Multi-nuclear Detection of Nuclear Spin Optical Rotation at Low Field

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Spectroscopy and Photochemistry; General Theory

Multi-nuclear Detection of Nuclear Spin Optical Rotation at Low Field Yue Zhu, Yuheng Gao, Shane Rodocker, Igor Savukov, and Christian Hilty J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01053 • Publication Date (Web): 22 May 2018 Downloaded from http://pubs.acs.org on May 22, 2018

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The Journal of Physical Chemistry Letters

Multi-nuclear Detection of Nuclear Spin Optical Rotation at Low Field Yue Zhu,† Yuheng Gao,† Shane Rodocker,† Igor Savukov‡,* and Christian Hilty†,* †

Chemistry Department, Texas A&M University, 3255 TAMU, College Station, TX 77843,

USA ‡

New Mexico Consortium, 100 Entrada Drive, Los Alamos, NM 87544, USA

Corresponding Author * e-mail: [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT. We describe the multi-nuclear detection of nuclear spin optical rotation (NSOR), an effect dependent on the hyperfine interaction between nuclear spins and electrons. Signals of 1

H and 19F are discriminated by frequency in a single spectrum acquired at sub-milli Tesla field.

The simultaneously acquired optical signal along with the nuclear magnetic resonance (NMR) signal allows the calculation of the relative magnitude of the NSOR constants corresponding to different nuclei within the sample molecules. This is illustrated by a larger NSOR signal measured at the 19F frequency despite a smaller corresponding spin concentration. Secondly, it is shown that heteronuclear J-coupling is observable in the NSOR signal, which can be used to retrieve chemical information. Multinuclear frequency and J resolution can localize optical signals in the molecule. Properties of electronic states at multiple sites in a molecule may therefore ultimately be determined by frequency resolved NSOR spectroscopy at low field.

TOC GRAPHICS

KEYWORDS. Low-field NMR, nuclear spin optical rotation, J-spectroscopy


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Optical detection of nuclear magnetic resonance (NMR) is currently being proposed for applications that benefit from sensitivity enhancement at low field, such as enabling spectroscopy and imaging at low cost.1–3 These detection methods are based on optical magnetometry, using nitrogen vacancy centers in diamond or optically pumped alkali vapor as sensitive probes for nuclear spin magnetization. A different magneto-optical effect, nuclear spin optical rotation (NSOR) exists, which is based on electronic transitions of a molecule. While not proposed for applications in sensitivity enhancement, this effect may instead be used to provide new spectroscopic information on the molecule.4–8 NSOR is in essence a nuclear spin induced Faraday rotation. The Faraday effect itself describes the rotation of optical polarization in a medium induced by a magnetic field.9,10 In NSOR, localization of electrons near the magnetic dipole moments of nuclear spins can result in an enhancement of the polarization rotation.11,12 The NSOR constant φNSOR, which describes the polarization rotation by proportionality, arises from the vector polarizability αv of electrons.

NSOR =

ℏ ⋅

v m

(1)

The vector polarizability in turn depends on the oscillator strength and frequency of an optical transition, in addition to the hyperfine interaction with a nuclear spin. Therefore, the NSOR effect relates the structure of ground and excited electronic states near a specific nucleus to its nuclear magnetic moment. For example, NSOR is strongly enhanced for heavy atoms and ions due to the increased electron cloud overlap, and it also depends on chemical identity.4 Methods to measure NSOR have been developed in several contexts. Most commonly, NSOR has been detected using a radio-frequency induced spin lock, which results in a continuously precessing nuclear spin magnetic moment, and concomitantly in an optical signal at the respective Larmor frequency.4,7,8 At high magnetic field, NSOR has been used with spin-echo 3 ACS Paragon Plus Environment


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pulse sequences to measure chemical shift resolved spectra of several compounds.5 Frequency resolution at low field does not contain chemical shift information. However, it does allow for the simultaneous detection of multiple nuclei, and for obtaining chemical information by Jspectroscopy.13–15 Here, we describe a frequency resolved measurement of NSOR at low field, which distinguishes signals from nuclei of different types and demonstrates a possibility for localized optical spectroscopy. NMR and NSOR signals of liquids containing

19

F and

1

H were

simultaneously measured in a cell transversed by a 405 nm laser for NSOR detection, and equipped with a coil to pick up NMR signal (Figure 1a). Sample liquid flowed through a 9.4 T magnet for nuclear spin polarization, before its entrance into a measurement cell. NMR and NSOR signals of recirculated water are shown in Figure 1b. The NSOR signal is detected based on light polarization rotation in the optical channel. The NMR signal acquired at the same time can serve as a control for nuclear spin polarization and the proper operation of data acquisition in the experimental apparatus. The NMR detection coil was not tuned, in order to avoid a Faraday effect caused by feedback that would interfere with NSOR detection. Both signals were obtained using the experimental scheme shown in the inset of Figure 1a, employing a Carr-PurcellMeiboom-Gill (CPMG) pulse train that refocuses nuclear spin coherence into echoes. CPMG alleviates signal loss due to magnetic field inhomogeneity, while preserving the ability for resolving individual frequencies. Because of the continuous nature of the CPMG signal, the Fourier transform can be performed over the entire echo train. This procedure results in a spectrum with a frequency resolution that is higher by a factor of the number of echoes, compared to the frequency resolution available from a single echo. The echo time of 20 ms then


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results in the observation of spectra with side-bands spaced every 50 Hz. The side bands are clearly visible in the NMR signal, but are below the noise level in the NSOR spectrum. Since the weaker signal in the NSOR channel is at the same frequency as that in the NMR channel, we further acquired control experiments with the laser light blocked (Figure 2c). In these experiments, no signals in the NSOR channel were detectable. This result confirms the absence of observable crosstalk between the NMR and NSOR signal channels. Comparison of the signals acquired from the optical channel with and without laser also indicates that the laser contributes to an increase in noise. The noise level contributed by the laser is 4.2 times larger than the expected shot noise

16

from the 100 mW laser radiation (shown in supporting

information), indicating further opportunities to increase the signal-to-noise ratio of the NSOR measurement in the future. The magnitude of optical rotation due to NSOR depends on the optical path length. The flow rate of the liquid can affect the velocity field inside of the cell, which ultimately changes the effective beam path length. This effect was quantified by measuring water NSOR signals at different flow rates. First, the flow rate dependence of the polarization level inside of the flow cell was determined (Figure 1d). Next, from the water NSOR signals and using Equation 2, the effective path length of the optical beam within the NMR excitation region was calculated as a function of the flow rate (Figure 1e). Within the parameter range investigated, the effective path length was found to linearly depend on the flow rate. At a low flow rate of 2.5 mL/s, the effective light path length is 20.5 cm, which is in good agreement with the three passages through the actual cell length of 7.5 cm. At higher flow rate, the effective path length decreases in an effect that could arise due to increased channeling of the flow field.



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Figure 1. a) Experimental setup for low-field NSOR and NMR measurement. 1 – Laser; 2 – RF excitation coil; 3 – NMR detection coil wound on sample cell; 4 – mirrors; 5 – half-wave plate; 6 – polarizer cube; 7 – photo diodes. b) NMR and NSOR signal of recirculating DI water. In the experimental scheme (inset), narrow and wide bars represent ⁄2 (0.45 ms; phase = , )

or π (0.9 ms; = ) NMR pulses, respectively. Each scan comprises 30 echoes with echo time τ = 20 ms. A total of 16,000 scans were averaged. c) Experiment as in (b), with laser turned off. d) Relationship between polarization level in the sample cell, and flow rate. The resulting fitted curve is = 3.2 ⋅ 10 ⋅ 1 ! .""#$ % ⋅ ! .&'#$ , where Q is the volumetric flow rate in unit 6 ACS Paragon Plus Environment

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of (mL/s). e) Calculated effective light path length correlated to flow rate. The resulting effective path length is ( = 3.35cm⋅s⋅mL ⋅ - + 29.2cm.

The capability for frequency resolved NMR and NSOR detection is demonstrated in Figure 2 with the acquisition of both proton and fluorine signals from a mixture of TFE and DI water at a ratio of 1:1 v/v. Because of a shorter signal lifetime compared to DI water, a shorter echo time of τ = 10 ms was chosen. The phase cycling almost completely removes contributions from the pulses, which become invisible in the time domain signal in Figure 2a. In the real spectrum of this data, two peaks corresponding to the fluorine (30,869 Hz) and proton (32,832 Hz) Larmor frequencies in the measurement field of 0.7711 mT are seen (Figure 2b). Likewise, the NSOR signal of TFE can be observed in the time domain (Figure 2c). In contrast, the NSOR signals of DI water shown in Figure 1 were not strong enough to visually observe in the time domain. Examination of the NSOR spectra of TFE reveals that they are mainly composed of fluorine signal. Comparing Figure 2b and 2d, relative height of 1H peak with 19F peak in NMR is similar to that in NSOR but with the species switched place, which indicates that fluorine has a substantially higher NSOR constant than proton. The reason for this higher NSOR constant is two-fold; a stronger hyperfine interaction in heavier atoms 4, and the high electronegativity of fluorine. The high electronegativity increases the NSOR constant by increasing the overlapping of electronic cloud and therefore creates a larger hyperfine interaction.7



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Table 1. Calculation of NSOR constant ratio.

H

F

UNMR (µV)

60.0

19.3

UNSOR (mV)

0.131

2.17

∆θ (nrad)

1.41

23.0

γ (106 rad s-1 T-1)

268

252

F H NSOR # NSOR

45.6

A potentially interesting feature of this measurement is the ability to obtain the ratio of NSOR constants of different nuclei observed from a single time domain trace, without the need for any external calibrations. This ratio is given by (see the derivation in supporting information):

F F H NSOR 2NSOR 2NMR 5F = 4 6 H H F 5H NSOR 2NSOR 2NMR

(2)

UNSOR and UNMR are the integrals of signal voltages measured from the peaks in the respective spectra, γ the gyromagnetic ratio of the corresponding spins. Here, the H/F signal ratio in the NSOR spectrum is about 50 times larger than in the NMR spectrum than in the NSOR spectrum, resulting in a ratio of F and H NSOR constants of 45.6 (Table 1). The NSOR constants depend on the hyperfine interaction and therefore on the properties of the electronic states coupled to the nucleus (Equation 3). Therefore, the ratios measured of multiple nuclei may enable the determination of properties of electronic states at multiple sites in the molecule, using the combination of optical detection with the localization to a nuclear spin resulting from the NSOR effect.


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Figure 2. NMR and NSOR signals of recirculated trifluoroethanol/water mixture measuerd simultaneously from an experiment averaging 72,000 scans, each comprising 25 echoes with echo time τ = 10 ms. a) Time domain NMR signals. b) Frequency spectrum of NMR signals. c) Time domain NSOR signals. d) Frequency spectrum of NSOR signals.

Absolute values for NSOR constants can be estimated if an internal standard consisting of a known substance is present. In the data from Figure 2, if the NSOR constant of H is assumed to H be the same as that of DI water with NSOR = 9.02 7 108 9:; ⋅ < 7 =,8 the fluorine NSOR

F constant is estimated as NSOR = 4.15 7 10 9:; ⋅ < 7 =. A calibration against the

constant of water appears reasonable, because the water/TFE mixture employed in the



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experiment contains 66.8 M of protons in water, along with 3.77 M of -OH protons and 7.54 M of CH2 protons in TFE, i.e. 83 % of protons are in water. Therefore, disregarding the effects of H protons in TFE and possible bulk effects affecting NSOR , the estimated NSOR constant for

fluorine in TFE is approximately three times larger than the previously detected NSOR constant of fluorine in C6F14, which was reported as 1.32 7 10 9:; ⋅ < 7 =.7 This variation appears to be within an expected range, considering previous reports that the NSOR constant of protons can vary by a factor of several (NSOR constant for water: 9.02 7 108 9:; ⋅ < 7 =; for cyclohexane: 2.3 7 10& 9:; ⋅ < 7 =),7 and calculations predicting that -CF3 has a larger

NSOR constant than -CF2 in C6F14.7 More than a half of the fluorine atoms in C6F14 are -CF2, while TFE has only a -CF3 group. The frequency dependent detection of two nuclei in the same spectrum allows for internal validation of signals. As evidenced in Figure 1d and e, internal calibration is especially useful when experimental conditions are changing, such as in the variation of effective light path length with flow rate. It can also be noted that the ratio of the gyromagnetic ratios in Equation 4 can be calculated from the observed spectral frequencies, therefore also not requiring the knowledge of these external parameters.


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Figure 3. Expanded view of the peaks and designated coupling patterns. a) Proton NMR peak, b) Fluorine NMR peak, c) Proton NSOR peak, d) Fluorine NSOR peak.

Frequency dependent NSOR signals, even measured at low field, contain information on chemical structure. The expanded fluorine NMR signal in Figure 3b clearly shows the multiplet structure due to heteronuclear J-coupling while the proton signal shows only one large singlet. The -CF3 peak appears as a triplet because of coupling to two protons, whereas -CH2 is expected to be a quartet because of coupling to three fluorine atoms. The major component of the proton signal does not show coupling, and therefore is attributed to protons of water and the -OH protons in TFE, which are in mutual chemical exchange. The coupling patterns appearing in the NMR spectrum are also reproduced in the NSOR signals. Therefore, chemical information



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through J-coupling would be available from NSOR measurements at low field even in the absence of simultaneous detection of NMR signals. Apart from resulting in chemical resolution through J-spectroscopy, an advantage of the CPMG based detection scheme compared to the application of a spin lock is that in the CPMG experiment, spins precess freely all the time even when the π pulses are applied. The absence of an applied radio-frequency field eliminates the possibility for electrical cross-talk that could affect the detection of the small optical signals. Further improvements of the experimental apparatus could lead to additional increases in signal-to-noise ratio (SNR).17,18 The light path length could be increased, either by lengthening the measurement cell or by increasing the number of reflections and passes of the laser beam though the cell. In the present experiment, a total of three passes through the cell were used. With the instrument described in this paper, at the limit of shot noise, the optimum passage number of the light is estimated to be 9, which is subject to increase if reflection and scattering losses in the optical path are reduced. In a different NSOR experiment, Shi et al. used 14 passes through a measurement cell in conjunction with a 0.85 T permanent magnet. In addition, SNR at the shot noise limit increases with the square root of light intensity. Combined, improvements in laser type and optical path along with adjustments in circulation time, and additional reduction in electrical noise in the optical channel may increase SNR by at least an order of magnitude and make this experiment accessible to low-cost implementation without a superconducting magnet. The NSOR signal is indicative of the electron distribution around the atom. The J-coupling patterns along with the ability of detecting multiple nuclei at the same time result in a means for identifying individual substances even in the absence of chemical shift resolution. Since the


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NSOR constants are typically higher in the larger molecules, such molecules could be observed selectively, in complement to the traditional NMR. In summary, we have demonstrated the ability to measure multinuclear, frequency resolved NSOR signals at low field. Using recirculating liquids in an optical cell containing NMR excitation and detection coils, we have determined the ratio between fluorine and proton NSOR constants in a mixture of DI water and trifluoroethanol. A CPMG based NMR pulse sequence maximized signal lifetime by refocusing spins dephased by magnetic field inhomogeneity, while at the same time retaining frequency resolution of pulsed NMR. High frequency resolution was further demonstrated in the observation of heteronuclear J-coupling multiplets. Since the NSOR constant depends on the hyperfine interaction, resolution of multiple nuclei potentially allows the characterization of electron configurations at multiple sites in a molecule, combining information on chemical and electronic structure.

Experimental Methods Sample was circulated from a glass bottle reservoir through a peristaltic pump head (040.MS1R.01S, Watson-Marlow, Wilmington, MA), a 9.4 T magnet (Bruker Biospin, Billerica, MA), and a sample cell for NMR and NSOR detection (Precision Glassblowing of Colorado, Centennial, CO) before returning to the glass bottle. The sample cell was located in previously described spectrometer

19

with a tetra-coil magnet

20

generating a magnetic field of 0.7328 –

0.7711 mT, which was shimmed to first order along three axes. An untuned coil (242 turns, length 7.5 cm, inner diameter 9.4 mm) wound around the sample cell was used to pick up the NMR signal, which is further processed by a second order band-pass filter (10 – 100 kHz) and amplifier with a gain of 9.67 (AD712JR, Analog Devices, Norwood, MA). Signals were then



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acquired using a data acquisition board (PCIe-6259, National Instruments, Austin, TX) and LabView software. The beam of a laser (100 mW, 405 nm; L4405M-100-TE/2mm/ESYS; Micro Laser Systems, Garden Grove, CA) was passed through the cell three times by reflection on two flat mirrors (Thorlabs, Newton, NJ), and subsequently divided by a beam splitter (PBS121, Thorlabs) to create two linearly polarized beams. Two calibrated photodiodes (FDS100-CAL, Thorlabs) in combination with an amplifier and filter chain consisting of a transimpedance and difference amplifier (OPA4131PJ, Texas Instruments, Dallas, TX and AD712, Analog Devices), an 8th order, 28 – 34 kHz bandpass filter (MAX274, Maxim Integrated, San Jose, CA), and a low-noise pre-amplifier (SR-560, Stanford Research Systems, Sunnyvale, CA) were used to prepare the optical channel signal for acquisition with the data acquisition board.

Acknowledgments Financial support from the National Science Foundation (Grants CHE-1404548 and CHE1404529) and the Welch Foundation (Grant A-1658) is gratefully acknowledged. Supporting information Detailed experimental methods and derivation of formulas are included in the support information. References

(1) Blanchard, J. W.; Ledbetter, M. P.; Theis, T.; Butler, M. C.; Budker, D.; Pines, A. HighResolution Zero-Field NMR J-Spectroscopy of Aromatic Compounds. J. Am. Chem. Soc. 2013, 135 (9), 3607–3612.


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(2) Shin, C.; Kim, C.; Kolesov, R.; Balasubramanian, G.; Jelezko, F.; Wrachtrup, J.; Hemmer, P. R. Sub-Optical Resolution of Single Spins Using Magnetic Resonance Imaging at Room Temperature in Diamond. J. Lumin. 2010, 130 (9), 1635–1645. (3) Theis, T.; Ganssle, P.; Kervern, G.; Knappe, S.; Kitching, J.; Ledbetter, M. P.; Budker, D.; Pines, A. Parahydrogen-Enhanced Zero-Field Nuclear Magnetic Resonance. Nat. Phys. 2011, 7 (7), 571–575. (4) Savukov, I. M.; Lee, S.-K.; Romalis, M. V. Optical Detection of Liquid-State NMR. Nature 2006, 442 (7106), 1021–1024. (5) Pagliero, D.; Meriles, C. A. Magneto-Optical Contrast in Liquid-State Optically Detected NMR Spectroscopy. Proc. Natl. Acad. Sci. 2011, 108 (49), 19510–19515. (6) Pagliero, D.; Dong, W.; Sakellariou, D.; Meriles, C. A. Time-Resolved, Optically Detected NMR of Fluids at High Magnetic Field. J. Chem. Phys. 2010, 133 (15), 154505. (7) Shi, J.; Ikäläinen, S.; Vaara, J.; Romalis, M. V. Observation of Optical Chemical Shift by Precision Nuclear Spin Optical Rotation Measurements and Calculations. J. Phys. Chem. Lett. 2013, 4 (3), 437–441. (8) Savukov, I. M.; Chen, H.-Y.; Karaulanov, T.; Hilty, C. Method for Accurate Measurements of Nuclear-Spin Optical Rotation for Applications in Correlated Optical-NMR Spectroscopy. J. Magn. Reson. 2013, 232, 31–38. (9) Brentjens, M. A.; Bruyn, A. G. de. Faraday Rotation Measure Synthesis. Astron. Astrophys. 2005, 441 (3), 1217–1228. (10) Crossley, W. A.; Cooper, R. W.; Page, J. L.; van Stapele, R. P. Faraday Rotation in RareEarth Iron Garnets. Phys. Rev. 1969, 181 (2), 896–904. (11) Yao, G.; He, M.; Chen, D.; He, T.; Liu, F. Analytical Theory of the Nuclear-Spin-Induced Optical Rotation in Liquids. Chem. Phys. 2011, 387 (1), 39–47. (12) Ikäläinen, S.; Romalis, M. V.; Lantto, P.; Vaara, J. Chemical Distinction by Nuclear Spin Optical Rotation. Phys. Rev. Lett. 2010, 105 (15), 153001. (13) McDermott, R.; Trabesinger, A. H.; Mück, M.; Hahn, E. L.; Pines, A.; Clarke, J. LiquidState NMR and Scalar Couplings in Microtesla Magnetic Fields. Science 2002, 295 (5563), 2247–2249. (14) Appelt, S.; Häsing, F. W.; Kühn, H.; Sieling, U.; Blümich, B. Analysis of Molecular Structures by Homo- and Hetero-Nuclear J-Coupled NMR in Ultra-Low Field. Chem. Phys. Lett. 2007, 440 (4–6), 308–312. (15) Ledbetter, M. P.; Crawford, C. W.; Pines, A.; Wemmer, D. E.; Knappe, S.; Kitching, J.; Budker, D. Optical Detection of NMR J-Spectra at Zero Magnetic Field. J. Magn. Reson. 2009, 199 (1), 25–29. (16) Rice, F. A Frequency-Domain Derivation of Shot-Noise. Am. J. Phys. 2015, 84 (1), 44–51. (17) Silver, J. A. Simple Dense-Pattern Optical Multipass Cells. Appl. Opt. 2005, 44 (31), 6545– 6556. (18) Li, S.; Vachaspati, P.; Sheng, D.; Dural, N.; Romalis, M. V. Optical Rotation in Excess of 100 Rad Generated by Rb Vapor in a Multipass Cell. Phys. Rev. A 2011, 84 (6), 061403. (19) Zhu, Y.; Chen, C.-H.; Wilson, Z.; Savukov, I.; Hilty, C. Milli-Tesla NMR and Spectrophotometry of Liquids Hyperpolarized by Dissolution Dynamic Nuclear Polarization. J. Magn. Reson. 2016, 270, 71–76. (20) Gottardi, G.; Mesirca, P.; Agostini, C.; Remondini, D.; Bersani, F. A Four Coil Exposure System (Tetracoil) Producing a Highly Uniform Magnetic Field. Bioelectromagnetics 2003, 24 (2), 125–133. 15 ACS Paragon Plus Environment


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Figure 1. a) Experimental setup for low-field NSOR and NMR measurement. 1 – Laser; 2 – RF excitation coil; 3 – NMR detection coil wound on sample cell; 4 – mirrors; 5 – half-wave plate; 6 – polarizer cube; 7 – photo diodes. b) NMR and NSOR signal of recirculating DI water. In the experimental scheme (inset), narrow and wide bars represent π/2 (0.45 ms; phase φ1 = x,–x) or π (0.9 ms; ) NMR pulses, respectively. Each scan comprises 30 echoes with echo time τ = 20 ms. A total of 16,000 scans were averaged. c) Experiment as in (b), with laser turned off. d) Relationship between polarization level in the sample cell, and flow rate. The resulting fitted curve is P = 3.2·10–5·(1–e–5.99/Q)·e–5.264/Q, where Q is the volumetric flow rate in unit of (mL/s). e) Calculated effective light path length correlated to flow rate. The resulting effective path length is l = –3.35 cm·s·mL–1·Q+29.2 cm. 190x337mm (600 x 600 DPI)

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Figure 2. NMR and NSOR signals of recirculated trifluoroethanol/water mixture measuerd simultaneously from an experiment averaging 72,000 scans, each comprising 25 echoes with echo time τ = 10 ms. a) Time domain NMR signals. b) Frequency spectrum of NMR signals. c) Time domain NSOR signals. d) Frequency spectrum of NSOR signals. 122x97mm (600 x 600 DPI)


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Figure 3. Expanded view of the peaks and designated coupling patterns. a) Proton NMR peak, b) Fluorine NMR peak, c) Proton NSOR peak, d) Fluorine NSOR peak. 117x90mm (600 x 600 DPI)



Table of Contents Figure 48x49mm (600 x 600 DPI)


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Multi-nuclear Detection of Nuclear Spin Optical Rotation at Low Field

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