Origin dependence is an unfortunate byproduct of approximations for standard LG calculations, but LG(OI) can remedy this for variational and nonvariational methods. In this work we have discussed two methods for locating the position and orientation of a molecule in space for which a standard LG-OR calculation is equivalent to LG(OI) in both the trace of the β tensor and its diagonal elements (within 1% relative error). While calculations with the coordinate origin at the COM or COC did not yield poor results for all cases, both the analytical and numerical procedure consistently showed substantial improvement over those choices of origin. When the COM was used as the starting point for the optimization routine, the resulting O Num proved to be essentially the same to O An (the agreement would improve if tighter thresholds were employed for the numerical procedure).