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Accessing long-lived disconnected spin-½ eigenstates through spins > ½ Kevin Claytor, Thomas Theis, Yesu Feng, Jin Yu, David Gooden, and Warren S. Warren J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 17 Sep 2014 Downloaded from http://pubs.acs.org on October 3, 2014
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Journal of the American Chemical Society
Accessing long-lived disconnected spin-½ eigenstates through spins >½ Kevin Claytor1, Thomas Theis2, Yesu Feng2, Jin Yu2, David Gooden3, and Warren S. Warren4* 1
Department of Physics, Duke University, Durham, NC 27708, USA
2
Department of Chemistry, Duke University, Durham, NC 27708, USA
3
Duke Small Molecule Synthesis Facility, Duke University, Durham, NC 27708, USA
4
Departments of Chemistry, Radiology, Biomedical Engineering, and Physics, Duke University, Durham, NC 27708, USA
Supporting Information Placeholder ABSTRACT: Pairs of chemically equivalent (or nearly equivalent) spin-1/2 nuclei have been shown to create disconnected eigenstates which are very long lived compared to the lifetime of pure magnetization (T1). Here the classes of molecules known to have accessible long-lived states is extended to include those with chemically equivalent spin-1/2 nuclei accessed by coupling to nuclei with spin > 1/2, in this case deuterium. At first, this appears surprising, because the quadrupolar interactions present in spin > 1/2 nuclei are known to cause fast relaxation. Yet it is shown that scalar couplings between deuterium and carbon can guide population into and out of long lived states, i.e. those immune from the dominant relaxation mechanisms. This implies that it 13 may be practical to consider compounds with C pairs di14 rectly bound to deuterium (or even N) as candidates for storage of polarization. In addition, experiments show that 13 simple deuteration of molecules with C pairs at their natural abundance is sufficient for successful lifetime measurements.
Hyperpolarization is a promising method for imaging a wide variety of metabolic pathways in-vivo. For instance, the conversion from pyruvate to lactate, useful for early stage 1 cancer detection, has been demonstrated in humans . The biggest limitation of hyperpolarized magnetic resonance imaging (HP-MRI) is that the hyperpolarization decays back to thermal equilibrium at a rate given by the nuclear spin relaxation time T1, which in solution is commonly seconds. These short relaxation times drastically limit the range of molecules and processes that can be studied. A powerful solution to the imaging time problem comes in the form of “disconnected eigenstates” with very long lifetimes, such as the singlet (αβ-βα) between a single pair of inequivalent 2 spins that can be maintained by going to low fields or by 3 spin locking . Another state, and one that can persist at any magnetic field without spin-locking, is the state (αββα)13C(αβ-βα)1H between pairs of chemically equivalent 4 spins . The case of chemically equivalent spins is particularly
interesting because high degrees of symmetry make the accessed states particularly long lived. At first glance, it is surprising that these disconnected states are even accessible without a chemical shift difference; however, the out-of-pair J-couplings break the magnetic equivalence and create a handle to access the disconnected eigenstates. Some of these disconnected eigenstates have been shown to have exceedingly long lifetimes, in excess of hundreds of seconds or over 5,6 80 times T1 . Previous experimental work on chemically equivalent spins has demonstrated long lived states on AA’XX’ (e.g. diacetylene, Figure 1) and AA’X2X2’ systems consisting entirely 4,5,7,8 of spin-1/2 nuclei . In these cases, the singlet-singlet state is only close to an eigenstate if JCH 1/2 experience quadrupolar relaxation which is absent for spin 1/2 nuclei, therefore analysis is necessary. Here, long-lived states are demonstrated to exist in deu13 terated 2,3- C diacetylene, shown in Figure 1B, and deuterated diphenylacetylene (DPA) labeled at the acetylenic car6 bons. A carbon-only pulse sequence (Figure S1) was applied to deuterated (but with carbon-13 at its natural abundance) diacetylene in a 700 MHz NMR spectrometer. A long-lived 13 state is observed from the statistically labeled 2,3- C2 fraction (only 0.01% of the molecules). In addition, deuterated, carbon-13 labeled DPA was synthesized and studied in a 360 MHz spectrometer, with much better SNR. The singlet states supported by protonated DPA were previously studied as the 5 DPA moiety can appear in antibiotic and anticancer drugs . The results are shown in Figure 2. A lifetime of TS = 83 ± 30 13 s is measured, five times the C T1 = 16.7 ± 0.9 s, ~160 times 2 the H T1 = 0.5 ± 0.2 s, and about twice the singlet relaxation 10 time reported in for protonated diacetylene (TS = 49 ± 23 s). The DPA sample was observed to have a deuterated singlet lifetime of TS = 479 ± 83s nearly 1.7 times the protonated sin5 glet lifetime reported in of TS = 274 ± 6.1 s. In the following, the form of the deuterium-carbon longlived states of AA’QQ’ systems, where A is spin-½ and Q is spin-1, is derived and some non-intuitive results are noted. For example, the long lived state in the AA’XX’ system is the spin-0 combination of each pair of spins (the singletAsingletX); the AA’QQ’ system also has a spin-0 combination for each spin pair, but that is not the most efficient or robust way to pump the long lived states. In addition, the lifetime of the shorter lived species (hydrogen in the AA’XX’ systems, deuterium in the AA’QQ’ system) plays almost no role. Although the spin-1 nuclei studied here is deuterium, systems 14 containing N may also prove useful. Overall, this implies a significantly wider range of labeled molecular targets that might be useful for long time hyperpolarized imaging.
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To understand why this works, consider the AA’XX’ case. Previous work has shown that the disconnected eigenstates for AA’XX’ systems can be accessed with two fundamentally 4,7 different pulse sequences in the high field limit . The first method is an adaption of the M2S (Magnetization-to-Singlet) sequence pioneered by Levitt and coworkers for a pair of 11,12 spin-1/2 nuclei with a small chemical shift difference . The interaction Hamiltonian of the coupled spin pairs of the four spin system is; H = 2π J AA ' S1 ⋅ S 2 + 2π J XX ' I1 ⋅ I 2 +2π J n ( I1z S1 z + I 2 z S 2 z )
(1)
+2π J f ( I1 z S 2 z + I 2 z S1 z ) where, by symmetry, Jn = JAX = JA’X’ and Jf = JAX’ = JA’X. Here the states of A (typically the species with the longer lived singlet, 13 such as C) and X (typically protons) are labeled in the singlet triplet basis; S = (αβ - αβ)/√2, T+1 = αα, T0 = (αβ + αβ)/√2, 4 T-1 = ββ. As has been shown previously , the Hamiltonian of Eq. (1) is not diagonal in this basis. Instead, the Hamiltonian is block diagonalized into two 2-level systems joining triplets A X A X and singlets; one block joins the states S S and T0 T0 and A X A X another block joins S T0 and T0 S . The elements that connect these states are those that break the magnetic equivalence and are proportional to ∆J = Jn – Jf, the difference between the two A-X couplings. For example, the singletsinglet and triplet-triplet block is;
T0AT0X T0AT0X S AS X
S AS X
π ( J AA + J XX ) −π∆J π π − ∆ J − J + J ( AA XX )
(2)
If ∆J 1/2, affects P and
Corresponding Author
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Experimental details (equipment, pulse sequence, and synthesis) and a full treatment of the spin-1 system (including the JDD terms) may be found in the supplement. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
[email protected] Notes The authors declare no competing financial interests.
ACKNOWLEDGMENT This work was supported by NSF under grant CHE-1058727.
i
M differently than Z and so the effect of a fluctuating electric field will be to mix 0,0 and 2,0 , and the latter has allowed dipolar transitions. Thus, quadrupolar relaxation is expected to be an issue with the deuterium states. Despite this, the systems studied here have a long-lived state where the extended lifetime depends on the carbon character of the disconnected state, not on the proton or deuterium component. If the proton or deuterium component relaxes to equilibrium the carbon singlet character can be preserved, and a significant fraction can be recalled into observable magnetization. In all of these systems, it is best to view the proton or deuterium as essentially an “auxiliary spin” which provides the couplings needed to guide the carbon into the singlet, but is not itself particularly long lived. For similar reasons, 14 spin-1 N may well be useful when combined with carbon or proton coherences. For example, that the SABRE method for 15–17 hyperpolarization generally uses molecules with this AA’XX’ motif (where here AA’ is para-hydrogen, and the XX’ (or QQ’) are spins on molecules bound to an iridium complex, such as pyridine). In conclusion, it is possible to generate long lived singlet states on chemically equivalent spin-1/2 pairs by coupling to a pair of chemically equivalent spin-1 pairs which breaks the magnetic equivalence of both pairs. At first glance, it may be surprising that long-lived states are obtained since even the disconnected (spin-0) state of the combined spin-1 nuclei is exposed to quadrupolar relaxation. Nevertheless, AA’QQ’ systems can store polarization for much longer than T1 in a singlet on the spin-1/2 nuclei. This allows singlet states in systems that were previously unattainable, such as chemically equivalent carbons directly 13 1 bonded to deuterium: In directly bonded C2- H2 systems the 13 1 13 13 C- H J-coupling is often stronger than the C- C J-coupling preventing a stable singlet state. The weaker deuterium coupling could support the singlet states in such one-bond coupled systems, extending the range of molecules of promise for long lived hyperpolarized MR.
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Lastly, by extending long lived singlet states to integer spin nuclei, molecules containing nitrogen-14 may also be considered as coupling partners to access long-lived singlets with15 out expensive and time consuming N labeling schemes.
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