Progress toward the reconstruction of molecular radial electron densities on the example of methane $2a_1$ and $1t_2$

The approach of photoemission orbital tomography (POT), i.e., the orbital density reconstruction from photoemission of planar molecular layers, is applied to measurements of the partial cross section from gas-phase methane $\left({\mathrm{CH}}_4\right)$. Within a central-field and one-electron model, the method previously validated on neon is tested on ${\mathrm{CH}}_4$'s molecular orbitals $2a_1$ and $1t_2$ with the goal to reconstruct absolute radial orbital densities. The reconstruction method is based on a Markov chain Monte Carlo optimization method, employing Bayesian inference, which additionally offers a reliable uncertainty evaluation. Applying the method to ${\mathrm{CH}}_4$, we aim to bridge the gap between simple single atoms and molecular layers, and to find a practical reference standard for the determination of orbital densities within POT.