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

Abstract

It is well-known experimentally that the positively charged muon and the muonium atom may bind to molecules and solids, and through muon’s magnetic interaction with unpaired electrons, valuable information on the local environment surrounding the muon is deduced. Theoretical understanding of the structure and properties of resulting muonic species requires accurate and efficient quantum mechanical computational methodologies. In this paper, the two-component density functional theory (TC-DFT), as a first principles method, which treats electrons and the positive muon on an equal footing as quantum particles, is introduced and implemented computationally. The main ingredient of this theory, apart from the electronic exchange–correlation functional, is the electron–positive muon correlation functional that is foreign to the purely electronic DFT. A Wigner-type local electron–positive muon correlation functional, termed eμc-1, is proposed in this paper and its capability is demonstrated through its computational application to a benchmark set of muonic organic molecules. The TC-DFT equations containing eμc-1 are not only capable of predicting the muon’s binding site correctly, but they also reproduce muon’s zero-point vibrational energies and the muonic densities much more accurately than the TC-DFT equations lacking eμc-1. Thus, this study sets the stage for developing accurate electron–positive muon functionals, which can be used within the context of the TC-DFT to elucidate the intricate interaction of the positive muon with complex molecular systems.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

“…130,141 The NEO methodology was originally implemented in the GAMESS quantum chemistry package, although the computations reported in the this paper have been derived via our in-house version of the NEO-GAMESS package. 85,123,142,143 Some details of the ab initio results are gathered in Table S1 in the ESI. †…”

Current status of deMon2k for the investigation of the early stages of matter irradiation by time-dependent DFT approaches

“…MC-DFT is rooted in an extension of the Hohenberg-Kohn theorems for composite systems where the total energy is a functional of the one-particle densities, which are built from reference non-interacting orbitals under the Kohn-Sham formalism [87]. MC-DFT has been employed to incorporate nuclear quantum effects beyond the Born-Oppenheimer approximation [88][89][90] and to analyze the interaction of atoms and molecules with exotic particles such as positrons [91] and muons [92]. The MC-DFT approach provides a more efficient framework for the inclusion of quantum effects as compared to traditional path integral methods [93].…”

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory

“…[5][6][7][8][9] Significant progress on this topic has been achieved in the last two decades, including the development of time-dependent MC-DFT, [10][11][12][13][14][15][16][17] electron-proton correlation functionals, 2,[18][19][20][21][22][23][24][25] and electron-muon correlation functionals. 26,27 The interaction between the different fermions in multicomponent DFT is of special interest, describing the intricate correlation in movement between, for example, electrons and protons or other femions. As outlined above, notable efforts have been put into the development of electron-proton correlation density functionals.…”