## Final Activity Report Summary - FROM DMFT TO DFT (From density matrix functionals to exchange-correlation functionals in density functional theory)

The main goal of all quantum chemistry methods is to replace the full many-electron Schroedinger equation, which is too complex to solve for more than a few electrons, with a simpler, however approximate, problem. It turns out that, in principle, the information contained in an N-electron wave function is also obtainable using a so-called one-electron reduced density matrix, 1-matrix, or even its diagonal part, i.e. electron density. A method based on the functionals of the latter, namely the Density functional theory (DFT), plays currently a crucial role in computational chemistry, since it combines relatively good accuracy with modest computational costs.

Density matrix functional theory (DMFT) that exploits 1-matrix as its main variable appears as an attractive alternative to DFT, since the kinetic energy term is explicitly known and the correlation effects are taken into account directly through fractional occupancies of the orbitals. In principle, both DFT and DMFT should be able to provide not only information about the ground state energy, through the energy functional, but also description of the excited states of the system.

The work performed during the fellowship concerned fundamental research which aimed at the development of methods exploiting functionals of one-electron density matrix. In particular, a time-dependent formulation of DMFT, the so-called Time-dependent density matrix functional theory (TD-DMFT) was proposed, enabling to obtain dynamic response properties and excitation energies from 1-matrix functionals. More precisely, we derived the equation of motion for 1-matrix in a functional form and showed how to approximate the resulting linear response equations to obtain simple scheme yielding dynamic properties.

The new methods were implemented and numerically analysed. Our achievement was an important step forward in rendering the DMFT a fully-fledged quantum chemistry method, thus providing both static and dynamic properties of electronic systems.

Density matrix functional theory (DMFT) that exploits 1-matrix as its main variable appears as an attractive alternative to DFT, since the kinetic energy term is explicitly known and the correlation effects are taken into account directly through fractional occupancies of the orbitals. In principle, both DFT and DMFT should be able to provide not only information about the ground state energy, through the energy functional, but also description of the excited states of the system.

The work performed during the fellowship concerned fundamental research which aimed at the development of methods exploiting functionals of one-electron density matrix. In particular, a time-dependent formulation of DMFT, the so-called Time-dependent density matrix functional theory (TD-DMFT) was proposed, enabling to obtain dynamic response properties and excitation energies from 1-matrix functionals. More precisely, we derived the equation of motion for 1-matrix in a functional form and showed how to approximate the resulting linear response equations to obtain simple scheme yielding dynamic properties.

The new methods were implemented and numerically analysed. Our achievement was an important step forward in rendering the DMFT a fully-fledged quantum chemistry method, thus providing both static and dynamic properties of electronic systems.