These are preliminary reports that have not been peer-reviewed. They should not be regarded as conclusive, guide clinical practice/health-related behavior, or be reported in news media as established information. For more information, please see our FAQs.
Preprints are manuscripts made publicly available before they have been submitted for formal peer review and publication. They might contain new research findings or data. Preprints can be a draft or final version of an author's research but must not have been accepted for publication at the time of submission.
Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact analysis of generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components - one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.