In the oxidation of a metal surface, the oxygen atoms transition from being in a diatomic molecular, where there is a covalent bond and each atom has a neutral charge, to being a part of an oxide phase, where they have a finite charge, and are subject to strong electrostatic forces. The metal atoms undergo a similar transition. To model such charge transfer in a molecular dynamics simulation, one must allow for the charges of the atoms to change as a function of time.

      The response of the electrons to a change in an atomic system will be much faster than that of the ions. Thus, to the electrons, the ions appear rigid. Implementing this fact in modeling is known as the adiabatic (or Born-Oppenheimer) approximation. In our MD simulations, this approximation is realized by relaxing the electrostatic energy at every time step.

      Following the method of Rappe and Goddard [1], the electrostatic energy can be written as

..... (1)

where E_i is the energy of atom i due to its charge (q_i), and V_ij is the electrostatic energy associated with atoms i and j. The driving force for charge transfer is the electronic chemical potential, given for atom i by

..... (2)

At charge equilibrium the electronic chemical potentials of the N atoms in the system will be equal. This condition generates N-1 equations. By requiring that the total charge be conserved, N equations are obtained that can be solved for the charges.

      In theory, the charges can be found by inverting an N×N matrix. In practice, however, this approach is not feasible for systems with hundreds of thousands of atoms. Instead, we solve for the charges by writing appropriate equations of motion that include a damping term. The charge system can then be annealed to arrive at the equilibrium configuration.

      The approach described above has been implemented for α-alumina using the Streitz-Mintmire potential [2]. We plan to investigate the α-Al₂O₃-Al interface, and the oxidation of an Al surface. We are adapting the Streitz-Mintmire potential to model a copper-oxygen system, where we also wish to model oxidation.