Theoretical studies of the temperature dependence of magnetic shielding tensors: H 2, HF, and LiH

Abstract

Shielding tensors are calculated for the nuclei in H 2, HF, and LiH over a range of internuclear separations using single-determinant wavefunctions of molecular orbitals expressed as linear combinations of a polarized basis set of gauge-invariant atomic functions. Such data are fitted by least-squares techniques to a power series in the reduced coordinate ξ, yielding a shielding function σ(ξ). Expansion of the potential function V( R) as a Dunham series in ξ allows the expectation values of powers of ξ in different low energy vibration-rotation staes, i.e. (ξ n ) υ j′ to be determined. Such values are combined with the shielding function data to calculate shielding tensor components, (σ αω) υ J′ for different vibration-rotation states. Using these σ cJ values, the shielding constant at temperature T, σ 0( T), is calculated as a Boltzmann average over the thermally accessible vibration-rotation states. For the shielding at nuclei in H 2 and HF, the agreement between calculated and experimental values of σ 0( T) at 300 K is excellent. In addition, there is good agreement between calculated and experimental isotope shifts in H 2, HD, D 2, HF and DF. For 19F shielding in HF, σ 0( T) is predicted to decrease with increasing temperature; in contrast, the 7Li shielding in 7LiH is predicted to increase slightly as the temperature is raised. These results are interpreted using simple molecular orbital ideas. In the temperature range accessible in the conventional NMR spectrometer, the temperature dependence of σ 0( T) arises principally from the term linear in ξ in σ(ξ). Although the quadratic term is relatively independent of temperature, nonetheless, the calculations presented here suggest that it can make a significant contribution to σ 0( T) even for proton shielding.