where N conf is the number of conformations of all molecules in the training set, n k is the number of atoms in the molecule corresponding to conformation k, µ ind, jkl is the induced dipole on atom j of conformer k with external field direction l, and r ijk is the vector from atom j to ESP point i for conformer k. The second quantity in parentheses is the potential at grid point i generated by the induced dipoles. Because we are using the direct approximation and are fitting polarizabilities to differences in ESP generated by an inducing field, the induced dipoles in Equation 2 are given simply by