  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. 20, 4466 (2018)]. In the present report we extend the muon-specific
effective electronic structure theory beyond the EHF level by introducing the
effective second order Muller-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.
