Parameter values for self-consistent charge equilibration (SCQEq) methods that include third- and fourth-order terms were determined for non-metallic compounds. Parameter fitting was performed to reproduce the restrained electrostatic potential (RESP) charges obtained by ab initio quantum chemical calculations. In addition, the calculated parameter values were validated by means of external test sets. The results indicate that SCQEq with higher-order terms can reproduce RESP charges for non-metallic compounds, especially for nitro derivatives, for which appropriate atomic charges cannot be obtained by traditional charge equilibration methods. (C) 2010 Elsevier B.V. All rights reserved.