NUCLEAR MAGNETIC SHIELDING OF $F^{19}$ IN HYDROGEN FLUORIDE MOLECULE
Loading...
Date
1963
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
“Unlike the magnetic shielding of protons in molecules, where a major part of the paramagnetic shielding constant $\sigma^{p}$ can be calculated from the ground-state wavefunction of the $molecule^{1,2}$ or alternatively by the Chan-Das $procedure^{3}$ from the dimensions of the molecule, for $F^{19}$ nuclei the major part of $\sigma^{p}$ is $\sigma^{p}_{exc}$, and so an accurate knowledge of the perturbed wave function of the molecule in the presence of magnetic field is required. For HF molecule, using the one center wave-function obtained by $Allen,^{4}$ we have computed $\sigma^{p}$ for $F^{19}$ nucleus by a variational $method.^{5}$ The result is $\sigma^{p} = 0.069 \times 10^{4}$ which is an order of magnitude smaller than the experimental value $-0.67 \times 10^{-4}$ and has a wrong $sigh.^{6}$ The calculated result is a difference of direct terms arising from the individual orbitals and exchange type terms arising out of interaction between $\pi$ and $\sigma$ orbitals and the latter outbalance the contribution from the direct terms. Since the convergence of the variation method is very good, the cause for the incorrectness of the theoretical result lies probably in the inaccuracy of the one-center wave function particularly near the nucleus. To test this point we have calculated the electric field at the fluorine nucleus due to the electrons. Neglecting small vibrational effects, the electric field due to the electrons should be equal and $opposite^{1,3}$ to that due to the proton by the Hellman - Feynman theorem. However we find the electric field due to the electrons as $-0.174 \frac{e}{a^{2}_{0}}$ while the field due to the proton is $0.332\frac{c}{a^{2}_{0}}$. The one-center wavefunctions thus seem to underestimate the p-character of the $\sigma$ orbitals near the nucleus and this may be partly the reason for the inaccuracy of the calculated $\sigma^{p}$. The implications of these results with reference to nuclear magnetic-shielding calculations using a non-over-lapping polarized-ion model for alkali halide molecules and crystals will be discussed.”
Description
$^{*}$ Supported by the National Science Foundation. $^{1}$ T. P. Das and R. Bersohn, Phys, Rev. 115, 897 (1959) $^{2}$ H. F. Hameka, Rev. Mod. Phys. 34, 87(1962). $^{3}$ S. I. Chan and T.P. Das. J. Chem. Phys. 37, 1527 (1962). $^{4}$ L. C. Allen, Quarterly Progress Reports of Solid State and Molecular Theory Group at M.I.T. (April 15, 1956 to January, 1958) $^{5}$ T. P. Das and M. Karplus, J. Chem. Phys. 36, 2275 (1962). $^{6}$ Baker, Nelson, Leavitt and Ramsey, Phys, Rev. 121, 807 (1961).
Author Institution: Department of Physics, University of California
Author Institution: Department of Physics, University of California