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Final Report Summary - TD-SCDFT (Time-dependent density functional theory for strongly-interacting electrons)

In the last few years a considerable amount of work on the strictly correlated electron (SCE) formalism within the framework of ground state Kohn–Sham (KS) density functional theory (DFT) has been carried out, showing great promise in describing strongly-correlated systems both in Physics and Chemistry.
The formalism owes its success to incorporating into the KS-DFT scheme an approximation for the so-called exchange-correlation energy functional which rests on a particular physical picture, the one of strictly correlated electrons, which describes very accurately the behaviour of particles in the regime of strong correlation. While a considerable amount of progress has been achieved in formulating and applying the SCE KS-DFT approach to ground state problems, excited state problems hadn’t been addressed until the start of the TD-SCDFT project. The aim of the project was to begin a systematic investigation of the SCE functional in the context of time dependent problems, in order to understand its fundamental aspects and its potential in tackling challenging problems for the standard approximations employed in time-dependent (TD) DFT.
The accuracy of TDDFT relies heavily on the approximations for the time-dependent potentials and for the linear response kernel that enter the theory. Just like in ground state DFT the use of non local functionals of the density can yield results which are superior to the one obtain with the more popular local and semi-local ones. The SCE functional, being highly non local, seemed a promising approximation already within the so-called adiabatic approximation, and thus our investigation begun from the properties of the adiabatic SCE (ASCE) functional.
Among the important results obtained, we showed how the ASCE satisfies important exact constraints of many-body theories, namely the generalized translational invariance (GTI) and the zero-force theorem (ZFT), which are desirable features to avoid incurring into unphysical results when describing the time evolution of a quantum system. Furthermore we obtained insights on the long standing issue of the so-called ultra non locality problem in TDDFT. Early works pointed out that non-locality in time requires non-locality in space as well in order to satisfy the ZFT, but it wasn’t obvious that the converse would be also true. Our derivations showed that it is not the case and indicated that the ASCE constitutes a privileged starting point in order to construct functionals with memory, which is a challenge of primary importance in TDDFT.
Subsequently we derived and analysed an expression for the exact ASCE exchange correlation (xc) kernel. The xc-kernel is a key ingredient of TDDFT and the exact one should exhibit a number of properties. Among them, in the particular case of long range charge transfer (CT) excitations, the xc-kernel should be able to account for a term which goes as the inverse of the distance between the donor and the acceptor of the transferred charge. When one employs approximations for the kernel with a local structure in space, such term is completely absent, which causes a severe underestimation of the charge transfer energy. We found that the ASCE kernel exhibits the well known divergence crucial to capture homolytic bond-breaking excitations and we tested it on a prototype system for the H2 molecule dissociation, obtaining very encouraging results. This finding is of great interest in the TDDFT community, since it showed that even a local in time (adiabatic) but non-local in space kernel, such as the ASCE one, is able to capture this type of excitations.
The TD-SCDFT project aimed also at the application of the method to interesting problems that occur in the time domain. Hence we pursued the idea of combining a TDDFT approach to quantum transport with the KS-SCE formalism, which was also generalized to fractional occupations, making it suitable for describing open systems. We aimed at exploiting one of the properties of the SCE potential, namely the fact that it exhibits the so-called derivative discontinuity, a feature which is missed by common local and semi-local density functionals and which has been proven to be crucial to describe phenomena like the Coloumb blockade (CB) in a DFT formulation of quantum transport.
To date, the CB has been captured only within a lattice formulation of TD transport.
The preliminary results have been promising, but this part of the project is still ongoing.
The main results of the project have been published in a long paper in a special issue of the Journal of Chemical Physics Physical Chemistry and they have been presented at a number of internal conferences, through talks and posters. Furthermore, the extension of the formalism to the realm of time dependent problems, brought it to the attention of an entirely new community, namely the TDDFT one, who judged it a very interesting and promising advance in the field.
Finally, two new international collaborations have been established: the first one with the group of Prof. R. van Leeuwen (University of Jyväskylä) and the second with Prof. S. Kurth (University of the Basque Country).
The project also included an outreach activity, consisting of editing further the Wikipedia page on the SCE formalism (https://en.wikipedia.org/wiki/Strictly-Correlated-Electrons_density_functional_theory) originally created by F. Malet (who was awarded an IEF grant in the group of P. Gori-Giorgi earlier).

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STICHTING VU-VUMC
Netherlands
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