I am looking for software to calculate the (approximate) molecular electrostatic potential for VERY big molecules without doing quantum-mechanical calculations. Any help is thanked.
If your molecule is composed of standard bioresidues (e.g. amino acids, DNA bases, etc.), another possibility would be to use the partial atomic charges from a molecular mechanics force field. Displaying each residue via surface rendering, and then coloring according to the partial atomic charges may provide you with what are looking for. The approximations in this would a) polarization would not be directly accounted for by neighboring residues (bonded and nonbonded), b) you strictly are not accounting for other quantum effects, c) you are trusting the original theory for developing the charges. The advantage would be that an MD simulation could be run, and then you can observe how the electrostatics would change based on your molecule's conformations (e.g. the opening of a binding cleft).
I suggest APBS solver for VMD, where you can prosper from other VMD functionality. http://www.poissonboltzmann.org/apbs/examples/visualization/apbs-electrostatics-in-vmd