Assessing the Nature of Chiral-Induced Spin Selectivity by Magnetic Resonance

Abstract

Understanding chiral-induced spin selectivity (CISS), resulting from charge transport through helical systems, has recently inspired many experimental and theoretical efforts but is still the object of intense debate. In order to assess the nature of CISS, we propose to focus on electron-transfer processes occurring at the single-molecule level. We design simple magnetic resonance experiments, exploiting a qubit as a highly sensitive and coherent magnetic sensor, to provide clear signatures of the acceptor polarization. Moreover, we show that information could even be obtained from time-resolved electron paramagnetic resonance experiments on a randomly oriented solution of molecules. The proposed experiments will unveil the role of chiral linkers in electron transfer and could also be exploited for quantum computing applications.

Figure 1

Scheme of the electron-transfer mechanism: (a) singlet initial state on the donor D (with two electrons both in the ground orbital). Photoexcitation (PE) brings it to the D*A singlet state in which one electron is excited (b), but the pair is still in an entangled state (dashed circle). After electron transfer (ET) of the excited electron to the acceptor (A), the final state is still either a correlated radical pair (RP, c) or a polarized state after transfer through a chiral bridge (d). Recombination to the initial singlet (or to the triplet) state occurs on a time scale T_R (dashed arrows). Top (bottom) inset: Scheme of the DA radical pair, linked by a linear (chiral) bridge.

Figure 2

(a) Q-band TR-EPR spectrum of a D⁺-χ-A^–-Q system (sketched on top) with the chiral axis aligned parallel to the external field (integrated from 100 to 300 ns) and for different initial states of the radical pair (with the qubit always in |↓⟩): singlet (blue line), corresponding to transfer along a linear bridge without CISS effect; fully polarized state (on both donor and acceptor, red); unpolarized state |ψ_U⟩ as suggested in ref (32), black. The gray-shaded area represents the signal from the donor–acceptor, while at larger field the absorption peaks are due to the qubit. (b) NMR spectrum as a function of frequency, probing nuclear excitations on a nuclear spin 1/2 (e.g., a ¹⁹F, Larmor frequency ν_L ≈ 40 MHz at 1 T) coupled by hyperfine interaction to the donor. The different intensity of the two peaks for p = 0 is due to different matrix elements for the two transitions. Variance from the p = 0 behavior directly measures the acceptor polarization. Parameters: hν = 34 GHz, J_AQ^z ≈ 200 MHz, r_DA = 25 Å, r_AQ = 8 Å, = 10 MHz, g_1,2 = g_e ∓ Δg/2, with Δg = 0.002, g_Q = (1.98, 1.98, 1.96), as typical for VO²⁺ or Ti³⁺,T₁ = 2 μs, T₂ = 0.5 μs, and T_R = 10 μs. Inhomogeneous broadening of the parameters is included by a Gaussian broadening of the peaks with fwhm 2.35 mT. To generalize our analysis, we did not include parameters of a specific qubit, such as hyperfine interaction.

Figure 3

Polarization transfer to the qubit probe: (a) and (b) Pulse sequence implementing the scheme on the AQ pair (D has opposite polarization compared to A and is not affected by the pulses; that is, rotations of A are independent from the state of D). Full (dashed) lines indicate occupied (empty) states, initially with fully polarized A, finally with polarization transferred to Q (red arrow). The two pulses on A (Q) are indicated by a purple (green) arrow. (c) TR-EPR spectrum (integrated from 100 to 300 ns) after application of the polarization transfer sequence for an unpolarized state (black line) or for a spin polarized one (red or blue, depending on the polarization), as expected after CISS induced by each of the two enantiomers. Transitions involving excitations of D (Q) are represented by peaks at low (high) field.

Figure 4

TR-EPR on a randomly oriented ensemble of D-χ-A molecules. Parameters: Δg = 0.002, r_DA = 25 Å, hν = 9.8 GHz. (a) and (b) Two-dimensional maps of ⟨S_y(t, B)⟩ for an initial singlet or polarized state, respectively. (c) Field dependence of the absorption TR-EPR spectrum, integrated in the time-window corresponding to the first maxima-minima in the maps of panels (a) and (b), for the states , ρ_p (with either p = −1 or p = 1, leading to the same result in solution). (d) Time dependence around B ≈ 349.5 mT, highlighting the opposite behavior at short times for polarized and unpolarized states. Simulations include relaxation, dephasing, and recombination of the radical pair, with T₁ = 2 μs, T₂ = 0.5 μs, T_R = 10 μs (in the singlet–triplet RP basis, see the Supporting Information), and Gaussian broadening with fwhm = 0.15 mT. Inset: schematic energy-level diagram, with states practically corresponding to eigenstates of S_zi. Allowed EPR transitions of D (A) are indicated by blue (purple) dashed lines.