Lattice, Time-Dependent Schrödinger Equation Solution for Ion-Atom Collisions

The conventional approach to treating charged defects in extended systems in first principles calculations is via the supercell approximation using a neutralizing jellium background charge. I explicitly demonstrate shortcomings of this standard approach and discuss the consequences. Errors in the electrostatic potential surface over the volume of a supercell are shown to be comparable to a band gap energy in semiconductor materials, for cell sizes typically used in first principles simulations. I present an alternate method for eliminating the divergence of the Coulomb potential in supercell calculations of charged defects in extended systems that embodies a correct treatment of the electrostatic potential in the local viciniq of the a charged defect, via a mixed boundary condition approach. I present results of first principles calculations of charged vacancies in NaCl that illustrate the importance of polarization effects once an accurate representation of the local potential is obtained. These polarization effects, poorly captured in small supercells, also impact the energetic on the scale of typical band gap energies