NMR Spectra

Diamagnetic shifts

Diamagnetic shifts are caused by the magnetic field from the electric current induced by the external magnetic field. This is the only source for the chemical NMR line shifts in diamagnetic molecules.

This contribution cannot be calculated in the framework of Hückel theory.

In the program MPorphW this is the input atomic parameters "Delta Shift" (see Manual).

Contact shifts

In paramagnetic molecules (radicals, complexes) there are two additional contributions. Direct interaction of electron spin with a nucleus (Fermi interaction) forms the contact NMR chemical shifts. The shift is proportional to the spin density at the atom :

 The factor Q_A is called the McConnel factor. It depends on the nature of the atom and it position in the molecule:

If the unpaired electron occupies the n-th MO 

then 

If the system has several unpaired electrons then the sum over all corresponding MO' should be taken. In the program MPorphW this is controlled by the numbers of and electrons.

Note that only the systems with unpaired electrons can be calculated with the Hückel method.

Dipolar shifts

 The second contribution to chemical shifts in paramagnetic systems is due to the dipole-dipole interaction between magnetic moments of the unpaired electron and a nucleus. 

Under certain assumptions [3] the chemical shifts of an atom at    due to this mechanism can be expressed as

Here g_x, g_y and g_z are the principal values of the g-tensor, and x, y and z label the corresponding principal axes, is the angle from the z-axis toward to the xy-plane and is the angle from the x-axis toward to the y-axis.

g-tensor principal values and axes

In the porphyrin ring plane (xy-plane) the above formula reduces to

Here    denotes the direction of the g-tensor x principal axis relative to the molecular x-axis. In general, it is necessary to distinguish the two coordinate systems. The rotation of the axial ligands relative to the porphyring ring can cause the g-tensor principal axes rotation. Two types of rotation can take place depending on the electronic structure of the complex [2]: 

g-tensor Co-Rotarion	g-tensor Counter-rotation

.In the case of non-symmetrical rings the g-tensor can be fixed relative to the ring.  

References

1. Nikolai V. Shokhirev and F. Ann Walker, "The effect of axial ligand plane orientation on the contact and pseudocontact shifts of low-spin ferriheme proteins". JBIC (1998)3:581-594.
2. Nikolai V. Shokhirev and F. Ann Walker, "Co- and Counterrotation of Magnetic axes and Axial Ligands in Low-Spin Ferriheme Systems". JACS (1998)120:981-990.
3. "NMR and EPR Spectroscopy of Paramagnetic Metalloporphyrins," Walker, F. A. In The Handbook of Porphyrins and Related Macrocycles; Kadish, K. M.; Guilard, R.; Smith, K. M., Eds.; Academic Press: Burlington, MA; 1999, Chapter 36, Vol. 5; pp. 81-183.

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ŠNikolai V. Shokhirev, F. Aann Walker 2003

nikolai@shokhirev.com