AutoSTOP-RT-TDDFT: Adaptive and Selected Real-Time Time-Dependent Density Functional Theory for Simulation of X-Ray...

It has recently been shown [J. Chem. Phys. 157, 074106 (2022)] that the propagator (P), step size (S) and total time (T) required by real-time time-dependent density functional theory (RT-TDDFT) simulation of X-ray absorptions (XAS) can be determined automatically (Auto) for whatever chemical systems described by whatever electronic Hamiltonians and basis sets, by making use only of the ground-state Kohn-Sham core orbital energies. The AutoPST algorithm is improved here in two aspects: (1) a universal bivariate linear relation is established for accurate predication of the time steps for both $K$ - and $L$ -edge XAS of any desired spectral accuracy; (2) an automated orbital selection scheme is introduced to pick up only those "active" core and virtual canonical molecular orbitals (CMO), thereby extending AutoPST to AutoSTOP. Such orbital selection is particularly necessary when an uncontracted basis set is used, which generates many high-lying CMOs that have no contributions to near-edge XAS but render the time step exceedingly small. The ratio of the number of active CMOs over the total number of CMOs decreases quickly as the increase of molecular size, thereby ensuring computational efficiency. It is also shown that both singlet and triplet core excited states of a closed-shell system can be obtained by RT-TDDFT with a weak spin-dependent external field. Spin-orbit couplings between the so-obtained singlet and triplet states can then readily be calculated to obtain the $L_2$ and $L_3$ spectra. Finally, the linearized variant of RT-TDDFT is briefly discussed.