Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation

X-ray absorption spectroscopy (XAS) in the metal K pre-edge is a standard probe of electronic and geometric structure of transition metal complexes. Simulating the K pre-edge spectra requires contributions beyond the electric dipole, but if that term is non-zero, the second-order terms, e.g. electric quadrupoles, are no longer origin-independent. In the velocity representation, complete origin independence can be achieved by including all terms to the same order in the oscillator strength. Here, we implement that approach in the length representation and use it for restricted active space (RAS) simulations of metal K pre-edges of iron monomers and dimers. Complete origin independence is not achieved and the size of the remaining errors depends on the electric dipole oscillator strength and its ratio in length and velocity representations. The error in the origin independence is in the ANO basis sets two orders of magnitude smaller than the value of the individual contributions. For systems with strong electric dipole contributions, the errors are not significant within 3 Å from a metal centre, far enough to handle many multi-metal systems. Furthermore, we discuss the convergence of the multipole expansion, the possibility to assign spectral contributions, and the origin of negative absorption intensities.