Multi-configuration density-functional theories for excited states – MCFUNEX

The formulation of a multi-state multiconfigurational DFT is obtained rigorously by using the range separation of the two-electron repulsion in the framework of ensemble DFT. The latter is an extension of DFT to excited states which relies on the so-called «ensemble density« which is the weighted sum of ground and excited state densities. The associated ensemble energy is then used to calculate excitation energies.
As an alternative to range-separated DFT, we recently started investigating the rigorous formulation of multiconfigurational DFT in the orbital space. When applied to model Hamiltonians like the Hubbard Hamiltonian, this approach leads to an exact site-occupation embedding theory (SOET).

Our main results in range-separated ensemble DFT are: (i) the formulation of a linear interpolation method (LIM) which provides a systematic way of calculating approximate (ensemble weight-independent) excitation energies, (ii) the combination of LIM with extrapolation techniques based on Taylor expansions in the range-separation parameter which gives more accurate excitation energies, and (iii) the formulation of a rigorous and general solution to the well-known «ghost-interaction problem« in ensemble DFT.
Turning to SOET, we recently developed the first local density approximation (LDA) in this context. It is based on the Hubbard dimer and gave promising results.

In the near future, we will focus on (i) the calibration of the various range-separated ensemble DFT schemes recently developed for modelling photochemical processes. Prototypical systems such as H4 or ethylene will be investigated first in order to highlight the strengths (and potential weaknesses) of the methods. We will also (ii) keep on developing SOET for model Hamiltonians (a potential application could be the modelling of quantum transport) and (iii) extend it to quantum chemistry. For that purpose we will combine SOET with reduced density matrix functional theory (RDMFT).

[1] “On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation” - E. Fromager, Mol. Phys. 113, 419 (2015)
[2] “Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states” - B. Senjean, S. Knecht, H. J. Aa. Jensen, and E. Fromager, Phys. Rev. A 92, 012518 (2015).
[3] “Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory” - B. Senjean, E. D. Hedegård, Md. M. Alam, S. Knecht, and E. Fromager, Mol. Phys. (2015), doi: 10.1080/00268976.2015.1119902
[4] “Local density approximation in site-occupation embedding theory” - B. Senjean, M. Tsuchiizu, V. Robert, and E. Fromager, submitted to Mol. Phys. (2016), arXiv preprint arXiv:1602.02547
[5] “Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation” - Md. M. Alam, S. Knecht, and E. Fromager, (2016), arXiv preprint arXiv:1603.05385

The purpose of the MCFUNEX project is to develop new computational tools for modeling excited-state properties in molecules (spectroscopy, photochemistry, ...). This includes the rigorous derivation of new quantum chemical models, as well as their computational implementation and their calibration. Our main focus is the proper treatment of strong correlation effects within density-functional theory (DFT) as well as the description of double and higher excitations, which are absent from conventional time-dependent DFT (TD-DFT) spectra, due to the adiabatic approximation. For that purpose, multi-configuration extensions of both DFT and TD-DFT are proposed, using the long-/short-range separation of the two-electron interaction. This choice is motivated by the fact that a long-range Multi-Configuration Self-Consistent Field (MCSCF) treatment, complemented by a short-range DFT (srDFT) description of the Coulomb hole, cannot double count correlation effects. This scheme, referred to as MC-srDFT, is appealing in this respect but, in practice, approximate short-range exchange-correlation density-functionals currently available are not accurate enough to make it always reliable. Indeed, strong correlation is generally not purely long-range which means that the short-range density-functionals should in principle be able to describe some part of it. In order to improve the MC-srDFT model in that respect, we propose to develop new short-range functionals, which depend not only on the density, but also on the on-top pair density or on the wave-function. In the latter case, the Optimized Effective Potential (OEP) approach will be adapted to a long-range MCSCF treatment, in order to avoid double-counting problems. For the purpose of extending the corresponding MC-srOEP model, which is not variational, to the TD regime, a Lagrangian formulation is proposed so that linear response properties (excitation energies, ...) can be computed efficiently. Finally, in order to model conical intersections, a multi-state extension of the MC-srDFT scheme will be explored in the framework of ensemble DFT (EDFT). As a preliminary work, a long-range Configuration Interaction (CI) treatment will be combined self-consistently with a srEDFT description. For the latter, approximate functionals will be developed from accurate adiabatic connection calculations. The output of the all project will be publications in international peer-reviewed journals where the formalism as well as calibration studies for well-known systems will be presented. The various models will be implemented in the DALTON program package which is freely distributed worldwide.