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The energetic disorder induced by fluctuating liquid environments acts in opposition to the precise control required for coherence-based sensing. Overcoming fluctuations requires a protected quantum subspace that only weakly interacts with the local environment. We report a ytterbium complex that exhibited an ultranarrow absorption linewidth in solution at room temperature with a full width at half maximum of 0.625 milli–electron volts. Using spectral hole burning, we measured an even narrower linewidth of 410 pico–electron volts at 77 kelvin. Narrow linewidths allowed low-field magnetic circular dichroism at room temperature, used to sense Earth-scale magnetic fields. These results demonstrated that ligand protection in lanthanide complexes could substantially diminish electronic state fluctuations. We have termed this system an “atomlike molecular sensor” (ALMS) and proposed approaches to improve its performance. 

Achieving ultranarrow absorption linewidths in the condensed phase enables optical state preparation of specific non-thermal states, a prerequisite for quantum-enabled technologies. 

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions. 

The robustness of nickelocene’s (NiCp2, Cp = cyclopentadienyl) magnetic anisotropy and addressability of its spin states make this molecular magnet attractive as a spin sensor. However, microscopic understanding of its magnetic anisotropy is still lacking, especially when NiCp2 is deposited on a surface to make quantum sensing devices. Quantum chemical calculations of such molecule/solid-state systems are limited to density functional theory (DFT) or DFT+U (Hubbard correction to DFT). We investigate the magnetic behavior of NiCp2 using the spin-flip variant of the equation-of-motion coupled-cluster (EOM-SF-CC) method and use the EOM-SF-CC results to benchmark SF-TD-DFT. Our first-principle calculations agree well with experimentally derived magnetic anisotropy and susceptibility values. The calculations show that magnetic anisotropy in NiCp2 originates from a large spin–orbit coupling (SOC) between the triplet ground state and the third singlet state, whereas the coupling with lower singlet excited states is negligible. We also considered a set of six ring-substituted NiCp2 derivatives and a model system of the NiCp2/MgO(001) adsorption complex, for which we used SF-TD-DFT method. To gain insight into the electronic structure of these systems, we analyze spinless transition density matrices and their natural transition orbitals (NTOs). The NTO analysis of SOCs explains how spin states and magnetic properties are retained upon modification of the NiCp2 coordination environment and upon its adsorption on a surface. Such resilience of the NiCp2 magnetic behavior supports using NiCp2 as a spin-probe molecule by functionalization of the tip of a scanning tunneling microscope. 

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.