skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, April 12 until 2:00 AM ET on Saturday, April 13 due to maintenance. We apologize for the inconvenience.

Title: Spin–orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations
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
Award ID(s):
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
The Journal of Chemical Physics
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The strong spin–orbit coupling (SOC) in lead halide perovskites, when inversion symmetry is lifted, has provided opportunities for investigating the Rashba effect in these systems. Moreover, the strong orbital moment, which, in turn, impacts the spin-pair in singlet and triplet electronic states, plays a significant role in enhancing the optoelectronic properties in the presence of external magnetic fields in lead halide perovskites. Here, we investigate the effect of weak magnetic fields (<1 T) on the photoluminescence (PL) properties of [Formula: see text] nanocrystals with and without Ruddlesden–Popper (RP) faults and single crystals of [Formula: see text]. Along with an enhancement in the PL intensity as a function of an external magnetic field, which is observed in both lead bromide perovskites, the PL emission red-shifts in [Formula: see text] nanocrystals. Density-functional theory calculations of the electronic band-edge in [Formula: see text] show almost no change in the energy gap as a function of the external magnetic field. The experimental results, thus, suggest the role of mixing of the triplet and singlet excitonic states under weak magnetic fields. This is further deduced from an enhancement in PL lifetimes as a function of the field in [Formula: see text]. In [Formula: see text], an increase in PL intensity is observed under weak magnetic fields; however, no changes in the peak energy or PL lifetimes are observed. The internal magnetic fields due to SOC are characterized for all three samples and found to be the highest for [Formula: see text] nanocrystals with RP faults.

    more » « less
  2. The D 5 Π–X 5 Δ (0,0) band of vanadium hydride at 654 nm has been recorded by laser excitation spectroscopy and represents the first analyzed spectrum of VH in the gas phase. The molecules were generated using a hollow cathode discharge source, with laser-induced fluorescence detected via the D 5 Π–A 5 Π (0,0) transition. All five main (ΔΩ = ΔΛ) subbands were observed as well as several satellite ones, which together create a rather complex and overlapped spectrum covering the region 15 180–15 500 cm −1 . The D 5 Π state displays the effects of three strong local perturbations, which are likely caused by interactions with high vibrational levels of the B 5 Σ − and c 3 Σ − states, identified in a previous multiconfigurational self-consistent field study by Koseki et al. [J. Phys. Chem. A 108, 4707 (2004)]. Molecular constants describing the X 5 Δ, A 5 Π, and D 5 Π states were determined in three separate least-squares fits using effective Hamiltonians written in a Hund’s case (a) basis. The fine structure of the ground state is found to be consistent with its assignment as a σπ 2 δ, 5 Δ electronic state. The fitted values of its first-order spin–orbit and rotational constants in the ground state are [Formula: see text] and B = 5.7579(13) cm −1 , the latter of which yields a bond length of [Formula: see text] Å. This experimental value is in good agreement with previous computational studies of the molecule and fits well within the overall trend of decreasing bond length across the series of 3d transition metal monohydrides. 
    more » « less
  3. The discovery of singular organic radical ligands is a formidable challenge due to high reactivity arising from the unpaired electron. Matching radical ligands with metal ions to engender magnetic coupling is crucial for eliciting preeminent physical properties such as conductivity and magnetism that are crucial for future technologies. The metal-radical approach is especially important for the lanthanide ions exhibiting deeply buried 4f-orbitals. The radicals must possess a high spin density on the donor atoms to promote strong coupling. Combining diamagnetic 89 Y ( I = 1/2) with organic radicals allows for invaluable insight into the electronic structure and spin-density distribution. This approach is hitherto underutilized, possibly owing to the challenging synthesis and purification of such molecules. Herein, evidence of an unprecedented bisbenzimidazole radical anion (Bbim 3− ˙) along with its metalation in the form of an yttrium complex, [K(crypt-222)][(Cp* 2 Y) 2 (μ-Bbim˙)] is provided. Access of Bbim 3− ˙ was feasible through double-coordination to the Lewis acidic metal ion and subsequent one-electron reduction, which is remarkable as Bbim 2− was explicitly stated to be redox-inactive in closed-shell complexes. Two molecules containing Bbim 2− (1) and Bbim 3− ˙ (2), respectively, were thoroughly investigated by X-ray crystallography, NMR and UV/Vis spectroscopy. Electrochemical studies unfolded a quasi-reversible feature and emphasize the role of the metal centre for the Bbim redox-activity as neither the free ligand nor the Bbim 2− complex led to analogous CV results. Excitingly, a strong delocalization of the electron density through the Bbim 3− ˙ ligand was revealed via temperature-dependent EPR spectroscopy and confirmed through DFT calculations and magnetometry, rendering Bbim 3− ˙ an ideal candidate for single-molecule magnet design. 
    more » « less
  4. 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 thezaxis,mJ. 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.

    more » « less
  5. Abstract

    Synchrotron‐based nuclear resonance vibrational spectroscopy (NRVS) using the Mössbauer isotope161Dy has been employed for the first time to study the vibrational properties of a single‐molecule magnet (SMM) incorporating DyIII, namely [Dy(Cy3PO)2(H2O)5]Br3⋅2 (Cy3PO)⋅2 H2O ⋅2 EtOH. The experimental partial phonon density of states (pDOS), which includes all vibrational modes involving a displacement of the DyIIIion, was reproduced by means of simulations using density functional theory (DFT), enabling the assignment of all intramolecular vibrational modes. This study proves that161Dy NRVS is a powerful experimental tool with significant potential to help to clarify the role of phonons in SMMs.

    more » « less