Generalization of internal density-functional theory and Kohn-Sham scheme to multicomponent self-bound systems, and link with traditional density-functional theory

Abstract

We generalize the recently developed "internal" density-functional theory (DFT) and Kohn-Sham scheme to multicomponent systems. We obtain a general formalism, applicable for the description of multicomponent self-bound systems (such as molecular systems where the nuclei are treated explicitly, atomic nuclei and mixtures of 3He and 4He droplets), where the fundamental translational symmetry has been treated correctly. The main difference with traditional DFT is the explicit inclusion of center-of-mass correlations in the functional. A large part of the paper is dedicated to the application to molecular systems, which permits us to clarify the approximations that underly traditional DFT

Minimal nuclear energy density functional

“…7. The next step is to account for correlation energies; the center-of-mass corrections, which, in the case of self-bound systems, present some challenges [223][224][225][226][227][228][229][230]. Accounting for the center of mass correction [217,231], the correction due to particle number projection [232], the vibration correlation energy correction [6,233], the angular momentum projection [6,70,173,216,220,234,235], and Wigner energy [7,8] should reduce the rms energy from about 1.7 MeV to about 0.5 MeV.…”

Alternate, well-founded way to treat center-of-mass correlations: Proposal of a local center-of-mass correlations potential

“…The c.m. correlations energy functional for Bosons condensates is obtained by replacing ϕ i int → ϕ int , thus ρ int = N |ϕ int | 2 , in (17). Setting ϕ int = ρ int /N , we obtain:…”

“…Applying the multicomponent internal DFT formalism developed in Ref. [17] (whose equations have a relatively similar form than the "one kind of particle" internal DFT ones recalled in §II A), we can rewrite the internal energy (ϕ (1) int and ϕ (2) int being the KS orbitals):…”

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional

“…68,69 While the e-DFT is intrinsically a single-component formalism, only assuming electrons as quantum particles, this is not an intrinsic limitation of the fundamental theorems of DFT, 70 and the multi-component versions of DFT, MC-DFT, have been also formulated for systems composed of multiple types of quantum particles. [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90] Particularly, and relevant to present study, is the recent developments in formulation and computational applications of the MC-DFT to molecular systems where one or some numbers of protons, or other isotopes of hydrogen, are treated as quantum particles instead of clamped point charges. In fact, since usually just two components of these systems are treated as quantum particles, for example electrons and protons, the general formulation of the MC-DFT is reduced to the two-component version, TC-DFT.…”