutron diffraction, consistent with a scenario where the magnetic moments are constrained to remain within an easy plane. For $B=1\phantom{\rule{0.28em}{0ex}}\mathrm{T}$, the unsaturated XMCD signal is reduced below ${T}_{MI}$ consistent with a magnetic transition to an easy-axis state that further reduces the powder-averaged magnetization in the field direction. For ${\mathrm{Ba}}_{2}{\mathrm{FeReO}}_{6}$, the field-aligned Fe spins are larger than for ${\mathrm{Ca}}_{2}{\mathrm{FeReO}}_{6}$ ($B=5\phantom{\rule{0.28em}{0ex}}\mathrm{T}$) and the temperature dependence of the Fe magnetic moment is consistent with the magnetic ordering transition at ${T}_{C}^{Ba}=305\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Our results illustrate the dramatic influence of the specific spin-orbital configuration of Re $5d$ electrons on the Fe $3d$ local magnetism of these Fe/Re double perovskites.