The experimental free ion 4f(2) energy level data sets comprising 12 or 13 J-multiplets of La+, Ce2+, Pr3+ and Nd4+ have been fitted by a semiempirical atomic Hamiltonian comprising 8, 10, or 12 freely-varying parameters. The root mean square errors were 16.1, 1.3, 0.3 and 0.3 cm(-1), respectively for fits with 10 parameters. The fitted inter-electronic repulsion and magnetic parameters vary linearly with ionic charge, i, but better linear fits are obtained with (4-i)(2), although the reason is unclear at present. The two-body configuration interaction parameters alpha and beta exhibit a linear relation with [Delta E(bc)](-1), where Delta E(bc) is the energy difference between the 4f(2) barycentre and that of the interacting configuration, namely 4f6p for La+, Ce2+, and Pr3+, and 5p(5)4f(3) for Nd4+. The linear fit provides the rationale for the negative value of alpha for the case of La+, where the interacting configuration is located below 4f(2). (C) 2013 Elsevier B. V. All rights reserved.