All atoms were described by the ANO-RCC basis set , with the contraction [8s7p5d3f2g1h] for Ln atoms, [4s3p2d1f] for O, [3s2p] for C and N, [2s] for H. Scalar relativistic terms were included in the one-electron part of the electrostatic Hamiltonian both in the CAHF and CASCI-SO steps, within the second order Douglas-Kroll-Hess (DKH2) approximation . SO always include both one-and two-centers SOC integrals. The CASCI-SO energies within a given multiplet have been compared with the CASCI-SO results which include the true H BP SO . The Cholesky representation of the 2e-SOC integrals as proposed in this paper was used to speed up the calculations when the atomic approximation is not used. Different Cholesky δ thresholds have been tested at first to reach the best compromise between time performance and accuracy. It has been fixed at δ = 10 -4 , which shows a significant speed up in the calculations with a loss of accuracy on the energy gaps smaller than 0.01 cm -1 with respect to the results which include all the 2e-SOC integrals.