Interpretation of the Longitudinal 13C Nuclear Spin Relaxation and

Article pubs.acs.org/JPCA

Interpretation of the Longitudinal 13C Nuclear Spin Relaxation and Chemical Shift Data for Five Bromoazaheterocycles Supported by Nonrelativistic and Relativistic DFT Calculations Artur Wodyński,† Anna Kraska-Dziadecka,‡ Dominika Kubica,‡ and Adam Gryff-Keller*,‡ †

Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa, Poland Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warszawa, Poland

‡

ABSTRACT: The longitudinal relaxation times of 13C nuclei and NOE enhancement factors for 2-bromopyridine (1), 6-bromo-9-methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5) have been measured at 25 °C and B0 = 11.7 T. The most important contributions to the overall relaxation rates of nonbrominated carbons, i.e., the relaxation rates due to the 13C−1H dipolar interactions and the shielding anisotropy mechanism, have been separated out. For 3 and 5, additionally, the T2,Q(14N) values have been established from 14 N NMR line widths. All of these data have been used to determine rotational diffusion tensors for the investigated molecules. The measured saturation recovery curves of brominated carbons have been decomposed into two components to yield relaxation times, which after proper corrections provided parameters characterizing the scalar relaxation of the second kind for 13C nuclei of 79 Br- and 81Br-bonded carbons. These parameters and theoretically calculated quadrupole coupling constants for bromine nuclei have allowed the values of one-bond 13C−79Br spin−spin coupling constants to be calculated. Independently, the coupling constants and magnetic shielding constants of the carbon nuclei have been calculated theoretically using the nonrelativistic and relativistic DFT methods F/6-311++G(2d,p)/PCM and so-ZORA/F/TZ2P/COSMO (F = BHandH or B3LYP), respectively. The agreement between the experimental and theoretical values of these parameters is remarkably dependent on the theoretical method used.

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INTRODUCTION The nuclear spin relaxation data for molecules in solid states as well as in solutions contain a wealth of information on molecular movements and molecular parameters.1−3 This fact has been recognized and exploited since the very beginning of NMR spectroscopy. Determination of the interesting parameters by this method demands that careful relaxation measurements be performed and involves interpretation of their results, which actually needs not be so straightforward. The general theory of nuclear spin relaxation phenomena was elaborated many years ago4−6 and has also been presented in a form suitable for practical applications.2,3,6,7 The quality of the relaxation data has improved in parallel with the technical progress in NMR equipment, although some methodological discussions concerning relaxation measurements and interpretation of their results are still being continued.8−11 Broader application of this methodology has been hampered for a long time by the limited access to exact molecular geometries and parameters such as magnetic shielding tensors and quadrupole coupling tensors, which are needed for the interpretation of relaxation data. Frequently, these parameters were determined indirectly just from relaxation measurements. Presently, thanks to the successful development of quantum-chemical calculation methods, those difficulties have largely been overcome.12−14 The experimental determination of the values of some parameters from NMR measurements and independent theoretical calculation of these values provide a possibility to control the data interpretation and/or to test the effectiveness © 2014 American Chemical Society

of the theoretical methods used. The study presented herein is a good example of such collaboration of experimental and theoretical methods. This work is a continuation of our studies exploiting the unique feature of bromine isotopes that is manifested as the SC2 relaxation mechanism contributing to the longitudinal relaxation of carbon nuclei. Preceding works were devoted to the more-or-less spherical CBrX3 molecules and to molecules possessing axial symmetry and collinear C−Br and C−H bonds.10,11 In this work, the 13C NMR chemical shifts and 13C longitudinal relaxation rates have been measured for CDCl3 solutions of five brominated azaheterocycles (Figure 1). Selection of the objects for this study was made to ensure a balance between the chemical similarity within the series (planar symmetry, azaheterocycle) and sufficient diversity. The chemical stability and accessibility of these compounds were also taken into account. The obtained experimental data have been carefully interpreted using the results of theoretical calculations. The latter have been performed by two nonrelativistic and two relativistic density functional theory (DFT) methods. The inclusion of relativity in the calculations seemed to be desired because of our molecules contain bromines, which possess heavy nuclei.15−19 Received: October 24, 2014 Revised: December 23, 2014 Published: December 23, 2014 517

DOI: 10.1021/jp510687x J. Phys. Chem. A 2015, 119, 517−524

Article

The Journal of Physical Chemistry A

The proton-decoupled 13C NMR spectra of these samples were recorded using a VNMRS NMR spectrometer working at B0 = 11.7 T. The deuterium signal of the solvent was used as a field/frequency lock, and its 13C signal, δ(CDCl3) = 77.16 ppm, was used as the internal reference to calibrate the carbon NMR chemical shifts. All of the measurements were done at the same temperature, 25 °C, which was controlled by the spectrometer variable-temperature (VT) accessory. Extensive zero filling of the free induction decay (FID) signals and, in the case of relaxation measurements, substantial line broadening (lb = 10) were applied prior to the Fourier transform (FT) operation. The signal assignments in the 13C NMR spectra of the investigated compounds were made by combining information from proton-coupled 13C NMR spectra and two-dimensional heteronuclear 1H−13C correlation (HSQC and HMBC) spectra. These assignments were later confirmed by the results of δexp/σcalc correlation analysis. The longitudinal relaxation times for compounds 1−5 (Tables 1 and 2) were measured by the saturation−recovery method23 and nuclear Overhauser effect (NOE) enhancement factors by the dynamic NOE procedure.24 Each measurement was repeated three to six times using slightly modified parameters defining the experiment. The set of signal intensities obtained in the course of all measurements of relaxation times or NOEs performed for a given compound were simultaneously subjected to nonlinear least-squares analysis.25 A more detailed description of the relaxation measurements and the numerical elaboration of the measurement results can be found in our preceding papers.10,11,25 The computer program developed to retrieve rotational diffusion parameters from DD, SA, and QQ relaxation data was described elsewhere.26 Other programs for data fitting were based on the Newton−Raphson algorithm of iterative nonlinear least-squares sum minimization. The differences between the resonance frequencies of brominated carbons and bromines were calculated according to the equation

Figure 1. Investigated compounds: 2-bromopyridine (1), 6-bromo-9methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5).

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EXPERIMENTAL SECTION 2-Bromopyridine (1) and all of the substrates and solvents were commercial products. 6-Bromo-9-methylpurine (2),20 3,5dibromopyridine (3),21 and 2,4,6-tribromopyrimidine (5)22 were synthesized from commercially available substrates according to literature procedures. 2,4-Dibromopyrimidine (4) was synthesized using the procedure elaborated for 2,4,6tribromopyrimidine22 from uracil (0.5 g, 4.5 mmol) and POBr3 (5 g, 18 mmol) in the presence of N,N-dimethylaniline (1.03 mL, 8.3 mmol) in 10 mL of toluene; purification by preparative TLC on silica gel using a 9:1 mixture of hexane and ethyl acetate as the eluent afforded a yield of 0.95 g (89%). NMR measurements were performed for the ca. 1 mol/dm3 solutions of compounds 1−5 in CDCl3. After the prepared solutions were deoxygenated and saturated with oxygen-free argon, 0.6 mL portions were transferred under an argon atmosphere into 5 mm NMR tubes and closed with airtight caps.

Table 1. Nuclear Spin Relaxation Data, Inertia Tensor Components, and Derived Rotational Diffusion Parameters Describing Molecular Reorientation of the Investigated Compounds in CDCl3 Solutions at 25 °C diffusion constants (1010 s−1)d compound 1

2 3

4 5

exptl relaxation times (s) C3 9.15 C4 8.22 C5 6.21 C6 9.08 C2 2.70 C8 2.45 C2 4.68 C4 6.22 N1 4.75 × 10−4 C5 4.18 C6 5.27 C5 2.95 N1, N3 2.45 × 10−4

a,b

T1,SA (s) C3 C4 C5 C6 C4 C5 C2 C4

a,b

49.2 40.9 32.5 40.3 22.6 28.9 27.3 49.5

C5 29.8 C6 31.7 C5 25.5

NOE factors C3 C4 C5 C6 C2 C8 C2 C4

1.62 1.59 1.61 1.53 1.73 1.83 1.64 1.74

C5 1.71 C6 1.64 C5 1.76

a

c

D1e

D2f

D3f

588

4.61(17)

3.24(11)

0.90(6)

1258

0.78(5)

1.09(7)

0.41(4)

1606

2.30(11)

2.18(9)

0.87(7)

1510

2.01(10)

1.94(9)

0.85(6)

2624

1.45(15)

0.73(8)

0.73(8)

inertia

a

The labels of the atom positions are followed by the appropriate relaxation times or NOE factors. bThe values of T1,SA for protonated carbons were calculated using eq 4. For C-4 and C-5 of 2, the measured T1 values (19.8 and 26.9 s, respectively) were corrected for both DD(1H) and DD(14N) relaxation contributions. The values of T2,Q(14N) were calculated from the measured 14N NMR line widths. cInertia tensor component (in u·Å2) corresponding to the out-of-plane inertia axis. dThe error estimates (in parentheses) were calculated using the Monte Carlo method from the errors in T1,DD (3%), T1,SA (12%), and T2,Q (20%). eDiffusion constant describing rotation about the axis perpendicular to the ring plane fDiffusion constants describing rotations about in-plane diffusion axes. 518


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Table 2. Relaxation Times and Other Physical Parameters Concerning Brominated Carbons and Bromines Used To Determine 1 13 79 J( C, Br) Spin−Spin Coupling Constants for the Investigated Compounds compound

carbon

Deff (1010 s−1)a

T1 (s)b

T1,SC (s)b

T1 (s)c

T1,SC (s)c

CQ (MHz)d

T2,Q (ns)

JCBr (Hz)e

|JCBr| (Hz)f

1 2 3 4 4 5 5

2 6 3, 5 2 4 2 4, 6

2.39 0.63 1.67 1.54 1.52 1.04 1.03

4.94 7.00 5.18 5.57 5.50 6.97 5.64

5.47 10.40 6.27 6.35 6.83 8.86 8.08

24.3 15.1 21.7 24.9 15.2 19.0 14.0

46.8 53.1 83.0 56.2 33.3 46.6 57.6

552.6 570.4 589.5 578.9 575.9 588.3 587.1

119 29 73 70 70 46 45

121 187 148 147 134 151 163

128(9) 182(13) 150(10) 152(10) 147(10) 159(11) 167(11)

a

Effective diffusion constant describing the reorientation rate of the given C−Br vector. bConcerns 79Br-bonded carbon(s). cConcerns 81Br-bonded carbon(s). dCalculated using the so-ZORA/B3LYP/TZ2P/COSMO(CHCl3) method. eThe values of 1J(13C,79Br) were calculated from the difference in SC relaxation rates for isotopomers containing 79Br and 81Br and the T2,Q(79Br) relaxation time calculated from Deff and CQ(79Br). fThe values of 1J(13C,79Br) were calculated from the SC relaxation time T1,SC(79Br) and the T2,Q(79Br) relaxation time calculated from Deff and CQ(79Br); errors (in parentheses) were calculated by Monte Carlo simulations assuming errors of 5% in T1,SC(79Br) and Deff and 10 MHz in CQ(79Br).

ΔωCX = [γC(1 − σC) − γX(1 − σX)]B0

diffusion parameters to only two. In the remaining cases, the directions of the in-plane diffusion axes had to be established on the basis of other indications. In the case of 1, we had at our disposal a sufficient number of independent relaxation data to treat the orientation of the in-plane diffusion axes during the data analysis as an additional unknown, while for 2 and 4 we assumed that all three diffusion axes coincided with the axes of the appropriate inertia tensors. The most important experimental data used to derive the rotational diffusion parameters were relaxation times characterizing the rates of longitudinal relaxation of 13C nuclei of protonated ring carbons caused by the dipolar 13C−1H mechanism. These T1,DD parameters could be established from the measured longitudinal relaxation times, T1, and NOE enhancement factors using the well-known relationship3,24

(1)

where X = 79Br or 81Br.27 The needed isotropic magnetic shielding constants of carbon nuclei were calculated using the measured 13C NMR chemical shifts and the relationship σ(13C) = σTMS − δ(13C)

(2)

where σTMS = 186.6 ppm stands for the isotropic magnetic shielding constant of tetramethylsilane carbons. The shielding constants of bromine nuclei for compounds 1−5 were calculated theoretically and corrected for relativistic effects using a method described elsewhere.27 These values were 2112, 2171, 2286, 1964, 2041, 1941, and 2027 ppm for 1, 2, 3, 2-Br of 4, 4-Br of 4, 2-Br of 5, and 4-Br of 5, respectively. The molecular geometry optimizations and calculations of NMR parameters were performed using in each case the same level of theory.28 The nonrelativistic quantum-chemical calculations, which included geometry optimizations and calculations of NMR parameters and electric field gradient (EFG) tensors, were performed with the aid of the Gaussian 03 program29 using DFT with either the BHandH30 or B3LYP31 hybrid functional and the standard 6-311++G(2d,p) basis set. The impact of the solvent was treated using the PCM solution model.32 The analogous relativistic calculations, which took into account both scalar and spin−orbit coupling terms using the two-component zeroth-order regular approximation (ZORA) Hamiltonian available in the ADF program,33−36 employed the same functionals, the TZ2P basis set or the jcpl basis set36 in the case of spin−spin coupling constants, and the COSMO solution model.37,38

T1,DD = (ηmax /η)T1

(3)

In the course of the analysis, for a given carbon, the dipolar interactions with all of the protons in the molecule were taken into account. The necessary interatomic distances were adopted from the optimized molecular geometries, except in the case of the directly bonded C−H atoms, where the distance was assumed to be equal to 1.12 Å to compensate for the effects of vibrations.26,40−43 Unfortunately, the data concerning the 13 C···1H dipolar relaxation alone did not allow separation of the diffusion parameters describing reorientations about the axis perpendicular to the ring plane and about the other two axes, as all of the C−H relaxation vectors lay in the ring planes. To overcome this difficulty, we included in the analysis the longitudinal relaxation rates due to the shielding anisotropy mechanism, T1,SA, estimated for the protonated carbons as

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RESULTS AND DISCUSSION Reorientation. The reorientation of the investigated molecules in solution has been described as rotational diffusion.39 In all cases, the plane of the heterocycle is a molecular symmetry plane, and thus, all of the molecules are planar rotors with one of the principal axes of the diffusion tensor being perpendicular to this plane. For 3 and 5, the directions of the two remaining diffusion axes result unambiguously from the C2v molecular symmetry, although in the case of 5 we had to introduce an additional assumption into the data analysis because of the shortage of accessible relaxation data. Specifically, taking advantage of the similarity of 5 and of 1,3,5-tribromobenzene, we assumed that our molecule behaved like a symmetric top with equivalent in-plane axes. This assumption allowed us to reduce the number of unknown

T1,SA = [ηmax /(ηmax − η)]T1

(4)

If necessary, the so-obtained values were corrected for dipolar relaxation due to 14N nuclei of directly bonded nitrogens. We realize that T1,SA values obtained in this way are only rough estimates of the true values, and in the relaxation data analyses we assigned to them weights 4 times smaller than those for T1,DD values. Moreover, in the case of 2, where the η values for protonated carbons were higher than in the other cases, we resigned from the procedure based on eq 4 and used the directly measured T1 values for C-4 and C-5 corrected for calculated contributions of the dipolar 13C···1H and 13C−14N mechanisms. In order to establish proper values of these corrections, two iteration steps were necessary. Additionally, for 3 and 5 the T2,Q(14N) values were used. These values were 519


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The Journal of Physical Chemistry A calculated from the 14N NMR line widths and were also not especially precise because of the broadness of these lines. In order to use T1,SA and T2,Q values in the analysis, the theoretically calculated shielding tensors of appropriate carbons and EFG tensors at the nitrogen nuclei were used. The experimental relaxation data and the diffusion parameters derived from them with the aid of the procedure described above are collected in Table 1. The similarity of the diffusion constants determined for all of the investigated molecules is striking. For four of the investigated molecules, the value of D1 coefficient, which describes the rate of reorientation about the axis perpendicular to the ring plane, is larger than the other two, which is probably a consequence of the flat shape of these molecules. The fact that compound 2 breaks out of this regularity can be attributed to other factors affecting molecular reorientation. One may suppose that in chloroform solution the nitrogen lone electron pairs of the investigated molecules are preferentially solvated by the formation of weak solute−solvent hydrogen bonds. The theoretical calculations support such a possibility. Such hydrogen-bonded complexes are, of course, very unstable, but nevertheless, they can slow down the reorientation. The larger the number of nitrogens, the stronger is the effect. The solvation effect also seems to explain the fact that the D1 reorientation of 4 is slightly slower than that of 3, despite the somewhat smaller inertia constants involved (however, see the error bars in Table 1). When changes in all of the other factors can be neglected, the increase in the appropriate component of the inertia tensor is expected to decrease the reorientation rate of the molecule. Indeed, in the investigated series such a tendency can be discerned for D1, keeping in mind, of course, the solvation effect. Relaxation of Brominated Carbons. Usually, longitudinal relaxation of brominated quaternary carbons in isotopomers containing 79Br is dominated by the scalar relaxation of the second kind (SC2) mechanism, while for such carbons in isotopomers containing 81Br other mechanisms can also play an important role.4,10,11,44−50 The SC2 relaxation rates of carbons in the two bromine isotopomers are different because of the different Larmor frequencies and different relaxation rates of the two bromine isotopes. The magnetization recovery curves obtained by saturation−recovery or inversion−recovery relaxation experiments are sums of two exponentials. The decomposition of such curves, which usually are recorded with permanent proton decoupling, into curves describing the recovery of the magnetization originating from particular isotopomers, demands that the influence of NOEs be taken into account.10,48 This problem, as well as an effective procedure allowing its solution, have been described in our previous paper.10 The parameters T1(79Br) and T1(81Br) obtained this way describe the overall relaxation rates of brominated carbons in appropriate isotopomers. In order to obtain the relaxation times concerning exclusively the SC2 mechanism, the T1(X) (X = 79Br, 81Br) parameters have to be corrected for contributions from all of the other relaxation mechanisms in operation:

measurement conditions. The remaining terms on the righthand side of the above equation can be calculated using the molecular geometries and diffusion tensors determined in the previous step of the relaxation data analysis. In the case of DD mechanisms, the contributions coming from dipolar interactions with all of the hydrogens in the molecule should essentially be included, while in the case of bromines and nitrogens, it is sufficient to take into account only the interactions with directly bonded atoms. Evaluation of the contribution of the shielding anisotropy mechanism demands either that relaxation measurements be performed at several magnetic fields or that the magnetic shielding tensor involved be calculating theoretically. We used the latter approach, remembering that for brominated carbons the shielding tensors are affected by relativistic effects. It has been found out that at B0 = 11.7 T the SA relaxation introduces the largest corrections to the measured relaxation rates for all of the brominated carbons in the investigated molecules. The uncorrected and corrected relaxation times (T1(X) and T1,SC(X), respectively) for brominated carbons in our molecules are collected in Table 2. Inspection of these results clearly shows that in the case of isotopomers containing 79Br, the correction procedure affects only slightly the relaxation parameter involved, although the correction is not negligible. On the other hand, in the case of isotopomers containing 81Br, the corrections are always large. Essentially, it is possible to derive simultaneously the bromine−carbon spin−spin coupling constants and the relaxation rates of bromines from the values of T1,SC(79Br) and T1,SC(81Br) without introducing any other experimental or theoretical data specific for a given molecule. It seems, however, that such a procedure may be unreliable, taking into account the possibility of cumulation of errors as well as several unavoidable assumptions adopted in the data analysis. We feel that the precision of the determined values of the T1,SC(81Br) parameters actually remains unknown and may be low. Taking this into account, we decided to resign from the experimental determination of the bromine relaxation times and to derive the carbon−bromine spin−spin coupling constants only. To do that, we exploited SC2 relaxation data and, additionally, the theoretically calculated quadrupole coupling constants, CQ, for bromines in our molecules. This allowed us to base our final results either on the more reliable values of T1,SC(79Br) or on the differences 1/T1,SC(79Br) − 1/ T1,SC(81Br). The latter approach seemed to be even more attractive, as it allowed us to avoid calculating most of the corrections appearing in eq 5. Actually, the two approaches yielded the same results within the experimental error (Table 2), which confirms the reliability of these results. Thus, in order to accomplish the data elaboration, we had to supplement our relaxation data with the CQ values (Table 2). These constants had been calculated theoretically with the use of the DFT soZORA method, including relativistic effects. Of course, the use of theoretical CQ data introduces additional error, but it should be lower than that which would be introduced by rough estimates of T1,SC(81Br) parameters. Possessing CQ data, we could calculate the transverse relaxation times of 79Br nuclei in our objects, as this relaxation is dominated by the quadrupole mechanism. The rate parameters describing reorientation of particular C−Br vectors (effective diffusion constants, Deff; Table 2) were calculated from the molecular geometries and the rotational diffusion tensors determined previously. Then the T2,Q values were calculated from the well-known formula4,51

T1,SC(X) = [T1(X)−1 − T1,DD(1H)−1 − T1,DD(X)−1 −1

− T1,DD(14 N)−1 − T1,SA −1 − T1,RF−1]

(5)

The contributions of relaxation caused by random fluctuating magnetic fields (RF), arising first of all from the spin−rotation interactions and intermolecular DD interactions, are expected to be negligible for our molecules under the applied 520


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Table 3. Values of 1J(13C,79Br) Spin−Spin Coupling Constants (in Hz) Calculated Theoretically Using Various DFT Methodsa and the Values Derived from the Relaxation Measurements compound

carbon

A

B

Rel-A

Rel-B

exptlb

1 2 3 4 4 5 5

2 6 3, 5 2 4 2 4, 6

−156.8 −185.3 −173.9 −184.9 −189.9 −197.1 −195.6

−139.6 −168.0 −154.0 −161.5 −170.5 −172.7 −176.8

−170.8 −203.6 −187.7 −202.7 −206.8 −214.8 −212.1

−174.0 −209.5 −189.5 −203.8 −209.5 −216.4 −216.1

−128(9) −182(13) −150(10) −152(10) −147(10) −159(11) −167(11)

a

The theoretical methods used in calculations were the following: (A) nonrelativistic DFT/B3LYP/6-311++G(2d,p)/PCM(CHCl3); (B) nonrelativistic DFT/BHandH/6-311++G(2d,p)/PCM(CHCl3); (Rel-A) DFT so-ZORA/B3LYP/jcpl/COSMO(CHCl3); (Rel-B) DFT so-ZORA/ BHandH/jcpl/COSMO(CHCl3). bThe sign established on the basis of theoretical calculations; numbers in parentheses denote error estimations.

Table 4. Comparison of the Effectiveness of Various DFT Methods in Predicting 13C NMR Chemical Shifts for the Investigated Compounds method

slopea

intercept (ppm)a

RMSD (ppm)a

mean dev. for C−Br (ppm)a

RMSD (ppm)b

DFT/B3LYP/6-311++G(2d,p)/PCM(CHCl3) DFT/BHandH/6-311++G(2d,p)/PCM(CHCl3) DFT/so-ZORA/B3LYP/TZ2P/COSMO(CHCl3) DFT/so-ZORA/BHandH/TZ2P/COSMO(CHCl3)

0.963 0.918 0.939 0.891

183.2 195.8 185.1 198.3

0.78 1.01 1.18 1.73

20.9 13.7 6.9 1.5

8.37 5.86 3.33 1.71

a

The regression parameters were derived from the correlation including the data for nonbrominated carbons only. bThese values were derived from the correlation including the data for all of the carbons.

0.3π 2(2IX + 3) 1 = 2 T2,Q (X) IX (2IX − 1)CQ (X)2 (1 + χX 2 /3)(6D⊥)−1

would be a still improper evaluation of the electron correlation effects by more rigorous relativistic theoretical methods and an accidental error compensation in the case of nonrelativistic methods. Shielding. The NMR data and DFT calculations for the investigated series of compounds also provide a good opportunity to compare the effectiveness of the popular DFT methods of theoretical prediction of the magnetic shielding constants for brominated aromatic carbons. The overall set of experimental data consists of 14 chemical shifts for nonbrominated carbons and seven chemical shifts for brominated carbons. The first group should be properly predicted by various DFT methods provided the scaling procedure is used.53,54 Indeed, the results of correlation analysis and especially the low root-mean-square deviation (RMSD) values found (0.78 to 1.18 ppm, depending on the computational method used) fully follow this expectation (Table 4; also see Figure 2). For brominated carbons, however, the situation is quite different. For three of the four theoretical methods used, the data for such carbons systematically and significantly diverge from the regression lines found for nonbrominated carbons (Figure 2). The size of these deviations is characteristic for a given DFT method and to a lesser extent depends on the electronic surroundings of a given carbon. Giesen and Zumbulyadisa53 observed similar features of the chemical shift data for chloro, bromo, and iodo compounds. They proposed to overcome this difficulty by correlating chemical shifts with shielding constants separately for nonhalogenated carbons and for carbons bonded to particular halogen atoms or by introducing special corrections to take into account the halogen effects. Obviously, a rigorous theoretical method should predict experimental chemical shifts without any artificial corrections. It is known that halogen effects arise from relativistic effects experienced by electrons moving in the space close to a heavy nucleus, causing a characteristic additional downfield shift of the NMR signals of the halogen-bonded carbons.16,18,55,56 The data collected in Table 4 clearly show that including relativity

(6)

For carbon-bonded bromines, the asymmetry parameter, χ, is small and may be neglected. Then, if T1,SC(79Br) is the only relaxation parameter used, the one-bond spin−spin coupling constant 1J(13C,79Br) can be calculated using the relationship 1 = T1,SC(A)

2 I (I 3 X X

+ 1)(2πJAX )2 T2(X)

1 + DωAX 2T2(X)2

(7)

where A = C, X = Br, and ΔωAX is the appropriate angular frequency difference between the A and X resonances. If the difference in relaxation times for the two isotopomers is used, the well-known relationships 13

79

γ81 J(13C, 81Br) = Br = 1.078 13 79 γ79Br J( C, Br)

(8)

and ⎛ Q 79 ⎞2 = ⎜⎜ Br ⎟⎟ = 0.7008 79 T2,Q ( Br) ⎝ Q 81Br ⎠ T2,Q (81Br)

(9)

in which QX is the nuclear quadrupole moment, have to be applied, and eq 7 has to be used twice, once for each isotopomer. The values of T2,Q(79Br) and 1J(13C,79Br) calculated in this way are collected in Table 2. The carbon−bromine spin−spin coupling constants were also calculated using several theoretical methods. The agreement between the experimental and theoretical values of 1 13 79 J( C, Br) for nonrelativistic computational methods is acceptable. Also, the agreement between the theoretical results obtained by the two relativistic methods is noticeable. However, these theoretical results generally overestimate the experimental values (Table 3). The reason for this unexpected discrepancy remains unclear (cf. refs 34 and 52). One possible explanation 521


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Figure 2. Deviations of the theoretically calculated 13C NMR chemical shifts from the δexp/σtheor regression lines derived using the data for nonbrominated carbons and various theoretical methods: (a) nonrelativistic DFT/B3LYP/6-311++G(2d,p)/PCM(CHCl3); (b) nonrelativistic DFT/BHandH/6-311++G(2d,p)/PCM(CHCl3); (c) DFT so-ZORA/B3LYP/jcpl/COSMO(CHCl3); (d) DFT so-ZORA/BHandH/jcpl/ COSMO(CHCl3). Blue bars are for nonbrominated carbons and red bars for brominated carbons.

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into the theoretical model by using the so-ZORA method reduces the deviations of points for brominated carbons from the regression line derived for nonbrominated ones, although with the B3LYP functional, deviations of the order of 7 ppm are still present. On the other hand, the results are much better with the BHandH functional, and the points for brominated carbons do not disturb the experiment/theory correlation. The relative effectiveness of the particular computational methods used in this study is well illustrated by Figure 2 and the data in the last column of Table 4.

CONCLUSIONS

The interpretation of the longitudinal DD and SA relaxation data (11.7 T, 25 °C, CDCl3) for nonbrominated carbons of 2bromopyridine (1), 6-bromo-9-methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5) allowed us to determine the rotational diffusion tensors describing reorientation of these molecules in the investigated solutions (Table 1). In most cases, the fastest reorientation occurred about the direction perpendicular to the aromatic ring planes. In the case of 2, such rotation was 522


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somewhat slower, probably because of preferential solvation of the electron lone pairs of the nitrogens. Subsequent analysis of the relaxation data of brominated carbons led to separation of the effects of the scalar relaxation of the second kind and determination of the one-bond carbon−bromine spin−spin coupling constants (Table 2). These values were compared with the results of the theoretical DFT calculations of these parameters (Table 3). It was observed that better agreement between the experimental and theoretical values was obtained for the theoretical methods DFT/F/6-311++G(2d,p)/PCM (F = BHandH, B3LYP), which neglect relativistic effects. On the other hand, the magnetic shielding constants for brominated carbons were proven to be predicted much better by the relativistic theoretical methods, especially by DFT so-ZORA/ BHandH/TZ2P/COSMO, than by nonrelativistic ones (Table 4).

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AUTHOR INFORMATION

Corresponding Author

*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. The MPD/2010/4 Project, realized within the MPD Programme of the Foundation for Polish Science, cofinanced by the European Union, Regional Development Fund, is acknowledged for a fellowship to A.W.

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Interpretation of the Longitudinal 13C Nuclear Spin Relaxation and

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