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Nuclear spin levels play an important role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for $^{161}$Dy and $^{163}$Dy nucleus in anionic DyPc$_2$ (Pc=phthalocyanine) single-molecule magnets, using multiconfigurational ab-initio methods (beyond density-functional theory) including spin-orbit interaction. The two isotopes of Dy are chosen because the others have zero nuclear spin. Both isotopes have the nuclear spin $I=5/2$, although the magnitude and sign of the nuclear magnetic moment differ from each other. The large energy gap between the electronic ground and first-excited Kramers doublets, allows us to map the microscopic hyperfine and quadrupole interaction Hamiltonian onto an effective Hamiltonian with an electronic pseudo-spin $S_{rm eff}=1/2$ that corresponds to the ground Kramers doublet. Our ab-initio calculations show that the coupling between the nuclear spin and electronic orbital angular momentum contributes the most to the hyperfine interaction and that both the hyperfine and nuclear quadrupole interactions for $^{161}$Dy and $^{163}$Dy nucleus are much smaller than those for $^{159}$Tb nucleus in TbPc$_2$ single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for $^{163}$DyPc$_2$. We demonstrate that hyperfine interaction for Dy Kramers ion leads to tunnel splitting (or quantum tunneling of magnetization) at zero field. This effect does not occur for TbPc$_2$ single-molecule magnets. The magnetic field values of the avoided level crossings for $^{161}$DyPc$_2$ and $^{163}$DyPc$_2$ are found to be noticeably different, which can be observed from experiment.
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Lanthanide-based single-ion magnetic molecules can have large magnetic hyperfine interactions as well as large magnetic anisotropy. Recent experimental studies reported tunability of these properties by changes of chemical environments or by application of external stimuli for device applications. In order to provide insight onto the origin and mechanism of such tunability, here we investigate the magnetic hyperfine and nuclear quadrupole interactions for $^{159}$Tb nucleus in TbPc$_2$ (Pc=phthalocyanine) single-molecule magnets using multireference ab-initio methods including spin-orbit interaction. Since the electronic ground and first-excited (quasi)doublets are well separated in energy, the microscopic Hamiltonian can be mapped onto an effective Hamiltonian with an electronic pseudo-spin $S=1/2$. From the ab-initio-calculated parameters, we find that the magnetic hyperfine coupling is dominated by the interaction of the Tb nuclear spin with electronic orbital angular momentum. The asymmetric $4f$-like electronic charge distribution leads to a strong nuclear quadrupole interaction with significant non-axial terms for the molecule with low symmetry. The ab-initio calculated electronic-nuclear spectrum including the magnetic hyperfine and quadrupole interactions is in excellent agreement with experiment. We further find that the non-axial quadrupole interactions significantly influence the avoided level crossings in magnetization dynamics and that the molecular distortions affect mostly the Fermi contact terms as well as the non-axial quadrupole interactions.
Molecular spin qubits with long spin coherence time as well as non-invasive operation methods on such qubits are in high demand. It was shown that both molecular electronic and nuclear spin levels can be used as qubits. In solid state systems with dopants, an electric field was shown to effectively change the spacing between the nuclear spin qubit levels when the electron spin density is high at the nucleus of the dopant. Inspired by such solid-state systems, we propose that divalent lanthanide (Ln) complexes with an unusual electronic configuration of Ln$^{2+}$ have a strong interaction between the Ln nuclear spin and the electronic degrees of freedom, which renders electrical tuning of the interaction. As an example, we study electronic structure and hyperfine interaction of the $^{159}$Tb nucleus in a neutral Tb(II)(Cp$^{rm{iPr5}}$)$_2$ single-molecule magnet (SMM) using the complete active space self-consistent field method with spin-orbit interaction included within the restricted active space state interaction. Our calculations show that the low-energy states arise from $4f^8(6s,5d_{z^2})^1$, 4$f^8$(5$d_{x^2-y^2}$)$^1$, and $4f^8(5d_{xy})^1$ configurations. We compute the hyperfine interaction parameters and the electronic-nuclear spectrum within our multiconfigurational approach. We find that the hyperfine interaction is about one order of magnitude greater than that for Tb(III)Pc$_2$ SMMs. This stems from the strong Fermi contact interaction between the Tb nuclear spin and the electron spin density at the nucleus that originates from the occupation of the $(6s,5d)$ orbitals. We also uncover that the response of the Fermi contact term to electric field results in electrical tuning of the electronic-nuclear level separations. This hyperfine Stark effect may be useful for applications of molecular nuclear spins for quantum computing.
We introduce a system-independent method to derive effective atomic C$_6$ coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C$_6$ coefficients as well as dispersion energies of weakly bound molecular dimers, organic crystals, and supramolecular complexes. We showcase the utility of our approach by incorporation of the recently developed many-body dispersion (MBD) method [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012)] into the semi-empirical Density Functional Tight-Binding (DFTB) method and propose the latter as a viable technique to study hybrid organic-inorganic interfaces.
The hyperfine interactions at the uranium site in the antiferromagnetic USb2 compound were calculated within the density functional theory (DFT) employing the augmented plane wave plus local orbital (APW+lo) method. We investigated the dependence of the nuclear quadruple interactions to the magnetic structure in USb2 compound. The investigation were performed applying the so called band correlated LDA+U theory self consistently. The self consistent LDA+U calculations were gradually added to the performed generalized gradient approximation (GGA) including scalar relativistic spin orbit interactions in a second variation scheme. The result, which is in agreement with experiment, shows that the 5f-electrons have the tendency to be hybridized with the conduction electrons in the ferromagnetic uranium planes.
The odd isotopologues of ytterbium monohydroxide, $^{171,173}$YbOH, have been identified as promising molecules in which to measure parity (P) and time reversal (T) violating physics. Here we characterize the $tilde{A}^{2}Pi_{1/2}(0,0,0)-tilde{X}^2Sigma^+(0,0,0)$ band near 577 nm for these odd isotopologues. Both laser-induced fluorescence (LIF) excitation spectra of a supersonic molecular beam sample and absorption spectra of a cryogenic buffer-gas cooled sample were recorded. Additionally, a novel spectroscopic technique based on laser-enhanced chemical reactions is demonstrated and utilized in the absorption measurements. This technique is especially powerful for disentangling congested spectra. An effective Hamiltonian model is used to extract the fine and hyperfine parameters for the $tilde{A}^{2}Pi_{1/2}(0,0,0)$ and $tilde{X}^2Sigma^+(0,0,0)$ states. A comparison of the determined $tilde{X}^2Sigma^+(0,0,0)$ hyperfine parameters with recently predicted values (M. Denis, et al., J. Chem. Phys. $bf{152}$, 084303 (2020), K. Gaul and R. Berger, Phys. Rev. A $bf{101}$, 012508 (2020), J. Liu et al., J. Chem. Phys. $bf{154}$, 064110 (2021)) is made. The measured hyperfine parameters provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants $W_d$ and $W_M$, which correlate P,T-violating physics to P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters of the $tilde{A}^{2}Pi_{1/2}(0,0,0)$ and $tilde{X}^2Sigma^+(0,0,0)$ states for all isotopologues of YbOH are discussed and a comparison to isoelectronic YbF is made.
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