The ground bound state in the positronium hydride molecule (HPs) is de
termined from extensive variational four-body calculations with the Ja
mes-Coolidge four-body variational expansion in the relative coordinat
es r(12), r(13), r(23), r(14), r(24), and r(34). For the positronium h
ydride with the infinitely heavy nucleus ((infinity)HPs) the total ene
rgy found, E = -0.789 1369 a.u., is one of the lowest variational valu
es published to date. A number of bound-state properties have been cal
culated also, including the delta-function expectation values, two-bod
y cusps, and the two-photon annihilation rate.