Local gauge origin

Here Uj and Uj are Cartesian unit vectors, a) and j3) are localized orbitals that are doubly occupied in the HF ground state, jm) and n) are virtual orbitals. Rq is the position vector of the local gauge origin assigned to orbital a) and = (r — R ) x p is the angular momentum relative to Re- Superscript 1 denotes terms to first order in the fluctuation potential, and = [A — is the principal propagator at the zero energy... 

This is a variant of the sum-over-states perturbation theory which applies the random phase approximation (RPA) to deal effectively with the paramagnetic contribution. A localised orbital scheme is utilised to ascribe the local gauge origins [12,13]. Complex (gauge-dependent) orbitals are not introduced. 

Technically, local gauge origins are introduced by non-canonical gauge-origin transformations. A standard canonical gauge-origin transformation of the form... 

Figure 6.4. Overview over quantum chemical methods for electron-correlated calculation of NMR chemical diifts using local gauge-origin methods.

For approximate variational wave functions, the origin independence of the trace of G is only achieved in the limit of a complete basis set. One way to overcome this problem is to introduce local gauge origins by using London atomic orbitals (Helgaker et al. 1994). 

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... 

---