Gauge origin problem

As described in Section 11, NMR chemical shifts can be computed as second derivatives [Eq. (6.8)]. With the development of analytic second derivative techniques for electron-correlated schemes [84], calculation of NMR chemical shifts thus became possible. In the last decade, a number of correlated approaches have been applied (together with appropriate measures for treating the gauge-origin problem) to the calculation of chemical shielding tensors, which has allowed its applications to several chemically interesting problems. 

It is still important in this formulation to deal correctly with the gauge-origin problem. The perturbation Hamiltonian contains terms involving the A vector of the magnetic field, related to the field B by ... 

A problem arising when a magnetic field is present in the Hamiltonian, such as in the calculation of magnetic properties, is the gauge origin problem. The vector potential representing the external magnetic field induction B is... 

Furthermore, one is faced with the gauge-origin problem, as discussed in Section 5.10. A popular solution to this problem is to work with perturbation-dependent basis sets. In the case of an external magnetic field as perturbation such basis functions... 

In the CTOCD-DZ approach for solving the gauge-origin problem in shielding calculations. Section 5.10, the diamagnetic contribution to the shielding tensor is... 

Geertsen, J. (1989). A solution of the gauge origin problem for the magnetic susceptibility. J. Chem. Phys., 90, 4892-4894. 

In contrast to the shielding constants, London orbitals are neither needed nor used in any calculation of spin-spin coupling constants. There is no dependence of the perturbing operators on the external magnetic field and thus no gauge origin problem. 

There are, in principle, two ways to solve the gauge origin problem (at least to a high degree of accuracy), (a) One tries to solve equation (9) as accurately as possible. In a basis expansion method this means that one uses nearly saturated basis sets, (b) One tries to find an optimum gauge origin R, for which the error with respect to an exact solution is as small as possible - even if the basis is small. 

The routine calculation of NMR chemical shifts " using quantum chemical methods has become possible since the introduction of local gauge-origin methods, " " which provide a solution to the gauge-origin problem within approximated schemes. In our formulation, we use gauge-including atomic orbitals... 

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