Progress Made Towards Context-free Molecular Structure Determination From Isotopologue Rotational Spectroscopy

\renewcommand{\thefootnote}{\alph{footnote}} Recent algorithms\footnote{N.A. Seifert et. al., Journal of Molecular Spectroscopy 312, 13 (2015).}\footnote{L. Yeh, L. Satterthwaite, and D. Patterson, The Journal of Chemical Physics 150, 204122 (2019).} have demonstrated context-free assignment of rotational constants---needing no knowledge of the chemical species other than the rotational spectrum. Efforts to date to subsequently determine molecular structure require further information including assignment of singly-substituted isotopologues\footnote{J. Yan and D. Patterson. Submitted to the 75th International Symposium on Molecular Spectroscopy (2021).}\footnote{K. Mayer et. al., Proceedings of the 74th International Symposium on Molecular Spectroscopy (2019).}, mass spectroscopy\footnotemark[\value{footnote}], and data mining\footnotemark[\value{footnote}]\footnote{M. Muckle, A. Mikhonin, D. McDaniel, and/or J. Neill, Proceedings of the 74th International Symposium on Molecular Spectroscopy (2019).}. We investigate two methodologies to resolve sign ambiguities of Kraitchman's substitution coordinates. The first methodology requires candidate rotational constants of doubly-substituted isotopologues. Given many such candidates, we have worked out how to determine 1) which candidates for singly- and doubly-substituted isotopologues are most probable, and 2) doubly-substituted atoms' relative position octant. This is realizable given resolution of doubly-substituted species in natural abundance, which is 10-100x order of magnitude above our instrument's present signal to noise. The second methodology requires precision measurement of the electric dipole moments and magnetic g-factors of both the parent and singly-substituted isotopologues. The magnetic g-factor is measured via application of a large magnetic field to our microwave spectrometer, as done by Flygare et. al. (1969). For a 6 carbon molecule, this could be realized given the ability to resolve a $\approx 10^{-5}$ percent difference between magnetic g-factors of the parent and singly-substituted isotopolog species, as well as resolve the electric dipole moment to 4 or 5 significant figures. Improving the capabilities of microwave spectrometers to within these thresholds would therefore enable context-free molecular structure determination