Ensemble Density Functional Theory of Neutral and Charged Excitations

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

“…Various decompositions have actually been proposed. [427][428][429][430]438 They all have their advantages and drawbacks. A dilemma already appears at the Hartree-only level of approximation.…”

“…Indeed, as each Kohn-Sham state generates its own Hartree potential, there is no single ensemble potential from which the minimizing Kohn-Sham orbitals can be determined (by diagonalization). 175,438,447,448 If we want to avoid the use of OEPs, this is essentially the price to pay for constructing ghost-interaction-free ensemble energies in a systematic and general way. Mapping the true interacting ensemble density onto such an approximate Hartree-only state-averaged ensemble leads to an alternative (in principle, exact) formulation of ensemble DFT.…”

DFT Exchange: Sharing Perspectives on the Workhorse of Quantum Chemistry and Materials Science

“…422,423,434,435 In particular, it has been shown that ensemble density-functional weight derivatives ∂ E ξ ξ ξ Hxc [ρ]/∂ ξ I are directly connected to the derivative discontinuities that the Hxc potential exhibits when a given excited state is incorporated into the ensemble. [436][437][438] In DFT for (canonical, for simplicity) thermal ensembles, 431,432,439 the ensemble weights are controlled by a single parameter -the temperature or, equivalently, the inverse temperature β . In thermal DFT, the variational principle is extended to the total (Helmholtz) energy, which contains an entropic contribution:…”

“…429,430 This can be seen in the regular ground-state limit of the theory, when the weights assigned to the excited states are equal to zero. 438 This specific feature of ensemble DFT is reflected in the implicit weight-dependence of the Kohn-Sham wave functions {Φ I }. 430 can be related to the concept of state-driven (SD) correlation.…”

Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach

“…Such ensemble calculations are increasingly being used in traditional and emerging electronic structure methods [18][19][20][21]. They are also at the center of (time-independent) density functional approaches to excited states [22][23][24][25][26][27][28][29][30].…”