Scalar Relaxation of the Second Kind. A Potential Source of

Article pubs.acs.org/JPCA

Scalar Relaxation of the Second Kind. A Potential Source of Information on the Dynamics of Molecular Movements. 4. Molecules with Collinear C−H and C−Br Bonds Piotr Bernatowicz,† Dominika Kubica,‡ Michał Ociepa,‡ Artur Wodyński,§ and Adam Gryff-Keller*,‡ †

Institute of Physical Chemistry, Polish Academy of Science, Kasprzaka 44/52, 01-224 Warszawa, Poland Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warszawa, Poland § Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa, Poland ‡

ABSTRACT: Continuing studies based on measurements of the nuclear spin relaxation rates running via the SC2 mechanism (scalar relaxation of the second kind), we present in this work the results obtained for three molecules: 9-bromotriptycene, 1,3,5tribromobenzene, and 1-(2-bromoethynyl)-4-ethynylbenzene in which C−Br bond and one of C−H bonds are collinear. Separation of saturation−recovery or inversion−recovery curves of 13C NMR signals of bromine-bonded carbons in the investigated compounds on two components has provided the longitudinal SC2 relaxation rates of these carbons in 79 Br- and 81Br-containing isotopomers. These data have enabled experimental determination of the bromine−carbon spin−spin coupling constants and relaxation rates of quadrupole bromine nuclei, hardly accessible by direct measurements. At the same time the rotational diffusion parameters describing the reorientation of the C−Br vectors have been determined for the investigated molecules on the basis of the dipolar relaxation of protonated carbons. These diffusion parameters are crucial for interpretation of the bromine relaxation rates. The values of the indirect 1J(13C,79Br) coupling constants, magnetic shielding of carbon nuclei and quadrupole coupling constants of bromines, determined for the investigated compounds, have been compared with the results of the theoretical calculations which take into account relativistic effects. The origin of some divergences between the results obtained by different methods has been discussed.

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INTRODUCTION For the nuclei possessing electric quadrupole moments, i.e., for I > 1/2 nuclei, random modulation of the interaction of this moment with the local electric field gradient, caused by molecular tumbling, usually provides the most efficient relaxation path.1−3 Thus, the parameters describing the rates of this relaxation carry valuable information on molecular movements. Unfortunately, for most quadrupole nuclei the direct measurements of relaxation times are possible only for species in which the nucleus occupies a point of a high local symmetry. In the case of 79Br and 81Br nuclei the direct measurements are feasible only for bromide and perbromide anions.4,5 In the case of bromoorganic compounds, with bromine covalently bonded to carbon, the quadrupole coupling constants, CQ(Br), are usually as high as 400−900 MHz,6 and the bromine NMR line widths in liquid samples are of a megahertz size. That is why the indirect determination of bromine relaxation times via investigation of the relaxation of the neighboring carbon appears as an attractive alternative. Such a possibility is provided by the impact of SC2 mechanism (scalar relaxation of the second kind) on the overall relaxation rate of the carbon.1,2,7 In the case of bromine isotopes, the measurements of the longitudinal relaxation of brominebonded carbon essentially suffice to accomplish the whole procedure. The rate of the longitudinal relaxation of nucleus A © 2014 American Chemical Society

running via SC2 mechanism depends on the involved scalar coupling constant, J(A,X), the transverse relaxation time of the quadrupole nucleus, T2,Q(X), and the resonance frequency difference ΔωAX:1,2,7 1/T1,SC2(A) = (2/3)IX(IX + 1)[2πJ(A,X)]2 T2,Q (X) /{1 + [ΔωAX T2,Q (X)]2 }

(1)

However, it has to be remembered that the SC2-relaxationbased method of retrieving parameters describing molecular movements is composed of several steps, each involving some assumptions and each carrying a jeopardy of introducing some errors to the final result.7−9 Moreover, the theory of SC2 relaxation and eq 1 are nothing but a phenomenological description of a limiting case of the relaxation of a pair of scalarcoupled spins, strictly valid only under extreme narrowing and some other conditions.1,2,8 Thus, the accuracy of the effective correlation times (or rotational diffusion parameters) obtainable by investigation of the SC2 relaxation of bromine-bonded carbons depends on a number of experimental and theoryrooted factors. Probably theoretical analysis of this problem is Received: April 16, 2014 Revised: May 14, 2014 Published: May 16, 2014 4063

dx.doi.org/10.1021/jp5037298 | J. Phys. Chem. A 2014, 118, 4063−4070

The Journal of Physical Chemistry A

Article

Table 1. 13C NMR Chemical Shifts, Longitudinal Relaxation Times, and NOE Enhancement Factors for Particular Carbons of 9-Bromotriptycene (1) in CDCl3 Solution Measured at B0 = 11.7 T and 25°C

feasible on the basis of the formalism developed by Werbelow and Kowalewski,8 but it seems to be quite a challenging task. The other possibility to tackle that problem is to accomplish some experimental tests. Below, we present the results of such tests performed for three molecules: 9-bromotriptycene (1), 1,3,5-tribromobenzene (2), and 1-(2-bromoethynyl)-4-ethynylbenzene (3), the brominated carbons of which have sp3, sp2, and sp hybridizations, respectively (Figure 1). An important

a

no.

assignment

δ [ppm]

T1 [s]

η

1 2 3 4 5 6 7 8

C-9a C-4a C-3 C-2 C-1 C-4 C-9 C-10

144.42 143.71 126.37 125.49 123.92 123.13 71.51 53.76

9.3 8.3 1.665 1.676 2.35 2.395 18.1, 49.7a 2.82

1.708 1.701 1.788 1.711

These values concern the respectively.

13

C carbons bonded to

1.98 79

Br and

81

Br,

measured 13C NMR chemical shifts and the relationship: σ(13C) = σTMS − δ(13C), where σTMS = 186.6 ppm stands for the isotropic magnetic shielding constant of TMS carbons. The shielding constants of bromine nuclei: 2568, 2224, and 2538 ppm for 1, 2, and 3, respectively, were calculated theoretically and corrected for relativistic effects, using a method described elsewhere.15 The values of these parameters were used to calculate the resonance frequency differences involved (ΔωAX parameters in eq 1).14 The longitudinal relaxation times for compounds 1 and 2 (Table 1 and 2) were measured by the saturation−recovery method15 and NOE enhancement factors by the dynamic NOE procedure.16 For compound 3 the longitudinal relaxation times (Table 3) were measured using the inversion−recovery method.15 Each measurement was repeated three times using slightly modified parameters defining the experiment. The sets of signal intensities obtained in the course of these measurements as a function of time were subjected to the nonlinear least-squares (l-s) analysis. The data from measurements performed at the same physical conditions were analyzed simultaneously.17 A more detailed description of the relaxation measurements and the numerical elaboration of the measurement results can be found in the preceding paper of this series.9 The nonlinear l-s method was also used to solve the overdetermined systems of equations connecting 13C relaxation data for brominated carbon at various magnetic fields with 1 13 79 J( C, Br), T2,Q(79Br), and Δσ(13C). Actually, T1,SA(13C) at 11.7 T was fitted rather than Δσ(13C) parameter. The numbers in parentheses that follow the parameter values represent the error estimates and concern the last (or two last) decimal places of the value throughout the paper. The nonrelativistic and relativistic quantum chemical calculations included geometry optimizations and calculations of NMR parameters and EFG tensors. The first were performed with the aid of Gaussian03 program18 using the DFT method with the B3LYP19 hybrid functional and the standard 6-311+ +G(2d,p) basis set. The impact of the solvent was treated using PCM solution model.20 The relativistic calculations took into account both scalar and spin−orbit coupling terms using twocomponent ZORA Hamiltonian available in ADF program.21−23 In these calculations the B3LYP functional and the TZ2P basis set, or in the case of spin−spin coupling constants the jcpl basis, were used. The solvent effects were estimated using COSMO solution model.24

Figure 1. Investigated compounds: 9-bromotriptycene (1), 1,3,5tribromobenzene (2), and 1-(2-bromoethynyl)-4-ethynylbenzene (3).

feature of the selected molecules is that they possess collinear C−H and C−Br bonds. This latter feature has allowed us to determine the effective correlation times describing molecular reorientation on the basis of the dipolar relaxation of the protonated carbon and to compare it with the value of that parameter obtained from the relaxation of bromine nucleus.

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EXPERIMENTAL SECTION 9-Bromotriptycene (1)10 was prepared from 9-bromoanthracene, anthranilic acid, and amyl nitrite using the slightly modified procedure elaborated for triptycene.11 1,3,5-Tribromobenzene (2) was synthesized from aniline according to the literature procedure.12 1-(2-Bromoethynyl)-4-ethynylbenzene (3) was obtained according to the literature method13 and purified by column chromatography (silica, hexane). NMR measurements were performed for the ca. 1 mol/dm3 solutions of compounds 1, 2, and 3 in CDCl3. The 0.6 mL portion of the prepared solution was placed in a 5 mm o.d. NMR tube, degassed, and sealed. The proton-decoupled 13C NMR spectra of these solutions were recorded using VNMRS, Bruker Avance II and Gemini 2000 NMR spectrometers working at 11.7, 7.05, and 4.7 T magnetic fields, respectively. In the case of 3 also Agilent NMR 600 MHz (14.1 T) and Varian Mercury 400 (9.4 T) spectrometers were used. The deuterium signal of the solvent was used as a field/frequency lock and its 13 C signal, δ(CDCl3) = 77.16 ppm, was used as the internal reference to calibrate carbon NMR chemical shifts. The measurement temperature (25 °C) was monitored by the same ethylene glycol (DMSO-d6) sample at all spectrometers. The extensive zero-filling of the FID signals and in the case of relaxation measurements the substantial line broadening (lb =10) were applied prior to the FT operation. The signal assignments in 13C NMR spectra of 1 (Table 1) and 3 (Table 3) have been accomplished by combining information coming from proton-coupled 13C NMR spectra and 2D heteronuclear 1H−13C correlation HSQC and HMBC spectra recorded at B0 = 11.7 T magnetic field. The isotropic magnetic shielding of carbon nuclei were calculated using the 4064



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Table 2. Longitudinal Relaxation Times, Tk (k = 79, 81), of 13C Carbons Bonded to the Particular Bromine Isotopes of 1,3,5Tribromobenzene (2), Determined at Various Magnetic Fields, and Calculated Contributions of Various Relaxation Mechanisms Taking Part in the Overall Relaxation, Given as the Partial Relaxation Timesa Tk [s] B0 [T]

k

total

DD(C···H)

DD(C−Br)

SA

SC

4.7

79 81 79 81 79 81

5.1(9) 13.8(9) 6.76(2) 18.52(4) 6.46(2) 18.64(3)

107 107 107 107 107 107

344 298 344 298 344 298

207 207 92 92 33.3 33.3

5.59 18.2 8.01 32.9 8.89 91.8

7.05 11.7

1

J(13C,79Br) [Hz]

T2,Q(79Br) [ns]

172(8)

62(8)

164(4)

47(2)

156(20)

48(32)

a The last two columns contain the values of 1J(13C,79Br) and T2,Q(79Br) calculated using the SC2 relaxation data determined at a given magnetic field and eqs 1, 5, and 6. DD(C···H) is the contribution due to dipolar interaction of 13C−Br with all the protons in the molecule, calculated from Deff and the molecular geometry. DD(C−Br) is the contribution due to dipolar interaction between 13C and the kBr nucleus, calculated from Deff and the molecular geometry. SA is the contribution due to the anisotropy of the magnetic shielding tensor of the brominated carbon, calculated from Deff and the effective Δσ parameter (169.1 ppm) taken from theoretical calculations. SC2 is the contribution due to the scalar relaxation of the second kind, calculated as a difference between the total (measured) relaxation rate and DD and SA contributions, exploiting the formula: 1/Tk = 1/ T1,SC(13C−kBr) + 1/T1,DD(13C···H) + 1/T1,DD(13C−kBr) + 1/T1,SA.

tops.2,25 The values of the appropriate rotational diffusion parameters: D∥ = 3.0(3) × 109 s−1 and D⊥ = 8.6(8) × 109 s−1 have been calculated using the measured T1 and η data for protonated carbons, the DFT optimized molecular geometry, and the computer program described elsewhere.26 During the analysis of the relaxation data the theoretically calculated equilibrium C−H bond lengths have been multiplied by a factor of 1.03 to compensate for the effect of molecular vibrations.26−30 The determined rotational diffusion coefficients and molecular geometry allowed us to calculate the contributions to the overall relaxation of C-9 carbon coming from the dipolar interactions2,26 with protons, T1,DD(13C···H) = 165 s, from the dipolar interactions with bromine isotopes, T1,DD(13C−79Br) = 271 s and T1,DD(13C−81Br) = 234 s, and from the contribution from the relaxation mechanism caused by the magnetic shielding anisotropy,1,2,26 T1,SA(13C-9) = 408 s. The last contribution has been estimated using the theoretically calculated Δσ(13C-9) = 39.2 ppm value. These contributions are hardly measurable and may seem unimportant, but it is not the case (see below). The saturation−recovery curve of brominated carbon signal is described by the function:

Table 3. Magnetic Field Dependence of the Longitudinal Relaxation Times of 13C Nuclei of 1-(2-Bromoethynyl)-4ethynylbenzene (3) T1 [s] assignment

δ [ppm]

4.7 T

7.05 T

9.4 T

11.7 T

14.1 T

C-3 C-2 C-1 C-4 C-1b C-1a C-2b C-2aa C-2aa,d C-2ab C-2ab,d

132.16 132.01 123.26 122.55 83.18 79.70 79.35 52.24 52.24 52.24 52.24

5.52 5.50 42 37 27.8 28.8 2.03 4.95c 5.18 4.95c 5.22

5.61 5.58

5.58 5.37 22.1 18.8 10.22 9.3 1.93 5.31 5.57 8.47 9.28

5.28 5.27 15.8 15.1 6.70 4.29 1.87 4.9 5.12 9.9 11.02

5.00 4.93 11.3 11.3 4.79

15.0 15.1 1.99 4.54 4.73 7.24 7.82

1.80 4.06 4.21 9.54 10.58

a

Isotopomer with 79Br. bIsotopomer with 81Br. cMonoexponential recovery curve. dValues corrected for C−Br dipolar relaxation: T1,DD(13C−79Br) = 112 s and T1,DD(13C−81Br) = 97.3 s.

■

RESULTS 9-Bromotriptycene (1). As the first step of the 13C relaxation data interpretation, the saturation−recovery curves for all carbons but C-9 recorded at B0 = 11.7 T have been subjected to l-s analysis assuming the monoexponential recovery: intensity(t ) = a[1 − exp( −t /T1)] + b

intensity(t ) = a[1 − p79 exp(−t /T79) − (1 − p79 ) exp( −t /T81)] + b

In the preceding paper of this series9 we have shown that knowledge of the impact of the dipolar relaxation due to protons on the relaxation of bromine-bonded carbon simplifies decomposition of the measured recovery curve into two exponents. Namely, the knowledge of T1,DD(13C···H) allows the adjustment of the apparent population parameter, p79, to be avoided during data analysis. Note that p79 differs from the natural abundance of 79Br isotope, due to nuclear Overhauser effects being different for the two isotopomers. The l-s analysis of the saturation−recovery data measured at B0 = 11.7 T, for the C-9 signal of 1 with the condition T1,DD(13C···H) = 165 s has yielded parameters T79 = 18.1 s and T81 = 49.7 s describing the longitudinal relaxation of C-9 in two bromine isotopomers of 1. Subtracting the above-listed relaxation contributions from the experimentally observed relaxation rates one obtains the SC2 relaxation rates (and relaxation times): T1,SC(13C−79Br) =

(2)

All three parameters, T1, a, and b have been adjusted, always yielding a b value close to the noise intensity. The mean values of the appropriate relaxation times are given in Table 1. These values have been used as fixed parameters in the analysis of the results of the dynamic NOE experiment, i.e., the stepwise increase of signal intensities from their equilibrium values to their intensities with NOE: d1 (proton decoupler off) − t (decoupler on) − (π/2-pulse) − acquisition (decoupler on).16 Such an increase has been described by the relationship intensity(t ) = a[1 + η − η exp( −t /T1)]

(4)

(3)

where η is the appropriate NOE factor. The determined η values are given in Table 1. Owing to the symmetry, the molecules of 1 reorient in isotropic solutions as symmetrical 4065



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23.2 s and T1,SC(13C−81Br) = 136.6 s. Finally, substituting these values to eq 1 and using the relationships1,2,6

magnetic shielding tensors do not ensure a reliable deconvolution of Deff into D∥ and D⊥. Thus, the contribution of the SA mechanism to the overall relaxation rate of brominated carbons has been calculated by assuming isotropic molecular reorientation and using the Deff value as a measure of the reorientation rate. Inspection of the data in Table 2 shows that at B0 = 11.7 T the SA contribution to the relaxation of brominated carbons has become substantial, and it is the second important difference between 1 and 2. The assumed 5% uncertainty of the Δσeff results causes very large uncertainty of 1 13 79 J( C, Br) and T2,Q(79Br), in spite of the relatively precise determination of the overall relaxation times in both isotopomers. This observation prompted us to supplement the relaxation data acquired at 11.7 and 7.05 T with the data measured at B0 = 4.7 T. The error estimates show that they are remarkably less precise, which is not a surprise for us, as the sensitivity and stability of our spectrometer is limited. On the other hand, these data are almost uninfluenced by SA relaxation. Having six independent relaxation data (T79 and T81 for three magnetic fields), we could perform the nonlinear l-s analysis by adjusting 1 13 79 J( C, Br), T2,Q(79Br), and additionally, the effective shielding anisotropy parameter. The results are as follows: 1J(13C,79Br) = 163(5) Hz, T2,Q(79Br) = 4.6(5) × 10−8 s and at 11.7 T T1,SA(13C−Br) = 35(5) s. The error estimates have been established using a Monte Carlo method (see below). All the relaxation data (apart from T79 at 4.7 T) have been reproduced perfectly during this analysis (Figure 2).

T2,Q (81Br)/T2,Q (79Br) = [eQ(79Br)/eQ(81Br)]2 = 1.438 (5) 1 13

J ( C,81Br)/1J(13C,79Br) = γ(79Br)/γ(81Br) = 0.9277

(6)

where eQ(X) and γ(X) are nuclear quadrupole moments and magnetogyric ratios, respectively, we have obtained a system of two equations with two unknowns. Solving it, one obtains 1 13 79 J( C, Br) = 112(10) Hz and T2,Q(79Br) = 3.5(6) × 10−8 s. Attempts at performing the analogous elaboration of the data acquired at B0 = 7.05 T have not been successful. Either the l-s analysis of the recovery curves yielded T79 = T81 or, after neglecting some data points, the error estimates for obtained relaxation parameters were unacceptably large. This numerical problem reflects strong parameter correlation and is typical for curves composed of two similar exponential components. In the case in hand, however, this problem could be overcome as the value of T79 can be easily predicted. Indeed, at 11.7 T magnetic field for the 79Br-containing isotopomer, the denominator of the RHS of eq 1 is close to unity and T79 values at two magnetic fields should practically differ only due to different contributions of SA relaxation mechanism. The appropriate correction is small and has yielded T79 = 18.5 s at 7.05 T. Introducing the latter value to the l-s analysis of recovery data as the fixed parameter, the experimental curve could be decomposed into two exponents yielding T81 = 28.7 s. Using the procedure described above, we have obtained T1,SC(13C−79Br) = 23.0 s and T1,SC(13C−81Br) = 42.4 s and finally 1J(13C,79Br) = 125(8) Hz and T2,Q(79Br) = 2.8(4) × 10−8 s. Taking into account the multistep procedure of elaborating the data and some assumptions involved, the agreement between the final results obtained from measurements performed at two magnetic fields, can be considered satisfactory. In further discussion, we use the following mean values of the final parameters: 1J(13C,79Br) = 119(10) Hz and T2,Q(79Br) = 3.1(5) × 10−8 s. A discussion on the error estimations is addressed later in this work. 1,3,5-Tribromobenzene (2). The relaxation data for this compound have been acquired and processed using the same methods as for 1. The results obtained are given in Table 2. There are, however, some differences between these two compounds, which are important from the point of view of our investigations. The first of them originates from different molecular geometry. Molecules of both compounds are of the similar symmetry and both possess collinear C−H and C−Br bonds; however, in the case of 2, as opposite to 1, these bonds are perpendicular to the symmetry axis. Thus, the dipolar relaxation rate of the ring carbons provides information only on a combination of the rotational diffusion coefficients, namely on Deff = 2D⊥(2D + D⊥)/(D + 5D⊥)

Figure 2. Result of the least-squares analysis of the 13C NMR relaxation data for brominated carbons of 1,3,5-tribromobenzene corrected for the dipolar carbon−hydrogen and carbon−bromine relaxation (Table 2) with adjustment of the values of three parameters: 1 13 79 J( C, Br) = 163(5) Hz, T2,Q(79Br) = 4.6(5) × 10−8 s−1, and T1,SA(13C−Br) = 35(5) s at 11.7 T.

1-(2-Bromoethynyl)-4-ethynylbenzene (3). The longitudinal relaxation times for 13C nuclei of 3 have been measured by the inversion−recovery method at five magnetic fields: 4.7, 7.05, 9.7, 11.5 and 14.1 T. The results of these measurements are given in Table 3. Inspection of these results shows the magnetic field dependence of relaxation rates for all carbons. Taking into account the size of the investigated molecule, one may expect that its reorientation rate fulfils the extreme narrowing condition and that magnetic field dependence reflects the impact of the shielding anisotropy (SA) relaxation mechanism.1,2,31 In the case of brominated carbon the SC2 mechanism contributes to this dependence as well. For protonated carbons the DD mechanism dominates, even at B0 = 14.1 T. The important feature of the molecule of 3 is that the distances of its peripheral C−H and C−Br carbons to the nearest ring protons are large, and that the dipolar interaction

(7)

Using the effective C−H distance, rC−H = 1.12 Å, we have obtained Deff = 1.3 × 1010 s−1. It is to be noticed that the same combined parameter governs the quadrupole relaxation of bromine nuclei, as the asymmetry of the EFG tensor involved is minimal. On the other hand, the shielding anisotropy tensors of the aromatic ring carbons are highly asymmetrical. It seems, however, that our relaxation data and theoretically calculated 4066



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with these protons may be neglected in the relaxation data analysis. The ex-post calculation of this contribution has fully confirmed validity of this expectation. This feature makes the analysis of the relaxation data for peripheral carbons much easier. Namely, the dipolar contribution to the relaxation of protonated carbons could be obtained by extrapolating the function: 1/T1,obs = 1/T1,DD + cSAB0 2

(8)

to B0 = 0. The coefficient cSA denotes the relaxation rate due to SA mechanism at B0 = 1 T. For the ethynyl C−H we have obtained: T1,DD = 2.064 s and the averaged value for protonated ring carbons T1,DD = 5.72 s. These data have been used to determine the rotational diffusion coefficients describing reorientation rate of the investigated molecule. The molecules of 3 are of C2v symmetry and their reorientation in a solution should essentially be described by three diffusion coefficients.25 However, owing to their elongated shape, the symmetrical top reorientation model still seems to be a very good approximation. It is a common practice to use such an approach when the shortage of the independent relaxation data prevents more rigorous reorientation description. The reorientation rate of the symmetry axis has been calculated from the dipolar relaxation rate of the ethynyl C−H carbon, giving D⊥ = 6.3(4) × 109 s−1. The rotation about the symmetry axis, described by the D∥ diffusion coefficient, is unimportant for the relaxation of the peripheral C−H and C− Br carbons. For the sake of completeness we have calculated the D∥ coefficient by using the dipolar relaxation rate of the ring carbons, diminished by 3% to compensate for the contribution of other than directly bonded protons. The result is D∥ = 5.0 × 1010 s−1. The l-s analysis of the recovery curves for the brominated carbon has shown that the relaxation rates for two isotopomers do not differ very much (Table 3). At B0 = 4.7 T the curve could not be separated into two exponents and we have had to assume the monoexponential recovery. The determined relaxation rates have been corrected for the carbon−bromine dipolar relaxation using the calculated T1,DD (13C−79Br) = 112 s and T1,DD(13C−81Br) = 97.3 s (Table 3). So corrected data have been subjected to l-s analysis, which has taken into account both SC2 and SA relaxation mechanisms. This analysis has yielded 1J(13C,79Br) = 276(17) Hz, T2,Q(79Br) = 2.31(28) × 10−8 s and at 11.7 T T1,SA(13C) = 30(8) s. It is worth noting that the magnetic field dependence of the relaxation data has been reproduced very well (Figure 3).

Figure 3. Result of the least-squares analysis of the 13C NMR relaxation data for brominated carbons of 1-(2-bromoethynyl)-4ethynylbenzene corrected for the dipolar carbon−bromine relaxation (Table 3) with adjustment of the values of three parameters: 1 13 79 J( C, Br) = 276(17) Hz, T2,Q(79Br) = 2.3(3) × 10−8 s, and T1,SA(13C−Br) = 30(8) s at 11.7 T.

order of 8−9%. In the course of elaborating the relaxation data of brominated carbons, this error propagates in a complicated manner through T1,DD(13C···H) and T1,DD(13C,79Br), and through T1,SA(13C) if not adjusted. Control of this propagation and proper inclusion of the effects of other possible errors are rather complex. To overcome this difficulty, at least partially, we applied the Monte Carlo simulation of 1J(13C,79Br), T2,Q(79Br), and Δσ(13C) errors. This method also involves some arbitrariness, but when applied cautiously, seems to provide reasonable results. Part of the data in Table 4 have been obtained by theoretical calculations or have been calculated using both experimental and theoretical data. In such cases the error estimates are not given. The first obvious conclusion coming from the obtained values of the diffusion coefficients is that the reorientation of the investigated molecules in the applied conditions is fast, so that the extreme narrowing condition is fulfilled (ωX/(6D⊥) ≪ 1, X = 13C, 79Br, 81Br), even at the highest magnetic field applied, B0 = 14.1 T. This fact justifies the usage of the concept of the scalar relaxation of the second kind throughout the elaboration of our relaxation data. Moreover, in such conditions the transverse nuclear magnetization due to high-spin nuclei decays exponentially and the relaxation parameter T2,Q(79Br) determined from eq 1 indeed has the meaning of the transverse relaxation time. The T2,Q(X) and the diffusion parameter DC−X, describing reorientation of C−X vector (i.e., D⊥ for compounds 1 and 3, and Deff for 2) are interconnected by the known relationship1,2,32

■

1/T2,Q (X) = 0.3π 2(2IX + 3)/[IX 2(2IX − 1)]CQ

DISCUSSION AND CONCLUSIONS The values of NMR parameters and rotational diffusion coefficients describing reorientation rates of the investigated molecules in CDCl3 solutions at 25 °C determined from the analysis of the relaxation data, as well as the values of some parameters calculated theoretically, are collected in Table 4. Before we undertake a discussion of these results, it is worth realizing that determination of the rotational diffusion coefficients on the basis of the dipolar relaxation due to C− H interactions can be burdened with some errors. The most important is the uncertainty concerning the effective, vibrationcorrected, C−H distance. One may expect that the frequently used rC−H = 1.12 Å can be connected with an error of 0.01 Å. After the measurement errors of T1 and η were added, the total error of the determined diffusion coefficients may be on the

(X)2 (1 + χX 2 /3)(6DC − X )−1

(9)

For carbon-bonded bromines the asymmetry parameter, χ, is small and may be neglected. If the quadrupole coupling constant, CQ(X), of the quadrupole nucleus in a given molecule is known, this equation can be used either to calculate the D⊥ value on the basis of the T2,Q(X) determined experimentally or to calculate T2,Q(X) from the D⊥ value determined earlier. To calculate CQ(79Br) values for compounds 1, 2 and 3, the electric field gradients at bromine nuclei have been calculated theoretically and multiplied by the appropriate nuclear quadrupole moment. The value eQ(79Br) = 31.3 × 10−30 m2 is presently considered to be the most reliable value of the quadrupole moment of 79Br nucleus and is recommended in the recent review articles by Pyykkö33 and by Bryce et al.3 The 4067



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Table 4. Parameter Values Determined for Compounds 1, 2, and 3 by the Interpretation of Nuclear Spin Relaxation Data or Calculated Theoretically with the Relativistic (rel) or Nonrelativistic (nr) DFT Method compound parameter D⊥

T2,Q(79Br)

units s−1

s

|1J(13C,79Br)| 1 13 79 J( C, Br)

Hz Hz

CQ(79Br)

MHz

Δσeff(13C−Br)

ppm

σ(13C−Br)

ppm

data source T1,DD CQ,rel(Br)a and CQ,rel(Br)b and T1,SC CQ,rel(Br)a and CQ,rel(Br)b and T1,SC calcrel calcnr T2,Q and D⊥ calcrela calcrelb calcnra T1,SC+SA calcrel calcnr expc calcrel calcnr

T2,Q T2,Q D⊥ D⊥

1

2

3

8.6(8) × 109 6.9 × 109 7.7 × 109 3.1(5) × 10−8 3.9 × 10−8 3.5 × 10−8 119(10) −128.6 −113.4 650(65) 582.6 616.1 546.6

1.3(1) × 1010 1.0 × 1010 1.15 × 1010 4.6(5) × 10−8 5.9 × 10−8 5.3 × 10−8 163(5) −177.6 −164.3 656(45) 582.3 615.8 565.6 164(17) 169.1 148.5 63.2 44.09 34.96

6.3(4) × 109 6.7 × 109 7.5 × 109 2.3(3) × 10−8 2.2 × 10−8 1.9 × 10−8 276(17) −373.8 −308.9 646(60) 662.8 700.9 635.9 124(20) 144.6 170.2 133.4 115.03 102.66

41.5 49.5 115.1 96.54 85.92

a Calculated by assuming eQ = 31.3 × 10−30 m2. bCalculated by assuming eQ = 33.1 × 10−30 m2. cObtained from the chemical shifts by assuming the relationship: σ(13C) = 186.6 − δ(13C).

same value was found by Bailey and Gonzalez34 as an effective value being optimal for the electric field gradients calculated by the theoretical method similar to that used in our work. Unfortunately, the calculational method of ref 34 was tested for molecules in gaseous state rather than in solution. Note, however, that a different value, eQ(79Br) = 33.1 × 10−30 m2 was also quoted.34,35 Obviously, the uncertainty of CQ(79Br) value propagates on the final parameters calculated by eq 9. Alternatively, it is possible to calculate the CQ(X) value from the experimental values of D⊥ and T2,Q(X). The results of all these calculations are given in Table 4. Inspection of these data shows that the values of D⊥ and T2,Q(79Br) determined experimentally from the relaxation data remain in agreement within experimental errors with the values obtained with the aid of eq 9. The same concerns the comparison of CQ(79Br) values obtained from eq 9 with the ones calculated theoretically. For compounds 1 and 2 a better agreement has been obtained for eQ(79Br) = 33.1 × 10−30 m2. It seems that the T2,Q( 79Br) values obtained through investigation of SC2 relaxation of brominated carbons do provide information on molecular dynamics. On the other hand, a high accuracy of these data should not be expected. Moreover, the perfect agreement between the shielding anisotropy parameters for brominated carbons determined for compounds 2 and 3 from the analysis of the relaxation data and the values calculated theoretically is noteworthy. It confirms independently the reliability of our relaxation data analysis and of the 1J(13C,79Br) values determined. Indeed, the values obtained for compounds 1−3 follow the trend observed by Hayashi et al.,36 who documented the increase of the absolute value of this spin−spin coupling constant with the hybridization of the carbon involved in the order sp3 < sp2 < sp. On the other hand, it is visible that there is another important factor affecting the value of this parameter. The value obtained here for 9bromotriptycene (1) matches well the values for CBrX3 compounds reported in the preceding paper:9 32 Hz for

(CH3)3CBr, 119 Hz for 1, 150 Hz for CBr4, and 170 Hz for CBrCl3. It seems that at the constant sp3 hybridization of the carbon the substituent electronegativity becomes a leading factor determining the 1J(13C,79Br) value. The importance of the substituent negativity for other 1J spin−spin couplings was documented many times.37−39 The carbon−bromine coupling constant determined here for 2 differs somewhat from the value 136 Hz, reported in ref 36. On the other hand, the value |1J(13C,79Br)| = 266 Hz determined for bromoacetylene,36 |1J(13C,79Br)| = 241(17) Hz for phenylacetylene,40 and |1J(13C,79Br)| = 264(9) Hz for bromoethynyltrimethylsilane41 are similar to the value determined for the compound 3. It has to be remembered, however, that these earlier results can be burdened by the errors caused by the neglect of magnetic shielding of bromine nuclei.14 Comparing the experimentally determined values of the 1 13 79 J( C, Br) coupling constants with the results of the theoretical calculations, we have found that the calculations based on the nonrelativistic theoretical method reproduce experimental values of this parameter better than those based on the relativistic one. The cause of the larger divergence in the case of the more rigorous theoretical method remains unclear,9,42 but taking into account the estimated experimental errors, the fault seems to lie rather on the side of the calculated values. Finally, the detailed comparison of the experimental and theoretically calculated NMR parameters would demand taking into account intermolecular interactions. For example, the remarkable changes of 1J(13C,13C) between acetylene carbons in phenylacetylene with the solvent polarity and proton donor/ acceptor ability were observed.43 It cannot be excluded that 1 13 79 J( C, Br) in compound 3 is also susceptible to the intermolecular interactions. The approximate solution models PCM or COSMO used in this work probably compensate partially for the medium effects but are certainly insufficient to treat specific intermolecular interactions. 4068



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(16) Neuhaus, D.; Williamson, M. P. Nuclear Overhauser Effect in Structural and Conformational Analysis; B. Verlag. Chemie: Weinheim, New York, 1989. (17) Gryff-Keller, A.; Ejchart, A.; Jackowski, K. Shielding Anisotropies of Acetylenic Carbons and Solution Molecular Dynamics Ethynyltrimethylsilane as Studied by 13C Nuclear Spin Relaxation and Theoretical Ab Initio Calculation. J. Magn. Reson. A 1994, 111 (2), 186−90. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03; Gaussian, Inc.: Wallingford, CT, 2004. (19) Becke, A. D. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (20) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105 (8), 2999−3093. (21) Klamt, A.; Jonas, V. Treatment of the Outlying Charge in Continuum Solvation Models. J. Chem. Phys. 1996, 105 (22), 9972− 9981. (22) Autschbach, J. On the Accuracy of the Hyperfine Integrals in Relativistic NMR Computations Based on the Zeroth-Order Regular Approximation. Theor. Chem. Acc. 2004, 112, 52−57. (23) Dyall, K. G. Relativistic Quadruple-Zeta and Revised Triple-Zeta and Double-Zeta Basis Sets for the 4p, 5p, and 6p Elements. Theor. Chem. Acc. 2006, 115, 441−447. (24) Pye, C. C.; Ziegler, T. An Implementation of the ConductorLike Screening Model of Solvation Within the Amsterdam Density Functional Package. Theor. Chem. Acc. 1999, 101, 396−408. (25) Dölle, A.; Bluhm, T. Orientation of the Rotational Diffusion Principal Axis System Determined by Nuclear Relaxation Data. Prog. Nucl. Magn. Reson. Spectrosc. 1989, 21, 175−201. (26) Kotsyubynskyy, D.; Gryff-Keller, A. Anisotropic Reorientation of 9-Methylpurine and 7-Methylpurine Molecules in Methanol Solution Studied by Combining 13C and 14N Nuclear Spin Relaxation Data and Quantum Chemical Calculations. J. Phys. Chem. A 2007, 111 (7), 1179−1187. (27) Sykora, S.; Vogt, J.; Bö siger, H.; Diehl, P. Vibrational Corrections in NMR Spectra of Oriented Molecules. J. Magn. Reson. 1979, 36 (1), 53−60. (28) Hardy, E. H.; Witt, R.; Dölle, A.; Zeidler, M. D. A New Method for the Determination of the Dynamic Isotope Effect and the Deuterium Quadrupole Coupling Constant in Liquids. J. Magn. Reson. 1998, 134 (2), 300−307. (29) Ejchart, A.; Zimniak, A.; Oszczapowicz, I.; Szatylowicz, H. Comparative 13C Relaxation Study of R and S Isomers of the 1Acetoxyethyl Ester of Cefuroxime. Influence of C-H Bond Lengths on Relaxation Data Consistency. Magn. Reson. Chem. 1998, 36 (8), 559− 564. (30) Kowalewski, J.; Effemey, M.; Jokisaari, J. Dipole−Dipole Coupling Constant for a Directly Bonded CH PairA Carbon-13 Relaxation Study. J. Magn. Reson. 2002, 157 (2), 171−177. (31) Anet, F. A. L.; O’Leary, D. The Shielding Tensor Part II: Understanding its Strange Effects on Relaxation. Concepts Magn. Reson. 1992, 4 (1), 35−52. (32) Gerothanassis, I. P.; Tsanaktsidis, C. G. Nuclear Electric Quadrupole Relaxation. Concepts Magn. Reson. 1996, 8 (1), 63−74. (33) Pyykkö, P. Year-2008 nuclear quadrupole moments. Mol. Phys. 2008, 106, 1965−1974. (34) Bailey, W. C.; Gonzalez, F. M. Calculation of Bromine Nuclear Quadrupole Coupling Constants in Gaseous State Molecules. J. Mol. Struct. 2003, 651−653, 689−695. (35) Stone, N. J. Table of Nuclear Magnetic Dipole and Electric Quadrupole Moments; IAEA Nuclear Data Section, Vienna International Centre: Vienna, Austria, 2011 (see www-nds.iaea.org/nsdd/ indc-nds-0594.pdf). (36) Hayashi, S.; Hayamizu, K.; Yamamoto, O. Spin-Spin Coupling Constants Between Carbon-13 and Bromine and Their Correlation With the S Character of the Carbon Hybridization. J. Magn. Reson. 1980, 37 (1), 17−29.

AUTHOR INFORMATION

Corresponding Author

*A. Gryff-Keller: e-mail, agryff@ch.pw.edu.pl; phone, +48 22 234 51 03. 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 no. 2466/B/H03/2011/40. The MPD/2010/4 project, realized within the MPD programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, is acknowledged for a fellowship to A. Wodyński.

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Scalar Relaxation of the Second Kind. A Potential Source of

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