Computational Estimation of the Binding Energies of POx and HPOx (x=2,3) Species

The distribution of molecules between the gas and solid phase during star and planet formation, determines the trajectory of gas and grain surface chemistry, as well as the delivery of elements to nascent planets. This distribution is primarily set by the binding energies of different molecules to water ice surfaces. We computationally estimated the binding energies of ten astrochemically relevant P-bearing species on water surface, we also validate our method for 20 species with known binding energies. We used DFT calculations (M06-2X/aug-cc-pVDZ) to calculate the energetics of molecules and water-molecule clusters (1-3 H$_2$O molecules) and from this determined the binding energy by comparing the complex and the separate molecule and cluster energies. We also explore whether these estimates can be improved by first calibrating our computational method using experimentally measured binding energies. Using the 20 reference molecules we find that the 2H$_2$O cluster size yields the best binding energy estimates and that the application of a calibration to the data may improve the results for some classes of molecules, including more refractory species. Based on these calculations we find that, small P-bearing molecules such as PH$_3$, PN, PO, HPO, PO$_2$ and POOH are relatively volatile and should desorb prior or concomitantly with water ice, while H$_2$PO, HPO$_2$, PO$_3$, PO$_2$OH can strongly bind to any hydroxylated surface, and will likely remain on the interstellar grains surface past the desorbtion of water ice. The depletion of P-carriers on grains constitute a pathway for the inclusion of Phosphorous molecules in planets and planetesimals.