Table 1 Retrieved molecular frame structure parameters for simulated NO₂.

Θ Parameters	Input	\({P}^{({{{{{{{\mathscr{N}}}}}}}})}\left({{{{{{{\bf{\Theta }}}}}}}}\| C\right)\)		\({P}^{(\delta )}\left({{{{{{{\bf{\Theta }}}}}}}}\| C\right)\)
		Θ^*	σ^Θ	Θ^*	σ^Θ
\(\langle {{{{{{{{\rm{NO}}}}}}}}}^{(1)}\rangle\) [Å]	1.35	1.3500	0.0005	1.3509	0.0004
\(\sigma ({{{{{{{{\rm{NO}}}}}}}}}^{(1)})\)[Å]	0.03	0.030	0.004	–	–
\(\langle {{{{{{{{\rm{NO}}}}}}}}}^{(2)}\rangle [{{\text{\AA}}}]\)	1.05	1.0500	0.0006	1.0485	0.0005
\(\sigma ({{{{{{{{\rm{NO}}}}}}}}}^{(2)})\)[Å]	0.02	0.020	0.007	–	–
\(\left\langle \angle {{{{{{{\rm{ONO}}}}}}}}\right\rangle\)[rad]	2.34	2.340	0.001	2.3401	0.0007
\(\sigma \left(\angle {{{{{{{\rm{ONO}}}}}}}}\right)\)[rad]	0.01	0.01	0.02	–	–

Our approximation of ∣Ψ(R)∣² (\(P\left({{{{{{{\bf{R}}}}}}}}\right\vert \left.{{{{{{{\bf{\Theta }}}}}}}},C\right)\)) is parameterized by molecular frame distances, angles, and their corresponding widths (Θ parameters). The optimal parameters, denoted as Θ^*, correspond to the mode of \(P\left({{{{{{{\bf{\Theta }}}}}}}}| C\right)\). We provide the retrieved Θ^* parameters along with their corresponding resolutions for the simulated NO₂. The input Θ parameters are those used to simulate the NO₂C_lmk(q) coefficients with a signal-to-noise ratio (SNR) of 400. The retrieved Θ^* parameters are those found when applying \({P}^{({{{{{{{\mathcal{N}}}}}}}})}\left({{{{{{{\bf{R}}}}}}}}\right\vert \left.{{{{{{{\bf{\Theta }}}}}}}},C\right)\) and \({P}^{(\delta )}\left({{{{{{{\bf{R}}}}}}}}\right\vert \left.{{{{{{{\bf{\Theta }}}}}}}},C\right)\) to the NO₂C_lmk(q) simulated using \({P}^{({{{{{{{\mathcal{N}}}}}}}})}\left({{{{{{{\bf{R}}}}}}}}\right\vert \left.{{{{{{{\bf{\Theta }}}}}}}},C\right)\). The σ^Θ values are the resolution of Θ^* and the uncorrelated widths of \({P}^{({{{{{{{\mathcal{N}}}}}}}})}\left({{{{{{{\bf{\Theta }}}}}}}}| C\right)\) and \({P}^{(\delta )}\left({{{{{{{\bf{\Theta }}}}}}}}| C\right)\), respectively.

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