$\Delta$SCF in \texttt{VASP} for excited-state defect computations: tips and pitfalls

Abstract

$\Delta$SCF with constrained occupations have been wildly used to investigate the excited-state and optical properties of defects. Recent studies have demonstrated that combining $\Delta$SCF with hybrid functionals yields good accuracy in predicting defect properties. The Vienna Ab initio Simulation Package (\texttt{VASP}) is one of the most widely used quantum mechanical packages based on plane-wave methods. Despite the increasing application of $\Delta$SCF as implemented in \texttt{VASP} for defect studies, detailed walkthroughs explaining how to conduct these calculations remain limited, making this approach a nontrivial task. Applying $\Delta$SCF with hybrid functionals can present convergence challenges; worse, it may sometimes converge to incorrect excited states and can go largely unnoticed. This document aims to serve as a concise guide outlining what we think might be the appropriate approach for performing $\Delta$SCF calculations in \texttt{VASP}. We benchmark this method by simulating excited states for a particularly challenging system: the neutral charge state of the silicon vacancy (SiV$^0$) defect in diamond. By highlighting potential pitfalls, we hope this document encourages further discussion within the community and assists researchers experiencing difficulties with this technique. The guidelines provided here are largely based on private discussions with Oscar Bulancea Lindvall from Link{\"o}ping University and Chris Ciccarino from Stanford University.