Electronic Structure Calculations of Filled Skutterudites RGe$_{4}$Pt$_{16}$*

We present a comparative study of the filled skutterudites RGe$_{4}$Pt$_{16}$ (R=La, Ce, Pr), based on T=0 density functional theory (DFT) calculations. To elicit possible role of the lanthanide f-electrons and f-f interaction U, we calculate band structures, Fermi surfaces and density of states (DOS) for different scenarios: (a) frozen f-electron GGA; (b) unfrozen f-electron GGA + U with spin-orbit coupling; (c) unfrozen f-electron GGA with spin-orbit coupling. Comparison of our DFT DOS with experimental electronic heat capacity suggest a modest values of m$^{*}$/m$_{\rm band}$. Our calculated Fermi surface topology near Fermi energy may provide clues into the occurrence of superconductivity in the La and Pr compounds and the non-occurrence in the Ce one. Our T=0 calculations of magnetism at zero doping and pressure show that Pr has a large moment and is ferrimagnetic; Ce has a very weak moment and marginally favors antiferromagnetism. We explore if the experimentally observed variation of superconducting T$_{C}$ with pressure in the Pr compound can be accounted for in terms of the variation of DOS with pressure.