The Connector Theory Approach: Principles and Development of New Density Functionals

Density Functional Theory (DFT) and Time-Dependent (TD) DFT allow us in principle to express observables as functionals of the density. Relatively efficient approximations exist for the ground state total energy, but major difficulties remain, for example to describe strongly correlated systems, or situations where long range correlation is important. For other observables, even less is known about how to build good density functionals.
One way of designing approximations is to use results of model systems. In this talk we will show how model results can be used in an in principle exact way, called “Connector Theory”, in order to describe observables and systems of interest. Within this approach, a quantity of interest is calculated for a model system as function of a parameter once and forever, and the results are stored. Under certain conditions, the result for an appropriate choice of parameter can then be used to replace a value of interest in a given real system. This choice of parameter is called “connector”.
We will discuss the principles and general properties of such an approach. Of course, in practice, the connector has to be approximated. We will show that formulating the problem in this way is a convenient starting point for approximations, and a strategy to build systematic approximations will be presented.
We will then focus more specifically on the use of the connector approach to design density functionals, both for DFT and TDDFT. Particular emphasis will be put on effects of non-locality in space and time, which are important to capture, e.g., image potentials or multiple excitations, respectively. Some discussion and results can be found in [1,2].

[1] M. Vanzini, A. Aouina, M. Panholzer, M. Gatti, and L. Reining, https://arxiv.org/abs/1903.07930
[2] M Panholzer, M Gatti, L Reining; Phys. Rev. Lett. 120, 166402 (2018).