Where to place the positive muon in the Periodic Table?

Abstract

In a recent study it was suggested that the positively charged muon is capable of forming its own "atoms in molecules" (AIM) in the muonic hydrogen-like molecules, composed of two electrons, a muon and one of the hydrogen's isotopes, thus deserves to be placed in the Periodic Table [Phys. Chem. Chem. Phys., 2014, 16, 6602]. In the present report, the capacity of the positively charged muon in forming its own AIM is considered in a large set of molecules replacing muons with all protons in the hydrides of the second and third rows of the Periodic Table. Accordingly, in a comparative study the wavefunctions of both sets of hydrides and their muonic congeners are first derived beyond the Born-Oppenheimer (BO) paradigm, assuming protons and muons as quantum waves instead of clamped particles. Then, the non-BO wavefunctions are used to derive the AIM structures of both hydrides and muonic congeners within the context of the multi-component quantum theory of atoms in molecules. The results of the analysis demonstrate that muons are generally capable of forming their own atomic basins and the properties of these basins are not fundamentally different from those AIM containing protons. Particularly, the bonding modes in the muonic species seem to be qualitatively similar to their congener hydrides and no new bonding model is required to describe the bonding of muons to a diverse set of neighboring atoms. All in all, the positively charged muon is similar to a proton from the structural and bonding viewpoint and deserves to be placed in the same box of hydrogen in the Periodic Table. This conclusion is in line with a large body of studies on the chemical kinetics of the muonic molecules portraying the positively charged muon as a lighter isotope of hydrogen.

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

“…On the other hand, the NEO methodology has been also used to study molecular systems containing exotic particles like positrons [13,15,17,42], or the positively charged muons [23][24][25][26]. In the case of the muonic (and positronic) systems the use of the NEO methodology is inevitable from outset since no "safe" adiabatic background has been justified yet and thus any comprehensive "muon-specific computational chemistry" must be based on the NEO.…”

“…, which has also been used in some previous ab initio NEO-HF calculations [23][24][25][26]36], is employed herein. In this function the two parameters, to be determined for each quantum nucleus, are the exponent, n  , and the center of the location of the function in space, , n c R  .…”

“…The Nuclear-electronic orbital (NEO) is particularly a promising non-BO ab initio methodology since various types of the NEO wavefunctions have been proposed with varying degree of complexity [1,[10][11][12][13][14][15][16][17][18][19][20][21][22]. Very recently, the NEO has also been successfully utilized for molecules containing exotic light quantum particles like the positively charged muons [23][24][25][26]. In this methodology certain types of nuclei or exotic light quantum particles are treated as quantum waves while adequate numbers of clamped nuclei are retained to avoid the complications emerging from treating total translational and rotational dynamics [27,28].…”

Toward the Computational Prediction of Muon Sites and Interaction Parameters

“…Promising results have been obtained with the nuclearelectronic orbital (NEO) method 102,118 which, by treating only a small subset of the atoms with non-BO approaches, improves the description of the muon and of other light nuclei with smaller computational costs with respect to other approaches like, for example, PIMD. For the cases where the computational cost of performing PIMD is sustainable, this approach has demonstrated high accuracy.…”

“…More accurate approaches may be provided by the NuclearElectronic Orbitals (NEO), 102 using Hartree-Fock methods 103 on an orthogonal basis for the muon and the electrons. Finally, path integral molecular dynamics (PIMD) [104][105][106][107][108] in principle can yield the most accurate calculations.…”