Polychromatic Excitation of Delocalized Long-Lived Proton Spin States in Aliphatic Chains

Anna Sonnefeld, Geoffrey Bodenhausen, and Kirill Sheberstov

Phys. Rev. Lett. 129, 183203 – Published 28 October 2022

Abstract

Long-lived states (LLS) involving pairs of magnetically inequivalent but chemically equivalent proton spins in aliphatic ${({CH}_{2})}_{n}$ chains can be excited by simultaneous application of weak selective radio frequency fields at $n$ chemical shifts by polychromatic spin-lock induced crossing. The LLS are delocalized throughout the aliphatic chains by mixing of intrapair singlet states and by excitation of LLS comprising products of four and six spin operators. The measured lifetimes $T_{LLS}$ in a model compound are about 5 times longer than $T_{1}$ and are strongly affected by interactions with macromolecules.

Received 18 April 2022
Revised 7 July 2022
Accepted 19 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.183203

Physics Subject Headings (PhySH)

Biomolecular interactions Chemical binding Coherent control Nuclear & electron resonance Zeeman effect

Atomic, Molecular & OpticalQuantum Information, Science & TechnologyPhysics of Living SystemsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Anna Sonnefeld , Geoffrey Bodenhausen , and Kirill Sheberstov ^*

Laboratoire des biomolécules, LBM, Département de chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France

^*Corresponding author. kirill.sheberstov@ens.psl.eu

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Vol. 129, Iss. 18 — 28 October 2022

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Images

Figure 1
Pulse sequences for poly-SLIC applied to an $A A^{'} M M^{'} X X^{'}$ system of a chain of three neighboring ${CH}_{2}$ groups. All nine methods start by exciting transverse magnetization by a “hard” ${(π / 2)}_{x}$ pulse, followed by the application of one, two, or three selective rf fields applied simultaneously at resonance frequencies (chemical shifts) $ν_{A}$ and/or $ν_{M}$ and/or $ν_{X}$ with phases $\pm y$ [43]. The SLIC pulses convert the magnetization into LLS. The rf amplitudes must be twice the magnitude of the intrapair geminal $J$ -coupling to achieve LLS excitation by single-quantum level anticrossing (SQ LAC), or equal to the magnitude of the intrapair $J$ -coupling for double-quantum (DQ) LAC. Maximum efficiency is achieved when the pulse duration is the inverse of the magnitude of the difference between the two out-of-pair $J$ -couplings for DQ LAC. For SQ LAC, maximum efficiency is achieved when the pulse duration is shorter by a factor of $\sqrt{2}$ (for the details see Supplemental Material). After a $T_{00}$ filter [42], further SLIC pulses allow one to reconvert LLS into observable magnetization.
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Figure 2
Numerical simulations of the excitation and reconversion of three types of LLS in Eq. (1). The superposition of two-spin product terms (yellow) has coefficients above 15% after triple SLIC excitation, the four-spin product terms (green) have negative coefficients close to $- 4 %$ , while the six-spin product term (red) has a negligible amplitude. The blue lines correspond to the trajectory of the total magnetization of the six spins that is partly converted into LLS and back. All simulations were carried out with SpinDynamica [44].
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Figure 3
(a) Molecular structure of ${NaSO}_{3} {CH}_{2} {CH}_{2} {CH}_{2} Si {({CH}_{3})}_{3}$ (DSS). (b) Multiplets of its $A A^{'} M M^{'} X X^{'}$ proton system, excited by a “hard” $π / 2$ pulse applied to the system in thermal equilibrium. Experimental multiplets (black) and simulated multiplets (blue) [46]. (c) Multiplets obtained by triple SLIC excitation of LLS followed, after a relaxation interval $τ_{rel} = 3 s$ and a $T_{00}$ filter, by reconversion into observable magnetization by triple SLIC irradiation. The arrows indicate at which chemical shifts the SLIC irradiation was applied. (d)–(f) Multiplets obtained in three separate experiments, each after triple SLIC excitation, evolution during $τ_{rel} = 3 s$ , and a $T_{00}$ filter. (d) Multiplet of the $A A^{'}$ pair obtained by single SLIC reconversion by irradiation at $ν_{A}$ . (e) Multiplet of the $M M^{'}$ pair after irradiation at $ν_{M}$ . (f) Multiplet of the $X X^{'}$ pair after irradiation at $ν_{X}$ . Note the agreement between experimental and simulated spectra (black and blue lines, respectively). The vertical scales of the experimental multiplets in (c)–(f) were amplified by a factor 10. All spectra were obtained by addition of eight transients.
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Figure 4
Typical decays of long-lived states. The arrows indicate at which sites the SLIC irradiation is applied. Blue dots: LLS excitation by triple SLIC, reconversion by single SLIC at $ν_{A}$ only ( $T_{LLS} = 9.3 \pm 0.4 s$ ). Green diamonds: LLS excitation and reconversion both by single SLIC at $ν_{A}$ ( $T_{LLS} = 8.0 \pm 0.4 s$ ). Orange triangles: LLS excitation by single SLIC at $ν_{M}$ and reconversion on a neighboring group by single SLIC at $ν_{A}$ ( $T_{LLS} = 9.6 \pm 0.5 s$ ). Red inverted triangles: LLS excitation by single SLIC at $ν_{X}$ and remote reconversion by single SLIC at $ν_{A}$ ( $T_{LLS} = 9.7 \pm 0.4 s$ ). The solid lines correspond to monoexponential fits for $τ_{rel} > 0.84 s$ , ignoring initial oscillations attributed to zero-quantum coherences. The largest amplitude is observed for triple SLIC excitation. The LLS lifetimes are at least 5 times longer than the corresponding longitudinal relaxation times $T_{1}^{A} \approx T_{1}^{M} \approx T_{1}^{X} \approx 1.5 \pm 0.03 s$ .
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