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Analysis of Carr—Purcell Spin‐Echo NMR Experiments on Multiple‐Spin Systems. I. The Effect of Homonuclear Coupling

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Adam Allerhand; Analysis of Carr—Purcell Spin‐Echo NMR Experiments on Multiple‐Spin Systems. I. The Effect of Homonuclear Coupling. J. Chem. Phys. 1 January 1966; 44 (1): 1–9. https://doi.org/10.1063/1.1726430

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The effect of homonuclear coupling in a molecule on Carr—Purcell spin‐echo (CPSE) nuclear magnetic resonance experiments is investigated. A density‐matrix approach is used to derive a general equation for the CPSE train of multiple‐spin molecules in the liquid state. This general equation predicts a CPSE train modulated with one or more frequencies, whose relative amplitudes are, in general, not equal. Unmodulated contributions may also arise. It is shown that the modulation frequencies and their relative amplitudes are functions not only of the relative chemical shifts and coupling constants, but are strongly dependent on the separation between the 180° pulses, t cp . In addition, the modulation can always be eliminated by making the pulse repetition rate, 1/ t cp , large with respect to all the relative chemical shifts and coupling constants. It is also shown that, for weak coupling, it is possible to derive simplified equations by neglecting the nonsecular part of the coupling Hamiltonian, but this approximation is valid only when 1/ t cp is of the order of, or smaller than the relative chemical shifts.

Procedures for solving the general equation to obtain closed formulas for the CPSE train of a specific system are discussed. Solutions for spin‐½ nuclei are treated in detail. Closed equations are derived for the AB, A 2 B, and A 3 B systems, and they are used in some numerical calculations. Simplified weak‐coupling formulas are also derived for these systems, and their range of validity is discussed.

A very brief discussion of heteronuclear coupling is presented.

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SHARPER-DOSY: Sensitivity enhanced diffusion-ordered NMR spectroscopy

George peat.

1 EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Rd, Edinburgh, EH9 3FJ UK

Patrick J. Boaler

Claire l. dickson.

2 Present Address: Oxford Instruments, Halifax Road, High Wycombe, HP12 3SE2 UK

Guy C. Lloyd-Jones

Dušan uhrín, associated data.

The NMR Data, Supplementary Software and Source Data Files generated in this study have been deposited in Edinburgh DataShare database 59 , under accession code 10.7488/ds/7472. Till August 31, 2023 the data are available from the corresponding author and freely available after this date.  Source data are provided with this paper.

Since its discovery in mid-20 th century, the sensitivity of Nuclear Magnetic Resonance (NMR) has increased steadily, in part due to the design of new, sophisticated NMR experiments. Here we report on a liquid-state NMR methodology that significantly increases the sensitivity of diffusion coefficient measurements of pure compounds, allowing to estimate their sizes using a much reduced amount of material. In this method, the diffusion coefficients are being measured by analysing narrow and intense singlets, which are invariant to magnetic field inhomogeneities. The singlets are obtained through signal acquisition embedded in short (<0.5 ms) spin-echo intervals separated by non-selective 180° or 90° pulses, suppressing the chemical shift evolution of resonances and their splitting due to J couplings. The achieved 10−100 sensitivity enhancement results in a 100−10000-fold time saving. Using high field cryoprobe NMR spectrometers, this makes it possible to measure a diffusion coefficient of a medium-size organic molecule in a matter of minutes with as little as a few hundred nanograms of material.

Since its discovery, the sensitivity of Nuclear Magnetic Resonance has increased steadily. Here the authors report on a liquid-state NMR methodology that increases the sensitivity of the diffusion coefficient measurements 10–100- fold, allowing to use microgram quantities of compounds, while reducing the measurement time to few minutes.

Introduction

NMR spectroscopy has impacted many areas of chemistry, biology and physics through to its ability to separate responses from nuclei of the same type along the chemical shift axis. Combined with another fundamental property of nuclei, scalar couplings, NMR has established itself as the leading technique for liquid-state molecular structure elucidation. However, many applications of NMR are limited by the inherently low sensitivity of the technique.

Splitting of signals due to J couplings reduces the signal-to-noise ratio (SNR) of NMR spectra, hence 13 C spectra are practically always acquired with 1 H decoupling. More recently, so called “pure shift” 1 H-detected experiments implemented real-time homonuclear decoupling 1 – 4 , aiming to simultaneously reduce spectral overlap and to increase the SNR of liquid-state NMR spectra.

One example, where significant sensitivity gains have been achieved by removing J splittings is SHARPER (Sensitive, Homogeneous And Resolved PEaks in Real time), a technique originally proposed to boost the sensitivity of reaction monitoring 5 . SHARPER removes hetero- and homonuclear splittings of a single selected signal in real time by interrupting data acquisition with 180° refocussing pulses. When non-selective pulses are used, all heteronuclear couplings are removed, while selective 180° pulses also remove homonuclear couplings; in both instances this only requires to pulse on the acquired nucleus. As SHARPER acquisition is embedded within a CPMG pulse sequence 6 , 7 , it eliminates the effects of magnetic field inhomogeneity and generates extremely narrow signals that approach their natural linewidth. Both of these factors contribute to significant sensitivity gains as recently demonstrated on benchtop NMR spectrometers 8 .

The original SHARPER experiments acquired signal during spin-echo intervals (referred to as acquisition chunk times, or just chunk times), τ, on the order <0.25/ J as required to eliminate J evolution. However, reducing the length of spin-echo intervals below 1.0 ms in combination with non-selective 180° refocusing pulses also removes J evolution 9 , the property which underpins the measurement of spin-spin relaxation times by the CPMG pulse sequence 7 .

We demonstrate here that a removal of frequency modulation on the chemical shift scale over thousands of Hz is entirely feasible and only requires a further reduction of the spin-echo intervals. The resulting collapsed signal contains a cumulative response from all selected protons, and serves as an intense molecular signature that can report on a compound concentration, or its molecular property. By applying this concept to the measurement of translational diffusion of molecules on high field NMR spectrometers, we have developed a protocol that boosts the sensitivity of Diffusion Ordered SpectroscopY (DOSY) up to two orders of magnitude, enabling fast and reliable determination of diffusion coefficients at very low sample concentrations. The proposed technique is referred to herein as SHARPER-DOSY. Its performance is demonstrated using three model compounds, 1-phenylethanol, 1 , cyclosporine, 2 , and sodium cholate, 3 (Fig.  1 )

1-phenylethanol, 1 , cyclosporine, 2 , and sodium cholate, 3 .

Collapsing NMR spectra into sharp singlets

Using a benchtop NMR instrument, we have recently presented a SABRE-SHARPER experiment 10 , in which the SHARPER acquisition module provided a further boost (up to 17-fold) to a hyperpolarised signal by removing inhomogeneous broadening, refocusing homo- and heteronuclear J couplings and chemical shift differences on the order of 75 Hz. Using the pulse sequence of Fig.  2a , we show here that this approach can be used to collapse signals spanning thousands of Hz.

a Pulse sequence of a non-selective SHARPER experiment (for explanation of symbols and details see Supplementary Note  1.1 ); b overlay of a 400 MHz 1D 1 H NMR spectrum (blue) of 1 in D 2 O, and its collapsed spectrum (red) acquired using, τ = 200 μs and 60 μs 180° refocusing pulses. Both real and imaginary SHARPER time domain points were used, no line broadening was applied. The 5.6–6.4 ppm region was scaled up vertically to illustrate that both spectra have identical noise levels; c expansions of the SHARPER singlet and the CH 3 doublet from the 1D spectrum using identical horizontal scales; the CH 3 signal was scaled up 25 times to equal the height of the SHARPER signal.

A 400 MHz 1 H NMR spectrum of 1 (Fig.  2b ) containing signals of nine non-exchangeable protons resonating across 6 ppm, was collapsed using the pulse sequence of Fig.  2a (Supplementary Note  1.1 ) into a SHARPER singlet shown in red in Fig.  2b . The 1D and SHARPER spectra presented in Fig.  2 were acquired using identical parameters and Fourier transformed without any apodisation. The obtained SHARPER singlet is 25 × taller and 5.4 × narrower than the CH 3 doublet of the 1D spectrum (Fig.  2c ). The SHARPER time domain points and the resulting spectrum are analysed in detail in Supplementary Note  2 .

To rationalise this level of signals enhancement, the efficiency of SHARPER acquisition was investigated. Using the HOD protons of a doped D 2 O sample, the SHARPER signal was inspected as a function of the frequency offset, Δν, of the HOD resonance frequency from the carrier frequency and its integral intensity across a 2400 Hz frequency range and chunk times τ = 100, 200 and 400 μs was monitored (Fig.  3a ). While practically identical on-resonance, the values decrease gradually to a level of 84, 63 and 3% at 2400 Hz, respectively, with increasing chunk time.

a Relative integral intensity, I Δ ν / I 0 , τ = 100 μ s , and ( b ) relative signal height, H Δ ν = T 2 S × I ( Δ ν ) / ( T 2 S ( τ = 100 μ s ) × I 0 , τ = 100 μ s ) , of the SHARPER singlet of HOD in doped D 2 O at 400 MHz as a function of the frequency offset, Δν. Data was normalised to the integral intensity ( a ) and the hight ( b ) of the on-resonance signal based on τ = 100 μs. Data for chunk times τ = 100 (blue), 200 (yellow) and 400 μs (red) are presented. Source data are provided as a Source Data Fig. 3.xlsx.

Another representation of the data, which quantifies the height of the signal and takes into account the effective spin-spin relaxation of the SHARPER signal, T 2 S , (see Supplementary Note  3 ) is presented in Fig.  3b . It can be seen that closer to the HOD frequency, the signal intensities are larger for longer chunk times. This is due to slower effective relaxation resulting from less frequent use of refocusing pulses, producing narrower, taller signals and ultimately higher SNRs. When collapsing narrower spectral regions, it is therefore beneficial to use longer chunk times.

Returning to the analysis of the SHARPER spectrum of 1 , its integral represents 87.1% of the integral of the entire reference 1D 1 H spectrum of 1 . This is in near perfect agreement with a weighted integral sum (87.8%) calculated by considering the positions of five aromatic, one methine and three methyl protons of 1 relative to the frequency of the SHARPER signal and the frequency profile presented in Fig.  3a . The 25:1 SHARPER: CH 3 signal intensity ratio is fully explained by accounting for the J -splitting of the CH 3 signal, number of protons contributing to the two signals, efficiency of the signal collapse and the narrowing of the SHARPER singlet (Supplementary Note  4 ).

As described previously 8 , the SNR of the SHARPER spectrum can be enhanced by a factor of 1.41, by removing the imaginary time domain data (Supplementary Note  5 ). Using matched filters to maximise independently the SNR 11 of both spectra, these were reprocessed using line-broadening of 0.11 and 0.59 Hz, respectively. After this treatment, a 11.4-fold higher SNR, as determined by comparing the SHARPER singlet and the CH 3 doublet, was obtained. Note that the magnetic field inhomogeneity can influence the SNR in standard 1D spectra, and hence the level of enhancement achieved. In contrast, the self-compensating nature of the SHARPER acquisition means that even severe magnetic field inhomogeneity has no or little effect on the intensity of the SHARPER singlet (Supplementary Note  6 ).

Managing the power deposition to the probe

When executing pulse sequences containing tens of thousands of high-power pulses, an important experimental consideration is the power deposition. This is limited for liquid-state NMR probes, in particular cryoprobes (Supplementary Note  7 ). One way to reduce the deposited power, is to reduce the flip angle, α, of the spin-echo pulses. This may seem inefficient at first, as signal recovery 12 , 13 during a train of spin-echoes over a 1/τ [Hz] frequency range scales with sin(α/2). For α = 90°, this means reduction to 71% relative to α = 180°. However, as demonstrated below, this loss of integral intensity is largely compensated for by narrowing of the SHARPER singlet, which originates from two sources. Firstly, the relative increase of the chunk time vs the pulse duration leads to longer T 2 S . Secondly, for 90° pulses, the spin-lattice relaxation contributes 14 towards T 2 S and for molecules outside of the extreme narrowing limit ( T 1  >  T 2 ) this increases T 2 S further. Both factor therefore contribute to the narrowing of the SHARPER signal and thus its increase intensity (Supplementary Note  7 ), while the power input into the probe is halved.

Selecting signals to be collapsed

When measuring a whole-molecule property, such as a diffusion coefficient of a pure compound, the chemical shift resolution can be sacrificed; the same information is much more efficiently obtained from a narrow SHARPER singlet – an intense signature of a molecule. Nevertheless, care must be taken not to include signals that could compromise the outcome of such experiments. The signals to be excluded may include those of the solvent, labile protons, which can be in exchange with the protons of the solvent, or in case of organic solvents, with traces of water and a signal of the chemical shift reference standard. The SHARPER-DOSY experiment therefore typically starts with a suppression of selected signals, followed by a band-selective excitation of the spectral region destined to be collapsed.

This process is illustrated at 800 MHz on a sample of 2 in benzene-d 6 (C 62 H 111 N 11 O 1 , M w  = 1,202.61 g/mol), which contains a small amount of H 2 O in slow exchange with one OH and four NH protons in 2 . The C 6 HD 5 signal at 7.2 ppm is particularly intense, while the H 2 O/OH signals resonating at ~ 1.55 ppm are relatively weak. It is well known from protein NMR spectroscopy that the water signal is best pre-saturated when the carrier frequency is set to the H 2 O frequency. However, the nature of the SHARPER acquisition dictates for the r.f. carrier to be placed in the middle of the collapsed region, which for 2 is at 3.27 ppm, in the middle of aliphatic resonances. This positions the C 6 HD 5 and OH signals off-resonance. Nevertheless, a protocol exists 15 , which produces an optimal suppression of off-resonance signals. It involves the use of ~20-80 ms phase-ramped, low power rectangular pulses applied in a loop with the pulse length adjusted to allow a 2 n π ( n is an integer) rotation for the off-resonance signal(s). With only one signal to be suppressed, this condition is easily fulfilled. We show here that for multiple signal suppression sites, a numerical solution can be found that allows each off-resonance signal to undergo close to a multiple number of full rotations, achieving optimal signal suppression (Supplementary Note  8 ). In the case of 2, 13 C satellites of C 6 HD 5 (Supplementary Note  9.1 ) were also saturated by applying a low power 13 C decoupling during the pre-saturation period.

In order to avoid the interference caused by the exchange of the NH protons of 2 with water, these were not included in the SHARPER signal. The remaining 106 protons were selected using a perfect echo 16 , 17 , in which short 180° ReBurp 18 pulses surrounded by pulsed field gradients (PFGs) replaced the non-selective 180° spin-echo pulses (Supplementary Note  1.2 ). The efficiency of signal selection by this band-selective perfect echo (BSPE) was 90% (Supplementary Note  9.2 ). The BSPE- SHARPER spectra of 2 obtained with 180° (90°) spin-echo pulses, resulted in 97% (75%) signal recovery relative to the entire BSPE spectrum. An overlay of the three spectra processed with matched exponential filters and with imaginary time domain data removed for the SHARPER data, is shown in Fig.  4 . In this presentation, the 1D spectrum was scaled up 32 times to achieve parity of the N-CH 3 singlets with the SHARPER singlets, revealing a 96-fold intensity increase of the SHARPER

Shown is an overlay of a partial 1D 1 H spectrum of 2 (blue) and two SHARPER spectra acquired using 90°(magenta, offset by +35 Hz for visibility) and 180°(red) 1 H spin-echo pulses. The vertical scale of the 1D spectrum was increased 32 times. The inset shows a close up of the two SHARPER singlets and the 3.72 ppm NCH 3 singlet. All spectra were produced using matched filters, hence the stated Δ 1/2 values are double the original linewidths.

signal relative to a hypothetical one proton singlet from a 1D spectrum – a remarkable sensitivity increase. The inset in Fig.  4 shows an expansion of the BSPE-SHARPER singlets obtained using 90° and 180° spin-echo pulses, respectively, and that of the NCH 3 signal at 3.722 ppm from the 1D spectrum. The SHARPER singlet obtained using 90°spin-echo pulses is the narrowest, compensating for the loss of integral intensity and surpassing the height of the SHARPER singlet acquired using 180°pulses.

SHARPER- DOSY

Inserting a DOSY module 19 , 20 between the signal pre-saturation and the BSPE block, leads to a SHARPER-DOSY pulse sequence (Fig.  5 ). Applied to acquire two 2D SHARPER-DOSY spectra of 2 using 90° and 180° spin-echo pulses these are overlaid with a regular

For explanation of symbols and details see Supplementary Note  1.3 .

DOSY spectrum of 2 in Fig.  6 (see also Supplementary Note  9.3 ). Also here a scaling factor of 32 was used for the regular DOSY spectrum, which shows a familiar smearing of signals in the DOSY dimension, while the SHARPER-DOSY spectra have much narrower F 1 profiles. All three diffusion axis projections overlap perfectly (inset in Fig.  6 ).

An overlay of the DOSY (blue) and two SHARPER-DOSY spectra of 2 acquired using 90° (magenta) and 180° (red) spin-echo pulses, which overlay perfectly. Red arrow points to the SHARPER-DOSY cross peaks. The inset shows an overlay of the F 1 projection of the three spectra. The DOSY spectrum and its projection were scaled up 32 times.

SHARPER-DOSY using μg quantities of sample

Having demonstrated a flawless performance of SHARPER-DOSY, the technique was tested at 800 MHz on a microgram quantity of a medium size organic molecule, sodium cholate (C 24 H 39 O 5 Na, M w  = 430.55 g/mol) containing 1.3 μg of the compound in 0.55 ml of D 2 O ([ 3 ] = 5.5 μM). Three deshielded HO-C H protons 3, 7 and 12 (Fig.  1 ) of 3 were excluded and the remaining 33 protons resonating within a ± 0.75 ppm range were collapsed into a SHARPER singlet. Such narrow frequency range allowed the chunk time to be increased to τ = 448μs, achieving >80% signal recovery. An overlay of a 1D BSPE spectrum of 3 acquired using 128 scans with a 8-scan BSPE-SHARPER spectrum (180° spin-echo pulses, Fig.  7a ) indicates that the SHARPER signal is 22-fold more intense than the CH 3 singlets of 3 . This is twice the 11-fold ratio calculated based on the proton count (33H/3H of a CH 3 singlet = 11). Narrowing of the SHARPER signal accounts for some of the observed excess gain, but does not explain it completely.

An overlay of 1D 1 H (blue and green, 128 scans) and BSPE-SHARPER spectra (red and magenta, 8 scans) of ( a ) 1.3 μg of 3 and ( b ) a blank D 2 O sample. Protons 3, 7 and 12 (Fig.  1 ) were not included in the collapsed signal. The regular 1D spectra were scaled up 16 times and the doublet at 1.28 ppm is indicated by an asterisk.

A closer inspection of the 1D BSPE spectrum of 3 revealed a doublet at 1.28 ppm that does not belong to this compound. Repeating the same experiments on a “pure” D 2 O sample showed that this and other signals are from solvent impurities (Fig.  7b ). These account for the rest of the intensity of the SHARPER signal of 3 and pose a problem for the acquisition of SHARPER-DOSY spectra. The collapsed signal is not solely from the compound of interest but contains the net and potentially significant contribution from a range of minor solvent impurities. A simple way around this problem is to collect two SHARPER-DOSY spectra; one of the sample and the other of the solvent, followed by a subtraction of the two 2D data sets (Bruker AU program, dosy_adsu, is provided in the  Supplementary Software ) before DOSY processing, as illustrated on 1D traces of the respective spectra in Fig.  8a . An overlay of F 1 projections of four DOSY spectra (Fig.  8b ) shows that before this treatment, the projection of the SHARPER-DOSY spectrum of 3 was broad.

a SHARPER-DOSY signals from 16 spectra acquired by increasing the strength of pulsed field gradients for sample of 3 , sample of D 2 O and their difference; b overlay of the F 1 projections of the DOSY spectrum (blue), the SHARPER-DOSY spectra of 3 in D 2 O (red), D 2 O impurities (black), and of their difference spectrum (magenta).

The projection of the D 2 O spectrum was yet broader, reflecting presence of several different size impurities. In contrast, the projection of the difference spectrum is narrower and much more intense than the projection of a regular DOSY spectrum, in which a contribution of the three CH 3 signals of 3 dominates the F 1 projection. With the experimental time of 10 min per a 2D SHARPER-DOSY spectrum, the diffusion coefficient of this medium size organic molecule was thus reliably determined using 1.3 μg of sample in 20 min on a 800 MHz cryoprobe NMR spectrometer.

The difference spectrum was used to compare the accuracy of the determination of a diffusion coefficient of low concentration compounds by analysing spectra or the time domain data. It was found that a more accurate value of a diffusion coefficient of 3 was obtained when time domain points up to 1.26 T 2 S were integrated 21 as opposed to using all time domain points or spectral integrals. For details see Supplementary Note  10 .

As demonstrate above, SHAREPR-DOSY technique provides significant sensitivity improvement for the measurement of diffusion coefficients of pure compounds. The experiment typically involves suppression of the residual 1 H signals of deuterated solvents and may use a band selective excitation to exclude some resonance. For example signals of labile protons, or isolated signals that would not contribute substantially to the SHARPER signal and their inclusion could invalidate the results. These two pulse sequence elements are also applicable when strong signals of co-solvents or buffers are present, potentially sacrificing more of the signal, focusing on narrower spectral regions only containing signals of the studied compound. Taking this approach to its limits, very selective techniques exist that can excite a single multiplet in a spectrum of a mixtures of compounds 22 , 23 . These can be implemented into the SHARPER-DOSY pulse sequence to achieve selectivity that is essential for accurate determination of diffusion coefficients of compounds in mixtures, while enhancing sensitivity by removing splittings and sharpening the acquired signal 5 , 8 . For mixtures of small and large compounds, preselection of small molecules can be achieved by including T 2 filters 24 , while large molecules can be selected using diffusion filters 24 , thus reducing the complexity of spectra. These techniques can be used e.g. to remove signals of co-solvents, buffers or small molecular impurities in samples of polymers. As exemplified in this work, solvent impurities can be dealt with by subtracting the SHARPER spectra of the solvent. Although only examples of 1 H NMR spectra are presented here, 19 F spectra are equally amenable to SHARPER-DOSY methodology. While attention must be paid to a wider chemical shift range of 19 F, the absence of a background signal due to lack of fluorinated endogenous compounds simplifies setting up of the DOSY experiments. Given the prevalence of manmade fluorinated drugs 25 and agrochemicals 26 , together with a recent interest in polyfluoroalkyl substances 27 , which typically are present at low concentrations, the SHARPER-DOSY technique is highly relevant to studies of fluorinated molecules.

The use of a CPMG acquisition loop is essential for NMR studies, typically carried out at low or very low magnetic fields, of a wide range of materials that affect the magnetic field homogeneity, including porous rocks 28 , oil and gas 29 , and dairy products 30 . A very short spin-echo times (0.1–0.5 ms) used in these experiments reduce primarily the effect of background gradients on decay of the NMR signal, while at the same time eliminate the chemical shift dispersion and J coupling evolution. On high-field solution-state NMR spectrometers, signal broadening due to magnetic field inhomogeneity is typically small (sub Hz to few Hz), nevertheless, the chemical shift dispersion on the order of thousands of Hz needs to be eliminated. Addressing this requirement, J evolution due HH couplings is therefore also suppressed 9 , as removing chemical shifts typically requires the use of spin-echo times below 0.5 ms. It is worth noting, that although a narrower chemical shift range is efficiently collapsed by 90° spin-echo pulses, the accompanying signal loss is compensated for by longer T 2 S relaxation times, resulting in narrower, more intense signals, while the power deposition into probes is reduced.

A recent extension of Laplace NMR—the ultrafast multidimensional Laplace NMR 31 – 33 ,—enabled correlation of relaxation and diffusion parameters as well as the observation of molecular exchange phenomena in single scan experiments. These experiments typically use longer spin echo times (5–30 ms) in combination with spatial encoding and therefore exhibit reduced sensitivity. In their basic form they do not eliminate J evolution; this can be achieved 32 by using perfect echos 16 , 17 in place of a CPMG sequence in the acquisition loop. Such pulse sequence element was not used in our work, as it would cause an undesirable line broadening of signals.

The CPMG acquisition module has also been utilised to enhance the sensitivity of solid- 34 – 38 and liquid-state 39 – 41 experiments, some applied in severally inhomogeneous magnetic fields 42 – 44 . Parallel efforts to increase the sensitivity of liquid-state NMR experiments such as manipulation of solvent exchange with labile sites in biomolecules 45 , the use of nanoliter non-resonant coils 46 , various forms of dynamic nuclear polarisation 47 – 49 , exploitation of electronic spins in nitrogen-vacancy centres 50 , or the use of para -hydrogen induced hyperpolarization (PHIP) based on chemical reactions 51 or reversible processes (SABRE) 52 , 53 are the focal point of many researcher groups. As demonstrated recently by the SABRE-SHARPER experiment 8 , the concept of collapsing resonances in high-resolution NMR is compatible with hyperpolarisation techniques and can produce significant additional sensitivity gains by removing frequency modulation of the NMR signal and importantly, also counter the magnetic field inhomogeneity.

Measurement of diffusion coefficients of low-micromolar samples in comparable time to those achieved by SHARPER-DOSY has been so far only possible for compounds that are amenable to SABRE hyperpolarisation 54 . In comparison, single-scan DOSY measurements, which utilise spatial encoding, require much more concentrated samples 55 , 56 .

In conclusion, the developed protocol for the measurement of diffusion coefficients of single compounds increased the sensitivity of standard DOSY experiments up to two orders of magnitude, with the exact gains depending on the number of collapsed resonance and their relaxation properties. Smaller molecules containing less protons, nevertheless have longer spin-spin relaxation times that narrow the SHARPER singlets (for comparison, △ 1 / 2 S α = 180 ∘  = 0.11, 1.45 and 1.1 Hz for compounds 1 , 2 and 3 , respectively). Achieving the SNR gains above those expected based on the proton count only is therefore possible. When used on high field cryoprobe NMR instruments, submicrogram quantities of compounds are sufficient to obtain high quality DOSY spectra. This e.g. allows to access low concentration samples in studies of molecular interactions and aggregation. As outlined in the Discussion, the SHARPER-DOSY technique can also be modified for applications to mixtures of varied complexity.

Due to the narrower frequency range, the relative gains at the lower magnetic fields, such as used in benchtop NMR instruments, will be higher than at very high fields. Finally, the concept of collapsing spectra or parts thereof by SHARPER acquisition as outlined here opens new possibilities for characterisation of molecules, or their mixtures, and is expected to find numerous applications in liquid-state NMR spectroscopy.

Doped water   A standard sample (0.1 mg GdCl 3 /ml D 2 O + 1% H 2 O + 0.1% 13 CH 3 OH) was used. The data was acquired on and processed in TopSpin3.2 a 400 MHz Bruker AVANCE III spectrometer using the sharper_collapse.du pulse sequence (see  Supplementary Software ) and following parameters: 1 s relaxation time (D1), 1.229 s nominal acquisition time (AQ), 2 dummy (DS) and 2 real (NS) scans, 20,000 Hz (49.983 ppm) spectral width (SW), 49152 time domain points (TD), p w 90 ∘ = 30 μ s , p w 180 ∘ = 60 μ s at 4.46 W, acquisition chunk times, τ, of 100, 200 and 400 μs, 25 μs dwell time (DW) with 4, 8 or 16 points per chunk, and 12,228, 6,144 or 3,072 spin echoes, respectively. The T 1 and T 2 relaxation time determined by inversion recovery and a CPMG methods were 230 and 180 ms, respectively.

Compound 1 (40 μL in 550 μL of D 2 O, c = 0.562 M). The 1D 1 H NMR spectrum was acquired and processed in TopSpin3.2 on a 400 MHz Bruker AVANCE III spectrometer using the following parameters: D1 = 16 s, AQ = 9.83 s, DS = 2, NS = 2, SW = 10,000 Hz (49.983 ppm), TD = 196608. The 1D SHARPER spectrum was acquired using the sharper_collapse.du pulse sequence and identical common parameters as for the 1D 1 H spectrum. The following specific parameters were used: τ = 200 μs, p w 90 ∘ = 30 μ s , p w 180 ∘ = 60 μ s at 4.46 W, DW = 50 μs (4 points per chunk, 49152 spin echoes). The actual acquisition time was AQ * ( τ + p w 18 0 ∘ ) / τ = 12.78 s .

Compound 2 ( M w  = 1,202.61 g/mol, 38 mg in 550 μL of benzene-d 6 , c = 3.67 mM). The data was acquired and processed in TopSpin4.1 on an 800 MHz BRUKER NEO NMR spectrometer equipped with a TCI cryoprobe. For all experiments, identical common parameters, as stated for the 1D 1 H spectrum, were used: D1 = 3.0 s, AQ = 1.652 s, DS = 4, NS = 8, SW = 39682.54 Hz (49.6384 ppm), TD = 128k. Presaturation parameters: pw = 25764.46 μs, l6 = 117, carrier frequency o1 = 2612.50 Hz, ν(C 6 HD 5 ) = (o1 + 3105.05) Hz; ν(H 2 O) = (o1 - 2173.57) Hz (optimised primarily for the suppression of C 6 HD 5 ). Pulse sequence zgpr_pulse.du (see  Supplementary Software ). For 13 C decoupling a xy32 super cycle 57 , 58 modified to implement composite 180° pulses ( 90 x o 180 y o 90 x o ) with p w 90 ∘ = 192 μ s was used with the 13 C carrier frequency at 128 ppm.

BSPE spectrum (pulse sequence zgpebs.du, see  Supplementary Software ) and the BSPE-SHARPER spectra (sharper_collapse.du) the following parameters were used: 1 ms ReBurp pulse, 600 μs PFG, G 1  = 7%, G 2  = 5% and G 3  = -12%. For the BSPE-SHARPER experiments the specific parameters were: τ = 100.8 μs, DW = 12.6 μs (8 points per chunk, 16,384 spin echoes), the spin echo pulses, p w 90 ∘ = 40 μ s , p w 180 ∘ = 80 μ s at 0.33 W resulting in the actual acquisition time = AQ * ( τ + p w 18 0 ∘ ) / τ = 2.96 s and = AQ * ( τ + p w 9 0 ∘ ) / τ = 2.30 s . Spectra were processed using matched filters, line broadening LB = 1.4 Hz for the 1D and BSPE spectra and LB = 1.45 and 1.07 Hz for BSPE-SHARPER with 180° and 90° spin-echo pulses, respectively.

A reference 2D DOSY spectrum (pulse sequence ledbpgp2s.compensated.dn, see  Supplementary Software ) was acquired using a modified Bruker pulse sequence, ledbpgp2s , to include a compensating PFGs before the start of the pulse sequence and off-resonance presaturation as explained above. The following DOSY specific parameters were used: diffusion time, d20 = 200 ms, diffusion PFGs, p30 = 1 ms, the spoil and compensation PFGs, p19 = 0.6 ms and the eddy current delay d21 = 5 ms. All PFGs were sine shaped and applied at the strength specified in the pulse programme. The diffusion gradients were ramped up in 16 increments using 5 to 95 % strength of the PFG coil (66.4 G/cm). Number of scans was 8 per increment, yielding total acquisition time of 11 min. The SHARPER-DOSY spectra (pulse sequence ledbpgp2s.sharper_collapse.du, see  Supplementary Software ) were acquired using the combination of parameters used for the BSPE-SHARPER and DOSY experiments stated above. The overall acquisition time was 14 and 12.5 min for the 180 and 90° spin echo pulses. The spectra were processed using matched filters, line broadening LB = 1.56 Hz for the 2D DOSY spectrum and LB = 1.39 and 1.02 Hz for SHARPER-DOSY with 180° or 90° spin-echo pulses, respectively. The number of points in the F 1 was 256, linear prediction was not used.

Compound 3 ( M w  = 430.55 g/mol, Sample 1: c = 5.5 μM, 1.3 μg; Sample 2: 7.7 mM, 1.82 mg in 550 μL of D 2 O). The data were acquired and processed in TopSpin4.1 on an 800 MHz BRUKER NEO NMR spectrometer equipped with a TCI cryoprobe. For all experiments, identical common parameters, as stated for the 1D 1 H spectrum (zgpr_pulse.du), were used: D1 = 3.0 s, AQ = 1.05 s, DS = 4, NS = 128, SW = 15625 Hz (19.5451 ppm), TD = 32 k. The HOD signal presaturation was performed using the PRESAT_JUMP option with γB 1 /2π = 96 Hz.

For the acquisition of the BSPE spectrum (zgpebs.du) and the BSPE-SHARPER spectra (sharper_collapse.du) the following parameters were used: 3 ms ReBurp pulse, 600 μs PFG, G 1  = 7%, G 2  = 5% and G 3  = 12%. For the BSPE-SHARPER experiments the specific parameters were: τ = 448 μs, DW = 32 μs (14 points per chunk, 2340 spin echoes), the spin echo pulses, p w 90 ∘ = 15.7 μ s , p w 180 ∘ = 31.3 μ s at 2.78 W resulting in the actual acquisition time =  AQ * ( τ + p w 180 ∘ ) / τ = 1.12 s .

The spectra were processed using matched exponential filters with broadening, LB = 1.5 and 0.8 Hz (BSPE and BSPE-SHARPER spectrum of the 3 ) and LB = 1.25 or 0.53 Hz (BSPE and BSPE-SHARPER spectrum of D 2 O impurities).

A reference 2D DOSY spectrum (ledbpgp2s.compensated.dn) was acquired using a modified Bruker pulse sequence, ledbpgp2s , to include a compensating PFGs before the start of the pulse sequence and off-resonance presaturation. The following DOSY specific parameters were used: diffusion time, d20 = 200 ms, diffusion PFGs, p30 = 1 ms, the spoil and compensation PFGs, p19 = 0.6 ms and the eddy current delay d21 = 5 ms. All PFGs were sine shaped and applied at the strength specified in the pulse programme. The diffusion gradients were ramped up in 16 increments using 5 to 95 % strength of the PFG coil (66.4 G/cm). Number of scans was 8 per increment, yielding total acquisition time of 10 min. The SHARPER-DOSY spectra (ledbpgp2s.sharper_collapse.du) were acquired using the combination of parameters used for the BSPE-SHARPER and DOSY experiments stated above.

Supplementary information

Acknowledgements.

This research was supported by EPSRC grants EP/S016139/1 (DU) and EP/R030065/1 (DU). We thank Megan Halse, University of York, for valuable discussion during the development of the project.

Source data

Source Data (573K, zip)

Author contributions

D.U., C.L.D. and G.P. contributed to the design of experiments. Spectra were acquired and analysed by D.U., G.P. and P.J.B.. P.J.B. has written the programmes for optimisation of signal suppression and removal of the imaginary time domain data. G.P. has written the A.U. programme for the subtraction of 2D DOSY data sets. D.U. has written the the first version of the manuscript. G.C.L.-J. contributed to the writing of the manuscript.

Peer review

Peer review information.

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

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Competing interests.

The authors declare no competing interests.

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The online version contains supplementary material available at 10.1038/s41467-023-40130-2.

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• Published: 27 August 2024

Enantiospecificity in NMR enabled by chirality-induced spin selectivity

• T. Georgiou 1 ,
• J. L. Palma   ORCID: orcid.org/0000-0002-2611-7560 2 ,
• V. Mujica   ORCID: orcid.org/0000-0002-5237-4851 3 ,
• S. Varela   ORCID: orcid.org/0000-0002-9608-0601 4 ,
• M. Galante 3 ,
• V. J. Santamaría-García   ORCID: orcid.org/0000-0001-9284-1218 5 , 6 ,
• L. Mboning 7 ,
• R. N. Schwartz 8 ,
• G. Cuniberti   ORCID: orcid.org/0000-0002-6574-7848 4 , 9 &
• L.-S. Bouchard   ORCID: orcid.org/0000-0003-4151-5628 1 , 7 , 10 , 11  

Nature Communications volume  15 , Article number:  7367 ( 2024 ) Cite this article

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• Chemical physics
• Theoretical chemistry

Spin polarization in chiral molecules is a magnetic molecular response associated with electron transport and enantioselective bond polarization that occurs even in the absence of an external magnetic field. An unexpected finding by Santos and co-workers reported enantiospecific NMR responses in solid-state cross-polarization (CP) experiments, suggesting a possible additional contribution to the indirect nuclear spin-spin coupling in chiral molecules induced by bond polarization in the presence of spin-orbit coupling. Herein we provide a theoretical treatment for this phenomenon, presenting an effective spin-Hamiltonian for helical molecules like DNA and density functional theory (DFT) results on amino acids that confirm the dependence of J-couplings on the choice of enantiomer. The connection between nuclear spin dynamics and chirality could offer insights for molecular sensing and quantum information sciences. These results establish NMR as a potential tool for chiral discrimination without external agents.

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Introduction.

Chirality is a structural property integral to various chemical and biological processes. It plays a significant role in diverse research fields, including asymmetric synthesis and drug design. The investigation of electron transport, electron transfer, and photo-ionization in chiral molecules has led to the discovery of the chiral-induced spin selectivity (CISS) effect. This discovery was made by Naaman and colleagues in 1999 1 . Electrons traversing chiral molecules experience a momentum-dependent effective magnetic field due to spin-orbit coupling (SOC). This leads to spin selectivity and polarization under conditions where time-reversal symmetry is not conserved. The CISS effect not only provides new perspectives on electron transport but also actively modifies it by limiting backscattering and altering electron flow rules. Different spin components have distinct transmission probabilities, resulting in unique distance and temperature dependencies. These dependencies are governed by the interactions between electrons and phonons, as well as electron-electron interactions. When chiral molecules interact with other structures, charge polarization occurs, resulting in distinct spin orientations with respect to the electric and magnetic fields. The CISS effect provides insights into electron transfer in chiral molecules and has implications for chemical reactions and biorecognition. It also emphasizes the spin-filtering capabilities of chiral structures, including DNA and peptides; for additional information, see ref. 2 .

Cross-polarization (CP), although seemingly unrelated, is a key technique in solid-state NMR used primarily to enhance the signals of less abundant nuclei with low gyromagnetic ratios, such as 31 P, 13 C, and 15 N. Magnetization is transferred from more abundant nuclei like 1 H using an RF field. The Hartmann-Hahn condition enables this transfer to occur in the presence of pairwise spin couplings. The primary mechanism involves nuclear magnetic dipole interactions, which are not influenced by chirality. CP is sensitive to the distance between nuclei and the dynamics of participating molecules or functional groups. It is thus valuable for identifying linked nuclei and observing molecular dynamics in solid structures. When augmented with techniques like magic-angle spinning (MAS), CP’s sensitivity to molecular geometry and dynamics is enhanced.

Another avenue for nuclear spin-spin coupling leading to CP is indirect coupling via electrons 3 . Two notable papers by Santos and colleagues 4 , 5 reported enantiospecific NMR responses in CP-MAS solid-state NMR experiments. While through-space dipolar coupling is likely the dominant contribution to the transfer of polarization in their experiments, it does not explain enantioselectivity in the measurement. While J couplings have been known to generate CP for quite some time 3 , these findings were unexpected, as there are no established links between nuclear magnetism and molecular chirality. The authors proposed a mechanism to explain these observations in terms of the CISS effect giving rise to or influencing the indirect J -coupling. In this scenario, bond polarization via a chiral center or a helical structure could lead to distinct contributions from different enantiomers. Such a mechanism would create a unique magnetic environment for the nuclei participating in these CP experiments. Despite these considerations, the exact mechanism for chirality-dependent indirect coupling remains unclear. These results generated controversy in the literature 6 . For example, particle size, sample preparation, and impurity content have been argued to contribute to the observed effect 6 .

In this study, we investigate the coupling between nuclear spins and electronic states in chiral molecules. We find that remote nuclear spins can couple effectively via conduction electrons, thereby creating a mechanism for chirality-dependent indirect spin-spin coupling between nuclei. A theoretical framework is introduced to assess the plausibility of potential spin-dependent mechanisms responsible for this effect and their role in probing enantioselectivity in CP. Our theoretical analysis addresses the DNA helix. We also present a more quantitative analysis via DFT, which suggests an underlying mechanism for the experimental observations of Santos and colleagues on amino acids 4 , 5 . These results help establish the plausibility of enantioselective bond polarization-mediated indirect nuclear spin-spin couplings involving either a chiral center or a helical structure. This uniquely described mechanism bridges nuclear spins and the CISS effect, augmenting our understanding of chiral molecular systems. The study thus contributes to our understanding of chirality-induced phenomena, and to the possible development of applications in NMR-based sensing and quantum information processing at the molecular level.

NMR and chirality

NMR, as described by D. Buckingham 7 , is “blind” to chirality since none of its standard parameters appear to be sensitive to it. Enantiomers display identical NMR spectra in an achiral environment. Thus, differentiating enantiomers using standard NMR techniques in the absence of a chiral resolvent or probe is challenging. We are aware of three methods to indirectly detect chirality by NMR: (1) chiral derivatizing agents (CDAs) 8 , 9 : These compounds react with a chiral substrate to produce diastereomers, which have distinct NMR spectra. For example, when a chiral alcohol reacts with a CDA like Mosher’s acid, the resultant diastereomeric esters can be distinguished by their NMR chemical shifts, revealing the absolute configuration of the alcohol. (2) Chiral Solvents 9 , 10 : In these solvents, enantiomers present slight differences in their NMR spectra due to unique interactions with the chiral environment. These differences can help deduce enantiomeric excess and sometimes the absolute configuration. (3) Chiral Lanthanide Shift Reagents 11 , 12 , 13 , 14 : These metal complexes can cause shifts in the NMR spectra of chiral compounds. Lanthanide ions, especially Eu, Yb, and Dy, have been used to distinguish the NMR signals of enantiomers by forming diastereomeric complexes detectable due to their differing chemical shifts. However, each of these methods has limitations. Mainly, they are indirect molecular effects that rely on external agents. To determine chirality conclusively, complementary analytical methods are often necessary. Alternatively, Buckingham, Harris, Jameson, and colleagues have proposed using electric fields for chiral discrimination 7 , 15 , 16 , 17 , 18 , 19 , though this remains to be demonstrated in experiments.

Indirect NMR methods to distinguish enantiomers are less accessible and often more cumbersome than non-NMR methods such as chiral chromatography, high-performance liquid chromatography, gas chromatography, capillary electrophoresis, circular dichroism spectroscopy, optical rotatory dispersion, X-ray crystallography or vibrational circular dichroism. The development of a method to directly probe the chirality of a molecule using NMR, without reliance on external agents or indirect techniques, would be an important development in the fields of stereochemistry and analytical chemistry. Direct enantiomeric detection via NMR would uniquely combine non-destructive, quantitative capabilities with reproducibility, while concurrently bypassing the need for reactive chiral derivatizing agents, chiral solvents, and chromatography columns.

CP and enantiospecificity

The experiments performed in refs. 4 , 5 demonstrated the existence of an enantiospecific response in CP. This effect was also observed recently by Bryce and co-workers 20 , but the authors argued that experimental artifacts such as particle size could contribute. Rossini and colleagues 6 suggested that impurities, crystallization, and particle size effects likely contribute to the observation. Although such factors may influence the measurements, the data presented in refs. 6 , 20 does not rule out the contribution from CISS. As to CP, it is the bread-and-butter of solid-state NMR thanks to its ability to dramatically increase the sensitivity of experiments involving nuclei in low concentrations. CP is a technique where magnetization is transferred from an abundant, high gamma nucleus ( I 1 ) to a low gamma, dilute nucleus ( I 2 ) that is coupled to the I 1 spin bath during a certain “contact” period 21 , 22 , 23 . During the contact time, radiofrequency (r.f.) fields for both I 1 and I 2 are turned on. Usually, the dominant magnetic coupling between pairs of nuclei is due to the magnetic dipole interaction. In the simplest solid-state NMR experiment, the enhanced magnetization of the dilute isotope is then detected while the abundant protons, or any other reference nuclei, are decoupled. The maximum gain in sensitivity is equal to the ratio of gyromagnetic ratios between the two nuclei (e.g., for 1 H and 13 C this ratio is approximately 4:1; a factor of 4 implies 16-fold SNR gains).

The method of using heteronuclear double resonance to transfer coherence between nuclei in a two-spin system was introduced by Hartmann and Hahn 21 , 22 , 23 , 24 and has since become widely employed in solid-state NMR. It is possible to do highly selective recoupling among nuclei 25 , 26 . Spectroscopists can also modulate the amplitude of spin-locking pulses to enhance CP dynamics, perform Lee-Goldburg decoupling to reduce homonuclear proton couplings during spin-locking or apply multiple-quantum CP to half-integer quadrupole systems 27 , 28 , 29 . CP is a highly useful experiment that facilitates high-resolution NMR in the solid state encompassing key principles of dipolar coupling (decoupling/recoupling) and MAS 30 .

The working principle of CP is illustrated in Fig.  1 a. If two nuclear spins I 1 and I 2 with gyromagnetic ratios γ I 1 and γ I 2 , respectively, are placed in an external magnetic field B 0 , they will be able to absorb r.f. photons at frequencies γ I 1 B 0 and γ I 2 B 0 , respectively, according to the Zeeman effect. They will not be able to exchange energy spontaneously, since the two frequencies γ I 1 B 0 and γ I 2 B 0 are different. If instead a bimodal oscillating r.f. field is applied at these two frequencies, with amplitudes such that ω I 1  =  ω I 2 (Hartmann-Hahn condition 24 ), where ω I 1  =  γ I 1 B 1, I 1 and ω I 2  =  γ I 2 B 1, I 2 . In the “doubly rotating frame” generated by these frequencies both nuclear spins I 1 and I 2 appear stationary. Photons can now be absorbed by either of these spins at the same frequency ω I 1  =  ω I 2 , the condition for resonant energy transfer.

The CISS effect gives rise to delocalized conduction bands. Delocalized electrons can in turn mediate indirect nuclear spin-spin couplings. a In the cross-polarization experiment of solid-state NMR energy transfers between heteronuclei are forbidden in the lab frame. Application of a bichromatic RF field oscillating at the resonance frequencies of both nuclei, enables energy transfer. At the Hartmann-Hahn condition γ I 1 B 1, I 1  =  γ I 2 B 1, I 2 , resonant energy transfer will lead to transfer of polarization from the cold to hot spin systems. b Indirect spin-spin coupling between two nuclei is mediated by conduction electrons. c Model for DNA helix, helicoidal coordinates ( a , b , φ ) and two nuclear spins I 1 , I 2 and their corresponding positions φ 1 , φ 2 along the helix. R is the distance whereas Δ φ is the angle between consecutive nucleotides. a is the helix radius and b is its pitch.

The CP experiment is often described using the concept of spin temperature 31 , 32 , 33 . The abundant spin system is prepared with an artificially low temperature. This is typically done by applying a π /2-pulse on the abundant nuclei, followed by a spin-locking field 31 . One then allows the dilute system to come into thermal contact with the cold system of abundant spins. Contact is typically established through the magnetic dipole-dipole interaction between nuclei. Heat flows from the sparse spin system to the cold abundant spins, which produces a drop in the temperature of the sparse spins. Physically, we observe resonance energy transfer if the natural frequencies of the two systems are close. This was Hahn’s ingenious concept 24 . This experiment requires the heat capacity of the abundant system to be larger than that of dilute spins. In the context of such experiments, to say that the spin temperature has dropped is nearly equivalent to the statement that population difference between the ground \(\left\vert g\right\rangle\) and excited \(\left\vert e\right\rangle\) states is increased, which leads to an increased sensitivity of the NMR experiment.

In the ref. 4 , 5 different efficiencies of CP were obtained depending on the choice of enantiomer. The existence of an enantiospecific bilinear coupling (see Fig.  1 b) of the form \({{{\bf{I}}}}_{1} \cdot {{{\mathbf{\sf{F}}}}} \cdot {{{\bf{I}}}}_{2}\) was postulated in those papers, where the coupling tensor \({{{\mathbf{\sf{F}}}}}\) depends on Rashba SOC, an interaction which is itself enantiospecific. Herein we argue that bond polarization and SOC provides a possible mechanism to mediate the interaction between two nuclear spins through the creation of enantiospecific delocalized electron conduction bands which, in turn, enable these electrons to couple to both nuclear spins simultaneously via magnetic dipole interaction.

A summary of all known CP results on enantiomers published to date (see refs. 4 , 5 ) is shown in Table 1 . According to the traditional view, NMR parameters are not supposed to depend on the handedness of enantiomers; therefore, the ratio I ( D )/ I ( L ) should be 1. Instead, for all CP-MAS results a clear trend I ( D )/ I ( L ) > 1 is observed indicating that the D enantiomer consistently inherits more polarization compared to the L enantiomer. This goes against all known mechanisms describing nuclear spin interactions in a diamagnetic molecule.

Santos and co-workers 4 , 5 postulated the existence of an effective nuclear spin-spin interaction mediated by SOC because the effective strength of the SOC interaction in molecules exhibiting CISS is enantiospecific (Fig.  1 b), leading to different transmission probabilities for the two values of electronic spin. However, the precise mechanism remains elusive, as SOC itself does not couple directly to nuclear spins, as far as fundamental interactions are concerned. SOC only directly affects the electronic wavefunction. We must then turn our attention to the nature of effective interactions affecting these nuclear spins. The hyperfine interaction defines the manner in which nuclear spins couple to electron spins. From this emerges a possible mechanism. The electron-nuclear hyperfine interaction is made up of three contributions: Fermi contact, electron-nuclear dipole interaction, and nuclear spin-electron orbital angular momentum. The first two interactions provide a possible mechanism for spin-spin coupling, albeit indirectly. Indirect couplings in NMR, also known as J couplings, were discovered independently by Hahn and Maxwell 34 as well as McCall, Slichter, and Gutowski 35 . While initially discovered in liquids, Slichter 36 has presented a theory for the solid state. For 3D Bloch wavefunctions in a solid the case of the Fermi contact interaction is discussed in ref. 36 whereas the case of the dipole-dipole interaction is discussed in Bloembergen and Rowland 37 . These theories, however, do not incorporate in any way the effects of chirality. We propose instead to investigate the following two pathways:

A classic example of chiral molecule is the DNA helix. DNA is also amenable to simple modeling. The hypothetical case of indirect coupling of nuclear spins I 1 and I 2 in a DNA molecule is illustrated in Fig.  1 c.

The key observation in the present work is that the electronic wavefunction in CISS differs from normal 3D Bloch wavefunctions (e.g., 36 ) in that it is enantiospecific 38 , 39 . Enantiospecificity is related to the SOC interaction and helicity, which takes into account the direction of electron propagation. Another difference is the 1D nature of helical molecules, giving rise to 1D wavefunctions in a band structure model 38 , 39 . The physics of one-dimensional systems involves unique mathematical considerations. In Supplementary Text  S1 we present a detailed theoretical treatment of the indirect coupling between pairs of nuclear spins in a helical molecule based on spin-dependent mechanisms (electron-nuclear dipole-dipole, Fermi contact). The main result is that both interactions are sufficiently strong to cause observable CP. The electron-nuclear dipolar contribution to the effective coupling tensor (derived in Supplementary Text  S1) depends on chirality. Amplitude estimates are shown in Fig.  2 a, where coupling strengths between pairs of nuclear spins (assumed to be protons for simplicity) can reach amplitudes that generate observing measurable effects by CP 3 for specific positions of the nuclear spins. The coupling strength depends on the position ( φ 1 , φ 2 ) of the nuclear spins along the helix. We remark that this calculation should not be considered quantitative due to the one-dimensional nature of the problem, which leads to the emergence of divergences. This calculation should instead serve to establish the plausibility of the mechanism. As to the Fermi contact interaction, it is generally weaker than dipole-dipole (see Fig.  2 b), yet sufficiently strong to produce measurable effects 3 . Weak Fermi contact interactions are generally due to low overlap of the electronic wavefunction at the site of the nuclei, possibly due to a stronger contribution from p -wave character of the wavefunction 38 , 39 than s -wave 36 . However, as explained in  SI for the case of high-field NMR the Fermi contact tensor is not enantioselective. The dipole-dipole term, on the other hand, is. This analysis applies to the DNA toy model only. The situation could be different for real chiral molecules and an independent analysis is warranted on a case-by-case basis.

Multiplication by 0.01 gives the coupling strength in Hz. a Contribution from the magnetic dipole interaction. Peak coupling strengths attain 100 kHz (white regions, right panel). b Contribution from the Fermi contact interaction (values should be multiplied by 0.01 to get units of Hz).

We sketch the main steps of the derivation presented in  SI . An effective Hamiltonian is derived using second-order perturbation theory:

The term on the first line describes the effects of the Fermi contact interaction ( \({{{{{{\mathcal{H}}}}}}}_{eff}^{FC}\) ), whereas term on the second line, the effects of the dipole-dipole interaction ( \({{{{{{\mathcal{H}}}}}}}_{eff}^{DD}\) ). The Varela spinors 38 , 39 , which were recently obtained by solving a minimal tight-binding model constructed from valence s and p orbitals of carbon atoms, describe the molecular orbitals of helical electrons in DNA molecules. These spinors can be used to compute the summations by considering them as the electronic states \(\left\vert j\right\rangle\) :

where \(\tilde{n}\) is analogous to a wavenumber, φ is the angular coordinate along the helix, θ depends on SOC and is the tilt of the spinor relative to the z axis, s  = ± 1 is the electron spin orientation and ζ  = ± 1 labels the enantiomer. By keeping track of ζ we can determine which contribution(s) depend on enantiomer. This leads to the result

where μ 0 , γ I , γ S , ∣ T ∣ are constants, \(f(\tilde{n})\) is a Fermi function, \({I}_{1}^{\alpha }\) are nuclear-spin operators (see  SI) and explicit expressions for the matrices \({M}_{1,\beta }^{\alpha \beta }({\tilde{n}}^{{\prime} },\tilde{n})\) ’s are given in Supplementary (SI) equations  2 – 4 .

This expression for the indirect coupling is enantiospecific. The effective Hamiltonian contains a product \({M}_{1,\beta }^{\alpha \beta }({\tilde{n}}^{{\prime} },\tilde{n}){M}_{2,{\beta }^{{\prime} }}^{{\alpha }^{{\prime} }{\beta }^{{\prime} }}(\tilde{n},{\tilde{n}}^{{\prime} })\) . Explicitly, this term is:

While M i , z is independent of ζ , both M i , x and M i , y depend linearly on ζ (see equations  2 - 4 in SI). The term \({M}_{1,z}^{\alpha,3}({\tilde{n}}^{{\prime} },\tilde{n}){M}_{2,z}^{{\alpha }^{{\prime} },3}(\tilde{n},{\tilde{n}}^{{\prime} })\) does not depend on ζ , since neither factor depends on ζ . Neither do \({M}_{1,x}^{\alpha,1}({\tilde{n}}^{{\prime} },\tilde{n}){M}_{2,x}^{{\alpha }^{{\prime} },1}(\tilde{n},{\tilde{n}}^{{\prime} })\) and \({M}_{1,y}^{\alpha,2}({\tilde{n}}^{{\prime} },\tilde{n}){M}_{2,y}^{{\alpha }^{{\prime} },2}(\tilde{n},{\tilde{n}}^{{\prime} })\) since ζ 2  = 1. On the other hand, terms such as M 1, z M 2, x depend linearly on ζ . The effect of enantiomer handedness is to flip the sign of this term, leading to a change in the magnitude of the indirect coupling mediated by dipole-dipole interaction. As explained in  SI (and as seen in Fig.  2 a) the magnitude of this term depends on the exact relative positions of the two nuclei of interest along the helix.

As mentioned earlier, the spin-dependent coupling mechanism could be different for real chiral molecules. For the amino acids in Table  1 , analytical expressions for the spinors of electronic states, which are essential for the computation of J couplings, are not available to us. We can instead use DFT calculations. In Fig.  3 we present calculations of J couplings between 1 H and 13 C nuclei for the two ( D , L ) enantiomers of alanine. As seen in the bar plot of Fig.  3 a, significant relative differences in the J couplings between enantiomers can be observed. In  SI we include DFT results for the remaining amino acids: phenylalanine, arginine, aspartic acid, cysteine, glutamic acid, glutamine, glyceraldehyde (non-amino acid), methionine, serine, threonine, tyrosine, and valine. There, we find that J coupling values depend on the choice of enantiomer for all the molecules.

Nonzero values of this relative difference constitute evidence of chiral selectivity of the scalar coupling. J couplings between 1 H and 13 C nuclei were computed by DFT using ORCA for the amino acids: alanine, arginine, aspartic acid, cysteine, glutamic acid, glutamine, glyceraldehyde, methionine, phenylalanine, serine, threonine, tyrosine and valine (see  SI for results). The case of alanine is shown here: a J coupling stereochemical deviation b labeling of atoms in alanine.

We propose a unique CISS-dependent contribution to the conventional indirect nuclear spin-spin coupling mechanism in chiral molecules based on a network of electron-nuclear spin-dependent interactions and enantioselective bond polarization. This finding suggests that NMR-based techniques could be capable of chiral discrimination. The dominant contribution to CP NMR experiments in such cases is, of course, likely due to standard dipole-dipole and non-chiral J couplings. However, our results show that an additive chiral contribution to J could provide observable enantiospecific effects on top of existing conventional mechanisms contributing to CP. For the DNA toy model, the electron-nuclear dipole interaction exhibits dependence on the choice of enantiomer, whereas the Fermi contact interaction does not. However, for real molecules, this mechanism may not always be the same; in which case, DFT calculations provide a more quantitative framework for the analysis of such contributions. Our work may provide a theoretical foundation for experiments that probe chirality by NMR, establishing the first link between the CISS effect and nuclear spins. The CISS effect gives rise to electronic wavefunctions that are enantiospecific owing to the effective SOC interaction, manifesting itself in the Rashba form, in the presence of a chiral structure. The effective nuclear spin-spin interaction consists of a nuclear spin coupled to delocalized conduction-band electrons, which in turn couple to another nuclear spin. When averaging this effective interaction over electronic degrees of freedom, we obtain a coupling tensor with components that are enantiospecific. We note that the idea of using NMR to probe chirality is not new. Theoretical studies by Buckingham and co-workers have proposed the use of electric fields (external, internal) for chiral discrimination by NMR 7 , 15 , 16 , 17 , 18 . A paper by Harris and Jameson 19 explains that the spin-spin ( J ) coupling has a chiral component: E  =  J   I 1   ⋅   I 2  +  J c h i r a l   E   ⋅   I 1  ×  I 2 , where J c h i r a l is a pseudoscalar that changes sign with chirality and E is an electric field. Different symmetry considerations are involved here, as we do not form a scalar interaction from the three vectors E, B (magnetic field) and a single spin I . Instead, we have a tensorial interaction originating from an effective magnetic coupling between two spins I 1 and I 2 where the effective scalar Hamiltonian involves a rank-2 tensor \({{{\mathbf{\sf{F}}}}}\) , that arises from the averaging of the electron spin-nuclear spin dipolar couplings over the electronic spinor wavefunction. The effective tensor interaction \({{{{{{\bf{I}}}}}}}_{1}\cdot {{{\mathbf{\sf{F}}}}}\cdot {{{{{{\bf{I}}}}}}}_{2}\) can be decomposed as the sum of three energies, \(F{{{{{{\bf{I}}}}}}}_{1}\cdot {{{{{{\bf{I}}}}}}}_{2}+\frac{1}{2}{\sum }_{ij}{F}_{ij}({I}_{1}^{i}{I}_{2}^{j}+{I}_{1}^{j}{I}_{2}^{i})+{{{{{\bf{f}}}}}}\cdot ({{{{{{\bf{I}}}}}}}_{1}\times {{{{{{\bf{I}}}}}}}_{2})\) , also known in the field of magnetism as the isotropic exchange, symmetric and antisymmetric parts of the anisotropic exchange, respectively. According to the discussion in Supplementary Text  S1 (see section 1.2.1. Enantiospecific NMR Response), all three coefficients F , F i j and f are enantiospecific for the DNA toy model. This is in contrast with the symmetry of the conventional J coupling tensor in NMR. For real molecules, this situation could be different from the helical structure toy model.

These results have at least four potential implications: 1) They establish NMR as a tool for probing chirality, at least as far as CP experiments are concerned, these two parameters could form building blocks of analytical pulse sequences that sense chirality. In terms of spectroscopy, solid powders have wide anisotropic lines making it difficult or impossible to observe splittings of resonances. Thus, chirality effects may be difficult to observe as coherent effects in standard NMR spectra. On the other hand, a wide range of specialized solid-state NMR experiments were developed by Emsley and co-workers for spectral editing or to probe fine structures in powder spectra 40 , 41 , 42 , 43 , 44 , 45 , 46 . These advanced spin control methods are building blocks that could be adapted for chiral discrimination purposes. 2) This establishes chiral molecules as potential components of quantum information systems through their ability to couple distant nuclear-spin qubits. 3) Our theory, while applied to nuclear spins, could also be extended to localized electronic spins, such as those found in transition metal ions, rare-earth ions, and molecular magnets. The spin-dependent interaction mechanism still holds, and its strength would be 6 orders of magnitude larger due to the higher moment of the Bohr magneton compared to the nuclear magneton. 4) Control of electronic spins could lead to control of nuclear spin states and vice-versa. It was remarked in a recent paper by Paltiel and co-workers 47 that the control of nuclear spins may lead to the control of chemical reactions, which would be remarkable. Control of electronic spins, of course, would generally not be possible if relaxation times were exceedingly short. But in the context of CISS, the electron spin is locked to its momentum, giving rise to new possibilities for quantum logic. For this example, the role of CISS is to create spin-polarized electronic conduction channels that can lead to indirect nuclear spin-spin coupling and associated benefits such as the transport of quantum information. Finally, we note that the application of an electric field for chiral discrimination, as was previously suggested [, 15 – 18 , is not needed here, as the CISS effect alone generates an observable response. In particular, an applied current is not required because of a nonzero quantum mechanical probability current (see Supplementary Text  S1 , Section 1.4. Is an Applied Current Needed to Drive this Effective Interaction?). As pointed out by Rossini and co-workers 6 impurities or crystallite size differences could potentially affect the CP process if they give rise to differences in spin-lattice relaxation. Such differences can be minimized by further purification and recrystallization. Independently from this, however, spin-lattice relaxation rates during the CP transfer step depend on the choice of enantiomer ( ζ ). This is because spin-lattice relaxation can be modulated by scalar coupling (see Supplementary Text  S2) , which itself depends on ζ . In other words, our analysis suggests that both T 1 and spin-spin couplings are intrinsically connected through the choice of enantiomer.

Finally, a word about potential applications. Chirality is a fundamental determinant of molecular behavior and interaction, notably in biological systems where it influences the specificity of biochemical reactions. Current enantiomeric differentiation techniques, which often necessitate chiral modifiers, can interfere with the native state of biological samples, thus obscuring intrinsic molecular dynamics. The advancement of a non-perturbative method, as described in this work, utilizing the CISS effect for direct chiral recognition, may represent an important leap forward. This approach would not only preserve the pristine condition of the sample but also offer insights into the chiral-driven phenomena at the molecular level. For example, this method could enhance our understanding of enzyme-catalyzed reactions and protein-ligand interactions, elucidating the role of chirality in fundamental biological processes and potentially advancing the design of more selective pharmaceuticals. Such experiments are crucial for investigating the core aspects of CISS as they bypass the effects of molecule-substrate couplings, instead directly probing the interactions among nuclei within chiral molecules through the electronic response governed by CISS principles.

The theoretical investigations into the NMR J couplings chiral amino acids as well as glyceraldehyde were conducted utilizing DFT as implemented in the ORCA quantum chemistry package 48 that includes routines for computing NMR parameters based on ref. 49 . The amino acids selected for this study were optimized at the B3LYP exchange-correlation 50 functional with the split-valence Pople basis set, 6-31G(d,p) 51 to ensure accurate geometries. Following geometry optimization, the NMR J couplings were calculated using the gauge-including atomic orbital method combined with the BP86 functional and TZVP basis set 52 . BP86, a widely utilized generalized gradient approximation functional, combines the Becke 1988 exchange function with the triple zeta valence polarization basis set. To account for solvent effects, the geometry optimization and NMR calculations were performed using the conductor-like polarizable continuum model with water as the solvent. This inclusion aims to more closely simulate the natural aqueous environment of molecules by modeling the solvent as a dielectric polarizable continuum medium.

Data availability

The raw J coupling values generated in this study are provided in the  Supplementary Information . The atomic coordinates used in this study are provided in Supplementary Data  1 .

Ray, K., Ananthavel, S., Waldeck, D. & Naaman, R. Asymmetric scattering of polarized electrons by organized organic films of chiral molecules. Science 283 , 814–816 (1999).

Article   ADS   PubMed   CAS   Google Scholar  

Aiello, C. D. et al. A chirality-based quantum leap. ACS Nano 16 , 4989–5035 (2022).

Article   PubMed   PubMed Central   CAS   Google Scholar  

Ernst, M., Griesinger, C., Ernst, R. R. & Bermel, W. Optimized heteronuclear cross polarization in liquids. Mol. Phys. 74 , 219–252 (1991).

Article   ADS   CAS   Google Scholar  

Santos, J. et al. Chirality-induced electron spin polarization and enantiospecific response in solid-state cross-polarization nuclear magnetic resonance. ACS Nano 12 , 11426–11433 (2018).

Article   PubMed   CAS   Google Scholar  

San Sebastian, E. et al. Enantiospecific response in cross-polarization solid-state nuclear magnetic resonance of optically active metal organic frameworks. J. Am. Chem. Soc. 142 , 17989–17996 (2020).

Venkatesh, A., Wijesekara, A. V., O’Dell, L. A. & Rossini, A. J. Comment on “chirality-induced electron spin polarization and enantiospecific response in solid-state cross-polarization nuclear magnetic resonance”. ACS Nano 13 , 6130–6132 (2019).

Buckingham, A. D. Chirality in NMR spectroscopy. Chem. Phys. Lett. 398 , 1–5 (2004).

Wenzel, T. J., Seco, J. M., Quiñoá, E. & Riguera, R. The assignment of the absolute configuration by nmr using chiral derivatizing agents: a practical guide. Anal. Bioanal. Chem. 407 , 8381–8382 (2015).

Article   CAS   Google Scholar  

Silva, M. S. Recent advances in multinuclear nmr spectroscopy for chiral recognition of organic compounds. Molecules 22 , 247, 21pp (2017).

Article   Google Scholar  

Sugiura, M., Kimura, A. & Fujiwara, H. Discrimination of enantiomers by means of nmr spectroscopy using chiral liquid crystalline solution: application to triazole fungicides, uniconazole and diniconazole. Magn. Reson. Chem. 44 , 121–126 (2006).

Parker, D. Excitement in f block: structure, dynamics and function of nine-coordinate chiral lanthanide complexes in aqueous media. Chem. Soc. Rev. 33 , 156–165 (2004).

Parker, D. Nmr determination of enantiomeric purity. Chem. Rev. 91 , 1441–1457 (1991).

Parker, D., Dickins, R. S., Puschmann, H., Crossland, C. & Howard, J. A. Being excited by lanthanide coordination complexes: aqua species, chirality, excited-state chemistry, and exchange dynamics. Chem. Rev. 102 , 1977–2010 (2002).

Morrill, T. C. Lanthanide shift reagents in stereochemical analysis (VCH Verlagsgesellschaft, Weinheim, 1986). https://api.semanticscholar.org/CorpusID:92955168 .

Garbacz, P. & Buckingham, A. Chirality-sensitive nuclear magnetic resonance effects induced by indirect spin-spin coupling. J. Chem. Phys. 145 , 204201 (2016).

Buckingham, A. D. Communication: permanent dipoles contribute to electric polarization in chiral NMR spectra. J. Chem. Phys. 140 , 011103 (2014).

Article   ADS   PubMed   Google Scholar  

Buckingham, A. & Fischer, P. Direct chiral discrimination in NMR spectroscopy. Chem. Phys. 324 , 111–116 (2006).

Walls, J. D., Harris, R. A. & Jameson, C. J. Measuring chirality in NMR in the presence of a static electric field. J. Chem. Phys. 128 , 154502 (2008).

Harris, R. & Jameson, C. J. A note on chirality in NMR spectroscopy. J. Chem. Phys. 124 , 096101 (2006).

Lafrance, A.-A., Girard, M. & Bryce, D. L. Solid-state NMR spectra of amino acid enantiomers and their relative intensities. Solid State Nucl. Magn. Reson. 131 , 101925 (2024).

Pines, A., Gibby, M. G. & Waugh, J. Proton-enhanced NMR of dilute spins in solids. J. Chem. Phys. 59 , 569–590 (1973).

Pines, A., Gibby, M. & Waugh, J. Proton-enhanced nuclear induction spectroscopy. a method for high resolution NMR of dilute spins in solids. J. Chem. Phys. 56 , 1776–1777 (1972).

Pines, A., Gibby, M. & Waugh, J. Proton-enhanced nuclear induction spectroscopy 13 C chemical shielding anisotropy in some organic solids. Chem. Phys. Lett. 15 , 373–376 (1972).

Hartmann, S. & Hahn, E. Nuclear double resonance in the rotating frame. Phys. Rev. 128 , 2042 (1962).

Baldus, M., Petkova, A. T., Herzfeld, J. & Griffin, R. G. Cross polarization in the tilted frame: assignment and spectral simplification in heteronuclear spin systems. Mol. Phys. 95 , 1197–1207 (1998).

Lewandowski, J. R., De Paëpe, G. & Griffin, R. G. Proton assisted insensitive nuclei cross polarization. J. Am. Chem. Soc. 129 , 728–729 (2007).

Ashbrook, S. E., Brown, S. P. & Wimperis, S. Multiple-quantum cross-polarization in MAS NMR of quadrupolar nuclei. Chem. Phys. Lett. 288 , 509–517 (1998).

Ashbrook, S. E. & Wimperis, S. Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei. J. Magn. Reson. 147 , 238–249 (2000).

Rovnyak, D., Baldus, M. & Griffin, R. G. Multiple-quantum cross polarization in quadrupolar spin systems during magic-angle spinning. J. Magn. Reson. 142 , 145–152 (2000).

Rovnyak, D. Tutorial on analytic theory for cross-polarization in solid state NMR. Concepts Magn. Reson. Part A: Educ. J. 32 , 254–276 (2008).

Stejskal, E. & Memory, J. High-resolution NMR in the solid state: fundamentals of CP/MAS , 1st edition. Oxford University Press (1994).

Abragam, A. The principles of nuclear magnetism (Oxford University Press, 1961).

Goldman, M. Spin temperature and nuclear magnetic resonance in solids , 1st ed. Clarendon Press (1970).

Hahn, E. & Maxwell, D. Chemical shift and field independent frequency modulation of the spin echo envelope. Phys. Rev. 84 , 1246–1247 (1951).

Article   ADS   Google Scholar  

Gutowsky, H., McCall, D. & Slichter, C. Coupling among nuclear magnetic dipoles in molecules. Phys. Rev. 84 , 589–590 (1951).

Slichter, C. Principles of magnetic resonance, corrected 3rd printing, vol. 1 of Springer Series in Solid-State Sciences (Springer, 1996).

Bloembergen, N. & Rowland, T. Nuclear spin exchange in solids: Tl 203 and Tl 205 magnetic resonance in thallium and thallic oxide. Phys. Rev. 97 , 1679 (1955).

Varela, S., Mujica, V. & Medina, E. Effective spin-orbit couplings in an analytical tight-binding model of dna: Spin filtering and chiral spin transport. Phys. Rev. B 93 , 155436 (2016).

López, A., Varela, S. & Medina, E. Radiation modulated spin coupling in a double-stranded dna model. J. Phys.: Condens. Matter 34 , 135301 (2022).

ADS   Google Scholar  

Duma, L. et al. Principles of spin-echo modulation by J-couplings in magic-angle-spinning solid-state NMR. ChemPhysChem 5 , 815–833 (2004).

Mifsud, N., Elena, B., Pickard, C. J., Lesage, A. & Emsley, L. Assigning powders to crystal structures by high-resolution 1 H– 1 H double quantum and 1 H– 13 C J-INEPT solid-state NMR spectroscopy and first principles computation. a case study of penicillin G. Phys. Chem. Chem. Phys. 8 , 3418–3422 (2006).

Duma, L., Hediger, S., Lesage, A. & Emsley, L. Spin-state selection in solid-state NMR. J. Magn. Reson. 164 , 187–195 (2003).

Lesage, A. et al. Experimental aspects of proton NMR spectroscopy in solids using phase-modulated homonuclear dipolar decoupling. J. Magn. Reson. 163 , 105–113 (2003).

Sakellariou, D., Lesage, A. & Emsley, L. Spectral editing in solid-state NMR using scalar multiple quantum filters. J. Magn. Reson. 151 , 40–47 (2001).

Lesage, A. & Emsley, L. Through-bond heteronuclear single-quantum correlation spectroscopy in solid-state NMR, and comparison to other through-bond and through-space experiments. J. Magn. Reson. 148 , 449–454 (2001).

Salager, E. et al. Enhanced sensitivity in high-resolution 1 H solid-state NMR spectroscopy with DUMBO dipolar decoupling under ultra-fast MAS. Chem. Phys. Lett. 469 , 336–341 (2009).

Vardi, O. et al. Nuclear spin effects in biological processes. Proc. Natl Acad. Sci. 120 , e2300828120 (2023).

Neese, F., Wennmohs, F., Becker, U. & Riplinger, C. The orca quantum chemistry program package. J. Chem Phys. 152 , 224108 (2020).

Cremer, D. & Gräfenstein, J. Calculation and analysis of nmr spin–spin coupling constants. Phys. Chem. Chem. Phys. 9 , 2791–2816 (2007).

Lee, C., Yang, W. & Parr, R. G. Development of the colle-salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37 , 785–789 (1988).

Safi, Z. S. & Wazzan, N. DFT calculations of 1 H-and 13 C-NMR chemical shifts of 3-methyl-1-phenyl-4-(phenyldiazenyl)- 1 H-pyrazol-5-amine in solution. Sci. Rep. 12 , 17798 (2022).

Article   ADS   PubMed   PubMed Central   CAS   Google Scholar  

Jensen, F. Segmented contracted basis sets optimized for nuclear magnetic shielding. J. Chem. Theory Comput. 11 , 132–138 (2015).

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Acknowledgements

L.-S.B. acknowledges partial support from NSF CHE-2002313 and would like to thank Alexej Jerschow, Jeffrey Yarger, Daniel Finkelstein-Shapiro, and Thomas Fay for helpful discussions (discussions do not imply endorsements). S.V. acknowledges the support given by the Eleonore-Trefftz-Programm and the Dresden Junior Fellowship Program by the Chair of Materials Science and Nanotechnology at the Dresden University of Technology. G.C. acknowledge the support of the German Research Foundation (DFG) within the project Theoretical Studies on Chirality-Induced Spin Selectivity (CU 44/55-1) and by the transCampus Research Award Disentangling the Design Principles of Chiral-Induced Spin Selectivity (CISS) at the Molecule-Electrode Interface for Practical Spintronic Applications (Grant No. tCRA 2020-01), and Program trans-Campus Interplay between vibrations and spin polarization in the CISS effect of helical molecules (Grant No. tC2023-03). V.M. acknowledges the support of Ikerbasque, the Basque Foundation for Science, the German Research Foundation for a Mercator Fellowship within the project Theoretical Studies on Chirality-Induced Spin Selectivity (CU 44/55-1), the W.M. Keck Foundation through the grant “Chirality, spin coherence and entanglement in quantum biology” and the National Science Foundation award (NSF, USA & Biotechnology and Biological Sciences Research Council BBSRC, UK) "Chirality-Induced Spin Selectivity in Biology: The Role of Spin-Polarized Electron Current in Biological Electron Transport and Redox Enzymatic Action".

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T.G. worked on certain aspects of the theory and performed all DFT computations. J.L.P. helped T.G. with DFT computations of NMR parameters, with inputs from V.M. and L.-S.B. V.M. and S.V. provided critical advice on the CISS effect in the context of the CP experiment. L.-S.B. developed the analytical theory for the helical model and wrote the first draft. R.N.S. provided critical inputs on the electron spin mechanism. V.S.G., M.G., L.B., S.V., V.M., and G.C. reviewed the manuscript. All authors conceived the project and contributed to the design of the study. All authors have critically examined the results and helped write and/or revise the manuscript.

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Georgiou, T., Palma, J.L., Mujica, V. et al. Enantiospecificity in NMR enabled by chirality-induced spin selectivity. Nat Commun 15 , 7367 (2024). https://doi.org/10.1038/s41467-024-49966-8

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Heterogeneous dynamics of diffusive motion in organic ionic plastic crystal studied using spin–spin relaxation time: N,N -diethylpyrrolidinium bis(fluorosulfonyl)amide

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Keiko Nishikawa, Kozo Fujii, Kazuhiko Matsumoto, Hiroshi Abe, Masahiro Yoshizawa-Fujita, Heterogeneous dynamics of diffusive motion in organic ionic plastic crystal studied using spin–spin relaxation time: N,N -diethylpyrrolidinium bis(fluorosulfonyl)amide, Bulletin of the Chemical Society of Japan , Volume 97, Issue 9, September 2024, uoae088, https://doi.org/10.1093/bulcsj/uoae088

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The temperature dependences of the spin–spin relaxation times ( T 2 ) of 1 H and 19 F nuclei were measured for N,N -diethylpyrrolidinium bis(fluorosulfonyl)amide with a plastic crystal phase. In the plastic crystal phase, 2 types of T 2 were observed in both 1 H and 19 F experiments, which were considered to be the appearance of heterogeneous dynamics of diffusive motion. By examining temperature dependences of the T 2 values and the existence ratios, the following conclusions were reached. (i) The prepared plastic crystal sample was in a polycrystalline state, and each crystallite comprised 2 phases: the core phase (plastic crystal phase) and the surface phase formed to relieve surface stress. (ii) The 1 H -T 2 ( 19 F -T 2 ) values of the 2 phases differed, and ions in the surface phase were more mobile. The 1 H -T 2 ( 19 F -T 2 ) values for the 2 phases increased with temperature rise. In particular, the 1 H -T 2 ( 19 F -T 2 ) values of the surface phase were smoothly connected to the liquid T 2 values. (iii) The cations and anions exhibited a cooperative diffusive motion. (iv) When the temperature was considerably lower than the melting point, the ratio of the surface phase did not significantly differ from when it first formed. However, it rapidly increased near the melting point and became liquid.

Free induction decay signal of 1 H-NMR for N,N -diethylpyrrolidinium bis(fluorosulfonyl)amide, [C 2 epyr][FSA], at 390 K. The chart shows that there are 2 types of diffusive motion of the [C 2 epyr] + cations, namely, a hard component (green curve, ratio 0.844) and a soft component (orange curve, ratio 0.156).

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