Electrostatic interactions play a critical role in determining the properties, structures, and dynamics of chemical, biochemical, and material systems. These interactions are described well at the level of quantum mechanics (QM) but not so well for the various models used in force field simulations of these systems. We propose and validate a new general methodology, denoted PQEq, to predict rapidly and dynamically the atomic charges and polarization underlying the electrostatic interactions. Here the polarization is described using an atomic sized Gaussian shaped electron density that can polarize away from the core in response to internal and external electric fields, while at the same time adjusting the charge on each core (described as a Gaussian function) so as to achieve a constant chemical potential across all atoms of the system. The parameters for PQEq are derived from experimental atomic properties of all elements up to Nobelium (atomic no. = 102). We validate PQEq by comparing to QM interaction energy as probe dipoles are brought along various directions up to 30 molecules containing H, C, N, O, F, Si, P, S, and Cl atoms. We find that PQEq predicts interaction energies in excellent agreement with QM, much better than other common charge models such as obtained from QM using Mulliken or ESP charges and those from standard force fields (OPLS and AMBER). Since PQEq increases the accuracy of electrostatic interactions and the response to external electric fields, we expect that PQEq will be useful for a large range of applications including ligand docking to proteins, catalytic reactions, electrocatalysis, ferroelectrics, and growth of ceramics and films, where it could be incorporated into standard force fields as OPLS, AMBER, CHARMM, Dreiding, ReaxFF, and UFF.