Prof. F. Ann Walker Research Group, Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA

Temperature dependence of NMR paramagnetic shifts

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

Estimation of Diamagnetic shifts

Diamagnetic contribution can be estimated in two ways:

1. If the temperature dependence really obeys the Curie law and the range of experimental points is wide enough, then the dependencies can be reliably extrapolated to the limit 1/T = 0 . The interceptions can be used as diamagnetic shifts.
2. The diamagnetic contribution depends mainly on the electronic density and is relatively insensitive to the details of electronic structure. If diamagnetic analog of a paramagnetic molecule can be found then its shifts can be used as diamagnetic parts in paramagnetic molecule.   

Two-Level system

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 w₁ = w₂.

P1/T (upper curve) and P2/T (lower curve)

 The combination of different values and signs can give quite different temperature dependences.

f2 / f1 = -1 quadratic dependence at x << 1

f2 / f1 = -10

f2 / f1 = 10

©Nikolai V. Shokhirev, F. Ann Walker, 2002

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