We present a new implementation for computing spin–orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin–flip variant (SF-TD-DFT). This approach employs the Breit–Pauli Hamiltonian and Wigner–Eckart’s theorem applied to the reduced one-particle transition density matrices, together with the spin–orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH 2 , [Formula: see text], SiH 2 , and [Formula: see text]) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, ωPBEh/cc-pVDZ) agrees well with the experimental estimate.
more »
« less
Constructing spin‐adiabatic states for the modeling of spin‐crossing reactions. I. A shared‐orbital implementation
In the modeling of spin‐crossing reactions, it has become popular to directly explore the spin‐adiabatic surfaces. Specifically, through constructing spin‐adiabatic states from a two‐state Hamiltonian (with spin‐orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a “transition state” structure, where the spin crossing occurs. In this work, we report the implementation of a fully‐variational spin‐adiabatic approach based on Kohn‐Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit‐Pauli one‐electron spin‐orbit operator. For three model spin‐crossing reactions (predissociation of N2O, singlet‐triplet conversion in CH2, and CO addition to Fe(CO)4), the spin‐crossing points were obtained. Our results also indicated the Breit‐Pauli one‐electron spin‐orbit coupling can vary significantly along the reaction pathway on the spin‐adiabatic energy surface. On the other hand, due to the restriction that low‐spin and high‐spin states share the same set of molecular orbitals, the acquired spin‐adiabatic energy surface shows a cusp (ie, a first‐order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin‐adiabatic surfaces.
more » « less- NSF-PAR ID:
- 10458768
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Quantum Chemistry
- Volume:
- 120
- Issue:
- 6
- ISSN:
- 0020-7608
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spinChemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom, there are few if any applicable and practical quasiclassical methods. Here, we show that for nonadiabatic dynamics with two electronic states and a complex-valued Hamiltonian that does not obey time-reversal symmetry (as relevant to many coupled nuclear-electronic-spin systems), the optimal semiclassical approach is to generalize Tully’s surface hopping dynamics from coordinate space to phase space. In order to generate the relevant phase-space adiabatic surfaces, one isolates a proper set of diabats, applies a phase gauge transformation, and then diagonalizes the total Hamiltonian (which is now parameterized by both R and P). The resulting algorithm is simple and valid in both the adiabatic and nonadiabatic limits, incorporating all Berry curvature effects. Most importantly, the resulting algorithm allows for the study of semiclassical nonadiabatic dynamics in the presence of spin–orbit coupling and/or external magnetic fields. One expects many simulations to follow as far as modeling cutting-edge experiments with entangled nuclear, electronic, and spin degrees of freedom, e.g., experiments displaying chiral-induced spin selectivity.more » « less
-
more » « less
Abstract Magnetic impurities at surfaces of superconductors can induce bound states referred to as Yu–Shiba–Rusinov states (i.e. Shiba states) within superconducting (SC) gaps. For superconductors with strong spin–orbit coupling (SOC), Shiba states arising from even single magnetic adatoms are too complex to be fully understood using effective models alone because SOC cannot be treated perturbatively and multiple orbitals are strongly mixed with spin projections. Here we investigate Shiba states of single magnetic adatoms at the surface of strongly spin-orbit coupled SC Pb, by solving the fully relativistic Dirac–Bogoliubov–de Gennes equations using multiple scattering Green’s function methods. For Fe and Co adatoms on Pb(110), we show that the Shiba states are better characterized by total angular momentum,
J , and its projections on thez axis,m J . As a hallmark of the SOC effect, the Shiba states show a strong dependence of the orientation of the adatom moment. As the orientation of the Fe/Co moment changes, the deepest Shiba states merge at zero energy. This zero-energy state disappears with an additional non-magnetic adatom next to the magnetic adatom, although the other Shiba states unchange. For a Mn adatom on Pb, our Shiba states overall agree with experiments. The characteristics of our Shiba states are also observed with the similar energies and characters in the experiments. The deepest Shiba states that we compute, however, do not appear as close to the Fermi level as the experimental data. It would be interesting to compute the Shiba states with continuously varying vertical distances of the Mn adatom from the surface or with varying the charge state of the adatom, and to calculate the spatial dependence of the spectral density. Our findings will be also useful for understanding of Shiba states for dimers and longer spin chains on the Pb surface considering noncollinear magnetic structures in them. -
The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas–Kroll–Hess Hamiltonian. Spin–orbit coupling was addressed with the Breit–Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin–orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.more » « less
-
null (Ed.)By coupling a newly developed quantum-electronic-state-selected supersonically cooled vanadium cation (V + ) beam source with a double quadrupole-double octopole (DQDO) ion–molecule reaction apparatus, we have investigated detailed absolute integral cross sections ( σ 's) for the reactions, V + [a 5 D J ( J = 0, 2), a 5 F J ( J = 1, 2), and a 3 F J ( J = 2, 3)] + CH 4 , covering the center-of-mass collision energy range of E cm = 0.1–10.0 eV. Three product channels, VH + + CH 3 , VCH 2 + + H 2 , and VCH 3 + + H, are unambiguously identified based on E cm -threshold measurements. No J -dependences for the σ curves ( σ versus E cm plots) of individual electronic states are discernible, which may indicate that the spin–orbit coupling is weak and has little effect on chemical reactivity. For all three product channels, the maximum σ values for the triplet a 3 F J state [ σ (a 3 F J )] are found to be more than ten times larger than those for the quintet σ (a 5 D J ) and σ (a 5 F J ) states, showing that a reaction mechanism favoring the conservation of total electron spin. Without performing a detailed theoretical study, we have tentatively interpreted that a weak quintet-to-triplet spin crossing is operative for the activation reaction. The σ (a 5 D 0 , a 5 F 1 , and a 3 F 2) measurements for the VH + , VCH 2 + , and VCH 3 + product ion channels along with accounting of the kinetic energy distribution due to the thermal broadening effect for CH 4 have allowed the determination of the 0 K bond dissociation energies: D 0 (V + –H) = 2.02 (0.05) eV, D 0 (V + –CH 2 ) = 3.40 (0.07) eV, and D 0 (V + –CH 3 ) = 2.07 (0.09) eV. Detailed branching ratios of product ion channels for the titled reaction have also been reported. Excellent simulations of the σ curves obtained previously for V + generated by surface ionization at 1800–2200 K can be achieved by the linear combination of the σ (a 5 D J , a 5 F J , and a 3 F J ) curves weighted by the corresponding Boltzmann populations of the electronic states. In addition to serving as a strong validation of the thermal equilibrium assumption for the populations of the V + electronic states in the hot filament ionization source, the agreement between these results also confirmed that the V + (a 5 D J , a 5 F J , and a 3 F J ) states prepared in this experiment are in single spin–orbit states with 100% purity.more » « less
