The experimental free ion 4f² 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 α and β exhibit a linear relation with [ΔE(bc)]⁻¹, where ΔE(bc) is the energy difference between the 4f² barycentre and that of the interacting configuration, namely 4f6p for La⁺, Ce²⁺, and Pr³⁺, and 5p⁵4f³ for Nd⁴⁺. The linear fit provides the rationale for the negative value of α for the case of La⁺, where the interacting configuration is located below 4f². Copyright © 2013 Elsevier B.V. All rights reserved.