Measurement of the cross sections for $e^{+}{e}^{-}\to p\bar{n}{\pi }^{-}$ at center of mass energies from 3.510 to 4.946 GeV

Using a data sample corresponding to an integrated luminosity of 43.8~fb${}^{-1}$ collected with the \mbox{BESIII} detector at 44 center-of-mass energy points between 3.510 and 4.946~GeV, the Born cross sections for the process $e^{+}{e}^{-}\to p\bar{n}{\pi }^{-}$ and its charge-conjugated process are measured. The energy dependence of the dressed cross sections is investigated to search for possible contributions from vector charmonium and charmonium-like states. No evidence for contributions from the $\psi (3770)$, $Y(4230)$, $Y(4360)$, $\psi (4415)$, $Y(4500)$, or $Y(4710)$ resonances is observed. The upper limits at the 90% confidence level are determined for the products of the electronic partial widths and the branching fractions for the decays of these resonances into the $p\bar{n}{\pi }^{-}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}$ final state.