11 and GGA calculations in order to estimate the value of the hybridization induced Pd and Al magnetic moments ( 4f in core and 4f in band as a Bloch states) and found values less than 0.1 µ$_{B}$ and 0.01 µ$_{B}$ , respectively. The Fermi level for SmPd$_{2}$Al$_{3}$ situated at the de- scending part of the DOS yielded N ( E$_{F}$ ) = 2.51 states 1/eV(f.u.). The orbital analysis of the DOS shows that mainly the Pd- 4d , Pr- 5d and Al- 3p states that contribute to the total DOS at E$_{F}$ . The value of the DOS at E$_{F}$ is too small to cause a spontaneous magnetic polarization of the Pd- 4d states. The value of the DOS at E$_{F}$ for SmPd$_{2}$Al$_{3}$ corresponds to an electronic specific heat coefficient γ = 5.9 mJ mol $_{−}$1 K $^{$_{−}$2}$, which is somewhat lower than the γ value of 7.0 mJ mol $_{−}$1 K $_{−}$2 derived from our specific heat data. This points to a rather low value of the mass-enhancement coefficient λ = 0.18 for SmPd$_{2}$Al$_{3}$ ( γ$_{exp.}$ = (1 + λ ) γ$_{band}$ ), indicating a weak electron-phonon interaction in the SmPd$_{2}$Al$_{3}$ compound. Next, the magnetic susceptibility was calculated on the basis of the CF scheme. The microscopic CF Hamiltonian for the Sm atomic configuration 4f 5 in the hexagonal symmetry has four independent parameters A m n . Reliable CF parameters were obtained for the NdPd$_{2}$Al$_{3}$ com- pound by fitting inelastic neutron data in 13 , $^{14}$; the values obtained were A 0 2 = -386 K, A 0 4 = 42 K, A 0 6 = 6.8 K and A 6 6 = -134 K. At first we decided to check these values by our first principles calculations. The first principles calculation of the crystal field parameters leads to the following values: A 0 2 = -308, A 0 4 = 25 A 0 6 = 1.9 and A 6 $_{6}$= -88. The second-order CF parameter has the correct sign, which determines the easy c -axis of SmPd$_{2}$Al$_{3}$ at low temperatures in agreement with the analysis of our susceptibility and magnetization data. The other parameters have also the correct sign and similar values compared to the CF parameters resulting from the analysis of inelastic neutron data in 13 , $^{14}$. Moreover the calculated gap between the ground and the first excited doublet is more than 100 K, which is in goof agreement with the Schottky specific heat analysis and this fact is also supported by the reliability of both the CF parameter sets obtained above. Since our theoretical approach is semi-quantitative only $^{20}$, we may state that a consistent description of the CF interaction in SmPd$_{2}$Al$_{3}$ compound is obtained. We would like to emphasize that we calculated a similar temperature dependence of magnetic susceptibility, which has an intersection of curves along the c - and a -axis (see Fig.11), as we found by experiment. The intersection was not obtained using the CF acting on the ground A 0 2 = -307 K, A 0 4 = 25 K, A 0 6 = 1.9 K and A 6 6 = -88 K for SmPd$_{2}$Al$_{3}$ using the GGA form 18 of the exchange-correlation potential. When we consider spin-orbit interaction the values were: