Hi Aleksei,
if overlaps cause your trouble, let me ask how you make your spheres big with the LJ potential? Do you vary sigma, or add the offset? If you vary sigma, then your spheres can normally approach each other to ~0.9 sigma (assuming epsilon=1kT). If you are seeking to model quite hard and big colloidal particles, I would suggest to control the sphere size by the LJ offset, keeping sigma=1.0. Then the spheres should never approach closer than offset+0.9sigma, which could resolve your problem with overlaps.
Note, that if you add offset, you have to set up your system such that there are no initial overlaps. Otherwise, Espresso complains. A possible solution is to start with zero offset and electrostatics OFF, gradually increase offset to the desired value, and then switch on the electrostatics.
Regards,
peter