The molecular docking method was used to calculate the binding free energies between biphenyl dioxygenase and 209 polychlorinated biphenyl (PCB) congeners. The relationships between the calculated binding free energies and migration (octanol–air partition coefficients, KOA), persistence (half-life, t1/2), toxicity (half maximal inhibitory concentration, IC50), and bioaccumulation (bioconcentration factor, BCF) values for the PCBs were used to gain insight into the degradation of PCBs in the presence of biphenyl dioxygenase. The relationships between the calculated binding free energies and the molecular weights, KOA, BCF, and t1/2 values for the PCBs were statistically significant (P < 0.01), whereas the relationship between the calculated binding free energies and the IC50 for the PCBs was not statistically significant (P > 0.05). The electrostatic field, derived from three-dimensional quantitative structure–activity relationship studies, was a primary factor governing the binding free energy, which agreed with literature findings for KOA, t1/2, and BCF. Comparative molecular field analysis and comparative molecular similarity indices analysis contour maps showed that the binding free energies, KOA, t1/2, and BCF values for the PCBs decreased simultaneously when substituents with electropositive groups at the 3-position or electronegative groups at the 3′-position were introduced. This indicated the binding free energy was correlated with the persistent organic pollutant characteristics of PCBs. Furthermore, low binding free energies improved the degradation of the PCBs and simultaneously decreased the KOA, t1/2, and BCF values, thereby reducing the persistent organic pollutant characteristics of PCBs in the environment. These results are expected to be beneficial in providing a theoretical foundation for further elucidation of the degradation and molecular modification of PCBs.Electronic supplementary materialThe online version of this article (10.1186/s13065-018-0389-2) contains supplementary material, which is available to authorized users.