Gauge problem

Early application of theoretical methods to the calculation of magnetic peroperties was hampered by the so called "gauge problem". The gauge problem arises firom the fact that the Schrodinger equation contains the vector... 

In principle (and using infinite basis sets), NMR chemical shifts can be computed using a single origin. However, practical (i.e. finite) basis sets require that the gauge problem be addressed. The several ways of doing this are listed below ... 

To quote from Schreckenback, Wolff, and Ziegler[67] chemical shifts are known to be sensitive to everything . Their list of factors include the following (1) relativity, (2) quantum mechanical approximation, (3) gauge problem, (4) basis set, (5) geometries, (6) reference compound, (7) condensed phase, temperature, and pressure. Relativistic effects, which are particularly important for heavy nuclei or light nucleus attached to a heavy one, will be discussed later. 

On top of the basic and complicated theoretical problem, real practical problems exist in actually performing a shielding calculation. As discussed earlier, one must select a suitable basis set and a molecular geometry, decide how or indeed whether to deal with rovibrational effects, and devise a strategy for combating the gauge problem. We discuss these problems in the examples presented later in this chapter. 

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