Article pubs.acs.org/JPCA
Cite This: J. Phys. Chem. A 2018, 122, 590−593
Isotope Effects on Nuclear Magnetic Shielding in Molecular Hydrogen Piotr Garbacz*,† and Grzegorz Łach‡ †
Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
‡
ABSTRACT: The secondary isotope shifts of six molecular hydrogen isotopologues (H2, D2, T2, HD, HT, and DT) were measured using gas-phase nuclear magnetic resonance spectroscopy. It was found that these isotope shifts are in satisfying agreement with performed ab initio quantum chemistry computations. However, there is a small systematic discrepancy between results of experiments and computations, i.e., the magnitudes of computed shifts are approximately 10% larger than those obtained from the experiments. This indicates that computations performed using the Born− Oppenheimer approximation are not sufficient for reproducing quantitatively the experimentally determined secondary isotope shifts of molecular hydrogen. nuclear magnetic shielding10−12 and comparing directly between the experiment and performed ab initio quantum chemistry computations, which for the system as small as the dihydrogen molecule give almost rigorous results. In the following text, names of hydrogen isotopes, 1H (protium) and H, 2H (deuterium) and D, and 3H (tritium) and T, are used interchangeably.
1. INTRODUCTION Studies of the influence of the isotope substitution on molecular spectral properties provide information about properties of materials and course of chemical reactions. An example of such spectroscopy that is sensitive to effects of the isotope substitution is nuclear magnetic resonance (NMR).1 The isotope effects on nuclear magnetic shielding are proportional to the range of chemical shifts for a given nucleus; therefore, for hydrogen, whose range of chemical shifts usually does not exceed 10 ppm (1 ppm = 10−6), these effects are weak.2,3 The primary 1H/2H isotope shifts (vide inf ra) are generally smaller than 0.1 ppm unless strong hydrogen bonds affect the chemical shift, e.g., in proton sponges, giving isotope shifts up to 0.7 ppm.4 The secondary 1H/2H isotope shifts have magnitudes of the same order.2 Isotope shifts are caused by perturbation of the electron distribution by rotations and vibrations of the molecule, whose frequencies are affected by the isotopic substitution.5,6 However, this description, which is based on the Born− Oppenheimer approximation, may not be sufficient for a system containing a very light atom (hydrogen). For instance, in the deuterium hydride molecule the isotropic nuclear magnetic shielding of the deuteron is larger than that of the proton even though averaging over rotational and vibrations states of the molecule is the same for both nuclei.7,8 In NMR studies of the isotope shifts, the secondary isotope shifts are commonly determined. In order to investigate the importance of the not yet computed nonadiabatic contributions to these shifts, we examined the gas-phase NMR spectra of several isotopologues of dihydrogen recorded under variable pressure. The studies of the secondary isotope shifts of hydrogen were extended on those hydrogen isotopologues, which contain tritium in comparison to the previously reported data (see refs 7 and 9 for details). Extrapolation of the obtained isotopic shifts to the zero-density limit allows to correct these shifts for the influence of the intermolecular interactions on © 2017 American Chemical Society
2. EXPERIMENTAL METHODS Tritium (activity 2.57 Ci/mL, pressure 0.48 bar, RC Tritec Ltd.), hydrogen deuteride (98% D; Isotec), and carbon dioxide (99.8%, Sigma-Aldrich) were used without further purification. 3 H is a radioactive isotope (beta minus emitter) and has to be handled in dedicated facilities with appropriate equipment for radioactive materials to avoid health risks caused by radiation exposure. The mixture of hydrogen isotopologues was obtained from the exchange reaction between tritium and hydrogen deuteride catalyzed by the platinum black. A small amount of this mixture was added to carbon dioxide, then the samples were sealed by a torch. Details of the preparation procedure of the samples are given in refs 13 and 14. Usage of CO2 as a solvent gas is beneficial in this experiment since hydrogen NMR peaks are practically at least an order of magnitude narrower in comparison to the case of pure gaseous hydrogen and, consequently, permits determining of the secondary isotope shifts of hydrogen with high precision. Four samples were prepared at pressures from 10 to 20 bar. Measurements of the 1H, 2H, and 3H NMR spectra of the mixture of hydrogen isotopologues were preformed using a Varian INOVA 500 spectrometer and a two-channel Varian switchable 5 mm probe at the magnetic field of strength B0 = 11.75 T and the temperature T = 300 K. The magnetic field Received: November 16, 2017 Revised: December 19, 2017 Published: December 21, 2017 590
DOI: 10.1021/acs.jpca.7b11342 J. Phys. Chem. A 2018, 122, 590−593
Article
The Journal of Physical Chemistry A was stabilized using as a reference the 2H NMR signal of benzene-d6 for 1H and 3H NMR spectra and the 19F NMR signal of hexafluorobenzene for 2H NMR spectra. The isotope effects on nuclear shielding were determined from the best fit of the line shape of a two-spin system derived from the Bloch−Redfield−Wangsness relaxation theory to the NMR spectra using the Mathematica computer program.15 This line shape analysis is described in refs 14 and 16. This procedure takes into account the influence of nuclear relaxation on the NMR spectrum and allows to determine the resonance frequency with precision an order of magnitude higher than the digital resolution of the spectrum (approximately 0.2 Hz). Then, the obtained spin precession frequency for each hydrogen isotopologue was extrapolated to the zerodensity limit.
Figure 1. Nuclear magnetic shielding of hydrogen isotopologues. The differences in the magnetic shielding between isotopologues originate from the zero point vibration (ZPV) correction, the temperature corrections, and the nonadiabatic effects. The latter correction is responsible for differences in shielding of nuclei for mixed hydrogen isotopologues. Notice that, ϵHD − ϵHT + ϵDT = 1ΔH(3/2H) − 1 ΔD(3/1H) + 1ΔT(2/1H). Nonadiabatic corrections do not necessarily shift nuclear shielding of mixed hydrogen isotopologues symmetrically with respect to the value obtained using the Born−Oppenheimer approximation.
3. COMPUTATIONAL METHODS The calculation of nuclear magnetic shielding of molecular hydrogen isotopologues were performed by ro-vibrational averaging of shielding computed within the Born−Oppenheimer approximation. The dependence of shielding on the internuclear distance was computed by Jaszuński et al.9 using the full configuration interaction (FCI) method extrapolated to the complete basis set and independently by Puchalski et al.17 using explicitly correlated functions. We used the latter values with the distance dependence fitted with cubic spline functions and inferred their accuracy by comparison with the fit to the nuclear shielding obtained using orbital methods. The potential energy curve was taken from analytic fit to the highly accurate results computed using the James−Coolidge basis set.18 The adiabatic and relativistic corrections to the Born−Oppenheimer energy curve were taken from ref 19. The ro-vibrational averaging has been done by the direct solution of the Schrödinger equation for nuclear motion for all the rovibrational states, using the numerical variable step method. Subsequently, the averaging was performed by numerical integration and direct summation over all the states allowed by symmetry with corresponding Boltzmann occupations. For instance, results for ditritium were averaged only over states of ortho-T2 since para-T2 does not contribute to the 3H NMR signal.
between the shielding of the nucleus X and nucleus Y in the molecule XY: X Y ϵXY = σXY − σXY
(1)
The primary isotope effect is a difference between the shielding of the nucleus X for the molecule XZ and the shielding of the nucleus Y for the molecule YZ:20 X Y ΔZ(Y /X ) = σXZ − σYZ
0
(2)
The secondary isotope effect is a change of shielding of the nucleus Z upon the substitution of the neighboring nuclei X by the nuclei Y in the molecule ZX: Z Z ΔZ(Y /X ) = σZX − σZY
1
(3)
In eqs 1−3, the isotope Y is heavier than the isotope X and {X, Y, Z} ∈ {H, D, T}. For molecular hydrogen, all isotope effects on nuclear shielding are negative. Application of eqs 1−3 gives 21 quantities, which describe molecular hydrogen shifts induced by the isotope substitution in which 13 are redundant as can be obtained from following equations:
4. RESULTS There are six isotopologues of molecular hydrogen containing 1 H, 2H, and 3H nuclei: dihydrogen (H2), dideuterium (D2), ditritium (T2), hydrogen deuteride (HD), hydrogen tritide (HT), and deuterium tritide (DT). At the theory level of the Born−Oppenheimer approximation, shielding of both nuclei for a given mixed hydrogen isotopologue is the same; therefore, five isotope shifts unambiguously determine changes of the shielding due to the isotope substitution (see Figure 1). These shifts are mainly determined by differences in fundamental oscillation frequencies of the molecules; the influence of temperature on shift magnitudes is less pronounced.9 However, if one takes into account nonadiabatic effects, then the degeneracy of shielding of mixed hydrogen isotopologues is lifted, and one has to determine eight isotope shifts. These isotope shifts can be characterized using differences between shielding of two nuclei, ϵ, primary shielding isotope shifts, 0Δ, and secondary shielding isotope shifts, 1Δ. The difference between shielding of two nuclei is the difference
0
ΔX(3/1H) = 0ΔX(3/2 H) + 0ΔX(2/1H)
1
(4)
ΔX(3/1H) = 1ΔX(3/2 H) + 1ΔX(2/1H)
(5)
ϵXY = 0ΔX(Y /X ) − 1ΔX(Y /X )
(6)
0
ΔX(Y /X ) + 0ΔY (Y /X ) = 1ΔX(Y /X ) + 1ΔY (Y /X )
(7)
ϵHD − ϵHT + ϵDT = 1ΔH(3/2 H) − 1ΔD(3/1H) + 1ΔT(2/1H) (8)
The choice of a convenient set of parameters describing effects of the isotope substitution on shielding for molecular hydrogen is determined by experimental factors. The quantity measured in the NMR experiment, the spin precession frequency, depends on the strength of the magnetic field B0 and the gyromagnetic ratio 591
DOI: 10.1021/acs.jpca.7b11342 J. Phys. Chem. A 2018, 122, 590−593
Article
The Journal of Physical Chemistry A X X νXY = γX(1 − σXY )B0
ppb mol/L. The second minor contribution to the slope is from interaction-induced shielding for which one can expect immeasurable small,
