Quantitative Structure-Based Prediction of Electron Spin Decoherence in Organic Radicals Elizabeth R

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Quantitative Structure-Based Prediction of Electron Spin Decoherence in Organic Radicals Elizabeth R Subscriber access provided by University of Washington | Libraries Physical Insights into Quantum Phenomena and Function Quantitative Structure-Based Prediction of Electron Spin Decoherence in Organic Radicals Elizabeth R. Canarie, Samuel M. Jahn, and Stefan Stoll J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.0c00768 • Publication Date (Web): 13 Apr 2020 Downloaded from pubs.acs.org on April 16, 2020 Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. 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ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts. is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties. Page 1 of 15 The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 Quantitative Structure-Based Prediction of Electron 8 9 10 11 12 Spin Decoherence in Organic Radicals 13 14 15 16 Elizabeth R. Canarie‡, Samuel M. Jahn‡, Stefan Stoll* 17 18 19 20 Department of Chemistry, University of Washington, Seattle, Washington, United States, 98195 21 22 23 Corresponding Author 24 25 *E-mail: [email protected] 26 27 28 29 ABSTRACT The decoherence, or dephasing, of electron spins in paramagnetic molecules limits 30 31 32 sensitivity and resolution in electron paramagnetic resonance (EPR) spectroscopy, and it repre- 33 34 sents a challenge for utilizing paramagnetic molecules as qubit units in quantum information de- 35 36 vices. For organic radicals in dilute frozen aqueous solution at cryogenic temperatures, electron 37 38 spin decoherence is driven by neighboring nuclear spins. Here, we show that this nuclear-spin- 39 40 41 driven decoherence can be quantitatively predicted from molecular structure and solvation geom- 42 43 etry of the radicals. We use a fully deterministic quantum model of the electron spin and up to 44 45 2000 neighboring protons with a static spin Hamiltonian that includes nucleus-nucleus couplings. 46 47 48 We present experiments and simulations on two nitroxide radicals and one trityl radical, which 49 50 have decoherence time scales of 4-5 μs below 60 K. We show that nuclei within 12 Å of the 51 52 electron spin contribute to decoherence, with the strongest impact from protons 4-8 Å away. 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment 1 The Journal of Physical Chemistry Letters Page 2 of 15 1 2 3 TOC GRAPHICS 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 KEYWORDS 23 24 25 26 nuclear spin diffusion, cluster correlation expansion, phase memory time, coherence, EPR, DNP 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment 2 Page 3 of 15 The Journal of Physical Chemistry Letters 1 2 3 The spins of unpaired electrons in organic radicals and metal ions are extensively used in 4 5 6 pulse electron paramagnetic resonance (EPR) spectroscopy to probe the structure and dynamics of 7 8 the nano-environment around the electrons.1–3 Molecule-based unpaired electrons are also inves- 9 10 tigated as potential building blocks for devices useful to quantum information science (QIS).4–6 In 11 12 13 this context, they are often referred to as “molecular spin qubits”. In both cases, a key limitation 14 15 is the fact that excited electron spins lose coherence over time. This process, called decoherence, 16 17 dephasing, or transverse relaxation, results in the loss of signal. In EPR, decoherence limits sen- 18 19 sitivity and spectral resolution. In QIS applications, it impacts the efficient transfer of information 20 21 22 between coupled qubits, and it limits the complexity of algorithms that can be executed. Extending 23 24 coherence times is therefore an important development goal in both fields. For this, a detailed 25 26 understanding of the physical origins of decoherence is crucial. 27 28 29 There are many processes that drive electron spin decoherence, including molecular mo- 30 31 tions and magnetic interactions7. It is possible to eliminate the effect of motions (librations, thermal 32 33 methyl rotations, etc.) on decoherence by operating at low temperatures. Magnetic interactions 34 35 36 among electron spins, and between electron spins and nearby nuclear spins, also contribute to 37 38 decoherence. Processes due to couplings between electron spins can be eliminated by dilution. At 39 40 sufficiently low temperatures and low electron spin concentrations, decoherence is driven by 41 42 nearby nuclear spins.8,9 This mechanism, often called nuclear spin diffusion, has been described 43 44 45 semi-classically as arising from stochastic energy-conserving flip-flops of pairs of nuclei, leading 46 47 to spectral diffusion of the electron spin resonance frequency and consequently to decoherence.10– 48 49 12 The problem with this stochastic model is that it is not predictive and does not provide insight 50 51 52 into the physical origin of the assumed flip-flop rate. 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment 3 The Journal of Physical Chemistry Letters Page 4 of 15 1 2 3 Here, we experimentally deter- 4 5 6 mine the decoherence behavior of three 7 8 prototypical organic radicals in frozen 9 10 aqueous solutions, at temperatures and Figure 1. Two-pulse echo pulse sequence. For a decoherence experi- 11 ment, the spin echo amplitude is recorded as a function of increasing τ. 12 13 concentrations low enough to eliminate 14 15 contributions of any motional or electron-electron processes to decoherence. We show that the 16 17 nuclear-spin-driven decoherence of the radicals can be quantitatively predicted directly from their 18 19 molecular geometry and solvation structure, using a combination of molecular dynamics (MD) 20 21 22 and quantum spin dynamics, without the need for any adjustable free parameters. 23 24 Electron spin decoherence can be measured using various pulse EPR techniques. The most 25 26 straightforward is the two-pulse echo decay (Figure 1). This technique uses the pulse sequence 27 28 29 2 echo and records the decay of the echo amplitude resulting from increasing 30 31 πthe⁄ inter− -pulse delay − π − . 32 33 We investigated the decoherence characteristics of three different radicals: 2,2,6,6-tetra- 34 35 36 methylpiperidine-1-oxyl (TEMPO), its perdeuterated isotopologue (d18-TEMPO), and a perdeu- 37 13 38 terated trityl radical (p1TAM) (Figure 2). TEMPO and d18-TEMPO both are N/O-centered radi- 39 40 cals with four neighboring methyl groups and differ only in that all 1H atoms in TEMPO are re- 41 42 2 43 placed with H atoms in d18-TEMPO. The trityl 44 45 radical, p1TAM, is a C-centered radical and has 46 47 12 deuterated methyl groups. The concentra- 48 49 tions of the radicals were kept low enough to 50 51 52 minimize additional decoherence effects aris- 53 Figure 2. Radicals used in this study. From left to right, TEMPO, 54 ing from instantaneous diffusion mediated by d18-TEMPO, and p1TAM. 55 56 57 58 59 60 ACS Paragon Plus Environment 4 Page 5 of 15 The Journal of Physical Chemistry Letters 1 2 3 14,15 electron-electron couplings. Electron T1 val- 4 5 6 ues are on the order of 0.1–1 s and do also not 7 8 contribute to decoherence. All samples were pre- 9 10 pared in a solution of 1:1 (w:w) H2O:glycerol 11 12 13 and were snap frozen in liquid nitrogen. The ex- 14 15 periments were performed from 20-60 K at Q- 16 17 band frequencies (ca. 33 GHz). 18 19 Figure 3 shows the experimental two- 20 21 Figure 3. Experimental decoherence behavior of the molecules pulse echo decays at 20 K, presented in black. used in this study (black), stretched exponential (SE) fits (gray), 22 and the structure-based simulations (red). From top to bottom, ap- 23 proximately 10 μM p1TAM, 100 μM d18-TEMPO, and 200 μM 24 For all samples, the coherence decays on a simi- TEMPO. The experiments were performed in 1:1 (w:w) H2O 25 :glycerol at 20 K and ca. 33 GHz. The SE fits gave x values of 3.37, 2.81, and 2.77 and TM values of 5.37, 4.23, and 4.33 μs for 26 lar timescale and is completely lost within 10 μs.
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