I generally have seen the pyramidal inversion of NH3 explained in terms of rehybridization. The sp3 hybridized NH3 changes to sp2, with the lone pair in the p orbital, and then reverts to sp3 in the opposite configuration. On the other hand, something like PH3 has a higher barrier to inversion, because the poor hybridization leads to the lone pair being placed in an orbital with higher s character, and moving this lone pair into a p orbital would require more energy than in NH3.
However, hybridization is an approximation for MO theory, so I am curious as to whether there is a molecular orbital justification for why we can assume molecules rehybridize. Is there an analogous idea in molecular orbital theory that can explain the pyramidal inversion of NH3, as well as why PH3 has a higher barrier to inversion?