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

Abstract

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the nuclear-electronic orbital theory [Phys. Chem. Chem. Phys., 2018, 20, 4466]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

On the Nature of the Positronic Bond

“…Using ab initio derived multi- component wavefunction of an exotic species, through a welldefined and unique machinery, which is system-independent and automated, the MC-QTAIM analysis derives the AIM and their properties. These properties may then be used to access the bonding modes of the AIM in the exotic molecule as has been previously done in the case of the positronic, [61][62][63] and the muonic, [64][65][66][67][68] species. Particularly, the previous MC-QTAIM analysis of the positronic species revealed that the positron is not capable of accumulating enough electrons around itself to form an independent atomic basin.…”

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

“…In the last decade, the QTAIM scheme has been extended to the partitioning of MC quantum systems, and the input to the extended algorithm, called MC-QTAIM, 98–117 are ab initio MC wavefunctions derived from solving the MC Schrödinger equation (written in atomic units):This equation governs a system with s types of distinguishable quantum particles, with spin-spatial variables x⃑ n , i = ( r⃑ n , i , σ n , i ) for the i th particle of the n th type, where there are N n particles with charge, q n , and mass, m n , interacting via the Coulomb law with each other and the clamped nuclei; there are Q of the latter carrying Z α charge and placed at R⃑ α . The zero-flux equation of the MC-QTAIM partitioning algorithm, used to derive the boundaries of the atomic basins, is as follows: 105,117 wherein, is the one-particle density of n th type particles.…”

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.…”