Where to place the positive muon in the Periodic Table?

On the nature of the two-positron bond: evidence for a novel bond type

The nature of the newly proposed two-positron bond in (PsH)2, which is composed of two protons, four electrons and two positrons, is considered in this contribution. The study is done at the multi-component-Hartree-Fock (MC-HF) and the Diffusion Monte Carlo (DMC) levels of theory by comparing ab initio data, analyzing the spatial structure of the DMC wavefunction, and applying the multi-component quantum theory of atoms in molecules and the two-component interacting quantum atoms energy partitioning schemes to the MC-HF wavefunction. The analysis demonstrates that (PsH)2 to a good approximation may be conceived of as two slightly perturbed PsH atoms, bonded through a two-positron bond. In contrast to the usual two-electron bonds, the positron exchange phenomenon is quite marginal in the considered two-positron bond. The dominant stabilizing mechanism of bonding is a novel type of classical electrostatic interaction between the positrons, which are mainly localized between nuclei, and the surrounding electrons. To emphasize its uniqueness, this mechanism of bonding is proposed to be called gluonic which has also been previously identified as the main driving mechanism behind formation of the one-positron bond in [H-,e+,H-]. We conclude that the studied two-positron bond should not be classified as a covalent bond and it must be seen as a brand-new type of bond, foreign to the electronic bonding modes discovered so far in the purely electronic systems.

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

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

Free Radical Chemistry of Phosphasilenes

Understanding the characteristics of radicals formed from silicon-containing heavy analogues of alkenes is of great importance for their application in radical polymerization. Steric and electronic substituent effects in compounds such as phosphasilenes not only stabilize the Si=P double bond, but also influence the structure and species of the formed radicals. Herein we report our first investigations of radicals derived from phosphasilenes with Mes, Tip, Dur, and NMe2 substituents on the P atom, using muon spin spectroscopy and DFT calculations. Adding muonium (a light isotope of hydrogen) to phosphasilenes reveals that: a) the electron-donor NMe2 and the bulkiest Tip-substituted phosphasilenes form several muoniated radicals with different rotamer conformations; b) bulky Dur-substituted phosphasilene forms two radicals (Si- and P-centred); and c) Mes-substituted phosphasilene mainly forms one species of radical, at the P centre. These significant differences result from intramolecular substituent effects.

The any particle molecular orbital/molecular mechanics approach

A computational scheme is proposed to broaden the range of applications of multicomponent methodologies for the study of local properties of big molecular systems existing in the gas phase and in solvated environments. This scheme extends the any particle molecular orbital (APMO) approach in the quantum mechanics/molecular mechanics (QM/MM) framework. As a first assessment of the performance of the proposed approach, we estimate the proton affinities (PAs) of seventy amines in the gas phase and the proton binding energies (PBEs) in the gas phase and in an explicitly solvated environment of the sixty-one protons present in the chignolin protein. These calculations are performed with the QM/MM versions of the APMO second-order proton propagator (APMO-PP2) and the APMO extended Koopmans' theorem (APMO-KT) approaches. Calculated PAs and PBEs show significant reductions in the computational effort with a reduced loss in accuracy. These results suggest that the APMO/MM scheme might be used as a low-cost multi-component alternative for studies of local properties in big molecular systems. Graphical Abstract QMMM regions and CPU times for the APMO/MM approach.

On the Nature of the Positronic Bond

Recently it has been proposed that the positron, the anti-particle analog of the electron, is capable of forming an anti-matter bond in a composite system consists of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859-8864 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates that the electron exchange phenomenon is virtually non-existent between the two atoms and no electronic covalent bond is conceivable in between. On the other hand, it is demonstrated that the positron density enclosed in each atom is capable of stabilizing interactions with the electron density of the neighboring atom. This electrostatic interaction suffices to make the whole system bonded against all dissociation channels. Thus, the positron indeed acts like an anti-matter glue between the two atoms.

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

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.

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

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.

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

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.

Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study

The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

Extending the Domain-Averaged Exchange-Correlation Energies Within the Context of the MC-QTAIM: Tracing Subtle Variations Induced by Isotope Substitution

Recently, it has been demonstrated that the domain-averaged exchange-correlation energies, V^xc , are capable of tracing the covalent character of atom-atom interactions unequivocally and thus pave the way for detailed bonding analysis within the context of the quantum theory of atoms in molecules (QTAIM) [M. García-Revilla, E. Francisco, P. L. Popelier, A. Martín Pendás, ChemPhysChem 2013, 14, 1211-1218]. Herein, the concept of V^xc is extended within the context of the newly developed multicomponent QTAIM (MC-QTAIM). The extended version, Veexc , is capable of analyzing nonadiabatic wavefunctions and thus is sensitive to the mass of nuclei and can trace "locally" the subtle electronic variations induced by isotope substitution. To demonstrate this capability in practice, ab initio nonadiabatic wavefunctions for three isotopically substituted hydrogen cyanide molecules, in which the hydrogen nucleus was assumed to be a proton, deuterium, or tritium, were derived. The resulting wavefunctions were then used to compute Veexc and it emerged that for the hydrogen-carbon bond, the Veexc was distinct for each isotopic composition and varied in line with chemical expectations. Indeed, the introduction of Veexc paves the way for the investigation of vast numbers of structural and kinetic isotope effects within the context of the MC-QTAIM.

Influence of vibration in the reactive scattering of D + MuH: the effect of dynamical bonding

The dynamics of the D + MuH(v = 1) reaction has been investigated using time-independent quantum mechanical calculations. The total reaction cross sections and rate coefficients have been calculated for the two exit channels of the reaction leading, respectively, to DMu + H and DH + Mu. Over the 100-1000 K temperature range investigated the rate coefficients for the DMu + H channel are of the order of 10(-10) cm(3) s(-1) and those for the DH + Mu channel vary between 1 × 10(-12) and 8 × 10(-11) cm(3) s(-1). These results point to a virtually barrierless reaction for the DMu + H channel and to the presence of a comparatively small barrier for the DH + Mu channel and are consistent with the profiles of their respective collinear vibrationally adiabatic potentials (VAPs). The effective barrier in the VAP of the DH + Mu channel is located in the reactant valley and, consequently, translation is found to be more efficient than vibration for the promotion of the reaction over a large energy interval in the post threshold region. Below this barrier, the DH + Mu channel can be accessible through an indirect mechanism implying crossing from the DMu + H pathway. The most salient feature found in the present study is revealed in the total reaction cross section for the DMu + H channel, which shows a sharp resonance caused by the presence of a deep well in the vibrationally adiabatic potential. This well has a dynamical origin, reminiscent of that found recently in the vibrationally bonded BrMuBr complex [Fleming, et al., Angew. Chem., Int. Ed., 2014, 53, 1], and is due to the stabilizing effect of the light Mu atom oscillating between the heavier H and D isotopes and to the bond softening associated with vibrational excitation of MuH.

Muon-Substituted Malonaldehyde: Transforming a Transition State into a Stable Structure by Isotope Substitution

Isotope substitutions are usually conceived to play a marginal role on the structure and bonding pattern of molecules. However, a recent study [Angew. Chem. Int. Ed. 2014, 53, 13706-13709; Angew. Chem. 2014, 126, 13925-13929] further demonstrates that upon replacing a proton with a positively charged muon, as the lightest radioisotope of hydrogen, radical changes in the nature of the structure and bonding of certain species may take place. The present report is a primary attempt to introduce another example of structural transformation on the basis of the malonaldehyde system. Accordingly, upon replacing the proton between the two oxygen atoms of malonaldehyde with the positively charged muon a serious structural transformation is observed. By using the ab initio nuclear-electronic orbital non-Born-Oppenheimer procedure, the nuclear configuration of the muon-substituted species is derived. The resulting nuclear configuration is much more similar to the transition state of the proton transfer in malonaldehyde rather than to the stable configuration of malonaldehyde. The comparison of the "atoms in molecules" (AIM) structure of the muon-substituted malonaldehyde and the AIM structure of the stable and the transition-state configurations of malonaldehyde also unequivocally demonstrates substantial similarities of the muon-substituted malonaldehyde to the transition state.