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Band calculations for Ce compounds with the AuCu$_{3}$-type crystal structurewere carried out on the basis of dynamical mean field theory (DMFT). Theauxiliary impurity problem was solved by a method named NCA$f^{2}$vc(noncrossing approximation including the $f^{2}$ state as a vertex correction).The calculations take into account the crystal-field splitting, the spin-orbitinteraction, and the correct exchange process of the $f^{1} \rightarrowf^{0},f^{2}$ virtual excitation. These are necessary features in thequantitative band theory for Ce compounds and in the calculation of theirexcitation spectra. The results of applying the calculation to CePd$_{3}$ andCeRh$_{3}$ are presented as the first in a series of papers. The experimentalresults of the photoemission spectrum (PES), the inverse PES, theangle-resolved PES, and the magnetic excitation spectra were reasonablyreproduced by the first-principles DMFT band calculation. At low temperatures,the Fermi surface (FS) structure of CePd$_{3}$ is similar to that of the bandobtained by the local density approximation. It gradually changes into a formthat is similar to the FS of LaPd$_{3}$ as the temperature increases, since the$4f$ band shifts to the high-energy side and the lifetime broadening becomeslarge.}

Band Calculations for Ce Compounds with AuCu$_{3}$-type Crystal Structure on the basis of Dynamical Mean Field Theory I. CePd$_{3}$ and CeRh$_{3}$