Ultrafast multidimensional Laplace NMR for a rapid and sensitive chemical analysis

Traditional nuclear magnetic resonance (NMR) spectroscopy relies on the versatile chemical information conveyed by spectra. To complement conventional NMR, Laplace NMR explores diffusion and relaxation phenomena to reveal details on molecular motions. Under a broad concept of ultrafast multidimensional Laplace NMR, here we introduce an ultrafast diffusion-relaxation correlation experiment enhancing the resolution and information content of corresponding 1D experiments as well as reducing the experiment time by one to two orders of magnitude or more as compared with its conventional 2D counterpart. We demonstrate that the method allows one to distinguish identical molecules in different physical environments and provides chemical resolution missing in NMR spectra. Although the sensitivity of the new method is reduced due to spatial encoding, the single-scan approach enables one to use hyperpolarized substances to boost the sensitivity by several orders of magnitude, significantly enhancing the overall sensitivity of multidimensional Laplace NMR.


Supplementary Fig. 2 | Ultrafast D-T 2 correlation experiment of hyperpolarized propene.
(a) Experimental data after the Fourier transform in the spatial frequency (k) dimension, the compensation of the spatial variations of the measurement coil sensitivity and the removal of the data not affected by the frequency sweep pulse. (b) The first row along the t direction. (c) The first column along the q direction. (d) The end portion of the last row, illustrating the noise level. SNR was estimated to be 80.

Supplementary Figure 3 | Simulated D-T 2 correlation LNMR data as well as 1D and 2D
Laplace inversions for two components with equal (0.5 and 0.5) amplitudes. The T 2 relaxation time of component 1 is T 2 1 = 100 ms and diffusion coefficient of component 2 is D 2 = 110 -9 m 2 /s. The relaxation time and diffusion coefficient ratio R = T 2 2 /T 2 1 = D 1 /D 2 vary from 2 (top) to 1.25 (bottom), and signal-to-noise ratio (SNR) from 10000 to 100. The integrals of the signals are indicated in the distributions. Parameter b = (G) 2 , where  is the gyromagnetic ratio, G is the strength of the magnetic field gradient,  is the length of the gradient pulse and  is the diffusion delay.

Supplementary Figure 4 | Simulated D-T 2 correlation LNMR data as well as 1D and 2D
Laplace inversions for two components with 9:1 amplitude ratio (amplitudes are 0.9 and 0.1). The T 2 relaxation time of component 1 is T 2 1 = 100 ms and diffusion coefficient of component 2 is D 2 = 110 -9 m 2 /s. The relaxation time and diffusion coefficient ratio R = T 2 2 /T 2 1 = D 1 /D 2 vary from 2 (top) to 1.5 (bottom), and signal-to-noise ratio (SNR) from 10000 to 1000. The integrals of the signals are indicated in the distributions.

Water in silica gel 60
Silica gel 60 (the average pore diameter of 6 nm and particle size of 60-200 m, purchased from Merck, Darmstadt, Germany) was immersed in an excess of water (1% H 2 O in D 2 O) in a 10 mm sample tube.
The experiments were carried out on a Bruker Avance III 300 MHz spectrometer equipped with a micro-imaging unit at room temperature.
Parameters of the ultrafast D-T 2 correlation experiment: Relaxation delay 4 s, chirp (frequencyswept) pulse duration 1 ms, chirp pulse bandwidth 151 kHz, amplitude of gradient G sweep = 27.9 G/cm, diffusion delay  = 50 ms, number of CPMG echoes 128, echo time 5 ms (t varying from 5 to 640 ms), amplitude of gradient G read = 7.86 G/cm, field of view in the z direction 3 cm, number of points collected in each echo 512, number of accumulated scans 32, experiment time 2 min 31 s.

Parameters of the conventional (reference) D-T 2 correlation experiment:
Relaxation delay 4 s, number of diffusion gradient steps 64, duration of diffusion gradient 2 ms, maximum diffusion gradient amplitude 49.13 G/cm, diffusion delay  = 50 ms, number of CPMG echoes 128, echo time 5 ms (t varying from 5 to 640 ms), number of accumulated scans 8, experiment time 41 min.

Hexane and pentadecane samples
Hexane sample composition: 167 L hexane and 600 L CCl 4 in a 5mm sample tube.
Pentadecane sample composition: 167 L pentadecane and 600 L CCl 4 in a 5mm sample tube.
The experiments were carried out on a Bruker Avance III 600 MHz spectrometer with a 5 mm BBO probe (equipped with a z gradient) at room temperature.
Parameters for the ultrafast D-T 2 correlation experiment: Relaxation delay 50 s, chirp (frequency-swept) pulse duration 1 ms, chirp pulse bandwidth 256 kHz, amplitude of gradient G sweep = 88.43 G/cm, diffusion delay  = 70 ms, number of PROJECT echoes 120, echo time 16 ms (t varying from 16 to 1920 ms), amplitude of gradient G read = 19.57 G/cm, field of view in the z direction 3 cm, number of points collected in each echo 512, number of accumulated scans 8 for the hexane and pentadecane samples and 128 for the mixture, experiment time 7 min for the hexane and pentadecane samples and 57 min for the mixture.
The data of the ultrafast D-T 2 correlation experiment as well as 1D T 2 and D distributions of the mixture are shown in Supplementary Fig. 1.

PHIP hyperpolarized propene
Parahydrogen-enriched H 2 (called simply parahydrogen) was produced by passing high purity hydrogen through 5 g of FeO(OH) ortho-para conversion catalyst kept at liquid nitrogen temperature (77 K), which decreased the ortho-para spin isomer ratio from the room temperature equilibrium value of 3 : 1 to the value of 1 : 1. Propyne and parahydrogen were premixed in the 1 : 4 ratio in a 1 L gas cylinder with the total absolute gas pressure of 5 bar 1 . Before acquiring the data, the gas mixture was bubbled through a solution of [Rh(COD)(DPPB)]BF 4 catalyst in deuterated acetone in a 5 mm sample tube inside the NMR spectrometer.
The experiments were carried out on a Bruker Avance III 600 MHz spectrometer with a 5 mm BBO probe (including a z gradient) at room temperature.
Parameters of the ultrafast D-T 2 correlation experiment with PHIP: Relaxation delay 0 s, length of the selective (at 4.9 ppm) /2 excitation pulse 10 ms, antiphase to inphase conversion delay  anti->in 25 ms, chirp (frequency-swept) pulse duration 1 ms, chirp pulse bandwidth 150 kHz, amplitude of gradient G sweep = 20.05 G/cm, diffusion delay  = 70 ms, number of PROJECT echoes 64, echo time 6 ms (t varying from 6 to 384 ms), amplitude of gradient G read = 19.57 G/cm, field of view in the z direction 3 cm, number of points collected in each echo 512, number of accumulated scans 1, experiment time 0.5 s.
The data of the ultrafast D-T 2 correlation experiment is shown in Supplementary Fig. 2.

DNP hyperpolarized DMSO
Parameters of the ultrafast D-T 2 correlation experiment with 1 H DNP: Stabilization time after injection of sample into flow cell 3 s, relaxation delay 0 s, chirp (frequency-swept) pulse duration 1 ms, chirp pulse bandwidth 107 kHz, amplitude of gradient G sweep = 19.90 G/cm, diffusion delay  = 100 ms, number of CPMG echoes 64, echo time 10 ms (t varying from 10 to 640 ms), amplitude of gradient G read = 7.83 G/cm, field of view in the z direction 3 cm, number of points collected in each echo 512, number of accumulated scans 1, experiment time 0.8 s.
Experimental method for the ultrafast D-T 2 correlation experiment with 13 C DNP: A 60 μL DMSO in D 2 O (v/v 18:7) with 15 mM sodium salt of tris-8-carboxyl-2,2,6,6 tetrakis[2-(1hydroxethyl)]-benzo(1,2-d:4,5-dS)bis(1,3)dithiole-4-ylmethyl free radical (OXO63; Oxford Instruments, Abingdon, U.K.) and 1 mM diethylenetriamine pentaacetic acid gadolinium complex (Gd-DTPA; Sigma-Aldrich, St. Louis, MO) was first hyperpolarized by irradiating 60 mW of microwaves at a frequency of 93.974 GHz at a temperature of 1.4 K in a field of 3.35 T for 3 hours. Subsequently, the sample was dissolved with superheated water. This sample solution was rapidly transferred to an injection loop, and driven into a flow cell in a 400 MHz NMR magnet using water from a high pressure pump.
Parameters of the ultrafast D-T 2 correlation experiment with 13 C DNP: Stabilization time after injection of sample into flow cell 3 s, relaxation delay 0 s, chirp (frequency-swept) pulse duration 2 ms, chirp pulse bandwidth 44.6 kHz, amplitude of gradient G sweep = 50 G/cm, diffusion delay Δ = 200 ms, number of CPMG echoes 64, echo time 30 ms, amplitude of gradient G read = 9.725 G/cm, field of view in the z direction 10 cm, number of points collected in each echo 512, number of accumulated scans 1, experiment time 3 s.
Here, "G 1 ", "G 2 " and "Acq" refer to diffusion encoding gradient, diffusion decoding gradient and data acquisition. The relaxation delay is denoted as d 1 . The sequence was repeated 16 times with amplitudes of both gradients simultaneously and linearly increased from 2% to 95% of the maximum strength; however, the duration of gradients were kept as 0.8 ms. The diffusion time (time between the first and last 2  pulses) was set to 100 ms. The maximum z-gradient was separately calibrated by applying a PFG spin echo sequence 2 to a phantom.

Laplace inversion
Laplace inversion program provided by P. Callaghan (Victoria University of Wellington, New Zealand) was used for determining the 1D and 2D relaxation time and diffusion coefficient distributions 22 . The program is based on the method published by Venkataramanan et al. 6,7 .