What do the letters A and B stand for?
It must have something to do with the well depth (epsilon) and the Re, but I would like to now more precise.
Van der Waals interactions are parameterized by Lennard-Jones (L-J) '6-12' potentials of the form
E = AiAj/r^6 - BiBj/r^12where A and B parameters for the types of atoms i and j are derived for the potential between two atoms of the same type. This same-type potential curve can also be defined by the radius (r*) corresponding to half the internuclear distance at the point of minimum energy, and the potential well depth ('e') at that internuclear distance. In this convention the potential energy for the van der Waals interaction between atoms 'i' and 'j' is defined as (rij*, eij), where rij* is (ri* + rj*)/2, and eij is sqrt(eiej). This is the convention which is used by AMBER.
The simple translation formulas one can derive to map Ai,Bi to r*i, 'e'i set the potential to be the same between atoms of the given type under both conventions. BUT, note that owing to the different combining rules, the per-atom potentials derived this way result in different distances of the minimum for pairs of atoms of different types (the depth of the potential is also different but is much less sensitive to the combining rules). Thus it was necessary to derive the r* values for the Aqvist monovalent cations to reproduce the ion-OH2 potential in the A,B scheme (rather than the ion-ion potential) in order to get the correct free energies of solvation in water.
Another representation of the parameters is sigma & 'e': According to Moore in his book "Physical Chemistry" (4th edition) page 128, sigma for the Lennard-Jones potential is the value of r (distance) where the potential energy equals zero, i.e. where the curve crosses the x-axis other than where r approaches infinity.
On the other hand, according to Hill in "Introduction to Statistical Thermodynamics", Appendix IV, pg 484, r* is the distance at the potential minimum. Thus r* = sigma * 2^(1/6).