These limitations revolve around a few key factors: the incompleteness of the basis set and of the treatment of electron correlation in practical calculations, the inability of treating quantum effects in electrons and nuclei on the same footing, and the inability to treat the environment around a chiral molecule at the quantum level. Although these limitations are common to simulations of many molecular properties, they are particularly important for OR due to its sensitivity to molecular structure and intermolecular interactions. Typically, vibrational contributions to OR are treated with perturbative formulas, but it is hard to determine the accuracy of this approach. For solvation the situation is even worse, as there is no standard recipe to accurately reproduce its effect, and the anomalous shift in OR going from gas to solution a) Electronic mail: mcaricato@ku.edu phase is largely not understood. For OR in the solid phase, a few efforts have begun to appear but simulations are not at a mature state. Electron correlation incompleteness is also difficult to overcome, because chiral molecules tend to be too large for high-level methods. Among the systematically improvable methods, the most accurate and yet affordable one is coupled cluster with single and double excitations (CCSD), but we have recently shown that CCSD may not be as close to convergence in terms of electron correlation treatment as one would hope. On the other hand, density functional theory (DFT) methods dominate the field of OR simulations because of their favorable cost to accuracy ratio. However, although it has been shown that the accuracy can be improved with range-tuning, the typical DFT issue of system dependent-accuracy is also present for this property. The basis set dependence in OR calculations has been well studied, and basis sets have been formulated specifically for OR calculations in an attempt to decrease computational cost while maintaining accuracy. A consequence of basis set and electron correlation incompleteness is that different choices of gauge for the external field representation provide different numerical values of the OR, contrary to exact calculations. Two common choices are the length gauge (LG) and the velocity gauge (VG), which differ in the representation of the electric dipole operator. VG calculations include an unphysical static limit, which must be calculated and subtracted out explicitly; a procedure called modified VG (MVG). Approximate LG-OR calculations are origin dependent, which is also unphysical. The issue can be solved using London orbitals , where a magnetic field dependent phase factor is included on each atomic basis function. This is a general approach that can be useful for many magnetic properties, but at the cost of significantly more complicated equations and implementations. Additionally, this approach requires the inclusion of the orbital response, which is standard in DFT but not in CCSD (unless complicated orbital optimization procedures are used ). We proposed a different approach, called origin-invariant LG or LG(OI), where the origin dependence of the OR is removed with a clever transformation of the OR tensor. The LG(OI) approach is considerably simpler to implement than London orbitals and it works equally well for variational and non-variational methods, but it is specific to OR calculations. In a recent work, we showed that LG(OI) converges to the complete basis set limit slightly faster than MVG. In this work, we investigate whether a meaningful choice of coordinate origin and molecular orientation can be made for a standard LG calculation so that it matches the LG(OI) result. In previous work, we have proposed an analytical approach to determine the spatial orientation of a molecule so that the diagonal elements of the OR tensor match between LG and LG(OI) calculations. Here we try to understand if that choice has any general physical characteristic and how the OR results compare with more common choices of coordinate origin (e.g., the center of mass or the center of nuclear charge). We also determine whether the choice of molecular orientation where the LG and LG(OI) OR match is unique, by using a numerical procedure that iteratively performs rigid rotations and translations of the molecule until the diagonal elements and the trace of the LG and LG(OI) OR tensors agree within a given threshold. Finally, we explore whether this choice of molecular orientation is transferable between different methods (for instance, from a specific functional to another one or to CCSD). This is important because while LG(OI) is trivial to implement for DFT and has no impact on the computational cost, it does require some effort for CCSD (both in terms of initial implementation and for the computational cost, if the symmetric version of the response function is used). Therefore, it may be useful to find a special LG origin for DFT and use it for a standard LG-OR CCSD calculation.