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1. Spin–orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations

   https://doi.org/10.1063/5.0130868  

   Kotaru, Saikiran ; Pokhilko, Pavel ; Krylov, Anna I. ( December 2022 , The Journal of Chemical Physics)

   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. 

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2. 31 P nuclear spin singlet lifetimes in a system with switchable magnetic inequivalence: experiment and simulation

   https://doi.org/10.1039/D1CP03085J  

   Korenchan, David E. ; Lu, Jiaqi ; Levitt, Malcolm H. ; Jerschow, Alexej ( September 2021 , Physical Chemistry Chemical Physics)

   31 P NMR spectroscopy and the study of nuclear spin singlet relaxation phenomena are of interest in particular due to the importance of phosphorus-containing compounds in physiology. We report the generation and measurement of relaxation of 31 P singlet order in a chemically equivalent but magnetically inequivalent case. Nuclear magnetic resonance singlet state lifetimes of 31 P pairs have heretofore not been reported. Couplings between 1 H and 31 P nuclei lead to magnetic inequivalence and serve as a mechanism of singlet state population conversion within this molecule. We show that in this molecule singlet relaxation occurs at a rate significantly faster than spin–lattice relaxation, and that anticorrelated chemical shift anisotropy can account for this observation. Calculations of this mechanism, with the help of molecular dynamics simulations and ab initio calculations, provide excellent agreement with the experimental findings. This study could provide guidance for the study of 31 P singlets within other compounds, including biomolecules. 

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3. Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh 3 ) 2 X 2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling

   https://doi.org/10.1002/chem.202100705  

   Bone, Alexandria N. ; Widener, Chelsea N. ; Moseley, Duncan H. ; Liu, Zhiming ; Lu, Zhengguang ; Cheng, Yongqiang ; Daemen, Luke L. ; Ozerov, Mykhaylo ; Telser, Joshua ; Thirunavukkuarasu, Komalavalli ; et al ( August 2021 , Chemistry – A European Journal)

   Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single‐molecule magnets (SMMs). Spin‐phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin‐phonon coupling in molecules is challenging. We have found that far‐IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂(Co‐X; X=Cl, Br, I) reveal rarely observed spin‐phonon coupling as avoided crossings between magnetic andu‐symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero‐field split (ZFS) levels of theS=3/2 electronic ground state were probed by INS, high‐frequency and ‐field EPR (HFEPR), FIRMS, and frequency‐domain FT terahertz EPR (FD‐FT THz‐EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) andgvalues. Ligand‐field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities inCo‐X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin‐phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

    

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4. Singlet excitation in the intermediate magnetic equivalence regime and field-dependent study of singlet–triplet leakage

   https://doi.org/10.1039/C8CP06883F  

   Kharkov, Boris ; Duan, Xueyou ; Tovar, Emily S. ; Canary, James W. ; Jerschow, Alexej ( January 2019 , Physical Chemistry Chemical Physics)

   The examination and optimized preparation of nuclear spin singlet order has enabled the development of new types of applications that rely on potentially long-term polarization storage. Lifetimes several orders of magnitude longer than T 1 have been observed. The efficient creation of such states relies on special pulse sequences. The extreme cases of very large and very small magnetic equivalence received primary attention, while relatively little effort has been directed towards studying singlet relaxation in the intermediate regime. The intermediate case is of interest as it is relevant for many spin systems, and would also apply to heteronuclear systems in very low magnetic fields. Experimental evidence for singlet–triplet leakage in the intermediate regime is sparse. Here we describe a pulse sequence for efficiently creating singlets in the intermediate regime in a broad-band fashion. Singlet lifetimes are studied with a specially synthesized molecule over a wide range of magnetic fields using a home-built sample-lift apparatus. The experimental results are supplemented with spin simulations using parameters obtained from ab initio calculations. This work indicates that the chemical shift anisotropy (CSA) mechanism is relatively weak compared to singlet–triplet leakage for the proton system observed over a large magnetic field range. These experiments provide a mechanism for expanding the scope of singlet NMR to a larger class of molecules, and provide new insights into singlet lifetime limiting factors. 

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5. Electron-phonon coupling and spin fluctuations in the Ising superconductor NbSe2

   https://doi.org/10.1038/s41524-023-01017-4  

   Das, S. ; Paudyal, H. ; Margine, E. R. ; Agterberg, D. F. ; Mazin, I. I. ( April 2023 , npj Computational Materials)

   Ising superconductivity, observed in NbSe₂and similar materials, has generated tremendous interest. Recently, attention was called to the possible role that spin fluctuations (SF) play in this phenomenon, in addition to the dominant electron–phonon coupling (EPC); the possibility of a predominantly triplet state was discussed and led to a conjecture of viable singlet–triplet Leggett oscillations. However, these hypotheses have not been put to a quantitative test. In this paper, we report first principle calculations of the EPC and also estimate coupling with SF, including full momentum dependence. We find that: (1) EPC is strongly anisotropic, largely coming from the$$K-{K}^{{\prime} }$$$K-K^{\prime }$scattering, and therefore excludes triplet symmetry even as an excited state; (2) superconductivity is substantially weakened by SF, but anisotropy remains as above; and, (3) we do find the possibility of a Leggett mode, not in a singlet–triplet but in ans₊₊–s_±channel.

    

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