CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201300718
Paramagnetic Relaxation of Long-Lived Coherences in Solution NMR Maninder Singh, Chinthalapalli Srinivas, Mayukh Deb, and Narayanan D. Kurur*[a] Long-lived coherences (LLCs) are known to have lifetimes much longer than transverse magnetization or single quantum coherences (SQCs). The effect of paramagnetic ions on the relaxation of LLCs is not known. This is particularly important, as LLCs have potential applications in various fields like analytical NMR, in vivo NMR and MR imaging methods. We study here the behaviour of LLCs in the presence of paramagnetic relaxation agents. The stepwise increase in the concentration of the metal ion is followed by measuring various relaxation rates. The effect of paramagnetic ions is analysed in terms of the external random field’s contribution to the relaxation of two coupled protons in 2,3,6-trichlorobenzaldehyde. The LLCs relax
faster than ordinary SQCs in the presence of paramagnetic ions of varying character. This is explained on the basis of an increase in the contribution of the external random field to relaxation due to a paramagnetic relaxation mechanism. Comparison is also made with ordinary Zeeman relaxation rates like R1, R2, R11 and also with rate of relaxation of longlived states RLLS which are known to be less sensitive to paramagnetically induced relaxation. Also, the extent of correlation of random fields at two proton sites is studied and is found to be strongly correlated with each other. The obtained correlation constant is found to be independent of the nature of added paramagnetic impurities.
1. Introduction Despite states and coherences in NMR having longer lifetimes relative to the other forms of spectroscopy,[1] there is a constant quest to increase them. Along these lines, long-lived states and coherences were introduced recently.[2–6] States that are anti-symmetric with respect to spin permutation have long lifetimes because the intramolecular dipole–dipole relaxation, which is the major relaxation mechanism in liquids, is symmetric to particle interchange.[2, 3] The symmetry forbidden coherence between the singlet and central triplet state can be induced by specifically designed pulse sequences.[4, 5] Such coherences have recently been shown to have long lifetimes.[4] The long lifetimes associated with the superposition of quantum states of different symmetry, termed long-lived coherences (LLCs), may be used to reduce line broadening in NMR. Such LLCs have been excited in systems with two homonuclear scalar-coupled spins I = 1/2.[4] The lifetime of an LLC is limited by the interaction of nuclei with other species, including that of unpaired electron spins. The inspiration for this work is the recent developments reported by Sarkar et al.,[4, 5] where they showed that the zeroquantum coherences (ZQCs) between singlet and triplet states in a two-spin system can be excited, although it is symmetryforbidden and unaffected by inhomogeneous broadening.[6, 7] They also reduce the homogeneous broadening effect caused [a] M. Singh, Dr. C. Srinivas, M. Deb, Prof. N. D. Kurur Department of Chemistry Indian Institute of Technology, Delhi Hauz Khas, New Delhi (India) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201300718.
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
by homonuclear dipole–dipole coupling. It was reported that the lifetimes of LLCs is considerably higher than the singlequantum coherences (SQCs). Due to the large difference in the magnetic moment of electrons and protons, paramagnetism has profound effects in NMR as evidenced by various studies of contrast agents in magnetic resonance imaging, in electron relaxation studies operative in various systems, and also in understanding the phenomenon of magnetic coupling in paramagnetic metal centres in various polymetallic systems.[8] These effects are also evident at greater distance from the paramagnetic centre and therefore are of particular interest in the study of biological macromolecules. Paramagnetic substances in liquids are known to reduce the relaxation time of nuclei which are present near it. This was first demonstrated by Bloch, Hansen and Packard[9] for protons in an aqueous solution of Fe3 + ions. It was further studied by Bloembergen, Purcell and Pound[10] for various paramagnetic ions such as Cu2 + and also in the presence of other ions. Relaxation in simple terms refers to the processes by which the nuclear spins and coherence returns to equilibrium. Unlike other spectroscopic methods, in NMR or ESR, the transitions between excited and ground states do not occur spontaneously by direct emission of photons of that energy. Instead, fluctuating magnetic fields that are randomly generated in the environment (by the motion of particles, electric charges and other magnetic dipoles) induce the spin system to undergo transitions. In systems containing paramagnetic ions, one of the main mechanisms of nuclear relaxation is dipole–dipole coupling of nuclei with fluctuating magnetic fields generated by electron magnetic moments. ChemPhysChem 2013, 14, 3977 – 3981
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Paramagnetic species are known to induce singlet-to-triplet conversion in various types of molecules.[11–13] Does their presence affect the relaxation rate of LLCs? If they do, in what manner? Answers to these questions are relevant for possible in vivo applications of LLCs because every living being contains a variety of paramagnetic ions in the organelles.[14–16] Various MRI techniques used for in vivo imaging and the magnetic tracers used for analyzing different biochemical processes currently require the measurement of longitudinal or transverse relaxation rate of diverse molecules present. Can singlet–triplet coherence rate be a useful probe in such measurements? Are they expected to persist for longer or shorter time than single or multiple quantum coherences? In order to characterize the influence of paramagnetic ions on relaxation of LLCs in scalar coupled nuclear spins, we studied the pair of chemically inequivalent spin 1/2 nuclei in 2,3,6-trichlorobenzaldehyde (TCB). Our studies reported here are also influenced by the observation of Tayler et al.[17] that the relaxation behaviour of longlived states (LLSs) in the presence of paramagnetic ions is 2–3 times less sensitive to paramagnetically induced relaxation than normal Zeeman magnetization since the main dipole– dipole relaxation mechanism is highly ineffective for singlet state relaxation.[18] The effect of paramagnetic ions on the relaxation of ZQC in the laboratory frame was earlier studied by Wokaun and Ernst.[19] LLCs are ZQC in the rotating frame. The aim of this paper is to study the relaxation behaviour of these coherences in a spin-1/2 system in the presence of paramagnetic agents.
Figure 1. Pulse sequence used for excitation of long-lived coherences in 2,3,6-trichlorobenzaldehyde (0.01 m solution at 7.1 T or 300 MHz and 300 K). Here d1 is the pre-scan delay which is 3–5 times T1, and the inter-pulse delay t = 1/(2Dn12) where Dn12 is the chemical shift difference between two aromatic protons. tr is the variable time used for spin-locking the continuouswave pulse. The carrier frequency is set in the middle of chemical shift frequencies of two nuclei. The first non-selective (p/2)0 pulse converts initial Zeeman magnetization into (I1yI2y) followed by delay t that converts it into opposite x magnetization (I1xI2x) which was then spin-locked using a resonant strong RF field such as continuous wave (CW), which suppresses the chemical shift difference and instantaneously switches the eigenstates of the Zeeman product basis to a symmetry-adapted singlet–triplet basis. The spin system evolution is governed by an effective Hamiltonian of the form H = 2 p[n1(I1x+I2x) + Dn(I1z+I2z) + J(I1.I2) + (Dn12/2)(I1zI2z)] where Dn is the offset and J is the coupling constant between the two spins.
ing from 0.0 mm to 0.4 mm are plotted in Figures 2 and 3. In the absence of paramagnetic ions, LLC relaxes more slowly than transverse magnetization. As the concentration of metal ions increases, the relaxation rate increases. This increase in the relaxation rate is due to the effect of fluctuating magnetic fields generated by unpaired electron density on the metal
Experimental Section All the experiments were performed on a BRUKER AV-III spectrometer at a frequency of 300 MHz for protons. The sample used was (0.01 m) 2,3,6-trichlorobenzaldehyde in [D6]DMSO solvent. The experiments were done at room temperature and without degassing the sample. The pulse sequence used to measure the long-lived coherence time constant TLLC for inequivalent spin pairs in high magnetic field is shown in Figure 1. A resonant field of amplitude corresponding to a nutation frequency of wrf was used during the locking interval. The relaxation rate of LLC follows Equation (1):[4] IðLLCÞ ¼ I0 cosð2 pJtr Þexpðtr =T LLC Þ
ð1Þ
where tr is the variable time for spin locking, I(LLC) and I0 represents the intensity of magnetization at time tr = t and 0 respectively. Here J is the coupling constant and TLLC is the lifetime of LLC. The relaxation times T1 and T2 were measured by standard inversion recovery (IR) and Carr–Purcell–Meiboom–Gill (CPMG) pulse sequences while the LLS was created and measured using the pulse sequence introduced by Levitt and co-workers.[3] All the relaxivity values were obtained by fitting the data to a linear equation in OriginPro 8.[20]
2. Results and Discussion The measured relaxation rate constants, Rx ( = 1/Tx where Tx is the relaxation time constant) for metal ion concentration rang 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 2. The experimental relaxation rates (R1, R2, R11, RLLS and RLLC) of 2,3,6trichlorobenzaldehyde protons as a function of concentrations of Cu2 + ions (0.0 mm to 0.4 mm with a step size of 0.1 mm).
ions with nuclei present nearby. The effect of an increase in the rate constants upon addition of Mn2 + ions to the sample is much more prominent than that of Cu2 + additions. We attribute this to the five unpaired electrons of the Mn2 + in the 3d orbital compared to one unpaired electron of Cu2 + . The variation in the rate constants R1, R2, RLLS, RLLC and R11 with concentration of paramagnetic ions, obeys the following linear equation [Eq. (2)]: Ri ð½XÞ ¼ k i ½X þ Ri ð0Þ
ð2Þ ChemPhysChem 2013, 14, 3977 – 3981
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www.chemphyschem.org spins present nearby. These randomly fluctuating magnetic fields interact with nuclear spins and this resonant interaction results in the relaxation of nuclear spins. Relaxation due to unpaired electrons is much faster compared to that due to nuclear spin since the gyromagnetic ratio of the electron is much larger than that of the nuclear spin. The relaxivity ratios kLLC/k2 and kLLS/k1 can be interpreted roughly by assuming the two protons each experience randomly fluctuating magnetic fields generated by paramagnetic centers.[18, 25] Tayler and Levitt analyzed the relaxation of LLS by paramagnetic interactions in terms of randomly fluctuating magnetic fields using the Redfield formalism.[18] The rate expression for RLLS(ERF), R1(ERF) is given by Equations (3) and (4):
Figure 3. The experimental relaxation rates (R1, R2, R11, RLLS and RLLC) of 2,3,6trichlorobenzaldehyde protons as a function of concentrations of Mn2 + ions (0.0 mm to 0.4 mm with a step size of 0.1 mm).
where [X] is the concentration of the paramagnetic ion, Ri(0) and Ri([X]) are the rate constants of type i at 0 and [X] concentration respectively, and ki is the change in the relaxation rate, that is, relaxivity. It is pertinent to point out that the samples were not degassed and hence the relaxation rate constants have the contribution of dissolved paramagnetic impurities. In the absence of paramagnet RLLC is lower than R2 as expected. On addition of Cu2 + it soon overtakes R2. In contrast, RLLS relaxes more slowly than R1 and is immune to the addition of paramagnet. In the case of Mn2 + , the increase in RLLC is more pronounced than in Cu2 + . The relaxivities of the various rates are tabulated in Table 1. On comparing the effect of Mn2 + and Cu2 + metal ions on all relaxivities (k1, k2, k11, kLLS, kLLC), it is observed that the Mn2 +
Table 1. Relaxivities of 2,3,6-trichloro benzaldehyde protons in the presence of Cu2 + and Mn2 + ions at room temperature (298 K) at a field of 7.1 T. X 2+
Cu Mn2 +
k1
k2
kLLS
kLLC
0.41 0.04 1.88 0.17
0.40 0.04 2.22 0.09
0.07 0.015 0.69 0.14
0.60 0.05 3.29 0.31
effect is five times larger than that of Cu2 + . The relaxivities are proportional to the square of the magnetic moment of the metal ion, which depends on the number of unpaired electrons.[17, 25, 29] From Figures 2 and 3, it is concluded that the relaxivity for LLC is highest while that of LLS is the lowest. The ratio kLLC/kLLS (see Table 1) shows that the singlet–triplet coherences are more sensitive to paramagnetic relaxation than singlet states by a factor of approximately 5 to 10. The values are given in the Supporting Information (Table S1). One approach to understand the factors responsible for the increase in the relaxation rate in presence of paramagnetic ions is to model them as external random fields. External random fields[21–24] include the dipolar interactions from all other intermolecular spins, CSA and also the unpaired electron 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
R1 ðERFÞ ¼ gH 2 ðB1 2 þ B2 2 Þj1 ðw0 Þ
ð3Þ
RLLS ðERFÞ ¼ 2 gH 2 ðB1 2 þ B2 2 2 CB1 B2 Þ½j1 ð0Þ þ 2 j1 ðw0 Þ=3
ð4Þ
By a similar analysis, we find that the relaxation rate of longlived coherences, RLLC(ERF), is given by Equation (5): RLLC ðERFÞ ¼ ðgH 2 =4ÞðB1 2 þ B2 2 Þ½j1 ð0Þ þ 2 j1 ðw0 Þ ðgH 2 =2ÞCB1 B2 j1 ð0Þ
ð5Þ
where Bi is the root mean square (rms) value of the random fields at the nuclear site i (= 1, 2), Bi = hBi.Bii1/2. The random field at nuclear site i is denoted by Bi, and C = hB1.B2i/B1B2 represents the extent of correlation of the fluctuating magnetic fields at the two proton sites. All the relaxation rates depend on the Bi and C. Also, gH represents the magnetogyric ratio of the proton and j1(w0) is the non-normalized rank 1 spectral density at frequency w0. Under the condition of extreme narrowing j1(0) = j1(w0) = j1(2w0) and equal rms field amplitudes B1 = B2, the ratios of relaxivities depend upon field correlation C.[17] The RMS values of random fields at the two nuclear sites were calculated and the correlation constant C at different concentrations of paramagnetic ions is obtained by using the above equations for R1(ERF) and RLLS(ERF) (see Table 2). Calculating C from RLLS(ERF) rather than RLLC(ERF) is advantageous since the LLS is not affected by intramolecular dipolar relaxation. As noted first by Redfield[25] the random fields at nuclear sites increase in proportion to the increase in the concentration of paramagnetic ion. The correlation constant is fairly independent of the nature of paramagnetic ions. Earlier, Wokaun and Ernst[19] used the random field model and obtained similar correlation values by comparing the single and multiple quantum line-widths of proton pairs. The C value is a measure of the mean distance of approach of the paramagnet to the nuclear spins and expectedly is independent of the paramagnetic ion. Quantitative information about the proton–paramagnetic distances would require more extensive theory[26] and a complete treatment of the spectral densities. From the values of B1, B2 and C obtained above and from the expression for RLLC(ERF), we calculated the ERF contributions to LLCs of paramagnetic ions at various concentrations. These ChemPhysChem 2013, 14, 3977 – 3981
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Table 2. The calculated rms values of random fields B using R1(avg) and extent of correlation C of the random fields using RLLS(ERF) at the two nuclear sites for various concentrations of Cu2 + and Mn2 + . Experimental measurements gave the longitudinal relaxation rate R2. Using Equation (3), with the approximation of equal rms amplitudes B1 = B2 = B, which is justified because the relaxation rates at the two spins are experimentally found to be nearly equal, the rms value of the random magnetic field B was determined. The extent of correlation of the random fields, C, at the two nuclear sites was determined from experimental values of RLLS using Equation (4) and the rms value of the random magnetic fields determined above. All the calculations were done under the condition of extreme narrowing j1(0) = j1(w0) = j1(2w0) and a rotational correlation time tc of 50 ps. B [mT]
C
Conc [mm]
Cu2 +
Mn2 +
Cu2 +
Mn2 +
0.0 0.1 0.2 0.3 0.4
1067 1210 1316 1394 1418
1067 1545 1783 2191 2329
0.806 0.812 0.825 0.830 0.837
0.806 0.815 0.844 0.868 0.872
were found to increase linearly with increase in concentration (see Figure 4). The increase in ERF contributions with increase in paramagnets were earlier explained by Bertini and Luchinat.[27] The theoretically obtained values of relaxivity of LLCs are found to be slightly less than experimental values. This small difference is assumed to be due to intramolecular dipole–dipole relaxation. The comparison of relaxation behavior of LLCs with various other experiments like T1, T2 and T11 is made to study the external random field contributions on their relaxation mechanisms. We found that the relaxivity of LLCs is higher than any of the experiments involving SQC. We envisage that it could serve as a potential means for discriminating tissues in MRI.[28] The molecular parameters on which the lifetime of LLCs depends are far from understood. Further studies on the relaxation behavior of LLCs are required to fully exploit its usefulness.
Figure 4. The variation in theoretically determined external random field relaxation rate of LLCs (RLLC(ERF)) with the concentration of paramagnetic ions Mn2 + and Cu2 + in 2,3,6-trichlorobenzaldehyde and its comparison with experimentally obtained relaxation rate of LLCs (RLLC).
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
3. Conclusions The influence of paramagnetic ions, Cu2 + and Mn2 + , on the relaxation behaviour of LLC was studied in a two-spin system 2,3,6-trichlorobenzaldehyde. We observed that in presence of paramagnetic substances, the rate of relaxation of the LLCs is faster than transverse relaxation, as seen from the ratio kLLC/k2, which is greater than unity for both Cu2 + and Mn2 + . The relaxation of LLS on the other hand in case of both of these ions is less than the relaxation of longitudinal magnetization. The addition of Mn2 + has a more pronounced effect than Cu2 + , as seen from the relaxivity ratio ki(Mn2+)/ki(Cu2+), which is greater than 1 for all relaxation mechanisms. The paramagnetic ion induced relaxation of LLC was modelled as external random field fluctuations within the Redfield relaxation formalism. Such an analysis of the experimental observations suggests that the random fields at the two sites are strongly correlated. The hypersensitivity of LLCs to the local field fluctuations at the spin sites due to the addition of paramagnet may be favourable for experiments involving contrast agents in magnetic resonance imaging while its complementary behaviour to LLS may prove useful in other experiments.
Acknowledgements We would like to thank the University Grants Commission (UGC), India for financial support. We thank Prof. M. H. Levitt for helpful comments and discussions. Keywords: long-lived coherences · long-lived states · nmr spectroscopy · paramagnetic relaxation · relaxivities [1] C. N. Banwell, E. M. McCash, Fundamentals of Molecular Spectroscopy, Tata McGraw-Hill, New Delhi, 2002. [2] M. Carravetta, O. G. Johannessen, M. H. Levitt, Phys. Rev. Lett. 2004, 92, 153003. [3] M. Carravetta, M. H. Levitt, J. Am. Chem. Soc. 2004, 126, 6228 – 6229. [4] R. Sarkar, P. Ahuja, P. R. Vasos, G. Bodenhausen, Phys. Rev. Lett. 2010, 104, 53001. [5] R. Sarkar, P. Ahuja, P. R. Vasos, A. Bornet, O. Wagnieres, G. Bodenhausen, Prog. Nucl. Magn. Reson. Spectrosc. 2011, 59, 83 – 90. [6] G. Pileio, M. Carravetta, M. H. Levitt, Phys. Rev. Lett. 2009, 103, 083002. [7] A. Wokaun, R. R. Ernst, Chem. Phys. Lett. 1977, 52, 407 – 412. [8] C. Luchinat, S. Ciurli, NMR of Paramagnetic Molecules, Springer, New York, 1993. [9] F. Bloch, W. W. Hansen, M. E. Packard, Phys. Rev. 1946, 70, 474 – 485. [10] N. Bloembergen, E. M. Purcell, R. V. Pound, Phys. Rev. 1948, 73, 679 – 712. [11] Y. N. Chiu, J. Chem. Phys. 1972, 56, 4882 – 4898. [12] Y. G. Porter, M. R. Wright, Discuss. Faraday Soc. 1959, 27, 18 – 27. [13] V. I. Makarov, I. V. Khmelinskii, Adv. Chem. Phys. 2001, 118, 45 – 98. [14] P. Marzola, S. Cannistraro, Physiol. Chem. Phys. Med. NMR 1986, 18, 263 – 273. [15] J. L. Barnhart, R. N. Berk, M. Andre, Physiol. Chem. Phys. Med. NMR 1985, 17, 53 – 60. [16] T. Theophanides, Int. J. Quantum Chem. 1984, 26, 933 – 941. [17] M. C. D. Tayler, M. H. Levitt, Phys. Chem. Chem. Phys. 2011, 13, 9128 – 9130. [18] M. Carravetta, M. H. Levitt, J. Chem. Phys. 2005, 122, 214505. [19] A. Wokaun, R. R. Ernst, Mol. Phys. 1978, 36, 317 – 341.
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CHEMPHYSCHEM ARTICLES [20] J. A. Wass, “OriginPro 8” to be found under http://www.scientificcomputing.com/articles/2008/02/originpro-8-%E2%80 %94-not-just-graphicsanymore#.UfuFLNJHJ2Y, 2008. [21] B. D. Nageswara Rao, Adv. Magn. Reson. 1970, 4, 271. [22] B. D. Nageswara Rao, Pure Appl. Chem. 1974, 40, 93 – 101. [23] A. Kumar, B. D. Nageswara Rao, J. Magn. Reson. 1972, 8, 1 – 6. [24] T. N. Khazanovich, V. Y. Zitserman, Mol. Phys. 1971, 21, 65 – 82. [25] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, London, 1961. [26] J. Kowalewski, L. Maler, Nuclear Spin Relaxation in Liquids, Taylor and Francis, New York, 2006.
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www.chemphyschem.org [27] I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin-Cummings, San Francisco, 1986. [28] E. Prez-Mayoral, V. Negri, J. S. Padrs, S. Cerdn, P. Ballesteros, Eur. J. Radiol. 2008, 67, 453 – 458. [29] P. W. Atkins, M. J. Clugston, Mol. Phys. 1974, 27, 1619 – 1631.
Received: August 3, 2013 Revised: October 1, 2013 Published online on October 22, 2013
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Paramagnetic Relaxation of Long-Lived Coherences in Solution NMR Maninder Singh, Chinthalapalli Srinivas, Mayukh Deb, and Narayanan D. Kurur*[a] Long-lived coherences (LLCs) are known to have lifetimes much longer than transverse magnetization or single quantum coherences (SQCs). The effect of paramagnetic ions on the relaxation of LLCs is not known. This is particularly important, as LLCs have potential applications in various fields like analytical NMR, in vivo NMR and MR imaging methods. We study here the behaviour of LLCs in the presence of paramagnetic relaxation agents. The stepwise increase in the concentration of the metal ion is followed by measuring various relaxation rates. The effect of paramagnetic ions is analysed in terms of the external random field’s contribution to the relaxation of two coupled protons in 2,3,6-trichlorobenzaldehyde. The LLCs relax
faster than ordinary SQCs in the presence of paramagnetic ions of varying character. This is explained on the basis of an increase in the contribution of the external random field to relaxation due to a paramagnetic relaxation mechanism. Comparison is also made with ordinary Zeeman relaxation rates like R1, R2, R11 and also with rate of relaxation of longlived states RLLS which are known to be less sensitive to paramagnetically induced relaxation. Also, the extent of correlation of random fields at two proton sites is studied and is found to be strongly correlated with each other. The obtained correlation constant is found to be independent of the nature of added paramagnetic impurities.
1. Introduction Despite states and coherences in NMR having longer lifetimes relative to the other forms of spectroscopy,[1] there is a constant quest to increase them. Along these lines, long-lived states and coherences were introduced recently.[2–6] States that are anti-symmetric with respect to spin permutation have long lifetimes because the intramolecular dipole–dipole relaxation, which is the major relaxation mechanism in liquids, is symmetric to particle interchange.[2, 3] The symmetry forbidden coherence between the singlet and central triplet state can be induced by specifically designed pulse sequences.[4, 5] Such coherences have recently been shown to have long lifetimes.[4] The long lifetimes associated with the superposition of quantum states of different symmetry, termed long-lived coherences (LLCs), may be used to reduce line broadening in NMR. Such LLCs have been excited in systems with two homonuclear scalar-coupled spins I = 1/2.[4] The lifetime of an LLC is limited by the interaction of nuclei with other species, including that of unpaired electron spins. The inspiration for this work is the recent developments reported by Sarkar et al.,[4, 5] where they showed that the zeroquantum coherences (ZQCs) between singlet and triplet states in a two-spin system can be excited, although it is symmetryforbidden and unaffected by inhomogeneous broadening.[6, 7] They also reduce the homogeneous broadening effect caused [a] M. Singh, Dr. C. Srinivas, M. Deb, Prof. N. D. Kurur Department of Chemistry Indian Institute of Technology, Delhi Hauz Khas, New Delhi (India) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201300718.
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
by homonuclear dipole–dipole coupling. It was reported that the lifetimes of LLCs is considerably higher than the singlequantum coherences (SQCs). Due to the large difference in the magnetic moment of electrons and protons, paramagnetism has profound effects in NMR as evidenced by various studies of contrast agents in magnetic resonance imaging, in electron relaxation studies operative in various systems, and also in understanding the phenomenon of magnetic coupling in paramagnetic metal centres in various polymetallic systems.[8] These effects are also evident at greater distance from the paramagnetic centre and therefore are of particular interest in the study of biological macromolecules. Paramagnetic substances in liquids are known to reduce the relaxation time of nuclei which are present near it. This was first demonstrated by Bloch, Hansen and Packard[9] for protons in an aqueous solution of Fe3 + ions. It was further studied by Bloembergen, Purcell and Pound[10] for various paramagnetic ions such as Cu2 + and also in the presence of other ions. Relaxation in simple terms refers to the processes by which the nuclear spins and coherence returns to equilibrium. Unlike other spectroscopic methods, in NMR or ESR, the transitions between excited and ground states do not occur spontaneously by direct emission of photons of that energy. Instead, fluctuating magnetic fields that are randomly generated in the environment (by the motion of particles, electric charges and other magnetic dipoles) induce the spin system to undergo transitions. In systems containing paramagnetic ions, one of the main mechanisms of nuclear relaxation is dipole–dipole coupling of nuclei with fluctuating magnetic fields generated by electron magnetic moments. ChemPhysChem 2013, 14, 3977 – 3981
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Paramagnetic species are known to induce singlet-to-triplet conversion in various types of molecules.[11–13] Does their presence affect the relaxation rate of LLCs? If they do, in what manner? Answers to these questions are relevant for possible in vivo applications of LLCs because every living being contains a variety of paramagnetic ions in the organelles.[14–16] Various MRI techniques used for in vivo imaging and the magnetic tracers used for analyzing different biochemical processes currently require the measurement of longitudinal or transverse relaxation rate of diverse molecules present. Can singlet–triplet coherence rate be a useful probe in such measurements? Are they expected to persist for longer or shorter time than single or multiple quantum coherences? In order to characterize the influence of paramagnetic ions on relaxation of LLCs in scalar coupled nuclear spins, we studied the pair of chemically inequivalent spin 1/2 nuclei in 2,3,6-trichlorobenzaldehyde (TCB). Our studies reported here are also influenced by the observation of Tayler et al.[17] that the relaxation behaviour of longlived states (LLSs) in the presence of paramagnetic ions is 2–3 times less sensitive to paramagnetically induced relaxation than normal Zeeman magnetization since the main dipole– dipole relaxation mechanism is highly ineffective for singlet state relaxation.[18] The effect of paramagnetic ions on the relaxation of ZQC in the laboratory frame was earlier studied by Wokaun and Ernst.[19] LLCs are ZQC in the rotating frame. The aim of this paper is to study the relaxation behaviour of these coherences in a spin-1/2 system in the presence of paramagnetic agents.
Figure 1. Pulse sequence used for excitation of long-lived coherences in 2,3,6-trichlorobenzaldehyde (0.01 m solution at 7.1 T or 300 MHz and 300 K). Here d1 is the pre-scan delay which is 3–5 times T1, and the inter-pulse delay t = 1/(2Dn12) where Dn12 is the chemical shift difference between two aromatic protons. tr is the variable time used for spin-locking the continuouswave pulse. The carrier frequency is set in the middle of chemical shift frequencies of two nuclei. The first non-selective (p/2)0 pulse converts initial Zeeman magnetization into (I1yI2y) followed by delay t that converts it into opposite x magnetization (I1xI2x) which was then spin-locked using a resonant strong RF field such as continuous wave (CW), which suppresses the chemical shift difference and instantaneously switches the eigenstates of the Zeeman product basis to a symmetry-adapted singlet–triplet basis. The spin system evolution is governed by an effective Hamiltonian of the form H = 2 p[n1(I1x+I2x) + Dn(I1z+I2z) + J(I1.I2) + (Dn12/2)(I1zI2z)] where Dn is the offset and J is the coupling constant between the two spins.
ing from 0.0 mm to 0.4 mm are plotted in Figures 2 and 3. In the absence of paramagnetic ions, LLC relaxes more slowly than transverse magnetization. As the concentration of metal ions increases, the relaxation rate increases. This increase in the relaxation rate is due to the effect of fluctuating magnetic fields generated by unpaired electron density on the metal
Experimental Section All the experiments were performed on a BRUKER AV-III spectrometer at a frequency of 300 MHz for protons. The sample used was (0.01 m) 2,3,6-trichlorobenzaldehyde in [D6]DMSO solvent. The experiments were done at room temperature and without degassing the sample. The pulse sequence used to measure the long-lived coherence time constant TLLC for inequivalent spin pairs in high magnetic field is shown in Figure 1. A resonant field of amplitude corresponding to a nutation frequency of wrf was used during the locking interval. The relaxation rate of LLC follows Equation (1):[4] IðLLCÞ ¼ I0 cosð2 pJtr Þexpðtr =T LLC Þ
ð1Þ
where tr is the variable time for spin locking, I(LLC) and I0 represents the intensity of magnetization at time tr = t and 0 respectively. Here J is the coupling constant and TLLC is the lifetime of LLC. The relaxation times T1 and T2 were measured by standard inversion recovery (IR) and Carr–Purcell–Meiboom–Gill (CPMG) pulse sequences while the LLS was created and measured using the pulse sequence introduced by Levitt and co-workers.[3] All the relaxivity values were obtained by fitting the data to a linear equation in OriginPro 8.[20]
2. Results and Discussion The measured relaxation rate constants, Rx ( = 1/Tx where Tx is the relaxation time constant) for metal ion concentration rang 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 2. The experimental relaxation rates (R1, R2, R11, RLLS and RLLC) of 2,3,6trichlorobenzaldehyde protons as a function of concentrations of Cu2 + ions (0.0 mm to 0.4 mm with a step size of 0.1 mm).
ions with nuclei present nearby. The effect of an increase in the rate constants upon addition of Mn2 + ions to the sample is much more prominent than that of Cu2 + additions. We attribute this to the five unpaired electrons of the Mn2 + in the 3d orbital compared to one unpaired electron of Cu2 + . The variation in the rate constants R1, R2, RLLS, RLLC and R11 with concentration of paramagnetic ions, obeys the following linear equation [Eq. (2)]: Ri ð½XÞ ¼ k i ½X þ Ri ð0Þ
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www.chemphyschem.org spins present nearby. These randomly fluctuating magnetic fields interact with nuclear spins and this resonant interaction results in the relaxation of nuclear spins. Relaxation due to unpaired electrons is much faster compared to that due to nuclear spin since the gyromagnetic ratio of the electron is much larger than that of the nuclear spin. The relaxivity ratios kLLC/k2 and kLLS/k1 can be interpreted roughly by assuming the two protons each experience randomly fluctuating magnetic fields generated by paramagnetic centers.[18, 25] Tayler and Levitt analyzed the relaxation of LLS by paramagnetic interactions in terms of randomly fluctuating magnetic fields using the Redfield formalism.[18] The rate expression for RLLS(ERF), R1(ERF) is given by Equations (3) and (4):
Figure 3. The experimental relaxation rates (R1, R2, R11, RLLS and RLLC) of 2,3,6trichlorobenzaldehyde protons as a function of concentrations of Mn2 + ions (0.0 mm to 0.4 mm with a step size of 0.1 mm).
where [X] is the concentration of the paramagnetic ion, Ri(0) and Ri([X]) are the rate constants of type i at 0 and [X] concentration respectively, and ki is the change in the relaxation rate, that is, relaxivity. It is pertinent to point out that the samples were not degassed and hence the relaxation rate constants have the contribution of dissolved paramagnetic impurities. In the absence of paramagnet RLLC is lower than R2 as expected. On addition of Cu2 + it soon overtakes R2. In contrast, RLLS relaxes more slowly than R1 and is immune to the addition of paramagnet. In the case of Mn2 + , the increase in RLLC is more pronounced than in Cu2 + . The relaxivities of the various rates are tabulated in Table 1. On comparing the effect of Mn2 + and Cu2 + metal ions on all relaxivities (k1, k2, k11, kLLS, kLLC), it is observed that the Mn2 +
Table 1. Relaxivities of 2,3,6-trichloro benzaldehyde protons in the presence of Cu2 + and Mn2 + ions at room temperature (298 K) at a field of 7.1 T. X 2+
Cu Mn2 +
k1
k2
kLLS
kLLC
0.41 0.04 1.88 0.17
0.40 0.04 2.22 0.09
0.07 0.015 0.69 0.14
0.60 0.05 3.29 0.31
effect is five times larger than that of Cu2 + . The relaxivities are proportional to the square of the magnetic moment of the metal ion, which depends on the number of unpaired electrons.[17, 25, 29] From Figures 2 and 3, it is concluded that the relaxivity for LLC is highest while that of LLS is the lowest. The ratio kLLC/kLLS (see Table 1) shows that the singlet–triplet coherences are more sensitive to paramagnetic relaxation than singlet states by a factor of approximately 5 to 10. The values are given in the Supporting Information (Table S1). One approach to understand the factors responsible for the increase in the relaxation rate in presence of paramagnetic ions is to model them as external random fields. External random fields[21–24] include the dipolar interactions from all other intermolecular spins, CSA and also the unpaired electron 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
R1 ðERFÞ ¼ gH 2 ðB1 2 þ B2 2 Þj1 ðw0 Þ
ð3Þ
RLLS ðERFÞ ¼ 2 gH 2 ðB1 2 þ B2 2 2 CB1 B2 Þ½j1 ð0Þ þ 2 j1 ðw0 Þ=3
ð4Þ
By a similar analysis, we find that the relaxation rate of longlived coherences, RLLC(ERF), is given by Equation (5): RLLC ðERFÞ ¼ ðgH 2 =4ÞðB1 2 þ B2 2 Þ½j1 ð0Þ þ 2 j1 ðw0 Þ ðgH 2 =2ÞCB1 B2 j1 ð0Þ
ð5Þ
where Bi is the root mean square (rms) value of the random fields at the nuclear site i (= 1, 2), Bi = hBi.Bii1/2. The random field at nuclear site i is denoted by Bi, and C = hB1.B2i/B1B2 represents the extent of correlation of the fluctuating magnetic fields at the two proton sites. All the relaxation rates depend on the Bi and C. Also, gH represents the magnetogyric ratio of the proton and j1(w0) is the non-normalized rank 1 spectral density at frequency w0. Under the condition of extreme narrowing j1(0) = j1(w0) = j1(2w0) and equal rms field amplitudes B1 = B2, the ratios of relaxivities depend upon field correlation C.[17] The RMS values of random fields at the two nuclear sites were calculated and the correlation constant C at different concentrations of paramagnetic ions is obtained by using the above equations for R1(ERF) and RLLS(ERF) (see Table 2). Calculating C from RLLS(ERF) rather than RLLC(ERF) is advantageous since the LLS is not affected by intramolecular dipolar relaxation. As noted first by Redfield[25] the random fields at nuclear sites increase in proportion to the increase in the concentration of paramagnetic ion. The correlation constant is fairly independent of the nature of paramagnetic ions. Earlier, Wokaun and Ernst[19] used the random field model and obtained similar correlation values by comparing the single and multiple quantum line-widths of proton pairs. The C value is a measure of the mean distance of approach of the paramagnet to the nuclear spins and expectedly is independent of the paramagnetic ion. Quantitative information about the proton–paramagnetic distances would require more extensive theory[26] and a complete treatment of the spectral densities. From the values of B1, B2 and C obtained above and from the expression for RLLC(ERF), we calculated the ERF contributions to LLCs of paramagnetic ions at various concentrations. These ChemPhysChem 2013, 14, 3977 – 3981
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Table 2. The calculated rms values of random fields B using R1(avg) and extent of correlation C of the random fields using RLLS(ERF) at the two nuclear sites for various concentrations of Cu2 + and Mn2 + . Experimental measurements gave the longitudinal relaxation rate R2. Using Equation (3), with the approximation of equal rms amplitudes B1 = B2 = B, which is justified because the relaxation rates at the two spins are experimentally found to be nearly equal, the rms value of the random magnetic field B was determined. The extent of correlation of the random fields, C, at the two nuclear sites was determined from experimental values of RLLS using Equation (4) and the rms value of the random magnetic fields determined above. All the calculations were done under the condition of extreme narrowing j1(0) = j1(w0) = j1(2w0) and a rotational correlation time tc of 50 ps. B [mT]
C
Conc [mm]
Cu2 +
Mn2 +
Cu2 +
Mn2 +
0.0 0.1 0.2 0.3 0.4
1067 1210 1316 1394 1418
1067 1545 1783 2191 2329
0.806 0.812 0.825 0.830 0.837
0.806 0.815 0.844 0.868 0.872
were found to increase linearly with increase in concentration (see Figure 4). The increase in ERF contributions with increase in paramagnets were earlier explained by Bertini and Luchinat.[27] The theoretically obtained values of relaxivity of LLCs are found to be slightly less than experimental values. This small difference is assumed to be due to intramolecular dipole–dipole relaxation. The comparison of relaxation behavior of LLCs with various other experiments like T1, T2 and T11 is made to study the external random field contributions on their relaxation mechanisms. We found that the relaxivity of LLCs is higher than any of the experiments involving SQC. We envisage that it could serve as a potential means for discriminating tissues in MRI.[28] The molecular parameters on which the lifetime of LLCs depends are far from understood. Further studies on the relaxation behavior of LLCs are required to fully exploit its usefulness.
Figure 4. The variation in theoretically determined external random field relaxation rate of LLCs (RLLC(ERF)) with the concentration of paramagnetic ions Mn2 + and Cu2 + in 2,3,6-trichlorobenzaldehyde and its comparison with experimentally obtained relaxation rate of LLCs (RLLC).
2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
3. Conclusions The influence of paramagnetic ions, Cu2 + and Mn2 + , on the relaxation behaviour of LLC was studied in a two-spin system 2,3,6-trichlorobenzaldehyde. We observed that in presence of paramagnetic substances, the rate of relaxation of the LLCs is faster than transverse relaxation, as seen from the ratio kLLC/k2, which is greater than unity for both Cu2 + and Mn2 + . The relaxation of LLS on the other hand in case of both of these ions is less than the relaxation of longitudinal magnetization. The addition of Mn2 + has a more pronounced effect than Cu2 + , as seen from the relaxivity ratio ki(Mn2+)/ki(Cu2+), which is greater than 1 for all relaxation mechanisms. The paramagnetic ion induced relaxation of LLC was modelled as external random field fluctuations within the Redfield relaxation formalism. Such an analysis of the experimental observations suggests that the random fields at the two sites are strongly correlated. The hypersensitivity of LLCs to the local field fluctuations at the spin sites due to the addition of paramagnet may be favourable for experiments involving contrast agents in magnetic resonance imaging while its complementary behaviour to LLS may prove useful in other experiments.
Acknowledgements We would like to thank the University Grants Commission (UGC), India for financial support. We thank Prof. M. H. Levitt for helpful comments and discussions. Keywords: long-lived coherences · long-lived states · nmr spectroscopy · paramagnetic relaxation · relaxivities [1] C. N. Banwell, E. M. McCash, Fundamentals of Molecular Spectroscopy, Tata McGraw-Hill, New Delhi, 2002. [2] M. Carravetta, O. G. Johannessen, M. H. Levitt, Phys. Rev. Lett. 2004, 92, 153003. [3] M. Carravetta, M. H. Levitt, J. Am. Chem. Soc. 2004, 126, 6228 – 6229. [4] R. Sarkar, P. Ahuja, P. R. Vasos, G. Bodenhausen, Phys. Rev. Lett. 2010, 104, 53001. [5] R. Sarkar, P. Ahuja, P. R. Vasos, A. Bornet, O. Wagnieres, G. Bodenhausen, Prog. Nucl. Magn. Reson. Spectrosc. 2011, 59, 83 – 90. [6] G. Pileio, M. Carravetta, M. H. Levitt, Phys. Rev. Lett. 2009, 103, 083002. [7] A. Wokaun, R. R. Ernst, Chem. Phys. Lett. 1977, 52, 407 – 412. [8] C. Luchinat, S. Ciurli, NMR of Paramagnetic Molecules, Springer, New York, 1993. [9] F. Bloch, W. W. Hansen, M. E. Packard, Phys. Rev. 1946, 70, 474 – 485. [10] N. Bloembergen, E. M. Purcell, R. V. Pound, Phys. Rev. 1948, 73, 679 – 712. [11] Y. N. Chiu, J. Chem. Phys. 1972, 56, 4882 – 4898. [12] Y. G. Porter, M. R. Wright, Discuss. Faraday Soc. 1959, 27, 18 – 27. [13] V. I. Makarov, I. V. Khmelinskii, Adv. Chem. Phys. 2001, 118, 45 – 98. [14] P. Marzola, S. Cannistraro, Physiol. Chem. Phys. Med. NMR 1986, 18, 263 – 273. [15] J. L. Barnhart, R. N. Berk, M. Andre, Physiol. Chem. Phys. Med. NMR 1985, 17, 53 – 60. [16] T. Theophanides, Int. J. Quantum Chem. 1984, 26, 933 – 941. [17] M. C. D. Tayler, M. H. Levitt, Phys. Chem. Chem. Phys. 2011, 13, 9128 – 9130. [18] M. Carravetta, M. H. Levitt, J. Chem. Phys. 2005, 122, 214505. [19] A. Wokaun, R. R. Ernst, Mol. Phys. 1978, 36, 317 – 341.
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CHEMPHYSCHEM ARTICLES [20] J. A. Wass, “OriginPro 8” to be found under http://www.scientificcomputing.com/articles/2008/02/originpro-8-%E2%80 %94-not-just-graphicsanymore#.UfuFLNJHJ2Y, 2008. [21] B. D. Nageswara Rao, Adv. Magn. Reson. 1970, 4, 271. [22] B. D. Nageswara Rao, Pure Appl. Chem. 1974, 40, 93 – 101. [23] A. Kumar, B. D. Nageswara Rao, J. Magn. Reson. 1972, 8, 1 – 6. [24] T. N. Khazanovich, V. Y. Zitserman, Mol. Phys. 1971, 21, 65 – 82. [25] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, London, 1961. [26] J. Kowalewski, L. Maler, Nuclear Spin Relaxation in Liquids, Taylor and Francis, New York, 2006.
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www.chemphyschem.org [27] I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin-Cummings, San Francisco, 1986. [28] E. Prez-Mayoral, V. Negri, J. S. Padrs, S. Cerdn, P. Ballesteros, Eur. J. Radiol. 2008, 67, 453 – 458. [29] P. W. Atkins, M. J. Clugston, Mol. Phys. 1974, 27, 1619 – 1631.
Received: August 3, 2013 Revised: October 1, 2013 Published online on October 22, 2013
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