The local contribution
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص521-522
2025-12-10
46
The local contribution
It is convenient to regard the local contribution to the shielding constant as the sum of a diamagnetic contribution, σd, and a paramagnetic contribution, σp:
σ(local) = σd + σp
A diamagnetic contribution to σ(local) opposes the applied magnetic field and shields the nucleus in question. A paramagnetic contribution to σ(local) reinforces the applied magnetic field and deshields the nucleus in question. Therefore, σd > 0 and σp < 0. The total local contribution is positive if the diamagnetic contribution dominates, and is negative if the paramagnetic contribution dominates. The diamagnetic contribution arises from the ability of the applied field to generate a circulation of charge in the ground-state electron distribution of the atom. The circulation generates a magnetic field that opposes the applied field and hence shields the nucleus. The magnitude of σd depends on the electron density close to the nucleus and can be calculated from the Lamb formula (see Further reading for a derivation):
where µ0 is the vacuum permeability (a fundamental constant, see inside the front cover) and r is the electron–nucleus distance.
The diamagnetic contribution is the only contribution in closed-shell free atoms. It is also the only contribution to the local shielding for electron distributions that have spherical or cylindrical symmetry. Thus, it is the only contribution to the local shield ing from inner cores of atoms, for cores remain spherical even though the atom may be a component of a molecule and its valence electron distribution highly distorted. The diamagnetic contribution is broadly proportional to the electron density of the atom containing the nucleus of interest. It follows that the shielding is decreased if the electron density on the atom is reduced by the influence of an electronegative atom nearby. That reduction in shielding translates into an increase in deshielding, and hence to an increase in the chemical shift δ as the electronegativity of a neighbouring atom increases (Fig. 15.7). That is, as the electronegativity increases, δ decreases. The local paramagnetic contribution, σp, arises from the ability of the applied field to force electrons to circulate through the molecule by making use of orbitals that are unoccupied in the ground state. It is zero in free atoms and around the axes of linear molecules (such as ethyne, HC≡CH) where the electrons can circulate freely and a field applied along the internuclear axis is unable to force them into other orbitals. We can expect large paramagnetic contributions from small atoms in molecules with low lying excited states. In fact, the paramagnetic contribution is the dominant local contribution for atoms other than hydrogen.
Fig. 15.7 The variation of chemical shielding with electronegativity. The shifts for the methylene protons agree with the trend expected with increasing electronegativity. However, to emphasize that chemical shifts are subtle phenomena, notice that the trend for the methyl protons is opposite to that expected. For these protons another contribution (the magnetic anisotropy of C-H and C-X bonds) is dominant.
الاكثر قراءة في مواضيع عامة في الكيمياء الفيزيائية
اخر الاخبار
اخبار العتبة العباسية المقدسة
