A precision measurement of the hyperfine structure of87Sr+

Relativistic Douglas-Kroll-Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Structural and electronic trends of optical cycling centers in polyatomic molecules revealed by microwave spectroscopy of MgCCH, CaCCH, and SrCCH

The unique optical cycling efficiency of alkaline earth metal-ligand molecules has enabled significant advances in polyatomic laser cooling and trapping. Rotational spectroscopy is an ideal tool for probing the molecular properties that underpin optical cycling, thereby elucidating the design principles for expanding the chemical diversity and scope of these platforms for quantum science. We present a comprehensive study of the structure and electronic properties in alkaline earth metal acetylides with high-resolution microwave spectra of 17 isotopologues of MgCCH, CaCCH, and SrCCH in their 2Σ+ ground electronic states. The precise semiexperimental equilibrium geometry of each species has been derived by correcting the measured rotational constants for electronic and zero-point vibrational contributions calculated with high-level quantum chemistry methods. The well-resolved hyperfine structure associated with the 1,2H, 13C, and metal nuclear spins provides further information on the distribution and hybridization of the metal-centered, optically active unpaired electron. Together, these measurements allow us to correlate trends in chemical bonding and structure with the electronic properties that promote efficient optical cycling essential to next-generation experiments in precision measurement and quantum control of complex polyatomic molecules.

Suppression of Clock Shifts at Magnetic-Field-Insensitive Transitions

We show that it is possible to significantly reduce rank 2 tensor shifts of a clock transition by operating at a judiciously chosen magnetic-field-insensitive point. In some cases shifts are almost completely eliminated making the transition an effective J=0 to J=0 candidate. This significantly improves the feasibility of a recent proposal for clock operation with large ion crystals. For such multi-ion clocks, geometric constraints and selection rules naturally divide clock operation into two categories based on the orientation of the magnetic field. We discuss the limitations imposed on each type and how calibrations might be carried out for clock operation.

Derivation and assessment of relativistic hyperfine-coupling tensors on the basis of orbital-optimized second-order Møller-Plesset perturbation theory and the second-order Douglas-Kroll-Hess transformation

The accurate calculation of hyperfine-coupling tensors requires a good description of the electronic spin density, especially close to and at the nucleus. Thus, dynamic correlation as well as relativistic effects have to be included in the quantum-chemical calculation of this quantity. In this paper, orbital-optimized second-order Møller-Plesset perturbation theory (MP2) is combined with the second-order Douglas-Kroll-Hess (DKH) transformation to yield an efficient and accurate ab initio method for the calculation of hyperfine couplings for larger molecules including heavy elements. Particular attention is paid to the derivation of the hyperfine-coupling tensor in the DKH framework. In the presence of a magnetic field, the DKH-transformation is not unique. Two different versions can be found in the literature. In this paper, a detailed derivation of one-electron contributions to the hyperfine-coupling tensor as they arise in linear-response theory is given for both DKH-transformations. It turns out that one of the two variants produces divergent hyperfine-coupling constants. The possibility to remove this divergence through a physically motivated finite-nucleus model taking into account the different extent of charge and magnetization distribution is discussed. Hyperfine-coupling values obtained at the orbital-optimized MP2 level with second-order DKH corrections for the non-divergent variant are presented. The influence of a Gaussian nucleus model is studied. The method is compared to four-component, high-accuracy calculations for a number of cations and atoms. Comparison to B3LYP and B2PLYP is made for a set of transition-metal complexes of moderate size.

Electron-spin polarization of photoions produced through photoionization from the laser-excited triplet state of Sr

We report the detailed experimental study on the production of electron-spin-polarized Sr+ ions through one-photon resonant two-photon ionization via laser-excited 5s5p 3P1 (MJ = +1) of Sr atoms produced by laser-ablation. We have experimentally confirmed that the use of laser-ablation for the production of Sr atoms prior to photoionization does not affect the electron-spin polarization. We have found that the degree of electron-spin polarization is 64+/-9%, which is in good agreement with our recent theoretical prediction. As we discuss in detail, we infer, from a simple analysis, that photoelectrons, being the counterpart of electron-spin-polarized Sr+ ions, have approximately the same degree of electron-spin polarization. Our experimental results demonstrate that the combined use of laser-ablation technique and pulsed lasers for photoionization would be a compact and effective way to realize a pulsed source for spin-polarized ions and electrons for the studies of various spin-dependent dynamics in chemical physics.