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The McGill Planar Hydrogen Atmosphere Code (McPHAC) v1.1 calculates the hydrostatic equilibrium structure and emergent spectrum of an unmagnetized hydrogen atmosphere in the plane-parallel approximation at surface gravities appropriate for neutron stars. McPHAC incorporates several improvements over previous codes for which tabulated model spectra are available: (1) Thomson scattering is treated anisotropically, which is shown to result in a 0.2%-3% correction in the emergent spectral flux across the 0.1-5 keV passband; (2) the McPHAC source code is made available to the community, allowing it to be scrutinized and modified by other researchers wishing to study or extend its capabilities; and (3) the numerical uncertainty resulting from the discrete and iterative solution is studied as a function of photon energy, indicating that McPHAC is capable of producing spectra with numerical uncertainties <0.01%. The accuracy of the spectra may at present be limited to ~1%, but McPHAC enables researchers to study the impact of uncertain inputs and additional physical effects, thereby supporting future efforts to reduce those inaccuracies. Comparison of McPHAC results with spectra from one of the previous model atmosphere codes (NSA) shows agreement to lsim1% near the peaks of the emergent spectra. However, in the Wien tail a significant deficit of flux in the spectra of the previous model is revealed, determined to be due to the previous work not considering large enough optical depths at the highest photon frequencies. The deficit is most significant for spectra with T eff < 105.6 K, though even there it may not be of much practical importance for most observations.