Erratum: Development of Electron-Proton Density Functionals for Multicomponent Density Functional Theory [Phys. Rev. Lett.101, 153001 (2008)]

Abstract

a Results from A. Chakraborty, M. V. Pak, and S. Hammes-Schiffer, J. Chem. Phys. 134, 079902 (2011). NEO-HF is Eq. (10) with g ¼ 0. b All calculations used an STO-2G electronic basis set. NEO calculations used the 5s nuclear basis sets for H, D, and T. c The electron-proton functional used a single geminal function with b ¼ 0:852 a:u: and ¼ 1:962 a:u. These parameters were fixed at their original values. d ÁE ¼ E NEO-DFT À E NEO-HF is the difference in total energies in a.u.

Theory of Coupled Electron and Proton Transfer Reactions

“…Note that the magnitude of the electronic coupling is usually similar for related PCET and ET reactions, but the PCET electron-proton vibronic coupling is substantially smaller due to inclusion of the overlap between the reactant and product proton vibrational wavefunctions. Currently methods for calculating the combined electron-proton vibronic coupling in terms of mixed nuclear-electronic wavefunctions are being developed 121–123…”

Calculation of the Positron Annihilation Rate in PsH with the Positronic Extension of the Explicitly Correlated Nuclear−Electronic Orbital Method

“…This type of NEO-DFT approach has been successfully applied to multicomponent systems involving quantum electrons and protons. 36 Another advantage of NEO-DFT is that electron-electron correlation can be included in a computationally efficient and consistent manner, 37 where δ e i p ≡ δ(r i e -r p ). Using the NEO-XCHF wave function in eq 2, this expectation value can be expressed as where the one-, two-, and three-particle operators resulting from combining the delta function operator δ e i p and the geminal operator are defined as We now provide the explicit expressions for these terms using the restricted Hartree-Fock (RHF) formulation for closed-shell electron systems.…”

The any particle molecular orbital approach: A short review of the theory and applications

“…The MC‐DFT approach can be utilized to study NQEs. In these calculations, the exchange‐correlation functional comprises three contributions: the electronic exchange‐correlation functional, , which is usually borrowed from electronic structure DFT; the nuclear exchange‐correlation, , which is neglected since it has been found to be negligible and the nuclear‐electron correlation, , for which local density approximation (LDA) functionals have been proposed . Still, in some applications of APMO‐DFT, the nuclear‐electronic correlation has been neglected …”

“…In these calculations, the exchange-correlation functional comprises three contributions: the electronic exchange-correlation functional, E e xc , which is usually borrowed from electronic structure DFT; the nuclear exchange-correlation, E n xc , which is neglected since it has been found to be negligible [37,39,40,59,60] and the nuclear-electron correlation, E en c , for which local density approximation (LDA) functionals have been proposed. [14,47,49,[61][62][63][64] Still, in some applications of APMO-DFT, the nuclear-electronic correlation has been neglected. [58,65] In MC studies of exotic atoms and molecules the system regularly comprises all electrons and only one exotic particle as quantum waves.…”