The conventional electrostatic charge models (PD-AC) are constructed so as to reproduce the molecular electrostatic potential (MESP) on and beyond the van der Waals’ (vdW) surface. The MESP distribution has recently [S R Gadre, S A Kulkarni and I H Shrivastava (1992)J. Chem. Phys.96 5253] been shown to exhibit rich topographical features. With this in view, a detailed topographical comparison of the MESP derived from the charge models, with the respectiveab initio (MO) ones is taken up for water, hydrogen sulphide, methane and benzene molecules as test cases. It is shown that the point charge models have a fundamental lacuna, viz. they fail to mimic the essential topographical features of MESP. A new model incorporating a small number of floating spherical Gaussians is shown to restore all the critical features of the molecules under study. A comparative study of the standard deviations of MESP derived from charge models on scaled vdW surfaces further reveals that the present model leads to a better representation ofab initio MESP.