Article pubs.acs.org/JPCA
Scalar Relaxation of the Second Kind: A Potential Source of Information on the Dynamics of Molecular Movements. 1. Investigation of Solution Reorientation of N‑Methylpyridone and 1,3Dimethyluracil Using Measurements of Longitudinal Relaxation Rates in the Rotating Frame Adam Gryff-Keller* and Dominika Kubica Faculty of Chemistry, Warsaw University of Technology, ul. Noakowskiego 3, PL-00-664 Warsaw, Poland ABSTRACT: The practical utility of the method of retrieving the relaxation rate of a quadrupole nucleus via the scalar relaxation of the second kind (SC2) of an I = 1/2 spin nucleus has been considered once again. The study was motivated by the fact that such data are frequently very useful in investigations of reorientational movements of molecules in solutions. At the same time, the parameters describing spin− spin and quadrupolar couplings, necessary in such studies, have become relatively easily accessible owing to a remarkable progress in theoretical methods. It was shown that even in the case of small N−C coupling constants (1J = 7−8 Hz) the classical method of approaching SC2 relaxation effects by measurements of the longitudinal relaxation rates in the rotating frame, although somewhat tedious, can yield acceptably accurate results. The whole procedure has been successfully applied in the investigation of molecular movements of N-methylpyridone (1) and 1,3-dimethyluracil (2) in acetone solution.
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INTRODUCTION In studies of molecular movements with the use of nuclear spin relaxation measurements, the dipolar relaxation rates of protonated carbons are most frequently used as a source of information. Also the longitudinal and transverse quadrupole relaxation rates (R1,Q and R2,Q) carry similar valuable information.1−3 The quadrupole relaxation mechanism is usually very effective, and contributions of other relaxation paths to the overall, experimentally accessible relaxation rate can safely be neglected during the data interpretation. Undoubtedly, it is an advantage of the quadrupole mechanism over the dipolar mechanism in the studies of molecular movements. In the past, a wider application of R1,Q and R2,Q measurements was prevented mainly because of limited accessibility of quadrupole coupling parameters (quadrupole coupling constant, e2Qq, and asymmetry parameter, ηQ) or electric field gradient (EFG) tensors, which are necessary for interpretation of the RQ data. Moreover, the direct measurements of RQ are difficult, with the exceptions of deuterium and lithium isotopes and cases of high symmetry of the electronic surrounding of the quadrupole nucleus. In most cases transverse relaxation of quadrupole nuclei is rapid and their signals are very broad. As a result, the measurements of liquid phase spectra of the nuclei such as those of chlorine, bromine, or iodine isotopes are usually very difficult. When several quadrupole nuclei of the same isotope occur in the investigated molecule, the spectra are usually useless. Even for 14N, the most © 2012 American Chemical Society
interesting quadrupole nucleus for organic and bioorganic chemistry, precise separation of more than two signals by line shape analysis is usually very difficult. In the cases when NMR spectra of the quadrupole nucleus are uninterpretable, the desired RQ values can sometimes be retrieved by measurements of the rate of the scalar relaxation of the second kind (RSC2) of the neighboring I = 1/2 nucleus.1,2,4 To use this method, however, the value of the involved spin− spin coupling constant has to be known. That is probably why this attractive procedure was used rather scarcely in the past. Nowadays, both the electric field gradient tensors and spin− spin coupling constants can be calculated using theoretical methods.5−8 Thus, the way of investigating the kinetics of molecular movements via scalar relaxation of the second kind and quadrupole relaxation seems to be open now. There are three methods of retrieving RSC2 data from NMR experiments. The contribution of the longitudinal relaxation R1,SC2 can be measured for carbon nuclei bonded to bromine or iodine and probably for many other systems at sufficiently low magnetic fields. The transverse R2,SC2 relaxation is much more common, and its effect can be observed as signal broadening, which in convenient circumstances can be monitored by the transverse relaxation rate measurements or, equivalently, by line Received: June 29, 2012 Revised: September 5, 2012 Published: September 12, 2012 9632
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calculation stages using the polarizable continuum model (PCM) of Tomasi et al.12 and defining the cavity according to the UAKS scheme.11 The computer program aimed at retrieving rotational diffusion parameters from relaxation data was described elsewhere.13 Other programs for data fitting and line shape analyses were based on the Newton−Raphson algorithm of iterative nonlinear least-squares sum minimization.
shape analysis. Owing to the scalar relaxation of the second kind, the R1,Q parameter can also be retrieved from the measurements of longitudinal relaxation in the rotating frame (R1ρ), of the signals of the I = 1/2 nucleus indirectly coupled to the quadrupole nucleus.1,2,4 Below, we discuss the possibilities and limitations of the last methodology and present the results of applying it to the molecules of N-methylpyridone and 1,3dimethyluracil (Figure 1). Other possibilities will be discussed in subsequent publications of this series.
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RESULTS AND DISCUSSION SC2 Relaxation Mechanism. It is well-known that the spectral pattern of an I = 1/2 nucleus A scalar-coupled to another nucleus X depends on the spin and relaxation rate of the latter. For slow relaxation of spin X (R1X ≪ JAX; JAX is an involved spin−spin coupling constant) the multiplet of 2IX + 1 equally intense components is observed in the NMR spectrum of A. For R1X comparable to JAX the characteristic broadenings and, finally, the collapse to one broad signal of A are observed. Finally, the spectrum of A becomes a singlet showing residual broadening. Pople was the first one who described quantitatively and discussed these changes for the most important case of quadrupole relaxation of nucleus X.14 A more general theory valid for any combination of various relaxation mechanisms was elaborated by Werbelow.15 In his fundamental monograph Abragam1 found out that in the limiting case of fast X relaxation (R1X ≫ JAX) the X nucleus can be conceptually incorporated into the thermal lattice surrounding the A nucleus, and that residual effects experienced by the A nucleus can be described as a new relaxation mechanism, which he named the scalar relaxation of the second kind.1
Figure 1. Investigated molecules: N-methylpyridone (1) and 1,3dimethyluracil (2).
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EXPERIMENTAL AND THEORETICAL METHODS The investigated compounds N-methylpyridone (1) and 1,3dimethyluracil (2) as well as acetone-d6 were commercial products (Aldrich). NMR measurements were performed for 1 M solutions of 1 and 2 in acetone-d6. Appropriate portions of these solutions were placed in 5 mm o.d. NMR tubes, which were degassed and sealed. 1H NMR, 13C NMR, and 14N NMR spectra were recorded at B0 = 11.7 T magnetic field using a VNMRS500 spectrometer, at the temperature stabilized at 25 °C. The longitudinal 13C relaxation times were measured by the standard inversion−recovery technique,9 using a three-parameter fit to retrieve relaxation parameters from the signal intensity vs recovery delay dependences. The 13C[1H] nuclear Overhauser effect (NOE) enhancement factors were determined using the dynamic NOE experiment based on the analysis of signal intensities in the spectra recorded with variable decoupling time. Decoupling executed during the delay just before the observing pulse (and acquisition) was preceded by a constant, sufficiently long resting time. During elaboration of these data, a two-parameter fitting procedure was applied in which the values of the relaxation times known from the former experiment were kept constant. The 13C longitudinal relaxation rates in the rotating frame of the methyl group carbons were measured by a standard spinlock technique.10 The strengths of the locking magnetic fields applied, as measured by the length of the π/2 pulse, were in the range 0.18−1.8 ms. Measurements were performed with onresonance continuous-wave proton decoupling. In order to determine a single T1ρ value, the signal intensities were measured for seven different locking times. All quantum chemical calculations were performed using the Gaussian 03 program.11 The molecular geometry optimization and the spin−spin constant calculations were performed using the DFT method with the B3LYP functional and the 6-311++G (2d,p) basis set. The electric field gradient calculations were made for previously optimized molecular geometries with the DFT/B3PW91/6-311+G (df,pd) method following Bailey.7 The impact of the solvent was taken into account at all
R1A,SC2 = (8/3)π 2JAX 2 IX(IX + 1)[R 2X /(R 2X 2 + Δω 2)] (1)
R 2A,SC2 = (4/3)π 2JAX 2 IX(IX + 1) [1/R1X + R 2X /(R 2X 2 + Δω 2)]
(2)
where Δω is the difference of the Larmor frequencies of A and X. It is noteworthy that Abragam’s contribution to the problem was much more than a clever description of the limiting case, as under convenient circumstances (R2X2 comparable to or greater than Δω2) the scalar relaxation of the second kind can contribute to not only the transverse but also the longitudinal relaxation of the nucleus A. Formulas 1 and 2 are valid only in the extreme narrowing limit (ω0τc ≪ 1). This is the case we are discussing below. For slower molecular motions a much more sophisticated approach is necessary.16,17 A recommended method for investigating the SC2 relaxation rate of nucleus A is based on measurements of the longitudinal relaxation rates in the rotating frame.2,4 After neglecting some unimportant (in most cases) terms, the dependence of an experimentally measured parameter R1ρ can be expressed as a function of the applied spin-lock field strengths (ωSL):2,4 R1Aρ = R 0 + (1/3)IX(IX + 1)(2πJAX )2 R1X,Q /[R1X,Q 2 + ωSL 2]
(3)
where in the idealized case R0 should be equal to the transverse relaxation rate of the nucleus A. However, in practice this parameter tends to absorb various experimental imperfections, such as those caused by nonideal proton decoupling, etc. In the 9633
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past the measurements of R1ρ as a function of ωSL were most frequently used for determination of the spin−spin coupling constants between I = 1/2 nuclei and quadrupole nuclei,4,18,19 but there are no precautions to using them to measure the relaxation rates of the fast relaxing nuclei. The only problem to be discussed in every case is the accuracy of such a procedure. As the above dependence is nonlinear, eq 3 used to be transformed into a form suitable for data analysis based on a linear regression between appropriate new variables. Such an approach may be helpful in overcoming some numerical problems.4,20 Application of the nonlinear least-squares (nls) procedure should essentially provide a possibility of simultaneous determination of all three unknown parameters R0, JAX, and R1,Q. The numerical tests described below have shown that, unfortunately, such an approach can lead to completely false results, at least for the experimental conditions we have encountered in the case of N-methylpyridone and 1,3dimethyluracil. It is to be stressed that this fact reflects a limited information content of the R1ρ data unavoidably burdened by experimental errors and, in our case, has nothing to do with convergence of the nls procedure. Determination of one R1,Q value from the series of R1ρ measurements could hardly be classified as an efficient procedure. The situation is different, however, when in one series of rotating frame measurements several R1,Q parameters are measured simultaneously. Such a determination can be accomplished provided that the offset effects are taken into account during the data elaboration.2 Relaxation Rates of 14N Nuclei of 1 and 2. The quadrupole relaxation rates of 14N nuclei in our objects dissolved in acetone-d6 can conveniently be determined on the basis of the line widths observed in their 14N NMR spectra. These line widths have been measured for 1 and 2 by performing line shape fitting to avoid possible errors due to signal overlapping or arbitrary choice of the baseline level. The line widths (w) determined were reproducible to within 1 Hz. Because of the predominance of the quadrupole relaxation mechanism for 14N nuclei and rapid molecular motions (extreme narrowing), the appropriate relaxation rates can be calculated as R1,Q = R 2,Q = πw
Figure 2. Dependence of the longitudinal rotating-frame relaxation rates of 13C nuclei in N-methyl groups of 1 and 2 on the strength of the spin-lock magnetic field represented by experimental points and the best-fit curves when adjusting R1,Q and R0 values.
parameters are strongly correlated and that our data set does not ensure a reliable simultaneous determination of their values. On the other hand, two other pairs of unknowns, either JAX and R0 or R1,Q and R0, can be determined quite reliably, provided that the value of the third parameter is kept constant during the fitting procedure. Table 1 contains the results of the numerical analyses of the R1ρ = f(ωSL) dependences performed in two variants. In the first we adjusted the values of R1X,Q and R0, whereas the JAX constant was fixed at the value calculated theoretically. In the second, JAX and R0 were adjusted keeping R1X,Q fixed at the value determined from the 14N line width (see below). Both variants allowed very good reproduction of the experimental R1ρ data (Figure 2). We have found that, despite the small value of 1J(13C,14N), the 14N relaxation rates determined for 1 and 2 remain in acceptable agreement with the values obtained on the basis of 14N line widths (Table 1). Theoretical Calculations of Spin−Spin and Quadrupole Coupling Constants. Another question that remains to be clarified is the accuracy of the theoretically calculated values of spin−spin coupling constants and its influence on the overall procedure of R1,Q determination. The form of eq 3 suggests that the relative error of J results in a twice as large error of the determined R1,Q value. A simple numerical simulation fully confirms this supposition. As it concerns the accuracy of the theoretical JAX values, there is no doubt that it depends on the level of the theoretical method applied. Particularly meaningful is the quality of the basis set used. Some authors recommend usage of basis sets augmented with functions enabling better description of the regions at the shortest distances from the nuclei of interest.5,21,22 Enlargement of the basis set strongly affects the computational effort, which may be troublesome for larger molecules. For purposes of this work we have checked whether a more or less standard level of theory used in NMR calculations, such as DFT B3LYP/6-311++G(2d,p) with PCM,23−25 could yield sufficiently good results for rigid compounds analogous to 1 and 2. Comparison of the calculated results for formamide, pyridine, 2,6-dimethylpyridine, and some uracil derivatives with the precise experimental J data available in the literature26−28 shows divergences smaller than 0.3 Hz, which after performance of the linear regression reduce to less than 0.2 Hz (Table 2). It is a surprisingly good result. Only one data point deviates by 0.4 Hz, but one cannot be sure that the fault lies in this case on the side of the calculations.
(4)
The method is very convenient and precise but, unfortunately, can hardly be applied for larger molecules, for viscous solutions, and for molecules possessing several nitrogen atoms. The data obtained for 1 and 2 are an excellent basis for checking the effectiveness of the method applicable in a more general case, based on the analysis of R1ρ vs ωSL dependence. Since there are many interesting objects for which the 14N line widths cannot be directly measured, we have used also this alternative method to determine relaxation rates of 14N nuclei in the investigated compounds. Namely, we measured the longitudinal relaxation rates in the rotating frame (R1ρ) for Nmethyl group carbons as a function of the spin-lock field strengths, ωSL (Figure 2). Then, we took advantage of the functional dependence, eq 3, and analyzed these data using the nonlinear least-squares fitting procedure. As mentioned, the attempt at simultaneous fitting of all three unknown parameters has resulted in perfect reproduction of experimental data by a theoretical curve, but it has yielded completely false parameter values. A Monte Carlo test performed for the simulated data, close to our experimental ones, with the assumption of 10% errors for particular R1ρ values, has shown that JAX and R1,Q 9634
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Table 1. Results of the Least-Squares Analysis of R1ρ(ωSL) Dependencesa nitrogen N-methylpyridone N-1 1,3-dimethyluracil N-3 1,3-dimethyluracil
J(14N,13C) [Hz]
T1,Q(14N) [s]
R1,Q(14N) [s−1]
errorb [%]
T0 [s]
R0 [s−1]
errorb [%]
7.12 6.75 ± 0.06 7.97 8.16 ± 0.21 7.49 7.53 ± 0.20
0.00309 0.0027 0.00128 0.0010 0.00130 0.0011
324 370 781 1000 769 909
2.3 − 9.4 − 14.6 −
5.62 5.66 3.78 4.46 4.03 4.37
0.178 0.177 0.265 0.224 0.248 0.229
1.4 1.4 4.8 6.5 6.7 6.9
1
a During particular runs of the fitting procedure the values given in italics (either the theoretically calculated value of 1J(14N,13C) or the value of T1,Q(14N) determined from the 14N NMR line widths) were kept constant. bError = (ΔR/R)·100% = (ΔT/T)·100%.
in the literature,26 and for compounds 1 and 2, are collected in Table 3. These results confirm once again the effectiveness of Bailey’s method and simultaneously show that it is very important to take into account the impact of the solvent in such calculations, especially in the case of hydroxylic solvents. In all cases the main axis of the EFG tensor is perpendicular to the molecular symmetry plane. The small ηQ values point out that the interaction tensors for 1 and 2 are approximately axially symmetrical. In the input to our computer program elaborating relaxation data,14 the whole (undiagonalized) EFG tensors in the molecular frame of axes are used. Molecular Reorientation. Also in the case of Nmethylpyridone and 1,3-dimethyluracil, investigated in this work, the basic experimental data allowing description of molecular motions are dipolar relaxation rates of 13C nuclei of protonated carbons. The longitudinal relaxation rates for all carbons have been determined by the conventional inversion− recovery and dynamic NOE experiments. The contributions of the dipolar mechanism to the overall relaxation, R1, for particular carbons have been calculated by a simple formula:
Table 2. Comparison of the Theoretically Calculated [B3LYP/6-311++g(2d,p), PCM] 14N−13C Spin−Spin Coupling Constants with Experimentally Determined Values of These Parameters in Formamide, Pyridine and Uracil Derivatives, and Compounds 1 and 2, Investigated in This Work 1
J(14N,13C) [Hz]
compound formamide N-methylpyridone (1) N1−CH3 pyridine N−C2 N−C3 N−C4 2,6-dimethylpyridine N−C2 N−C3 N−C4 N−C5 uracil N1−C6 N3−C4 N1−C2 1-methyluracil N1−C6 3-methyluracil N1−C6 1,3-dimethyluracil (2) N1−C6 N1-CH3 N3-CH3 1-methyluracil monoanion N1−C6
experimentala
calculated
10.57
10.66
6.75
7.12
−0.52 −1.8 2.7
−0.86 −1.8 2.76
0.7 −1.9 1.7 6.98
0.4 −1.94 1.71 7.04
8 6.1 12
8 5.9 12.2
9.1
8.6
8.3
8
8.7 8.16 7.53
8.6 7.97 7.49
9.1
9.1
R1,DD = R1
η ηmax
(5)
where η is the NOE coefficient. Its maximum value, ηmax, in the extreme narrowing limit amounts to 1.988 for the 13C[1H] pair.31 The data obtained this way are collected in Table 4 together with R1,Q for 14N nuclei. It is to be realized that R1,DD are burdened with errors of R1 and η determinations. Moreover, during the interpretation of R1,DD the vibrational corrections to interatomic distances have to be taken into account. In our analysis we assumed 3% elongation of C−H bonds in 1 and 2 compared to their optimum equilibrium values.32−34 The collected relaxation data allow us to describe reorientational motion of the molecules of 1 and 2 in the investigated solutions in terms of rotational diffusion parameters.35 The crude, but simplest, approach has involved treatment of the molecule as a rigid spherical top and description of the reorientation by a single diffusion parameter or reorientation correlation time (Table 5). Such results should be and actually are roughly reproduced by simple hydrodynamic models. Actually, the investigated molecules are planar rotors with one of the principal axes of the rotational diffusion tensor (z-axis) perpendicular to the molecular symmetry plane. The reorientation of such objects in solutions may be described either as the rotational diffusion of a symmetrical top, defined by 0z direction and two diffusion coefficients (Dz and D⊥) or, more adequately, within the four-parameter reorientation model.35 In the latter case, apart from three diffusion coefficients (Dx, Dy, Dz), one angle parameter defining the directions of two in-plane diffusion axes has to be determined.
a
The values for formamide, pyridine derivatives, and uracil derivatives are taken from refs 26, 27, and 28, respectively, whereas data for compounds 1 and 2 originate from relaxation measurements (this article, Table 1).
Retrieving information on molecular motions from RQ data yet demands the knowledge of the values of parameters describing quadrupole interactions of the involved nuclei with their surroundings. There are numerous reports on successful theoretical calculations of EFG tensors and quadrupole coupling parameters for nuclei in various molecules.7,8,12,29,30 Especially convincing are the results of Bailey,7 who found a correcting factor that enables achieving precise values of e2Qq for nitrogen nuclei from theoretically calculated EFG data. The results obtained in this work with the aid of exactly the same method for formamide, which has been thoroughly investigated 9635
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Table 3. Theoretically Calculateda and Experimentally Determined Quadrupole Coupling Constants (e2Qq in MHz) and Asymmetries of EFG Tensors for 14N Nuclei in Formamide (FA), N-Methylpyridone (1), and 1,3-Dimethyluracil (2) calculated
experimental
compound
medium
e2Qq
ηQ
exptl method
e2Qq
ηQ
FA FA FA dimer 1 1 1 1 1 1 1·2MeOH 1·2H2O N1 of 2 N1 of 2 N3 of 2 N3 of 2
gas water water gas acetone CCl4 toluene methanol water methanol water gas acetone gas acetone
3.95 3.22 2.81 2.62 2.46 2.55 2.55 2.34 2.33 2.17 2.18 3.68 3.47 3.44 3.38
0.026 0.095 0.262 0.229 0.187 0.21 0.21 0.159 0.157 0.12 0.116 0.055 0.047 0.115 0.109
MWb LC NMRd R1 NMR
3.85c 2.6−3.2c 2.84c,e
0.028c
R1 NMRf
2.55e,f
R1 NMRf
3.36e,f
R1 NMRf
3.20e,f
a
7
2
14
Following the procedure of Bailey, the corrected e Qq values in MHz for N nuclei were calculated as 3.0331(3/2)eQz, where the Qz component is given in au.13 bMicrowave spectroscopy. cReference 26. dNuclear magnetic resonance spectroscopy in liquid crystalline solutions. eThe determined value of e2Qq[1 + (Q2/3)]1/2 is given. fThis work; the value was based on the 14N line width and dipolar relaxation data interpreted within the spherical top reorientation model.
Table 4. Longitudinal Relaxation Data for 13C Nuclei of the Investigated Compounds in Acetone Solutions carbon N-methylpyridone C2 C3 C4 C5 C6 CH3 1,3-dimethyluracil C2 C4 C5 C6 CH3(N1) CH3(N3)
T1 [s]
R1 [s−1]
η
R1,DD [s−1]
57.73 11.7 9.86 11.19 11.18 13.81
0.017 0.085 0.101 0.089 0.089 0.072
0.34 1.61 1.76 1.59 1.63 1.38
0.003 0.069 0.090 0.071 0.073 0.050
45.65 38.97 7.95 6.83 11.02 11.78
0.022 0.026 0.126 0.146 0.091 0.085
1.24 1.27 1.78 1.63 1.35 1.24
0.014 0.016 0.113 0.120 0.062 0.053
based on such data have to be treated with caution. Moreover, in the investigated molecules all C−H vectors lie in the molecular symmetry plane and all elementary dipolar relaxation mechanisms depend on the same combination of Dz and D⊥ diffusion coefficients.36 This feature in practice precludes application of the symmetrical top model, as separation of these two parameters and determination of their values is impossible. Thus, it is apparent that inclusion of R1,Q data for 14 N nuclei into the analysis is highly desirable for a complete description of the solution reorientation of our objects. In the determinations of the rotational diffusion parameters we used the transverse relaxation rates of 14N nuclei determined directly from the line widths of the appropriate 14N signals, although the data obtained using both methods described above were similar (Table 1). As mentioned above, the EFG tensors of all nitrogens are almost axially symmetrical with their distinguished axes perpendicular to the molecular symmetry planes. This means that the rotation about the z-axis practically does not affect the R1,Q relaxation. Nevertheless, R1,Q is relevant for Dz determination in our case, since quadrupole relaxation depends on the remaining diffusion parameters. For relaxation data analyses the program implemented earlier in our laboratory,13 based on Canet’s formulation of the appropriate formalism connecting relaxation and rotational diffusion parameters,37 was used. The least-squares fitting of the diffusion parameters was convergent in all cases, i.e., for both investigated compounds and for three diffusion models. For the four-parameter model the reproduction of the experimental
Unfortunately, in the case of 1, only three independent R1,DD(C−H) values concerned with the molecular skeleton are available, since two C−H vectors are approximately parallel, whereas in 2 only two R1,DD values for protonated carbons exist. Obviously, the dipolar relaxation of nonprotonated carbons and, in general, relaxation data concerned with dipolar interactions between carbons and protons which are not directly bonded, do provide some additional information. Such relaxation effects are, however, relatively weak and the results
Table 5. Rotational Diffusion Parameters for Molecules of the Investigated Compounds in Acetone Solutions Determined from Analysis of the Relaxation Rates of 13C and 14N Nuclei spherical top
a
symmetrical top
planar rotor
compound
log D0
log Dz
log D⊥
log Dz
log Dx
log Dy
αa [deg]
1-methyluracil 1,3-dimethyluracil
10.6317 10.4628
10.6612 10.406
10.611 10.4806
10.6153 10.433
10.7672 10.5515
10.4715 10.4036
−27.1 −70.3
The angle between the inertia and diffusion principal axis frames. 9636
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Figure 3. Reproduction of the experimental relaxation rates for 1 and 2 by particular reorientation models.
the acetone solution the molecular shape and the electric dipole moment are of importance for molecular reorientation. The results obtained for 1 can be compared with those of Ancian et al.,38 who investigated magnetic relaxation of 1 in four solvents at 305 K. Thus, our diffusion coefficients had first to be rescaled for compensating temperature and viscosity changes. According to the Stokes−Einstein−Debye equation they should be multiplied by a factor x = 1.076 composed of the absolute temperature and viscosity ratios. Since relaxation data were processed in ref 37 under some restrictive assumptions, which can now be avoided, we have interpreted them once again assuming that apart from the dominant dipolar relaxation mechanism the chemical shift anisotropy mechanism introduces some small contribution. Moreover, the quadrupole coupling parameters have been calculated for 1 in particular solutions, taking into account the formation of doubly solvated species in methanol and water suggested by Ancian et al.38 Also, exploiting the procedure used for compounds 1 and 2, we need not assume the coincidence of the diffusion and inertia principal axes. The results of such recalculation are given in Table 6. The diffusion coefficients represent a large spread, which, however, originates mainly from the differences in solvent viscosity. The second part of Table 6 contains the diffusion coefficients renormalized to a common viscosity. Now the spread of values is much smaller. The changes of the reduced diffusion coefficients reflect better the solvent specificity. It is apparent that dx, dy, and dz values are smaller for two hydroxylic solvents expected to form stable solvates of 1, which are actual reorienting species. The dz coefficient for 1 in methanol solution is noticeably smaller than in other solvents. It may reflect the formation of dimethanolate. On the other hand, it should be remembered that the entire mathematical problem is rather poorly conditioned and the numbers obtained are susceptible to the values of quadrupole coupling parameters used in data analysis and to experimental errors of relaxation data. Keeping in mind all the precautions, we can conclude that our results remain in very good agreement with the results of Ancian et al.38
parameters (Table 5) are internally consistent. For molecule 1, which is smaller and has a more elongated shape than 2, the reorientation is faster and more anisotropic. In both cases the fastest-reorientation axis is oriented roughly parallel to the direction defined by N-1 and C-4 atoms. The frames of the principal axes of the appropriate diffusion tensors do not coincide with the frames of the inertia tensors. Apparently, in
CONCLUSIONS Investigation of the molecular reorientation of N-methylpyridone (1) and 1,3-dimethyluracil (2) in acetone solution, performed in this work, as well as various test calculations, prove that measurements of longitudinal relaxation rates in the rotating frame (R1ρ) for 13C carbon nuclei bonded to 14N nitrogen can be effectively used to measure their transverse
relaxation data was perfect and remarkably better than for two simpler models (Figure 3). The obtained rotational diffusion
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Table 6. Rotational Diffusion Coefficients, Dq, and Appropriate Viscosity Renormalized Coefficients, dq, Describing Reorientation of N-Methylpyridone Molecule in Various Solvents at 305 Ka Dq [1010 s−1]
dq [1010 s−1]
solvent
ν [cP]
Dx
Dy
Dz
α [deg]
dx
dy
dz
CCl4 toluene acetone methanol water methanolb waterb
0.77 0.51 0.291 0.51 0.778 0.51 0.778
3.31 6.2 6.3 4.66 2.37 3.96 2.03
2.47 4.2 3.19 3.69 1.67 3.09 1.47
1.43 1.89 4.44 0.45 1.15 0.85 1.09
5.4 −0.6 −27.1 32.2 10.4 −32.5 −12.6
3.31 4.11 2.38 3.08 2.4 2.62 2.05
2.47 2.78 1.2 2.44 1.69 2.05 1.49
1.43 1.25 1.68 0.3 1.16 0.56 1.1
dq is defined as dq = Dq(ν/νCCl4), where ν is the viscosity of the solvent used. α denotes the angle between the principal x-axis of the diffusion tensor and the smallest inertia axis. Most of the results are based on the relaxation data of ref 38 (see text). bThe e2Qq and ηQ values calculated for dimethanolate and dihydrate, respectively, have been used. a
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relaxation rates caused by the scalar relaxation of the second kind mechanism (R2,SC2) and to determine the longitudinal relaxation rate (R1,Q) of the involved nitrogen. Even the values of 13C−14N coupling constants, which are generally small, need not be a restrictive precaution for applying the method. However, the reliability of the result should be better checked by a Monte Carlo simulation of the experiment being performed. Determination of R1,Q values from the R 1ρ measurements is rather a tedious procedure. This problem becomes less important when in one series of rotating frame measurements several R1,Q parameters can be measured simultaneously. Our work confirms that spin−spin coupling constants and quadrupole parameters needed for relaxation data interpretation can be relatively easily calculated with the use of routine quantum chemistry methods. It is to be remembered, however, that theoretical calculation of reliable values of quadrupole coupling parameters demands including the impact of the solvent into the theoretical model.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +4822 234 5103. E-mail: agryff@ch.pw.edu.pl. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by the National Science Centre (Poland) within Grant 2466/B/H03/2011/40. REFERENCES
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dx.doi.org/10.1021/jp306422c | J. Phys. Chem. A 2012, 116, 9632−9638
