Time-dependent density functional theory with the orthogonal projector augmented wave method

The projector augmented wave (PAW) method maps smooth pseudo wavefunctions to highly oscillatory all-electron wavefunctions. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic energy cutoffs and larger grid spacing at the cost of having to solve for non-orthogonal wavefunctions. Orthogonal PAW (OPAW) was developed to allow the use of PAW when orthogonal wavefunctions are required. In OPAW, the pseudo wavefunctions are transformed through the efficient application of powers of the overlap operator with essentially no extra cost compared to NCPP methods. Previously, OPAW was applied to density functional theory (DFT). To make OPAW viable for post-DFT methods, we implement it in real-time time-dependent (TD) DFT. We compare calculations of absorption spectra for various organic and biological molecules and show that very large grid spacings are sufficient, 0.6–0.7 Bohr in OPAW-TDDFT rather than the 0.4–0.5 Bohr used in traditional NCPP-TDDFT calculations. Our method would be directly applicable to any post-DFT methods that require time-dependent propagations such as the GW approximation and the Bethe–Salpeter equation.