A crude but computationally cheap approach for modeling excited states is to use DFT with non-Aufbau occupations assigned to the Kohn-Sham states. This approach is known as ΔSCF or constrained DFT (cDFT) – though the latter term can also refer to constraints on charge or spin localization. Despite the availability of more sophisticated approaches, cDFT remains useful in contexts such as charge-transfer excitations, Gill’s maximum overlap method, non-adiabatic dynamics, and TDDFT for excited-state structural or electronic dynamics. Indeed it is perhaps the only available approach for thermalized or otherwise incoherent electronic excitations in solids. Within ordinary DFT, vibrational and dielectric linear-response calculations have become routine with the Sternheimer equation of density-functional perturbation theory (DFPT), which needs only the occupied states. This technique works at zero temperature or with an effective temperature described through a smearing function, and can be used in both static and TDDFT calculations. However, the formalism has not been available for calculation of states with arbitrary occupations, as can arise in the cDFT description of excited states. I derive a simple modification to extend DFPT to arbitrary fractional occupations, implemented in the Octopus real-space DFT/TDDFT code, and show example applications for excited-state absorption of transition-metal complexes.

Density-functional perturbation theory for excited states from constrained DFT

2019 Fall National Meeting

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