Effective electronic-only Kohn–Sham equations for the muonic molecules

Abstract

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

How intrinsic nuclear nonadiabaticity affects molecular structure, electronic density, and conformational stability: Insights from the multicomponent DFT calculations of Mu/H isotopologues

“…Subsequently, a single ghost (Bq) atom has been introduced to represent the center of expansions of electronic and muonic orbitals for the binding muonium atom. The uncontracted [4s1p] electronic and [5s5p] muonic basis functions of muonium atom are gathered in Supporting Information Tables S1 and S2, respectively, while the detailed account of devising the muon‐specific basis functions are published elsewhere and will not be reiterated herein . A brief glance at the exponents of electronic basis functions of the muonium atom (ranged from 0.805 to 3.925) highlights the importance of incorporating muon‐specific basis functions in any rigorous study of the muonium adducts beyond the BO paradigm.…”

“…In addition, the exponents of muonic basis functions were carefully arranged to have enough flexibility in the description of muon vibrational anharmonicity. The competence and efficiency of the combined set of electronic and muonic basis functions of the muonium atom in characterizing the muon's anharmonic and anisotropic vibrations have been recently shown within the framework of the effective electronic‐only formalism at Hartree‐Fock and Kohn‐Sham levels of theory . The overall levels of theory are denoted as UB3LYP/[6‐311++g(d,p)/4s1p:5s5p] and UB3LYP/6‐311++g(d,p) for the muoniated and hydrogenated adducts hereafter, respectively.…”

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

“…The eµc-1 functional may also be used to introduce novel effective non-Coulombic potentials, within the context of the newly proposed effective electronic-only Kohn-Sham equations, 119,120 which may overcome the mentioned problem of overlocalization in this context. Let us stress the fact that also from the computational perspective the single-component effective electronic-only equations are extremely cost effective.…”

“…Let us stress that in our previous computational studies on muonic molecules, [114][115][116][117][118] the electron-muon correlation was completely neglected and our recent formulation of the "effective electronic-only" DFT for muonic systems also does not contain this ingredient. 119,120 The present paper is organized as follows. First, we will try to computationally justify the above proposed SAA(eµ/n) framework in a benchmark set of simple muonic organic molecules.…”

Developing effective electronic-only coupled-cluster and Møller–Plesset perturbation theories for the muonic molecules

“…It is timely to stress that we have recently extended the idea of the effective theory to the NEO density functional theory (NEO-DFT) and derived an effective set of electronic-only Kohn-Sham (EKS) equations for the muonic molecules. 57 In this report, the effective theory is extended beyond the mean-field approximation and the ee correlation is accounted for using an effective Hamiltonian for the muonic molecules. This is done within the context of the second order Møller-Plesset (MP2) perturbation theory and the coupled-cluster (CC) theory as well-known examples of nonvariational methods.…”