Report No xxxx - Instytut Fizyki JÄ drowej PAN

A DETERMINATION OF ABSOLUTE SHIELDING CONSTANTS
AND SPIN-SPIN COUPLINGS FOR ISOLATED MOLECULES
Karol Jackowski
Laboratory of NMR Spectroscopy, Department of Chemistry, Warsaw University,
ul. Pasteura 1, 02-093 Warszawa; kjack@chem.uw.edu.pl
In a gas of low density, the nuclear magnetic shielding (σ) and spin-spin coupling (J)
can be written as expansions in powers of density (ρ):
σ(ρ,T) = σ 0 (T) + σ 1 (T) ρ + σ 2 (T) ρ 2 + ... (1)
J(ρ,T) = J 0 (T) + J 1 (T) ρ + J 2 (T) ρ 2 + ... (2)
where σ 0 (T), J 0 (T) are the shielding and coupling constants for an isolated molecule and
σ 1 (T), σ 2 (T), J 1 (T), J 2 (T)... terms are due to intermolecular effects. The higher order terms,
starting from σ 2 (T) and J 2 (T) are usually negligible for low-density samples. Then the
dependence on density is linear and the spectral parameters (σ 0 (T), σ 1 (T), J 0 (T) and J 1 (T)) are
available. According to Eqs. 1 and 2 extrapolation of gas-phase measurements to the zerodensity
limit gives the σ 0 (T) and J 0 (T) values which are free from intermolecular interactions.
Such results are especially attractive for ab initio studies since the calculations can actually
model the shielding and spin-spin coupling tensors with high accuracy only for isolated
molecules. The σ 1 (T) and J 1 (T) parameters reveal the influence of intermolecular interactions.
The J 0 (T) values are straightforward ready for the comparison with theoretical data because
the spin-spin couplings are independent of an external magnetic field. On the other hand the
σ 0 (T) measurements require the determination of an absolute shielding scale for a given
nucleus since the applied magnetic field itself cannot be measured with high precision. It can
be done using the relationship between the paramagnetic part of shielding (σ p ) and the spinrotation
constant measured by high-resolution microwave spectroscopy. Combined with an
accurate calculation of the diamagnetic part of shielding (σ d ) in a molecule, the absolute
shielding of a suitable primary reference molecule can be obtained. For 13 C and 17 O the
primary reference molecule is CO, for 15 N and 14 N it is NH 3 , for 33 S the molecule of OCS is
used, etc. Once the absolute shielding is determined for at least one molecule all the other
measurements of σ 0 for the studied nucleus can be expressed as the absolute shielding
constants suitable for the verification of ab initio results. An NMR multinuclear spectrometer
(Varian, 500 MHz) has enabled us to observe extremely weak 17 O and 33 S spectra for a set of
gaseous molecules: (CH 3 ) 2 CO, (CH 3 ) 2 O, (CD 3 ) 2 O, CO, CO 2 , N 2 O, OCS, SO 2 , SO 3 and SF 6 .
Similar 1 H, 13 C, 15 N and 19 F NMR experiments were used for the investigation of other
compounds: CH 3 13 C 15 N, 13 CH 3 13 CN, CH 3 15 NH 2 , H 13 C 13 CH, H 2 13 C 13 CH 2 , CH 3 F, CH 2 DF,
CHD 2 F, CD 3 F, CH 2 F 2 , CHF 3 and CF 4 . Some of the molecules were exclusively studied in
gaseous solvents (Xe, CO 2 and SF 6 ). For the first time we could measure the appropriate
shielding and spin-spin coupling constants as the function of density. Our new results include
NMR parameters for isolated molecules (σ 0 (T) and J 0 (T)), their isotope effects and the second
virial coefficients (σ 1 (T) and J 1 (T)). It was shown that at least some spin-spin coupling
constants were strongly affected by intermolecular interactions.
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