Molecular Design for Optically Induced Magnetization: Targeting Excited State Orbital Degeneracy in Tungsten(V) Complexes

Abstract

The rise of quantum information science has spurred chemists to prepare new molecules that serve as useful building blocks in quantum technologies of the future. Implementation of molecular spin-based qubits requires new methods to induce high spin polarization of samples. Herein, we report design criteria to develop axially symmetric spin-1/2 molecules amenable to optically induced magnetization (OIM), a technique using circularly polarized (CP) excitation to deliver spin polarization. We apply these criteria to develop a series of tungsten­(V) chalcogenide complexes that are demonstrated to have large spin-sensitive responses to CP light using magnetic circular dichroism (MCD) that could allow up to ∼20% spin polarization through OIM. Pulsed electron paramagnetic resonance (EPR) spectra reveal these systems have improved relaxation times over molecules like K₂IrCl₆, a species recently investigated by OIM, and field-swept electron spin–echo (FS-ESE) experiments show they have a remarkable lack of anisotropy in their phase-memory T _m times. The design criteria are general and point toward future ways to improve OIM-initializable qubits.

The development of molecular spin-based qubits requires that spins fulfill several criteria outlined by DiVincenzo for quantum computing or Degen for quantum sensing. Of these criteria, use of molecular spin most prominently demands advancement in methods of “initialization,” the process of selective spin polarization into a pure |0⟩ or |1⟩ state. Spin polarization is usually done thermally: application of an external magnetic field splits the M _S levels, and a Boltzmann population of these levels is then achieved on the timescale of the spin–lattice (T ₁) relaxation time. Conceptually, greater spin polarization can be easily reached by applying a larger magnetic field or cooling a sample further. Practically, this is difficult. The combination of low temperatures and high fields does provide high polarization, but such instrumentation can be prohibitively costly, and cooling below helium temperatures can cause increasingly slow T ₁ relaxation. ,

Nonthermal ways to polarize spin sidestep these issues, and optical methods have proven especially promising. − These techniques leverage electronic excitation and molecular design to influence spin, allowing chemists to untether spin polarization from Boltzmann population and spin T ₁ relaxation. We are interested in a spin-sensitive optical phenomenon known as “optically induced magnetization” (OIM). OIM is deeply intertwined with a technique more familiar to chemists, magnetic circular dichroism (MCD): MCD measures the differential response of M _S levels to circularly polarized (CP) light (Δϵ = ϵ_LCP – ϵ_RCP), , whereas OIM exploits this differential response to preferentially bleach one M _S level. Despite demonstration of OIM in a wide variety of systems, − the method has not been well-explored to manipulate molecular spin. This will surely change after a recent report demonstrating the usefulness of OIM to explore ultrafast spin dynamics of K₂IrCl₆.

Selection of K₂IrCl₆ relied on its octahedral geometry and its ² T _2g ground state (GS) orbital angular momentum (OAM), promoting a large MCD/OIM response but also causing exceedingly short coherence (phase-memory) T _m times, even at 20 K. Such rapid decoherence impairs many applications in quantum technologies by limiting the computations that can be performed or the information that may be sensed by a qubit. , Herein, we report a more flexible molecular design strategy to optimize OIM responses that allows us to explore the preparation of S = 1/2 molecules of axial symmetry that lack any GS OAM. Our design strategy led us to a series of tungsten­(V) chalcogenide complexes [1·E]⁻ (Figure a) that could give up to ∼20% spin polarization by OIM. Pulsed electron paramagnetic resonance (EPR) experiments reveal improved spin relaxation characteristics for these complexes due to their lack of GS OAM or a low-lying excited state (ES), and field-swept electron spin–echo (FS-ESE) EPR measurements reveal a remarkable insensitivity of phase-memory (T _m) times to magnetic field.

1.

(a) The [1·E]⁻ compounds have bulky aryloxide ligands that enforce pseudo-C _4v geometry, confirmed by (b) the crystal structure of [Na­(THF)₆]­[1·O]. (c) The d orbital splittings for [1·O]⁻ are shown with C _4v irrep labels. (d) SOC splits the ² E state into two components labeled by C _4v double group irreps.

Using the language of MCD theory, maximization of OIM is equivalent to maximization of the “C term” MCD response, something driven by spin–orbit coupling (SOC) in transition-metal systems. The K₂IrCl₆ system experienced strong SOC due to the residual (“fictitious”) OAM in its GS, but there is no reason SOC splitting must come from the GS. Instead, we were inspired by ruby, where OIM can be performed from its orbitally nondegenerate ⁴ A ₂ GS to a degenerate ² E ES. This ² E ES of ruby lacks residual OAM; yet, SOC still causes splitting into two Kramers doublets. Because SOC is the dominant driver of this splitting, spin and orbital angular momenta strongly mix to deliver a highly M _S-selective MCD/OIM response. Clearly, threefold orbital degeneracy is not required for OIM.

Simply put, any point group possessing degenerate irreducible representations (irreps) may allow for orbital-based optimization of OIM. This certainly includes cubic point groups (O _h , T _d , etc.), but also all axial point groups of threefold-or-higher symmetry. At its simplest, OIM maximization should therefore incorporate

• axial (C _{(n ≥ 3)(v/h)}, D _{(n ≥ 3)(h)}, D _(n ≥ 2)d , S _2n ≥ 4) or isometric (T _(d/h), O _(h), I _(h)) point groups

• an optical transition involving an orbitally degenerate state

• SOC splitting of similar or greater magnitude to the line width of the electronic transition

. An OIM-initializable qubit should additionally target increased spin coherence through

• avoidance of GS OAM and low-lying ESs

• a large absorptivity (ϵ) to allow more dilute samples

Of the few examples of molecular OIM we are aware of,^18,19 every system fails to satisfy at least one of these five criteria.

We selected tungsten­(V)–oxo complex [1·O]⁻ as a promising system: tetragonal d ¹ oxos generally have a low-lying ² E ES (Figure c), and 5d metals have strong SOC (ζ_W(V) = 3483 cm^–1). Heating a THF solution of WOCl₃(THF)₂ and sodium 2,6-diisopropylphenoxide (NaODipp, 4 equiv) overnight (69 °C, 18 h) provided deep blue [Na­(THF)₆]­[1·O] in 50% recrystallized yield. A preliminary X-ray diffraction study (Figure b) revealed a nearly C ₄-symmetric anion with a geometry close to an ideal square pyramid (τ₅ = 0.052(6)). An optical ² B ₂ → ² E transition was observed in the UV–vis–NIR absorption spectrum (16 100 cm^–1, Figure a) with a prominent shoulder due to tungsten­(V) SOC, and a relatively large absorptivity for a d–d transition (270 M^–1 cm^–1). Thus, [1·O]⁻ satisfied all our design requirements.

2.

(a) Room-temperature UV–vis–NIR absorption and MCD spectra of [Na­(THF)₆]­[1·O] (THF solution). (b) The maximum spin polarization through OIM is |Δϵ_satlim/2ϵ|, estimated here for [1·O]⁻ in two ways (see text and the SI). (c) The absorption and MCD spectra of the heavier chalcogenide complexes reveal a ² A ₁ transition.

We were pleased to find the MCD spectrum of [1·O]⁻ shows large intensities associated with its ² E ES. The SOC splitting of this state was clearly indicated by the characteristic bisignate (“pseudo-A”) line shape, the negative and positive features corresponding to E _1/2 and E _3/2 levels, respectively (see the SI). The MCD intensities of these levels were quantified through their “C ₀/D ₀” ratios, a ratio of MCD C term intensity (“C ₀”) to absorption intensity (“D ₀”). For a simple spin-1/2 GS lacking OAM and low-lying ESs, the maximum possible magnitude of |C ₀/D ₀| is g/2, half the GS g value (see the derivation given in the SI); however, molecules typically feature ratios far smaller (Chart ). The values for the [1·O]^{− 2} B ₂  → ² E transitions (−0.46(3) and +0.32(4)) were quite large, multiple times larger than those of TEMPO^• and Cu­(acac)₂ exemplars, and approach the values for ${[{\mathrm{I}\mathrm{r}\mathrm{C}\mathrm{l}}_6]}^{\mathrm{2-}}$ , , an ion specifically chosen for OIM studies due to its residual GS OAM.

1. ² B ₂ → ² E Transitions of [1·E]⁻ Species Have Far Stronger MCD Intensities than Other S = 1/2 Organic or Transition Metal Species with Smaller SOC; Their C ₀/D ₀ Ratios Approach Those of [IrCl₆]^2– , a System with GS OAM.

The MCD C ₀/D ₀ ratio is a useful heuristic, but more direct insight for OIM would come from measuring Δϵ for each individual M _S level. This can be accomplished in the saturation limit. Magnetic saturation occurs under sufficiently low temperatures or high fields that most molecules populate a single M _S level. In the limit of complete saturation, the MCD spectrum reveals the intrinsic Δϵ for the single lowest-energy M _S level. MCD intensity in the presence of saturation is nonlinear,

$$\frac{\mathrm{\Delta }ϵ}{E}=\gamma \frac{2C_0}{g}\tanh \left(\frac{g{\mu }_{\mathrm{B}}B}{2k_{\mathrm{B}}T}\right)f(E)$$ 1

where E is the excitation energy, γ a proportionality constant, μ_B the Bohr magneton, B the magnetic field, k _B the Boltzmann constant, T the temperature, and f(E) a line shape function (see the SI). We used eq to estimate MCD in the saturation limit Δϵ_satlim in two ways: from room-temperature data, and from cryogenic MCD data (5 K, 7 T). The maximum spin polarization that can be achieved by OIM is |Δϵ_satlim/2ϵ| (see the SI), and both methods of estimating Δϵ_satlim/2ϵ reveal that CP excitation of the ² B ₂ → ² E transition can deliver up to 15% (E _3/2) or 20% (E _1/2) spin polarization, depending on wavelength of excitation (Figure b). For context, such a large polarization can only be achieved thermally at 1–1.5 K in X-band EPR experiments.

Analogous chalcogen congeners [1·S]⁻ and [1·Se]⁻ were also synthesized to explore their MCD intensities. The former was prepared by treating W­(ODipp)₄ with NaSCPh₃ (1 equiv, THF), a convenient source of S^• – upon release of CPh₃ . Stirring overnight then washing with ether provided teal [Na­(THF)₆]­[1·S] in 36% yield after recrystallization. The latter complex was prepared in a two-step one-pot procedure: W­(ODipp)₄ was first treated with PPh₃Se to form the terminal selenide complex, and then reduction with NaCPh₃ formed the tungsten­(V) anion. Recrystallization provided vibrant green [Na­(THF) _x (Et₂O) _y ]­[1·Se] in 26% isolated yield.

The MCD spectra of [1·S/Se]⁻ show the appearance of the ² B ₂ → ² A ₁ ligand field transition, likely caused by weaker σ_WE interactions in the heavier chalcogenides. This assignment follows from its negative MCD response, indicating E _1/2 symmetry, and is corroborated by model CASSCF/RI-NEVPT2 calculations (see the SI). We ascribe the weaker |C ₀/D ₀| ratios (Chart ) of the ² B ₂ → ² A ₁ transitions to a lack of ES orbital degeneracy. For such nondegenerate states, the sum-over-states perturbation theory formalism says C term intensity is proportional to the reciprocal energy difference to other states coupling through SOC. This is an important distinction from ² E states, underscoring that design of molecules with large MCD/OIM responses should target transitions involving orbital degeneracy.

All three chalcogenide complexes can be observed by continuous-wave (CW) EPR experiments at temperatures at least up to 80 K due to their lack of GS OAM and thus slower relaxation properties. Inversion recovery and Hahn-echo X-band EPR experiments were used to directly measure T ₁ and T _m times (Figure ), giving values higher than those of K₂IrCl₆ (10–100 times higher at 20 K); in fact, even higher values may be attainable through techniques like deuteration, picket-fence saturation recovery experiments, and Carr–Purcell–Meiboom–Gill (CPMG) pulse sequences. Despite this increase in coherence for [1·E]⁻ complexes, these T _m relaxation times are still modest likely due to the strong SOC within the systems. A balance clearly needs to be struck between maximizing MCD/OIM using heavy atom SOC while avoiding the collapse of spin coherence, and this will be a fascinating area for future exploration.

3.

(a) The CW EPR spectra show approximate C ₄ symmetry for all anions with slight rhombic distortions for [1·S/Se]⁻. (b) Spin T ₁ and T _m measurements show slower relaxation for [1·E]⁻ anions than K₂IrCl₆ (values from ref ) due to the latter’s GS OAM. (c) Normalized contours in the FS-ESE spectrum of [1·Se]⁻ show nearly flat T _m times independent of field.

The T ₁ and T _m measurements also showed unexpectedly consistent relaxation times when measured in the g _∥ and g _⊥ regions of the spectra. Such behavior differs from related species, which often show large variations across the spectra. This insensitivity to magnetic field was demonstrated using a 2D FS-ESE EPR experiment conducted on [1·Se]⁻, showing nearly constant T _m times across the entire spectrum. Studies are ongoing to uncover correlations between relaxation times, molecular symmetry, and MCD/OIM intensity.

With this work, we hope to highlight that a large synthetic space remains to be explored in the development of optimal molecules for OIM. Our results ease the restrictive O _h design strategy for OIM, showing that chemists can exploit axial symmetry to deliver large MCD responses. This increased flexibility should allow targeting of other properties important for qubits, especially spin relaxation times. Ligand design may be particularly useful, as the ODipp ligands here were selected for ease of use rather than promotion of spin coherence. − We are conducting experiments toward these ends, and toward balancing spin and optical lifetimes for future implementation of OIM in molecular qubit systems on the nanosecond time scale.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.5c03783.

• Experimental details, spectroscopic characterization, crystallographic information, computational details, and theoretical derivations (PDF)

The authors declare no competing financial interest.