On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

Abstract

The exact formulation of multi-configuration density-functional theory (DFT) is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of Configuration Interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact Site-Occupation Embedding Theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with Density Matrix Embedding Theory (DMET) is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact Complete Active Space Site-Occupation Functional Theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described with an orbital occupation functional. The computational implementation of SOET and CASSOFT as well as the development of approximate functionals are left for future work.

Density matrix renormalization group with efficient dynamical electron correlation through range separation

“…In turn, the coupling of DFT to a CAS-type wave function method provides the required flexibility for cases where static correlation becomes important and where DFT is likely to fail [41][42][43][44] . Although hybrid approaches between wave function theory (WFT) and DFT have not been considered for DMRG yet, they have already been studied with other wave func-tion methods [45][46][47][48][49][50][51] . While approximate DFT functionals will introduce errors on the absolute scale, relative energies for hybrid WFT-DFT approaches can be obtained with good accuracy [52][53][54][55][56] .…”

Polarizable Embedding Density Matrix Renormalization Group

“…For this analysis, the DMRG (20,27)[1024] active space encompassed the π-system and higher lying σ/σ * orbitals. The same active space was employed in the DMRG (20,27)[1024]-srDFT calculations.…”

“…For this analysis, the DMRG (20,27)[1024] active space encompassed the π-system and higher lying σ/σ * orbitals. The same active space was employed in the DMRG (20,27)[1024]-srDFT calculations. The latter calculations were performed with the tailored short-range PBE functional by Goll, Werner, and Stoll [124], and we denote these calculations DMRG (20,27)[1024]-srPBE in the following.…”

“…The same active space was employed in the DMRG (20,27)[1024]-srDFT calculations. The latter calculations were performed with the tailored short-range PBE functional by Goll, Werner, and Stoll [124], and we denote these calculations DMRG (20,27)[1024]-srPBE in the following. All calculations on retinylidene employed a 6-31G* basis set because this very small basis had already been chosen for studies on related rhodopsins [103,125] and hence makes a comparison possible.…”

“…The FDE method is not restricted to DFT and the embedded subsystem can also be described by a wave function which is usually denoted WFT-in-DFT [14][15][16][17][18][19][20][21]. WFT-in-WFT embedding schemes have also been investigated, e.g., by Chan and co-workers [22][23][24], by Scuseria and co-workers [25,26], and by Fromager and co-workers [27,28].…”