Recent synthesis and NMR spectroscopy of neutral Ir(V) complexes hydridotris(3,5-dimethylpyrazol-1-yl)borato tetrahydride (Tp*IrH4) and hydridotris(pyrazol-1-yl)borato tetrahydride (TplrH(4)) have been interpreted as supporting face-capped octahedral structures (C-3v) with each of three Ir-H bonds trans to an Ir-N bond and the fourth hydride capping the IrH3 face. Here, density functional geometry optimizations and coupled cluster calculations on hydridotris(pyrazol-1-yl)borato iridium tetrahydrogen find that a C-s edge-bridged octahedral tetrahydride structure and a C-1 eta (2)-dihydrogen, dihydride structure are local minima and find that the C-3v structure is a local maximum (second-order saddle point). Several low energy transition states connecting the local minima have been located, and these minima can be used to simulate the experimental NMR spectra. A comparison of the experimental infrared spectrum of Tp*IrH4 and the harmonic frequency calculations on the C-s, C-1, and C-3, structures also supports the assignment of the C-s and C-1 structures as the observed ones.