Formulation and Implementation of the Spin-Restricted Ensemble-Referenced Kohn–Sham Method in the Context of the Density Functional Tight Binding Approach

The spin-restricted ensemble-referenced Kohn-Sham (REKS) method and its state-interaction state-averaged variant (SI-SA-REKS, or SSR) provide computational platform for seamless inclusion of multi-reference effects into the density functional calculations. The SSR method enables an accurate calculation of the vertical excitation energies for the molecules with multi-reference ground states and describes conical intersections between the ground and excited states with the accuracy matching the most sophisticated ab initio multi-reference wavefunction methods. In this work, the SSR method is formulated and implemented in the context of the long-range corrected density functional tight binding (LC-DFTB) approach. The new LC-DFTB/SSR method enables calculation of the excited electronic states and the S1/S0 conical intersections of very large molecules. The LC-DFTB/SSR method is benchmarked against vertical excitation energies and conical intersection energies and geometries of several organic molecules with π...