The spatial and temporal interplay of the association, dissociation, and translocation of proteins along DNA is of central importance to genome regulation. Brownian dynamics (BD) is employed to study the energetics of nonspecific binding of 434 Cro repressor protein (Cro) to model B-DNA as a function of ionic strength. BD simulates the diffusional dynamics as Cro encounters the DNA surface including the steric effects of encounter between the irregular surfaces of the protein and DNA and the electrostatic effects based on a finite difference numerical solution of the Poisson-Boltzmarm (PB) equation. The free energy of a Cro-DNA encounter is determined by computing the potential of mean force versus the radial distance from the protein center to the DNA helix axis. The PB equation is solved by two approximations, the linearized form (LPB) and the full PB form (FPB); periodic boundary conditions are implemented for both solutions. The effect of the solution of the PB equation on the predicted free energy curve shows that both methods give qualitatively similar results but statistically the best results are achieved using the full PB. Both methods show that the depth of the free energy curve dramatically decreases as ionic strength increases from 0.01 to 0.50 M, For example, the full PB gives average depths of the free energy curves at -7 +/- 2 and -0.51 +/- 0.09 kcal/mol for ionic strengths of 0.01 and 0.50 M, respectively. The lifetimes of nonspecifically docked states, estimated from the free energy BD profile, depend on the ionic strength and are approximately 1000 and 0.03 ps for ionic strength of 0.01 and 0.50 M, respectively.