Length-gauge formulation

This ensures basis set convergence comparable with that of the optical rotation in the length-gauge formulation, while not affecting origin independence. 

As was the case for the optical rotation, the length-gauge formulation is origin dependent for finite basis set calculations, but we note that origin-independent results can be obtained using London atomic orbitals [24,25],... 

The key quantity for the computational simulation of an BCD spectrum is the scalar rotational strength for a transition from the ground state 0) to an excited state n), which can be evaluated from the residue of a linear response function. In the so-called length-gauge (LG) formulation, see also Bqs. 2.46, we have... 

It can be shown that the trace of the tensor G, and hence the computed optical rotation of a sample of randomly oriented chiral molecules, is independent of the origin provided that the linear response function satisfies O Eq. 5.46 and that the commutator of O Eq. 5.47 is fulfilled. Consequently, approximate linear response calculations of the length gauge optical rotation depend on the chosen coordinate origin. On the other hand, the trace of the velocity gauge formulation of the electric dipole - magnetic dipole polarizability... 

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