Article pubs.acs.org/JPCA
Shielding and Indirect Spin−Spin Coupling Tensors in the Presence of a Heavy Atom: An Experimental and Theoretical Study of Bis(phenylethynyl)mercury† Adam Gryff-Keller,‡,§ Anna Kraska-Dziadecka,*,‡ Sergey Molchanov,‡ and Artur Wodyński∥ ‡
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
∥
S Supporting Information *
ABSTRACT: Magnetic shielding and indirect spin−spin coupling phenomena are tensorial properties and both their isotropic and anisotropic parts do affect NMR spectra. The involved interaction tensors, σ̂ and J,̂ can nowadays be theoretically calculated, although the reliability of such methods in the case of anisotropic parameters, Δσ and ΔJ, in systems involving heavy nuclei, yet demands testing. In this communication the results of the experimental and theoretical investigations of bis(phenylethynyl)mercury (I) labeled with 13C isotope at positions neighboring Hg are reported. The theoretical calculations of molecular geometry and values of NMR parameters for I have been performed by the ZORA/DFT method, including the relativistic scalar and spin−orbit coupling contributions, using the PBE0 functional and TZP (or jcpl) basis set. These values have been confronted with the experimentally measured ones. The isotropic parameters have been measured by the standard 13C and 199Hg NMR spectra. The shielding anisotropies for the atoms in the central part of molecule I have been determined in a liquid sample using magnetic relaxation measurements. The relaxation data have been interpreted within the rotational diffusion theory, assuming the symmetrical top reorientation model. The anisotropies of onebond 13C−199Hg and two-bond 13C−Hg−13C spin−spin couplings have been determined exploiting the temperature-dependent 13 C NMR spectra of I in the ZLI1167 liquid-crystal phase. We have found that our theoretical calculations reproduce experimental values of both isotropic and anisotropic NMR parameters very well.
■
INTRODUCTION Sixty years ago Ramsey1−3 published the series of fundamental papers containing the microscopic theory of NMR parameters. This theory predicted that both the shielding and the indirect spin−spin coupling phenomena are tensorial properties and that even in the case of axial symmetry of the electronic environment of the considered nuclei not only the isotropic parts, Tiso, of the involved tensors but also their anisotropies ΔT, can affect NMR spectra. These parameters are usually defined as Tiso = (1/3)tr(T̂ ) = (1/3)T + (2/3)T⊥
(1)
Taniso = (2/3)ΔT = (2/3)(T − T⊥)
(2)
determine NMR spectral patterns recorded for isotropic liquids. In a more general case of an anisotropic phase, however, both isotropic and anisotropic parameters affect the spectra. There are many examples of determination of Δσ and ΔJ from spectral patterns observed in liquid crystals and solids (e.g., refs 7−18). Actually, even in isotropic solutions Δσ and ΔJ do affect relaxation rates, although an experimental example in which the mechanism due to ΔJ seems to dominate the dipolar relaxation, has been presented only recently.19 Determination of the anisotropy of the indirect spin−spin coupling is, in general, a nontrivial task as the ΔJ effects are always heavily masked by the dipolar coupling between the same nuclei. On the other hand, there are numerous examples of determination of Δσ by nuclear spin relaxation studies in liquids (e.g., refs 20−23). The whole tensors of magnetic interactions can nowadays be theoretically calculated. Such calculations become more and more popular among the NMR community thanks to development of efficient calculation methods and generalpurpose quantum chemistry programs. It is clear that the theoretical approach is especially attractive for evaluating ΔJ parameters. It seems, however, that the reliability of calculation
where T∥ and T⊥ denote the parallel and perpendicular principal components of the appropriate shielding, dipolar coupling or indirect spin−spin coupling tensors. The dipolar (direct) coupling tensors, D̂ , are traceless and so their isotropic parts vanish. For molecular systems composed of atoms possessing light nuclei Ramsey’s theory has survived to present times without modifications, whereas for systems involving heavy atoms this theory has had to be adapted to include relativistic effects.4−8 Indeed, the isotropic parts of those tensors: shielding constants, σ, or equivalently chemical shifts, δ, and spin−spin coupling constants, J, are easily measurable parameters as they © 2012 American Chemical Society
Received: August 7, 2012 Revised: October 8, 2012 Published: October 10, 2012 10615
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
The Journal of Physical Chemistry A
Article
PBE0 functional and TZ2P basis were used, whereas in indirect spin−spin coupling calculations the same functional and jcpl (a suitably augmented TZ2P) basis were applied. The calculations were carried out using the Gaussian charge distribution nuclear model (SCF step/perturbation operator). Solvent effects were neglected.36
results for systems involving heavy nuclei should yet be tested experimentally, especially in the case of anisotropy parameters. We have performed such a test in this communication, taking as an investigated object the molecule of bis(phenylethynyl)mercury (I; Figure 1), a compound that was thoroughly studied at least two times in the past.23,24 The results of this test are encouraging.
Figure 1. Bis(phenylethynyl)mercury (I) labeled with positions.
13
■
RESULTS AND DISCUSSION The molecular geometry optimization of I (neglecting solvent effects) yields the structure of D2d symmetry. However, test calculations performed using nonrelativistic level of theory have shown that energies for D2 and D2h structures are only marginally higher (the differences below 0.7 kJ/mol). We realize that in solutions, especially in solvents of high donicity, such as DMSO, this is only an approximate description of molecular shape of I. Indeed, nonrelativistic calculations confirm formation of a solvation complex with DMSO in which solvent molecule is bonded to Hg and the solute molecule is bent by ca. 10°. Formation of unstable solvates could explain the extraordinarily high sensitivity of the 1 199 J( Hg,13C) coupling constant to the solvent. The change of this constant by about 200 Hz when passing from weakly interacting solvents to DMSO was reported previously18 and has also been observed in this study. More detailed treatment of the solvation problem, however, exceeds the frame of this work. In the remaining part of the discussion the “gas phase” molecular geometry of I is adopted. Such a simplifying assumption seems to be a necessity and, on the other hand, does not seem to influence our results and conclusions. Within this proviso, one can expect coincidence of the principal axes systems of δ̂, σ̂, D̂ , and J ̂ tensors for nuclei or pairs of nuclei belonging to the central fragment −CCHgCC− of the investigated molecule. Moreover, one can expect that all these tensors are (almost) axially symmetrical. Validity of these expectations has been confirmed by our theoretical calculations. These features remarkably simplify the quantitative description of the observed spectroscopic phenomena.
C in α-
■
EXPERIMENTAL AND THEORETICAL METHODS Deuterated solvents, 1 3 C-labeled phenylacetylene (C6H5C13CH) and ZLI1167 liquid crystal phase were commercial products. Bis(phenylethynyl)mercury, doubly labeled with 13C (I), was prepared according to the literature25 procedure using C6H5C13CH as a substrate. Most of the NMR spectra were recorded using VNMRS NMR spectrometer working at B0 = 11.7 T; during relaxation measurements other spectrometers were also used. The 0.1 M solutions of I in CDCl3 and DMSO-d6 were prepared directly in 5 mm o.d. NMR tubes. The sample for relaxation measurements was thoroughly degassed and sealed. The longitudinal 13C relaxation rates were measured using the standard inversion−recovery method26 at four magnetic fields 4.7 T (Gemini2000), 7.05 T (Bruker Avance II), 9.4 T (Mercury VX), and 11.7 T (VNMRS). The measurement temperature (25 °C) was monitored by a methanol sample. The recovery curves were analyzed by the nonlinear leastsquares procedure, fitting three adjustable parameters. Further details concerning the methodology applied in our relaxation measurements were described previously.22,23 The linewidths of the central line of 13Cα and 199Hg satellites in 13C NMR spectra were measured by performing line shape analysis assuming the Lorentzian shape of these NMR lines. Oriented (and isotropic) phase 13C NMR spectra of I in Merck ZLI-1167 phase (ca. 20% w/v) were measured at temperatures 25−90 °C. The investigated solution was placed in the 3 mm o.d. NMR tube inserted into a standard 5 mm o.d. tube. Between the walls of these tubes an amount of DMSO-d6 was added, which provided a lock and 13C reference signal. Some initial test calculations which included geometry optimizations and NMR shielding calculations were performed with the aid of Gaussian03 program27 using nonrelativistic DFT method with PBE1PBE hybrid functional (also known as PBE0)28 and the standard 6-311++G(2d,p) basis set for H and C atoms, and for Hg the LANL2DZ29 basis which includes the effective core potential replacing core electrons. The final results of theoretical calculations were achieved by two-component relativistic ZORA/DFT method with the use of ADF program.30−32 The molecular geometry was optimized on the BVP8633−35 TZ2P level, including scalar relativistic effects. In this calculation the innermost atomic shells, namely 1s of carbon and 1s-4d of mercury, have been approximated by the frozen core densities. During the calculations of NMR parameters the contribution due to spin−orbit coupling was also taken into account. In the magnetic shielding calculations
Figure 2. Deviations of the experimental 13C chemical shifts of bis(phenylethynyl)mercury from the regression line: δ calc = 0.939(188.7 − σcalc) = −0.939σcalc + 177.2, RMSD = 1.47 ppm.
Figure 2 and Table 1 show that the applied level of theory ensures very good reproduction of the experimental values of the isotropic 13C NMR chemical shifts of I. The comparison of the values measured for DMSO-d6 solution and the theoretical values of the isotropic shielding constants has been performed using the two-parameter scaling procedure37 which yielded the root-mean-squares deviation as low as 1.47 ppm and reasonable values of the slope (−0.939) and intersept (estimated σTMS = 10616
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
The Journal of Physical Chemistry A
Article
Table 1. Experimental (DMSO-d6, 25°C) and Theoretically Calculated Isotropic NMR Parameters for Bis(phenylethynyl)mercury X δ(X)
a
Cα
|J(Hg,X)|
exp calc exp
J(Hg,X) |J(Cα,X)| J(Cα,X)
calc exp calc
123.21 124.91 2692 2472a 2532 58.7b 69.9b
Ci
Co
Cm
Cp
104.05 104.55 675
Cβ
123.34 122.70 57.5
131.46 133.06 15.0
128.55 126.01
127.99 127.36
720 135.4, 10.4b 161.3, 12.9b
66.5
−30.9
6.1
−7.3
Measured in ZLI-1167 at 90 °C. bThe value concerns nJ(Cα−Hg ···X).
188.7 ppm) of the δexp vs σtheor regression. Also the reproduction of the experimental values of the spin−spin coupling constants involving 199Hg nucleus by our theoretical calculations (Table 1) is fully satisfying, taking into account the high solvent sensitivity of these parameters in the investigated molecule. Theoretical calculations, as opposed to experimental measurements, allow us to establish the absolute signs of those constants. It is interesting that 2J(13C−Hg-13C) and 3J(13C− Hg−C13C) coupling constants, which do not involve the nuclear spin but do involve the electrons of mercury atom, have also been reproduced very well. The experimental values of these constants could be determined by the laocoon-type analysis of the ABX pattern of the isotopomer of I possessing three 13C nuclei (PhC13CHg13C13CPh, ca. 2% abundance). It is noteworthy that the 2J(13CHg13C) coupling constant is positive, similar to 2J(13CC199Hg) and some other geminal couplings involving alkyne fragments.38 The question of accuracy of the results of our theoretical calculations is even more intriguing in the case of shielding anisotropy parameters. The values of these parameters for central atoms of I were determined previously23 using a method based on the interpretation of magnetic relaxation data concerning 13C and 199Hg nuclei. Because that interpretation involved some simplifying assumptions and hypotheses, we have decided to check validity of those results and to repeat the measurements and interpret them once again. This time we measured the longitudinal relaxation rates for 13C nuclei at single temperature but at four magnetic fields 4.7, 7.05, 9.4, and 11.7 T (Table S1, Supporting Information). Moreover, we measured the line widths of 199Hg satellites in 13C NMR spectra, wsat. These widths were established by line shape analysis and used to evaluate the longitudinal relaxation rates of 199 Hg nucleus, using the relationship R1(199Hg) = 2π (wsat − w0)
mechanisms can be safely neglected in the interpretation of the discussed relaxation data. The reorientation of molecule I in solution has been described within the rotational diffusion model of the symmetrical top.39 The diffusion constants, D∥ and D⊥, were determined from the relaxation data for protonated carbons, using a computer program based on Canet’s formulation of magnetic relaxation equations40 and described elsewhere.41 Next, the shielding anisotropy parameters for acetylene carbons were calculated, taking into account the corrections from the dipolar interactions of these carbons with protons. A similar method was used to determine the magnetic shielding anisotropy parameter of the mercury nucleus. Because the corrections due to CSA mechanism for protonated carbons are small and the molecular geometry of I is well established, the vibrational corrections to C−H bond lengths are the main factor determining accuracy of the diffusion parameters and in consequence the shielding anisotropy parameter of Cα. This bottleneck is characteristic for dipolar-relaxation-based studies of molecular movements.22,23,42−44 Assuming a reasonable C− H distance (rC−H = 0.112 nm) we have come to the results being in agreement with those obtained in the previous work (Table 2).23 Eventually, we have found that the shielding anisotropy parameters for Cα, Cβ, and Hg atoms of I have been reproduced reasonably well by our theoretical calculations. Table 2. Rotational Diffusion Constants and Shielding Anisotropy Parameters for Central Atoms of I Determined on the Basis of the Longitudinal Relaxation Rates of 13C and 199 Hg Nuclei (rC−H = 0.112 nm, DMSO-d6, 25 °C) log(D∥) −log(s)
log(D⊥) −log(s)
Δσ(Cα), ppm
Δσ(Cβ), ppm
Δσ(Hg), ppm
10.19 10.294
8.72 8.843
238 260
301 330a
5340 5478
249
339
5296
(3)
where w0 denotes the width of the central line. On the other hand, we have resigned from NOE measurements, as NOE parameters tend to be burdened with systematic errors, and, actually, under convenient circumstances become redundant. Indeed, in the case in hand one can expect that relaxation rates of protonated carbons are dominated by 1H−13C dipolar mechanism. Small contributions to the overall relaxation of those carbons due to carbon shielding anisotropy (CSA) can be estimated with sufficient accuracy, adopting the shielding tensors calculated theoretically, and introduced as corrections during the analysis of the relaxation data. The reverse situation occurs for the acetylene carbons, which relax mainly through CSA mechanism with only small admixture of dipolar mechanism. For the 199Hg nucleus, CSA is practically the only relaxation mechanism. We believe that other relaxation
notes ref 23 measured in this work calculated in this work
Based on Δσ(Cα) and Δσ(Cα)/Δσ(Cβ) = 0.788 determined in ref 23.
a
Experimental determination of ΔJ parameters is always a challenging task. Few examples of such studies dealing with organomercury compounds, based on the advanced interpretation of their nematic phase7,9 or solid state11,12,18 NMR spectra, have been reported. In most cases the determined values of ΔJ parameters are burdened by a relatively high uncertainty, because of severe experimental and interpretational difficulties. To the best of our knowledge, the experimentally determined ΔJ values involving heavy atoms have been confronted with the results of theoretical calculations only 10617
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
The Journal of Physical Chemistry A
Article
few times.15,18 In this study, taking advantage of labeling I with 13 C in both α-positions, we have determined the anisotropies of one-bond 199Hg−13C and two-bond 13C−Hg−13C couplings, exploiting the 13C NMR spectra of I in ZLI1167. This nematic phase is composed of three hydrogenated 4-cyano-4′alkylbiphenyls. A remarkable similarity of the solvent and solute molecules as it concerns molecular shape and molecular size has resulted in preserving the nematic order of the solutions even for relatively high solute concentrations and in a broad temperature range. Such feature of an investigated system is highly desirable in NMR studies. A typical 13C NMR oriented-phase spectrum of the investigated compound is shown in Figure 3. The signal
Figure 3. ZLI-1167 nematic phase spectrum of bis(phenylethynyl)mercury at 50 °C.
Figure 4. Relationships of signal splittings due to 199Hg−13C and 13C− Hg−13C couplings and signal position (■, 1J; ▲, 2J) for various orientations of bis(phenylethynyl)mercury molecule in ZLI-1167 phase observed in the spectra recorded in 25−90 °C temperature range.
pattern is very well visible and can easily be rationalized. The central doublet originates from isotopomers possessing nonmagnetic Hg isotopes and represents the oriented-phase A2 pattern of 13C nuclei of two equivalent alpha carbons,7,9 whereas the remaining two doublets are 199Hg satellites constituting the A2 part of A2X spin system. The relative integral intensities of the central doublet and satellites point out that dependently on measurement conditions the spectrum of isotopomer containing the 201Hg isotope (I = 3/2; 16% abundance) either overlaps the central doublet or is smeared out over a broad frequency range due to the rapid 201Hg relaxation and very large effective 201Hg−13C coupling constant. Thus, neglecting the undetectable isotope effect, the spectra depend on two effective coupling constants and one chemical shift. The signal splittings as well as the signal position are temperature-dependent due to changes of the effective orientation of the solute molecules with respect to the spectrometer magnetic field. Owing to the molecular shape, these three effective spectral parameters depend linearly on the same order parameter7,9 and in consequence are linearly interdependent. The observed dependences of the effective coupling constants on the signal position in the spectra recorded at various temperatures are shown in Figure 4. Let us recall that in the case in hand all tensors governing the spectra under discussion are axially symmetrical, with the common symmetry axis. As a result, the tensors describing the direct and indirect spin−spin magnetic couplings form a common tensor, whose anisotropy ΔTcoupling = 3D + ΔJ
affects the oriented phase spectra.7,9 The numerical factor before dipolar coupling constant, D, in the above equation comes from the commonly adopted definition of the dipolar coupling tensor: ⎡2 0 0 ⎤ ⎢ ⎥ D̂ = D⎢ 2 −1 0 ⎥ ⎣ 0 0 −1⎦
(5)
Furthermore, the coaxiality of the internuclear coupling and magnetic shielding tensors in I causes the basic relationships between the values of anisotropy parameters of these tensors to be particularly simple. Indeed, in the case in hand the basic dependence of the signal position observed in nematic phase spectra on isotropic chemical shift and anisotropy of the involved shielding tensor, reads δobs = δiso − (2/3)sΔσ
(6)
where s describes the orientation of the symmetry axis of the shielding tensor with respect to the magnetic field direction. Simultaneously, the effective splitting of the 13C signal (Jobs) due to the coupling with 199Hg spin (a part of the weakly coupled AX spin system) can be expressed as Jobs = Jiso + (2/3)s(3D + ΔJ )
(7)
These relationships denote the linear interdependence between Jobs and δobs parameters and lead to the operational formula:
(4) 10618
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
The Journal of Physical Chemistry A
Article
Table 3. Parameters Describing Magnetic Interactions between Bis(phenylethynyl)mercury 199
Jiso exp value calc value a
2472 2532
199
Hg−13C
ΔJ 742a 801
13
C−Hg−13C
D
3D + ΔJ
−674 −737.4a
−1470 −1221 −1411a
Assuming 3% reduction of the interatomic distances.
3D + ΔJ = −slope(Jobs vs δobs)Δσ
J ′obs = s(3D + ΔJ ′)
■
D
3D + ΔJ
−119 −130a
−377 −342 −376a
REFERENCES
(1) Ramsey, N. F. Phys. Rev. 1950, 78 (6), 699−703. (2) Ramsey, N. F. Phys. Rev. 1951, 83 (3), 540−541. (3) Ramsey, N. F. Phys. Rev. 1953, 91 (2), 303−307. (4) Pyykko, P. Theor. Chem. Acc. 2000, 103 (3−4), 214−216. (5) Visscher, L.; Enevoldsen, T.; Saue, T.; Jensen, H. J. A.; Oddershede, J. J. Comput. Chem. 1999, 20 (12), 1262−1273. (6) Vaara, J.; Malkina, O. L.; Stoll, H.; Malkin, V. G.; Kaupp, M. J. Chem. Phys. 2001, 114 (1), 61−71. (7) Vaara, J.; Jokisaari, J.; Wasylishen, R. E.; Bryce, D. L. Prog. Nucl. Magn. Reson. Spectrosc. 2002, 41, 233−304. (8) Helgaker, T.; Jaszunski, M.; Pecul, M. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 53, 249−268. (9) Lounila, J.; Jokisaari, J. Prog. NMR Spectrosc. 1982, 15, 249. (10) Kroeker, S.; Hanna, J. V.; Wasylishen, R. E.; Ainscough, E. W.; Brodie, A. M. J. Magn. Reson. 1998, 135 (1), 208−215. (11) Power, W. P.; Lumsden, M. D.; Wasylishen, R. E. Inorg. Chem. 1991, 30 (15), 2997−3002. (12) Power, W. P.; Lumsden, M. D.; Wasylishen, R. E. J. Am. Chem. Soc. 1991, 113 (22), 8257−8262. (13) Iijima, T.; Hashi, K.; Goto, A.; Shimizu, T.; Ohki, S. Chem. Phys. Lett. 2006, 419 (1−3), 28−32. (14) Facelli, J. C. Prog. Nucl. Magn. Reson. Spectrosc. 2011, 58, 176− 201. (15) Jokisaari, J.; Autschbach, J. Phys. Chem. Chem. Phys. 2003, 5 (20), 4551−4555. (16) Willans, M. J.; Demko, B. A.; Wasylishen, R. E. Phys. Chem. Chem. Phys. 2006, 8 (23), 2733−2743. (17) Bryce, D. L.; Autschbach, J. Can. J. Chem. 2009, 87 (7), 927− 941. (18) Bryce, D. L.; Courchesne, N. M. D.; Perras, F. A. Solid State Nucl. Magn. Reson. 2009, 36 (4), 182−191. (19) Gryff-Keller, A.; Kraska-Dziadecka, A.; Molchanov, S.; Wodyński, A. VII Symposium Nuclear Magnetic Resonance in Chemistry, Physics and Biological Science, Warsaw, Poland; 26−28 September, 2012; poster. (20) (a) Anet, F. A. L.; O’Leary, D. Concepts Magn. Reson. 1991, 3, 193. (b) Anet, F. A. L.; O’Leary, D. Concepts Magn. Reson 1992, 4, 35. (21) Cisnetti, F.; Loth, K.; Pelupessy, P.; Bodenhausen, G. ChemPhysChem. 2004, 5 (6), 807−814. (22) Molchanov, S.; Gryff-Keller, A. Magn. Reson. Chem. 2003, 41 (10), 788−793. (23) Molchanov, S.; Gryff-Keller, A. Magn. Reson. Chem. 2000, 38 (1), 17. (24) Sebald, A.; Wrackmeyer, B. Spectrochim. Acta 1982, 38A (2), 163−173. (25) Makarova, L. G.; Nesmeyanov, A. N. The Organic Compounds of Mercury; North-Holland: Amsterdam, 1967. Makarova, L. G.;
(9)
(10)
To use the above equation, the vibrationally corrected internuclear distances, ⟨r−3⟩−1/3, have to be known. One may expect that in the ground vibrational state the instantaneous internuclear distances in the central fragment of I molecule are modified primarily by the harmonic vibrations. As a result, the effective distances are shortened as compared to the equilibrium ones.
■
CONCLUSION All the results obtained for the molecule investigated in this work confirm the effectiveness of a sufficiently advanced although rutinely accessible theoretical approach allowing the satisfactorily accurate values of isotropic as well as anisotropic NMR parameters to be calculated, even for systems involving heavy atoms. This method can be especially useful when the ΔJ parameter, difficult to measure, is to be estimated. ASSOCIATED CONTENT
S Supporting Information *
Table S1. The longithudinal relaxation times of 13C nuclei of bis(phenylethynyl)mercury in DMSO solution at 25 °C and at various magnetic fields. Table S2. Calculated magnetic shielding constants for nuclei of carbon atoms of bis-(phenylethynyl)mercury. The optimum energy molecular geometry of bis(phenylethynyl)mercury. This material is available free of charge via the Internet at http://pubs.acs.org
■
ΔJ 13a 14.5
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 the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, is acknowledged for a fellowship to A.W.
Taking into account eqs 6 and 9, one can interconnect the anisotropy parameters of the involved coupling and shielding tensors by 3D + ΔJ ′ = −(2/3)slope(J ′obs vs δobs)Δσ
Jiso 61.3 69.9
■
(8)
where slope(Jobs vs δobs) denotes the slope of the line representing the relationship between the observed signal splitting due to the 199Hg−13C coupling and the signal position (Figure 3). In oriented phases also the signal of A2-type spin system, such as 13C−Hg−13C involving NMR-silent Hg isotopes, splits into doublet due to residual dipolar and anisotropic J-coupling. The apparent coupling constant amounts to
■
Hg−13C and between 13C−Hg−13C Nuclear Spins in
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest. § E-mail: agryff@ch.pw.edu.pl † Preliminary results of this work were presented on EUROMAR conference in Dublin in July 2012. 10619
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
The Journal of Physical Chemistry A
Article
Nesmeyanov, A. N. Metody Elementno-Organicheskoy Khimii, Hg; Nauka: Moscow, 1965. (26) Braun, S.; Kalinowski, H. O.; Berger, S. 150 and more basic NMR experiments: a practical course; Wiley-VCH Verlag: Weinheim, Federal Republic of Germany, 1998; pp 160−161. (27) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, Revision C.02; Gaussian, Inc., Wallingford, CT, 2004. (28) Vetere, V.; Adamo, C.; Maldivi, P. Chem. Phys. Lett. 2000, 325, 99. (29) Hay, P. J.; Wadt, W. R J. Chem. Phys. 1985, 82, 270−83. (30) Velde, G. T.; Bickelhaupt, F. M.; Baerends, E. J.; Guerra, C. F.; Van Gisbergen, S. J. A.; Snijders, J. G.; et al. J. Comput. Chem. 2001, 22, 931−967. (31) Fonseca Guerra, C.; Snijders, J. G.; Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391. (32) ADF2012, SCM. Theoretical Chemistry; Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com. (33) Vosko, S.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (34) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (35) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (36) Autschbach, J. ChemPhysChem 2009, 10, 2274. (37) Gryff-Keller, A. Concepts Magn. Reson. A 2011, 38A, 289−307. (38) Jaszunski, M.; Ruud, K. Chem. Phys. Lett. 2001, 336 (5−6), 473−478. (39) Dölle, A.; Bluhm, T. Prog. Nucl. Magn. Reson. Spectrosc. 1989, 21, 175−201. (40) Canet, D. Concepts Magn. Reson. 1998, 10, 291−297. (41) Kotsyubynskyy, D.; Gryff-Keller, A. J. Phys. Chem. A 2007, 111, 1179−1187. (42) Farrar, T. C.; Jablonsky, M. J.; Schwartz, J. L. J. Phys. Chem. 1994, 98 (18), 4780−4786. (43) Ejchart, A.; Zimniak, A.; Oszczapowicz, I.; Szatylowicz, H. Magn. Reson. Chem. 1998, 36, 559−564. (44) Kowalewski, J.; Effemey, M.; Jokisaari, J. J. Magn. Reson. 2002, 157, 171−177.
10620
dx.doi.org/10.1021/jp307828e | J. Phys. Chem. A 2012, 116, 10615−10620
