Polarization Transfer via Field Sweeping in Parahydrogen-Enhanced Nuclear Magnetic Resonance

Abstract

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We show that in a spin system of two magnetically inequivalent protons coupled to a heteronucleus such as 13C, an adiabatic magnetic field sweep, passing through zero field, transfers proton singlet order into magnetization of the coupled heteronucleus. This effect is potentially useful in parahydrogen-enhanced nuclear magnetic resonance, and is demonstrated on singlet-hyperpolarized [1-13C]maleic acid, which is prepared via the reaction between [1-13C]acetylene dicarboxylic acid and para-enriched hydrogen gas. The magnetic field sweeps are of microtesla amplitudes, and have durations on the order of seconds. We show a polarization enhancement by a factor of 10⁴ in the 13C spectra of [1-13C]maleic acid in a 1.4 T magnetic field. </div

Full text

Polarization transfer via field sweeping in parahydrogen-enhanced nuclear
magnetic resonance
James Eills,1, 2, a) John W. Blanchard,2Teng Wu,2Christian Bengs,1Julia Hollenbach,1Dmitry Budker,2, 3 and
Malcolm H. Levitt1
1)University of Southampton, Southampton, United Kingdom
2)Helmholtz Institute, Johannes-Gutenberg University, Mainz, Germany
3)University of California, Berkeley, California, USA
(Dated: 2 April 2019)
We show that in a spin system of two magnetically inequivalent protons coupled to a heteronucleus such
as 13C, an adiabatic magnetic field sweep, passing through zero field, transfers proton singlet order into
magnetization of the coupled heteronucleus. This effect is potentially useful in parahydrogen-enhanced nuclear
magnetic resonance, and is demonstrated on singlet-hyperpolarized [1-13C]maleic acid, which is prepared via
the reaction between [1-13C]acetylene dicarboxylic acid and para-enriched hydrogen gas. The magnetic field
sweeps are of microtesla amplitudes, and have durations on the order of seconds. We show a polarization
enhancement by a factor of 104in the 13C spectra of [1-13C]maleic acid in a 1.4 T magnetic field.
Keywords: NMR, Hyperpolarization, Adiabaticity, Zero-field NMR
I. INTRODUCTION
Magnetic resonance spectroscopy and magnetic reso-
nance imaging are widely applied techniques, but are of-
ten limited by the very low polarization of nuclear spins
at ordinary temperatures even in the highest available
magnetic fields. Nuclear hyperpolarization techniques
overcome this limitation by strongly polarizing the nu-
clear spins, with polarization levels of several percent
regularly achieved 1–4.
One hyperpolarization method is parahydrogen-
induced polarization (PHIP) which engenders nuclear
spin polarization from the nuclear spin-singlet (I= 0)
para isomer of hydrogen gas5–9 . In hydrogenative PHIP,
a molecule of para-enriched hydrogen undergoes pairwise
addition to a substrate molecule. If the protons in the
product retain magnetic equivalence (i.e. the Hamilto-
nian is invarant with respect to exchange of the pro-
ton spins), the hyperpolarized singlet state population
remains locked in an unobservable form. If their mag-
netic equivalence is strongly broken (with respect to the
magnitude of the proton-proton J-coupling), as is the
case for the original demonstrations 5, the hyperpolar-
ized magnetization may be directly observed. However,
if the breaking of magnetic equivalence is only slight, as
is the case in this work, magnetic field or pulse manipu-
lations are needed to convert the hyperpolarized singlet
order into magnetization 10–33 . The breaking of magnetic
equivalence may be through a chemical shift difference,
or as in our case, asymmetric coupling to a third nucleus.
Transfer of the parahydrogen proton spin polarization to
heteronuclear magnetization may be achieved by using
high-field rf (radio frequency) pulses 11–22, hydrogenating
at ultra-low field matching conditions23–26, or by mag-
netic field cycling techniques involving a sudden jump
a)Electronic mail: eills@soton.ac.uk
Rh
Ph2
P
P
Ph2
CH2
Acetone-d6
4
para-H2
PF
6
H
H
13C OH
OOH
O
13C
HO
O O
OH
H
H
13COH
OOH
O
Field sweep
Catalyst:
FIG. 1. a) Para-enriched hydrogen gas under-
goes pairwise addition to [1-13 C]acetylene dicar-
boxylic acid to form [1-13C]maleic acid. The reac-
tion catalyst is [1,4-bis(diphenylphosphino)butane](1,5-
cyclooctadiene)rhodium(I) tetrafluoroborate. The proton
singlet order is transformed into 13C magnetization by
applying a field sweep, passing through zero field.
in the magnetic field to a low value followed by a slow
increase in the field 27–31.
We demonstrate an alternative field-cycling method in
which proton singlet order is efficiently converted into
heteronuclear magnetization by adiabatically sweeping
an applied magnetic field from a negative value to a pos-
itive value, passing through zero. In this work we study
the 2% natural abundance [1-13C]maleic acid molecules
formed after hydrogenating acetylene dicarboxylic acid
(see Fig. 1). The method is depicted in Fig.2: (1) react
[1-13C]acetylene dicarboxylic acid with para-enriched hy-
drogen in the presence of a magnetic field (magnetic field
= +2 µT); (2) perform a non-adiabatic (rapid) field rever-
sal to -2 µT; (3) adiabatically (slowly) reverse the sign of
the magnetic field, passing through zero; (4) shuttle the
sample to a high-field benchtop NMR (nuclear magnetic
resonance) magnet, and (5) observe the 13C NMR sig-
nals. To perform the field sweeps, we employ a ZULF

2
Desktop NMR
Gas flow
Pulse coil
Guiding coil +8 μT+8 μT
+2 μT+2 μT
-2 μT+2 μT
60 s 0.5 s 2 s
pH2 @ 5 bar He @ 6 bar
Shuttle sample to SpinSolve
0.1 s
FIG. 2. Event sequence for the experiments performed, unless stated otherwise in the text. Further details are given in the
Materials and Methods section.
(zero and ultra-low field) NMR setup 34 , which allows for
precise control over the magnetic fields required for po-
larization transfer. The apparatus is described in more
detail in the Materials and Methods section. Adiabatic
field sweeps passing through zero have also been used in
the context of chemically induced dynamic nuclear po-
larization (CIDNP) 35.
[1-13C]maleic acid is a 3-spin-1/2, AA0X system.
These types of systems have been studied in the con-
text of SABRE (signal amplification by reversible ex-
change) 32,33. The J-coupling network is shown in
Fig. 3a, along with experimental (Fig.3b) and simulated
(Fig. 3c) 13C NMR spectra for a system at thermal equi-
librium. The proton-proton J-coupling is of the same
order of magnitude as the difference in proton-carbon J-
couplings, so the proton singlet state, which is populated
from parahydrogen addition, is close to being an eigen-
state of the spin Hamiltonian. An energy level diagram
with the single-quantum 13C transitions highlighted is
shown in Fig. 3d, to illustrate the origin of the spectral
lines. The finite amplitude of the outer transitions (5)
and (6) is due to singlet-triplet mixing, induced by the
heteronuclear J-couplings.
II. THEORY
A. State Bases and Hamiltonians
In this article we study three-spin systems, with two
protons, I1and I2, from the parahydrogen pair, and a
heteronuclear 13C spin, S3. It is convenient to discuss the
dynamics of this spin system using a set of orthogonal ba-
sis states termed here the STZ (Singlet-Triplet-Zeeman)
basis, defined as the tensor product of the singlet-triplet
states for spins 1 and 2, and the Zeeman states for spin
3:
STZ ={|S12
0i,|T12
+1i,|T12
0i,|T12
−1i} ⊗ {|α3i,|β3i}, (1)
where the singlet and triplet states of the proton pair are
defined as follows:
|S12
0i=1
√2(|α1β2i−|β1α2i)
|T12
+1i=|α1α2i
|T12
0i=1
√2(|α1β2i+|β1α2i)
|T12
−1i=|β1β2i. (2)
|αiand |βiare the Zeeman spin states for an isolated spin
in a magnetic field, with angular-momentum projection
+1/2 and −1/2 along the external field axis (defined here
as z), i.e. Iz|αi= + 1
2|αi, and Iz|βi=−1
2|βi, where
~= 1. The indices indicate the spin label.
For example, the state |S0αi=1
√2(|αβαi−|βααi)
signifies a proton singlet state, with the third spin (13C
in the case here) being in the |αiZeeman state. The spin
labels will be dropped henceforth.
The spin Hamiltonian for a solution-state sample is
H=H0+H1, (3)
which is split into two parts for convenience (discussed
below), with
H0= 2πJII I1.I2+ 2πJ13 I1zS3z+ 2πJ23 I2zS3z
+ω0
I(I1z+I2z) + ω0
SS3z, (4)
and
H1= 2πJ13 1
2(I+
1S−
3+I−
1S+
3)
+ 2πJ23 1
2(I+
2S−
3+I−
2S+
3), (5)
where ω0
j=−γjB, with ja spin label that corresponds
to a specific nuclear isotope, and J13 is the J-coupling
between spins I1and S3. The following symbols are in-
troduced now for brevity in later discussions:
ωII = 2πJII
ω∆
IS = 2π(J13 −J23)
ωΣ
IS = 2π(J13 +J23)
Ω = q4(ωII)2+ (ω∆
IS)2.

3
13C Chemical Shift
①②
③ ④
⑤ ⑥
+
H
H
13C OH
OOH
O
C
H
H
a
b
①
②
③
④
⑤
⑥
d
JIS
13C Chemical Shift
c
J23 = 2.1 Hz
JII = 12.2 Hz
J13 = 13.6 Hz
JII
`
`
`
`
`
`
`
`
FIG. 3. a) The product of the hydrogenation reaction, [1-13C]maleic acid, alongside a schematic showing the J-coupling
network. b) An experimental 13 C NMR spectrum without proton decoupling acquired with 16 transients on a sample of
1 M maleic acid in methanol-d4, showing just the carbonyl 13C peak. c) A simulation of the thermal polarization 13C NMR
spectrum of the carbonyl peak in [1-13 C]maleic acid. d) The nuclear spin energy levels of [1-13C]maleic acid with the 13C
single quantum transitions labelled. The label on each state indicates the STZ basis state which corresponds most closely to
the energy eigenstate. The dotted red lines labelled (5)+(6) show weak transitions which would be rigorously forbidden if the
singlet and triplet states were exact Hamiltonian eigenstates, but become weakly allowed through singlet-triplet mixing by the
heteronuclear J-couplings.
The eigenbasis of H0is termed here the STZ0basis, and
consists of the following states:
|1i=|S0αi0= cos θG
2|βααi − sin θG
2|αβαi
|2i=|T+1αi0=|αααi
|3i=|T0αi0= cos θG
2|αβαi+ sin θG
2|βααi
|4i=|T−1αi0=|ββαi
|5i=|S0βi0= cos θG
2|αββi − sin θG
2|βαβi
|6i=|T+1βi0=|ααβi
|7i=|T0βi0= cos θG
2|βαβi+ sin θG
2|αββi
|8i=|T−1βi0=|βββi, (6)
where the ’Goldman angle’ 13 is given by θG=
arctan(2ωII/ω∆
IS). In the case of magnetic equivalence,
θG=π/2, while for strong inequivalence, θG→0. Note:
some workers in the field use θ=π/2−θG.
The heteronuclear J-coupling terms in H0mix the |S0i
and |T0istates. The eigenvalues for H0are given in
Table I, along with the corresponding STZ0eigenstate.
Note that although the eigenvalues of H0depend on the
applied field, the eigenstates do not.
B. Avoided Crossings
At specific matching conditions of the external field B,
eigenvalues of H0can become degenerate. The flip-flop
components of the heteronuclear J-couplings, contained
in H1, mix the basis states of the full Hamiltonian H,
Eigenstate of H04∗State Energy / rad s-1
|1i=|S0αi0−ωII −Ω + 2ω0
S
|2i=|T+1αi0ωII +ωΣ
IS + 4ω0
I+ 2ω0
S
|3i=|T0αi0−ωII + Ω + 2ω0
S
|4i=|T−1αi0ωII −ωΣ
IS −4ω0
I+ 2ω0
S
|5i=|S0βi0−ωII −Ω−2ω0
S
|6i=|T+1βi0ωII −ωΣ
IS + 4ω0
I−2ω0
S
|7i=|T0βi0−ωII + Ω −2ω0
S
|8i=|T−1βi0ωII +ωΣ
IS −4ω0
I−2ω0
S
TABLE I. The symbols are defined as follows: ω0
j=−γjB,
and Ω = q4(ωII )2+ (ω∆
IS)2.
which leads to avoided crossings between the mixed states
at the positions of the H0degeneracies. The Bfield
positions of these avoided crossings are given (in units of
tesla) by:
B(1)
AC →2ωII + Ω −ωΣ
IS
4(γI−γS), (7)
and
B(2)
AC →2ωII −Ω−ωΣ
IS)
4(γI−γS). (8)

4
-300
-200
-100
0
100
200
300
-1 10-0.5 0.5
Magnetic Field / µT
Energy / rad s-1
J23 = 0 Hz
JII = 12 Hz
J13 = 1 Hz
C
H
H
`
`
`
`
`
`
`
`
a
b c
`
`
`
`
`
`
`
`
`
`
`
`
FIG. 4. Eigenvalues of the Hamiltonian Hfor the model three-spin-1/2 system shown in the inset, as a function of applied
field. There are four avoided crossings at -369nT, -8 nT, +8nT, and +369 nT (shown enlarged in panels a, b, and c). The line
colours label eigenvalues corresponding to eigenstates that transform smoothly into each other as the magnetic field changes.
The thick black and blue lines indicate the evolution of singlet order during a (fully) adiabatic -1 →+1 µT field sweep from
proton S0polarization at -1 µT into 13Cβpolarization at +1 µT. The avoided crossing of a pair of Hamiltonian eigenvalues is
shown in the inset. The corresponding eigenvalues of H0are shown by the dashed lines; the corresponding eigenstates of H0
are termed the diabatic states and belong to the STZ0basis (Eqn. 6). The Heigenstates are denoted |ψ1iand |ψ2i. Further
details are given in the text.
When |ωII||ω∆
IS|these equations simplify to:
B(1)
AC →4ωII −ωΣ
IS
4(γI−γS), (9)
and
B(2)
AC →−ωΣ
IS
4(γI−γS). (10)
Table II shows the states which have an avoided cross-
ing at the field values given, and gives the mixing terms
in the Hamiltonian H1that cause these avoided cross-
ings. The energy separation between the two states at
the position of the avoided crossing is given by twice the
magnitude of the mixing term.
The 8 eigenvalues of H0are plotted against the field
strength Bin Fig. 4, for the case of a model spin system
with JII = 12 Hz, J13 = 1 Hz, and J23 = 0 Hz. These val-
ues were chosen for clarity. 12 Hz is a typical J-coupling
for two protons in a cis conformation across a double
bond (as is often the case for parahydrogen products).
The four avoided crossings in this system, connecting the
states in Table II, are visible.
To understand the role of the avoided crossings, con-
sider the inset in Fig. 4, which shows the avoided crossing
between the H0eigenvalues corresponding to the diabatic
Crossing states Field Mixing term
|S0βi0↔ |T−1αi0−B(1)
AC π(J13 cos θG
2−J23 sin θG
2)
|S0αi0↔ |T+1βi0B(1)
AC π(J13 cos θG
2−J23 sin θG
2)
|T0βi0↔ |T−1αi0−B(2)
AC π(J13 sin θG
2+J23 cos θG
2)
|T0αi0↔ |T+1βi0B(2)
AC π(J13 sin θG
2+J23 cos θG
2)
TABLE II.
states |S0αi0and |T+1βi0. The eigenvalues of the dia-
batic states (i.e. the eigenstates of H0) are shown by
dotted black lines, and the coresponding eigenvalues of
Has thick coloured lines. If the system is prepared in
the state ψ1, and the magnetic field is varied adiabat-
ically (slowly) to take the system through the avoided
crossing, the system will remain in the same eigenstate
(i.e. follow the thick pink line), assuming the absence of
incoherent effects such as relaxation.

5
C. The field-sweep experiment
We now consider the density operator evolution for the
procedure sketched in Fig. 2; (1) sample hydrogenation
at a static field strength of +2 µT, (2) an instantaneous
(diabatic) field reversal to -2 µT, (3) a field sweep from
-2 µT to +2 µT under the adiabatic approximation.
1. Sample hydrogenation
Immediately after hydrogenation of the precursor with
para-enriched hydrogen, the spin density operator ρ0is
given by expressing the density operator
ρsinglet =1
2(|S0αihS0α|+|S0βihS0β|) (11)
in the Hamiltonian eigenbasis, and removing off-diagonal
elements between non-degenerate eigenvalues. The off-
diagonal elements are coherences, which are assumed to
be averaged to zero during the long hydrogenation period
(long in comparison to the inverse of the coherences).
The result is of the form
ρ0=X
ψ
pini
ψ|ψihψ|, (12)
where |ψiis a Hamiltonian eigenstate, and pini
ψis the
population of state ψ.
Since the hydrogenation field is not at an avoided cross-
ing, the eigenstates of H0are close to the eigenstates of
H. The initial populations of the H0eigenstates, assum-
ing pure pH2, are
pini
1=|hS0|S0αi0|2=(1 + sinθG)
4
pini
2=|hS0|T+1αi0|2= 0
pini
3=|hS0|T0αi0|2=(1 −sin θG)
4
pini
4=|hS0|T−1αi0|2= 0
pini
5=|hS0|S0βi0|2=(1 + sinθG)
4
pini
6=|hS0|T+1βi0|2= 0
pini
7=|hS0|T0βi0|2=(1 −sin θG)
4
pini
8=|hS0|T−1βi0|2= 0, (13)
where hS0|is shorthand for (hS0α|+hS0β|)/2.
2. Diabatic field reversal
Diabatic field reversal from +2 µT to -2 µT projects
the density operator ρ0onto the Hamiltonian eigenbasis
at this new field, and this operation has no effect on the
density operator. The states |S0αi0and |S0βi0retain
their populations.
0.5
0.4
0.3
0.2
0.1
0.0
-2 10-1 2
Magnetic Field / µT
J23 = 2.1 Hz
JII = 12.2 Hz
J13 = 13.6 Hz
C
H
H
State population
`
`
`
`
`
`
FIG. 5. State populations during an adiabatic -2 to +2 µT
field sweep for the 3-spin-1/2 system of maleic acid. The J-
couplings are shown in the inset figure.
3. Adiabatic field sweep
Applying a perfectly adiabatic field sweep from -2 µT
to +2 µT causes the state populations to evolve along
with the Hamiltonian eigenstates. Hence, the popula-
tions of states |S0αi0and |S0βi0are transferred into pop-
ulations of states |T+1βi0and |T0βi0, respectively, cor-
responding to 13C|βipolarization. This can be seen
visually by following the thick eigenvalue lines in Fig. 4.
The state populations during the field sweep are shown
in Fig. 5 for two differently J-coupled spin systems.
In cases for which the proton singlet state is an ex-
act Hamiltonian eigenstate, this process can give rise, in
principle, to unity 13C polarization. However, for [1-13C]
maleic acid, the incomplete magnetic equivalence of the
two protons means that the proton singlet state is not an
exact eigenstate of the initial spin Hamiltonian, leading
to a limit of 90% 13 C polarization, neglecting relaxation
and instrumental imperfections.
III. MATERIALS AND METHODS
For ultralow-field experiments, a magnetic shield (MS-
1F, Twinleaf LLC, Princeton, U.S.) was used to provide
a 106shielding factor against external magnetic fields.
Static internal magnetic fields for shimming were pro-
duced using built-in Bx,By, and Bzcoils, powered with
computer-controlled DC calibrators (Krohn-Hite, model
523, Brockton, U.S.), providing three-axis field control.
Time-dependent “pulse” fields were generated with three
nested Helmholtz coils wound on a 3D-printed former,

6
where each coil was driven with a separate isolated power
amplifier (AE Techron 7224-P, Elkhart, U.S.), with wave-
forms produced with the gradient controller of a low-field
NMR spectrometer (Kea II, Magritek GmbH, Aachen,
Germany).
NMR tubes held in the ZULF chamber and 1.4 T
SpinSolve were connected with PEEK tubing (1/16inch
O.D., 0.02 inch I.D.), as shown in Fig.6. Gas and liq-
uid flow were controlled by pneumatically actuated valves
(Swagelok, Solon, U.S.); the pneumatic valves were con-
trolled via TTL outputs of the Magritek spectrometer.
Sample hydrogenation was followed by shuttling into the
SpinSolve by reversing the gas flow. The sample trans-
port was performed with helium gas (any unreactive gas
could be used), and took 1 s. In order to prevent the
sample from passing through any fields that could lead to
undesired state-mixing during sample transport, a pene-
trating solenoid was used to provide a guiding field during
transit out of the magnetic shield.
Guiding Field
Solenoid
Static Field Coils
(Flexible PCB)
Pulse Field
Coils
-Metal
Shields
Ferrite
Shield
Benchtop NMR
Spectrometer
⁄” PEEK Tubing
NMR
Sample
Stainless Steel
Swagelok Fittings
Pressurisable
(J Young)
NMR Tube
NMR Pickup
Coil
FIG. 6. Schematic of the experimental apparatus. The sam-
ple was hydrogenated in the magnetically shielded chamber,
and field manipulations were performed using the pulse field
coils. The sample was then pneumatically shuttled into the
SpinSolve for signal acquisition.
To generate parahydrogen gas at 92% para en-
richment, regular hydrogen gas (purity 99.995%)
was passed through a Bruker parahydrogen gen-
erator operating at 36 K. Unless stated otherwise
in the text, the solution prior to hydrogenation
was 5 mM 1,4-bis(diphenylphosphino)butane(1,5-
cyclooctadiene)rhodium tetrafluoroborate and 100 mM
acetylene dicarboxylic acid in 300 µL acetone.
The events sequence is shown in Fig. 2. Initially the
sample is in the ZULF chamber in a 5 mm NMR tube, in
a +10 µT field provided by the pulse and guiding coils.
The field was stepped down to +2 µT (chosen as a rel-
atively low field that is still high enough for the Hamil-
tonian eigenstates to be, to a good approximation, the
STZ0basis states) by turning off the guiding field, and
parahydrogen gas was bubbled in at 5bar for 60 s. Af-
ter a 0.5 s delay to allow the sample to settle, a field
manipulation was applied using the pulse coils. The field
manipulation shown in Fig. 2 is a sudden step to -2 µT (in
∼10 µs), followed by a linear sweep to +2 µT in 1 s. The
field was then stepped to +2 µT (or in the case shown,
kept there). The guiding field was switched back on to
provide a +10 µT total field, and helium gas at 6 bar was
used to shuttle the sample into the SpinSolve. A π/2
pulse was applied followed by data acquisition triggered
by a TTL signal from the Kea II.
IV. RESULTS
To evaluate the field sweep methodology we perform
the hydrogenation, field sweep, and shuttling to high field
procedure, and detect the 13 C NMR signals. We first
show the effect of performing the sweep, and then study
the effects of sweep direction (i.e. sweeping from -2 to
+2 µT vs sweeping from +2 to -2 µT), sweep rate, and
finally provide an estimate of the achieved polarization
enhancement.
A. Field-sweep hyperpolarization of 13C NMR signals
To see the effect of the field sweep, a sample of acety-
lene dicarboxylic acid was hyperpolarized as described in
the Materials and Methods section, a linear field sweep
from -2 to +2 µT was performed with a duration of 1 s,
and the sample was shuttled into the SpinSolve for 13C
detection. For comparison, the experiment was repeated,
but instead of performing the field sweep, the field was
kept static at +2 µT for 1 s. The NMR signal of the hy-
perpolarized sample was allowed to relax, and a thermal
equilibrium spectrum was acquired. The 13C NMR spec-
tra are shown in Fig. 7. The field sweep spectrum shows
a dramatic 13C signal enhancement compared with ther-
mal equilibrium where no signal is observed.
When a field sweep is not used, two relatively weak
13C signals of opposite phase are observed (Fig. 7b).
These signals derive from the initial singlet polarization
of the protons which leads to weakly allowed transitions
through singlet-triplet state mixing (see Fig. 3).
B. Reversal of the field-sweep direction
To study the influence of the field-sweep direction,
the hyperpolarization procedure was repeated and the

7
180 170 160
Chemical Shift / ppm
150
a
b
cThermal
FIG. 7. Single-scan 13C NMR spectra of the reaction mixture
acquired without proton decoupling showing a) the signal af-
ter performing a -2 to +2 µT field sweep, b) the signal after
keeping the sample in a static +2 µT field, c) the thermal
equilibrium signal. The outermost spectral lines in (a) and
the only visible spectral lines in (b) are caused by S0↔T0
state mixing (see text).
field sweep was performed in the positive direction (-2 to
+2 µT) to polarize the 13C spins in the |βistate, and the
negative direction (+2 to -2 µT) to polarize the 13C spins
in the |αistate. The results are shown in Fig.8. Note
that helium bubbling for excess parahydrogen removal
was not performed in this experiment, so the signal-to-
noise is higher than in Fig. 7a.
Reversal of the sweep direction manifests as an in-
verted peak phase for the two spectra, and a reflection
about the central resonance. This is because, in the ideal
case, a positive field sweep polarizes states |T0βi0and
|T+1βi0, whereas a negative field sweep polarizes states
|T0αi0and |T−1αi0.
Simulations of the spectral lineshape were performed
by using SpinDynamica, a package for Mathematica 36.
For the simulations, the density operator at the start of
the field sweep was taken as ρ0from Eqn. 12. ρ0is then
propagated under the time-dependent Hamiltonian as the
field is swept. Proton relaxation from fluctuating exter-
nal random fields (as described in Ref. 37) is included.
The correlation between the random field fluctuations at
the two spin-sites was set to 0.9. The best-fit estimates of
the correlation time τcand root-mean-square amplitude
of the fluctuating external random fields were given by
(Brms
ran )2τc= 6 ×10−16 T2s.
Although the sample is in precisely zero field at the
centre of the sweep, it still matters whether the field is
increased from zero in the positive or negative sense. This
is because the quantum state in zero field depends on its
preparation history, and in particular whether the zero-
field state was prepared by an approach from the positive
or negative field direction.
180 170 160
Chemical Shift / ppm
150
a
b
FIG. 8. Single-scan 13C NMR spectra without proton decou-
pling showing a) the hyperpolarized [1-13C]maleic acid signal
acquired after performing a -2 to +2 µT field sweep, b) the
hyperpolarized sample signal acquired after performing a +2
to -2µT field sweep. Simulations of the spectra are shown in
blue.
C. Effect of field sweep duration on polarization transfer
efficiency
To understand the effect of the field sweep duration on
the degree of polarization transfer to the 13C spin, the
hyperpolarization step was performed on a series of re-
action mixtures, and a field sweep from -2 to +2µT was
applied with a different duration for each. In Fig. 9 the
13C signal intensities (as measured by peak integration)
are shown, along with a SpinDynamica simulation of the
13C polarization. The SpinDynamica simulations were
performed with the same parameters as used for Fig. 8,
but with the fluctuating external random field charac-
terised by the parameters (Brms
ran )2τc= 2 ×10−16 T2s,
which represents a weaker random field than that used
in the simulations in Fig. 8. The reason for the discrep-
ancy is unknown, but might reflect a variation in the
oxygen content of the solutions.
For efficient polarization transfer, the adiabatic condi-
tion needs to be met. Therefore, for longer sweep du-
rations the 13C signal is larger, as the process becomes
more adiabatic. This is true up to a point, but for the
longest sweep durations (2 s and 5 s), the signal is notably
attenuated by relaxation.

8
0 1 2
Sweep duration / s
3 4 5
0.2
0.0
0.6
0.4
0.8
Signal Amplitude
1.0
FIG. 9. Signal intensity measured for the 13C spins after
applying a -2 to +2 µT field sweep of variable duration, shown
by black circles. A SpinDynamica simulation of the transfer
efficiency is shown by the blue line. Details of the simulation
are given in the text. The signal intensity is normalized to
the maximum conversion amplitude of ∼0.9 in the absence of
relaxation.
D. Polarization Enhancement
To estimate the polarization level, a sample of 1 mM [1-
13C]acetylene dicarboxylic acid (13C-enriched) and 5 mM
rhodium catalyst in acetone was hydrogenated for 10 s
at 1 bar parahydrogen pressure, before performing a -2
to +2 µT field sweep in 1 s and shuttling to the Spin-
Solve for detection. After letting the polarized signal
decay, a 32 scan thermal spectrum was acquired on the
same sample. These results are shown in Fig. 10. The
[1-13C]maleic acid peak is not visible in the thermal spec-
trum, so the polarization was estimated by comparison
to the 13.5 M natural abundance acetone solvent peak
at 207 ppm. The signal enhancement on the product [1-
13C]maleic acid was estimated to be by a factor of 10,500,
corresponding to a polarization level of >1% in the 1.4 T
field.
V. CONCLUSIONS
We have presented a method to polarize the 13 C spin in
[1-13C]maleic acid by transferring the proton singlet or-
der, originating from the parahydrogen proton pair, using
a field sweep. The field sweeps used are typically -2 to
+2 µT and performed in 1 s, although variations of this
were used to evaluate the technique. This method can
in theory lead to up to 100% 13C polarization, although
this depends on the singlet order polarization level of
the hydrogenated molecule prior to the sweep, and the
degree of adiabaticity of the sweep used. We have pro-
vided a theoretical framework for understanding these
field sweep experiments, which is also applicable to the
more commonly used ‘field cycling’ method in AA0X spin
200 150 100 50
Succinate
Maleate
Acetone
Chemical Shift / ppm
4 transients
1 transient
Enhancement: 10,500
Polarization level: >1%
a
b
FIG. 10. Proton decoupled 13C NMR spectra with 2 Hz line
broadening showing a) hyperpolarized [1-13C]maleic acid af-
ter performing a 1 s -2 to +2 µT field sweep, b) thermal-
equilibrium signal acquired with 32 transients. The product
peak is not visible in the thermal equilibrium spectrum, so the
signal enhancement was estimated by integral comparison to
the acetone peak at 207 ppm.
systems 27–31.
We hope to combine this technique with an ex-
periment in which the hyperpolarized metabolite [1-
13C]fumarate can be produced via parahydrogen by
trans-hydrogenation38. This may allow for the produc-
tion of hyperpolarized metabolites for in vivo imaging in
a continuous-flow manner.
The required sweep duration for adiabaticity is in-
versely proportional to |ω∆
IS|. Given the relatively large
sweep range used in these experiments (4 µT), this corre-
sponds to a duration in the order of 1 s for [1-13C]maleic
acid, in which ω∆
IS = 2π×10.5 Hz. For [1-13C]fumaric
acid, ω∆
IS = 2π×3.4 Hz 21, which means longer sweep du-
rations will be necessary to maintain adiabaticity, and
signal losses due to relaxation might become significant.
For this reason, we are working to employ ’constant adi-
abaticity’ field sweep profiles39, which will reduce the
necessary field sweep duration as compared to the nonop-
timal linear profiles used in this work.
VI. ACKNOWLEDGEMENTS
This work was supported by the Engineering and
Physical Sciences Research Council (grant numbers
EP/N002482/1, EP/M508147/1, EP/P009980), the
Royal Society, and Bruker BioSpin. This project has re-
ceived funding from the European Union’s Horizon 2020
research and innovation programme under the Marie
Sk lodowska-Curie grant agreement number 766402. J.

9
E. would like to thank the Royal Society of Chemistry
for a researcher mobility grant.
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