I have the positions of a large number of charges (the strengths are known, but are also variables). Are there any tools that will allow me to visualize the electric field induced by these charges (or by a subset of these charges)? Are there such tools that are connected to visualization routines, so that these can be converted into figures for presentations or articles?
-Short answer for small molecules
PQR is one line per atom. Field_name should always be
If you already have partial charges (I'm going to assume you already have coordinates), it should be straightforward to write a script that will create your PQR file. If you don't already have partial charges, or if your molecule happens to be in certain accepted formats (MOL2, PDB, or XML), you should probably figure out how to use the PDB2PQR tool in order to make your PQR file.
Install APBS and VMD, and then just follow the instructions here. One thing to note: since you have no implicit solvent, in step 3 of "Running the electrostatics calculation" you will need to set your solvent and solute dielectric constant equal to whatever dielectric constant you used in your MD simulation (if you don't know what it was, setting them both to 1 should be fine).
That should be it. If you have any questions, or if it doesn't work, please add some comments and I'll see what I can do to answer/fix it.
If the number of charges isn't too large, hand-coding the formula for the potential and then taking the derivative symbolically with Sage or Mathematica should be easy enough.
If you have an enormous number of charges (several tens or more, in a file to long to convert to something by hand), you could read the charges and their positions into a python list, calculate the potential for each of them separately, and then add all the potentials together.