Ions from Rh XIII to Cd XVI belong to the arsenic isoelectronic sequence ions. Their ground configuration is 4s²4p³, and the lower excited configurations are 4s4p⁴, 4s²4p²4d and 4s²4p²5s etc. The present study aims to predict the energy levels and transition data unknown in experiment for configurations 4s²4p³ and 4s4p⁴ from Rh XIII to Cd XVI ions, by analyzing the trend of the variation of Slater-Condon parameters along the As-like sequence based on the experimental energy levels available in the literature. So, the theoretical analyses of fine-structure energy levels of these configurations are conducted for the sequence ions from Rb V to Cd XVI by Hartree-Fock with Relativistic correction (HFR) method in Cowan’ code. The Slater-Condon parameter values of energy levels are obtained by least-square-fit (LSF) technique for ions mentioned above with the available experimental data. For the unknown parameters, the generalized-least-square-fit (GLSF) technique is used together with the extra (or inter)-polation method. With these new parameter values, the energy levels of 4s²4p³ and 4s4p⁴, the wavelengths and oscillator strengths of the transition array 4s²4p³−4s4p⁴ are computed. This research shows that for 4s²4p³, the single-configuration approximation of HFR calculation can present the satisfactory results, however, for 4s4p⁴, the reasonable good results can be achieved only by multi-configuration(4s4p⁴ + 4s²4p²4d) approximation, which can be verified by the obtained data. Comparing the absolute differences between observed and present LSF calculated levels’ values (including multi-configuration interaction) for the 4s4p⁴ configuration in ions from Rb V to Mo X with the results computed in a similar Hartree-Fock single-configuration approximate method by Person and Pettersson (Person W, Pettersson S G 1984 Phys. Scr. 29 308), we can see that the present LSF energy levels are improved substantially. For example, the LSF minimum and maximum absolute deviation value at present are 1 cm^–1 and 140 cm^–1, respectively, much more accurate than the results presented by Person et al., which are 45 cm^–1 and 382 cm^–1. The predicted data are in good agreement with the experimental results. For obtaining more information, the energy levels of 4s²4p³ and 4s4p⁴ configurations are computed by grasp2K-DEV package in valence-valence correlation scheme, which is based on the fully relativistic multi-configuration Dirac-Hartree-Fock (MCDHF) theory. The overall MCDHF energy levels are generally in accordance with the experimental results. The data obtained in this research are expected to be used in the future relevant theoretical and experimental investigations.