Repulsive interatomic potentials calculated at three levels of theory

The high-energy repulsive interaction between nuclei at distances much smaller than the equilibrium bond length is the key quantity determining the nuclear stopping power and atom scattering in keV and MeV radiation events. This interaction is traditionally modeled within orbital-free density functional theory with frozen atomic electron densities, following the Ziegler-Biersack-Littmark (ZBL) model. In this work, we calculate atom pair-specific repulsive interatomic potentials with the ZBL model, and compare them to two kinds of quantum chemical calculations (second-order Møller-Plesset perturbation theory in flexible Gaussian basis sets as well as density functional theory with numerical atomic orbital basis sets) which go well beyond the limitations in the ZBL model, allowing the density to relax in the calculations. We show that the repulsive interatomic potentials predicted by the two quantum chemical models agree within <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mo>∼</a:mo><a:mn>1</a:mn><a:mo>%</a:mo></a:math> for potential energies above 30 eV, while the ZBL pair-specific potentials and universal ZBL potentials differ much more from either of these calculations. We provide pair-specific fits of the screening functions in terms of three exponentials to the calculations for all pairs <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>Z</b:mi><b:mn>1</b:mn></b:msub><b:mtext>−</b:mtext><b:msub><b:mi>Z</b:mi><b:mn>2</b:mn></b:msub></b:mrow></b:math> for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1</c:mn><c:mo>≤</c:mo><c:msub><c:mi>Z</c:mi><c:mi>i</c:mi></c:msub><c:mo>≤</c:mo><c:mn>92</c:mn></c:mrow></c:math>, and show that they agree within <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>∼</d:mo><d:mn>2</d:mn></d:mrow></d:math>% with the raw data. We use these potentials to simulate ion implantation depth profiles in single-crystalline Si and show very good agreement with experiment. However, we also show that under channeling conditions, the attractive part of the potential can affect the depth profiles.