Recent synthesis and NMR spectroscopy of neutral Ir(V) complexes hydridotris(3,5-dimethylpyrazol-1-yl)borato tetrahydride (Tp*IrH(4)) and hydridotris(pyrazol-1-yl)borato tetrahydride (TpIrH(4)) have been interpreted as supporting face-capped octahedral structures (C(3upsilon)) with each of three Ir-H bonds trans to an Ir-N bond and the fourth hydride capping the IrH(3) 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(3upsilon) 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*IrH(4) and the harmonic frequency calculations on the C(s), C(1), and C(3upsilon) structures also supports the assignment of the C(s)and C(1) structures as the observed ones.