The Notorious Diamagnetic Term

It is known from Pauli theory that two one-electron terms should emerge in the nonrelativistic limit, as is evident from Eq. (5.143). One of these terms is quadratic (bilinear) with respect to the vector potentials. 

This is called the diamagnetic term. Since a term bilinear in the vector potentials is not present in the fully relativistic four-component formulation, the 

Property operators which include the interaction with the magnetic part of the electromagnetic field, B, induce a gauge-origin dependence in the calculations. Translation of the molecule in space thus yields different results before and after the translation, which is physically not sensible. 

If we define the vector potential of a homogeneous magnetic field B as A(r) = B X (r — Ro)/2, then the gauge origin Rq dependence can be understood as a gauge transformation with the gauge function defined by x = —(B X Ro) rl1 (compare section 2.4). This vector potential then produces terms that depend on the arbitrary position Rq- Only for exact wave functions do these terms vanish (complete basis set), while they carmot be neglected in any (small) finite one-electron basis set. 

To avoid these artifacts, London atomic orbitals X t(B,Byi,r) are often employed [948,949], 

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