Electronic structure of new multiple band Pt-pnictide superconductors APt$_3$P

We report LDA calculated band structure, densities of states and Fermi surfaces for recently discovered Pt-pnictide superconductors APt$_3$P (A${}={}$Ca, Sr, La), confirming their multiple band nature. Electronic structure is essentially three dimensional, in contrast to Fe pnictides and chalcogenides. LDA calculated Sommerfeld coefficient agrees rather well with experimental data, leaving little space for very strong coupling superconductivity, suggested by experimental data on specific heat of SrPt$_3$P. Elementary estimates show, that the values of critical temperature can be explained by rather weak or moderately strong coupling, while the decrease of superconducting transition temperature $T_c$ from Sr to La compound can be explained by corresponding decrease of total density of states at the Fermi level $N(E_{\rm F})$. The shape of the density of states near the Fermi level suggests that in SrPt$_3$P electron doping (such as replacement Sr by La) decreases $N(E_{\rm F})$ and $T_c$, while hole doping (e.g. partial replacement of Sr with K, Rb or Cs, if possible) would increase $N(E_{\rm F})$ and possibly $T_c$.