Preparation of Nuclear Spin Singlet States Using Spin-Lock Induced Crossing

We introduce a broadly applicable technique to create nuclear spin singlet states in organic molecules and other many-atom systems. We employ a novel pulse sequence to produce a spin-lock induced crossing (SLIC) of the spin singlet and triplet energy levels, which enables triplet-singlet polarization transfer and singlet-state preparation. We demonstrate the utility of the SLIC method by producing a long-lived nuclear spin singlet state on two strongly coupled proton pairs in the tripeptide molecule phenylalanine-glycine-glycine dissolved in ${\mathrm{D}}_2\mathrm{O}$ and by using SLIC to measure the $J$ couplings, chemical shift differences, and singlet lifetimes of the proton pairs. We show that SLIC is more efficient at creating nearly equivalent nuclear spin singlet states than previous pulse sequence techniques, especially when triplet-singlet polarization transfer occurs on the same time scale as spin-lattice relaxation.

Figure 1

Simulated comparison of M2S and SLIC techniques applied to singlet state creation, evolution, and readout for a proton spin pair with chemical shift $\delta =3.71\mathrm{ppm}$ in the phe-gly-gly molecule. Guide lines connect points in the sequence with corresponding times in the simulation. (a) Schematic of M2S experiment. Following an initial 90 deg pulse to create transverse triplet polarization, the M2S pulse sequence creates singlet-state population by applying pulse trains with appropriate length and pulse spacing synchronized with the proton pair’s $J$ coupling and resonance frequency difference. The system then evolves over ${\tau }_{\mathrm{evolve}}$, and the M2S sequence is applied in reverse order to convert singlet population back to transverse triplet polarization for inductive NMR detection. (b) Simulation of M2S experiment. Transfer, in a series of stages, of transverse ($x$ axis) triplet polarization to singlet-triplet coherences and finally to singlet- and triplet-state populations of equal magnitudes. Transfer to the singlet-state population only occurs in the final $1/3$ of the M2S preparation sequence. (c) Schematic of SLIC experiment. Transverse triplet polarization is created via an initial 90 deg pulse and is then transferred to singlet-state population by the application of a spin-locking field with ${\nu }_n=J$ for period ${\tau }_{\mathrm{SL}}$. For spin locking, the transmitter frequency is set to the average resonance frequency of the nearly equivalent spin pair. The system then evolves for ${\tau }_{\mathrm{evolve}}$ and an identical spin-locking field converts singlet population back to transverse triplet polarization for detection. (d) Simulation of SLIC experiment. Transfer of transverse triplet polarization to singlet-state population begins immediately and occurs during a single spin-locking stage.

Figure 2

Simulations of ideal triplet-singlet polarization transfer efficiency for M2S (blue) and SLIC (red). Results are shown for $T_S\gg T_1$ and $T_S=3T_1$. M2S was modeled in two steps: first, polarization transfer from $I_{1x}+I_{2x}$ with lifetime $T_2=T_1$ to $I_{1y}-I_{2y}$ with lifetime $T_1/3$; second, polarization transfer from $I_{1z}-I_{2z}$ with lifetime $T_1/3$ to singlet state $S_0$ with lifetime $T_S$. Only one polarization transfer needed to be modeled for SLIC, between $I_{1x}+I_{2x}$ with lifetime $T_2=T_1$ and $S_0$ with lifetime $T_S$. A maximum of 50% polarization transfer to the singlet state can be achieved by both sequences, which we define to be an efficiency of 100%. Note that both sequences are less efficient for smaller $T_S/T_1$ due to singlet relaxation.

Figure 3

Experimental application of the SLIC technique to nuclear spin singlet state creation in the phe-gly-gly molecule. Results for $\delta =3.71\mathrm{ppm}$ proton pair: (a) The NMR signal (normalized $x$-axis magnetization, proportional to transverse triplet polarization) following the first SLIC spin lock as a function of nutation frequency for ${\tau }_{\mathrm{SL}}=300\mathrm{ms}$ exhibits a pronounced dip when the spin-lock frequency equals the $J$ coupling. A Lorentzian is fit to the measurement to determine ${\nu }_n=J=17.5\pm 0.3\mathrm{Hz}$. (b) NMR signal after the complete SLIC experiment with ${\tau }_{\mathrm{evolve}}=5\mathrm{s}$ (proportional to final transverse triplet polarization surviving transfer to singlet and back) as a function of spin lock duration. Maximal singlet-state creation is found for ${\tau }_{\mathrm{SL}}\approx 280–360\mathrm{ms}$. We fit for amplitude, $A$, and $\Delta \nu$ with the function $I=A{sin}^4(\pi {\tau }_{\mathrm{SL}}\Delta \nu /\sqrt{2})$, and we find $\Delta \nu =2.15\pm 0.02\mathrm{Hz}$. Results for $\delta =3.20\mathrm{ppm}$ proton pair: (c) NMR signal following the first SLIC spin lock as a function of nutation frequency for ${\tau }_{\mathrm{SL}}=332\mathrm{ms}$, with a Lorentzian fit to the data yielding optimal ${\nu }_n=J=13.5\pm 0.2\mathrm{Hz}$. (d) NMR signal after the complete SLIC experiment with ${\tau }_{\mathrm{evolve}}=500\mathrm{ms}$ as a function of spin lock duration. Maximal singlet state creation is found for ${\tau }_{\mathrm{SL}}\approx 300–400\mathrm{ms}$. From a fit with the function $I=A{sin}^4(\pi {\tau }_{\mathrm{SL}}\Delta \nu /\sqrt{2})+c$, we find $\Delta \nu =2.13\pm 0.06\mathrm{Hz}$.