  Realistic prediction of the superconducting transition temperature (Tc) for
PdH is a long-standing challenge, because it depends on robust calculations of
the electron and phonon band structures to obtain the electron-phonon
scattering matrix element. To date, first-principles calculations employing
density functional theory (DFT) have been based on selected
exchange-correlation and core-electron approximations. Incorporating
anharmonicity produced a more realistic value of Tc that nevertheless still
disagreed strongly with experiment unless adjustable parameters were
introduced. Here we consider how the value of Tc predicted using DFT in the
harmonic approximation depends on the DFT scheme employed. The rationale for
this work is that unless the calculation of Tc within the harmonic
approximation is robust, albeit incorrect, there is not a solid foundation for
incorporating anharmonicity meaningfully. Six combinations of
exchange-correlation approximation (LDA, PBE, PBEsol) and core-electron
approximation (PAW, USPP) were tested. Following a carefully systematic
methodology, the calculated Tc was found to vary by a factor exceeding two
across the tested DFT schemes. This suggests strongly that "standard" DFT, even
including anharmonicity, is not reliable for PdH, implying that a higher-rung
method will be needed to calculate a realistic lattice constant and phonon band
structure, and so predict Tc accurately.
