Prof. F. Ann Walker Research Group, Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
The positions of NMR lines are determined both by diamagnetic and paramagnetic shifts. The diamagnetic part is determined by the distribution of electronic density as a whole and does not depend on temperature. Subtracting the diamagnetic shifts (different for different lines) we get pure Curie dependencies
Original temperature dependence |
Corrected temperature dependence |
Diamagnetic contribution can be estimated in two ways:
Let us again consider the molecule that can be in two states
We assume that the diamagnetic shifts are already subtracted.
Remark. The information about the excited state is less available and reliable. Usually it is assumed that the electronic density and the diamagnetic shifts are approximately the same as for the ground state.
The probabilities to find the molecule in the states 1 and 2 are
Here the weights w_{n} take into account the degeneracy due to the electronic spin.
Let us denote the paramagnetic shift for the line k of the state n as
then the average shift for the line k is
In the examples below it is assumed that w_{1} = w_{2}.
P_{1}/T (upper curve) and P_{2}/T (lower curve) |
The combination of different values and signs can give quite different temperature dependences.
f_{2} / f_{1} = -1 quadratic dependence at x << 1 |
f_{2} / f_{1} = -10 |
f_{2} / f_{1} = 10 |
©Nikolai V. Shokhirev, F. Ann Walker, 2002