Some implications of the Hartree product treatment of the quantum nuclei in the ab initio nuclear–electronic orbital methodology

2018

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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.

Section: Discussionsupporting

confidence: 55%

Section: Theorymentioning

confidence: 99%

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

Rayka

2018

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“…To have a more quantitative view on the mass dependence of the optimized nuclear exponents, the exponent of the s-type gaussian function is re-expressed based on the parameters of the harmonic oscillator model taking into account the fact that the s-type gaussian function is also the ground eigenfunction of the 3D isotropic harmonic oscillator. 92 One easily drives: Table S3 demonstrating that knowing just the exponent of one of the isotopically substituted species suffices to fairly well predict the exponents of the same species with other isotopic constitutions. However, some small but systematic deviations are observable from this simple relation stemming from the fact that the effective force constant experienced by a heavier isotope is larger than a lighter isotope.…”

Section: A the Optimized Exponents Of The Muonic Basis Setsmentioning

confidence: 99%

Toward a muon-specific electronic structure theory: effective electronic Hartree–Fock equations for muonic molecules

Rayka

2018

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An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

“…The present study is part of our ongoing programme to devise a muonic-specific ab initio electronic theory that tackles the computational study of the muonic molecules, trying to combine theoretical simplicity and computational feasibility. [55][56][57] While it is customary to use the conventional adiabatic electronic structure theory to model the muonic molecules, 21,[129][130][131][132][133][134][135][136][159][160][161] assuming that a hydrogen atom with a clamped nucleus may be used to model the muonium atom, our studies do not confirm that this viewpoint is always a legitimate computational strategy. On the contrary, the present study demonstrates that both muonic bond lengths and the relative stabilities of the muonic adducts are nonnegligibly underestimated within context of the adiabatic strategy.…”

Section: Discussionmentioning

confidence: 99%

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

2018

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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.