Binding Matter with Antimatter: The Covalent Positron Bond

We report sufficient theoretical evidence of the energy stability of the e⁺?H₂^2? molecule, formed by two H^? anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e⁺?H₂^2? molecule is 74 kJ mol^?1 (0.77 eV), accounting for the zero‐point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations

The foundations of the two-component quantum theory of atoms in molecules (TC-QTAIM) are addressed in this contribution. In this regard, the theory is presented in an axiomatic manner and the main theorems describing regional properties of atoms in molecules are considered in detail. This is an extension of the orthodox quantum theory of atoms in molecules (QTAIM) for dealing with non-adiabatic wavefunctions of usual molecules as well as extracting the regional quantum structure of exotic species from the corresponding wavefunctions. The best examples of the latter are positronic and muonic species. The computational study of a model system consisting of a clamped lithium nucleus, four electrons, and a positively charged quantum particle carrying a unit of positive charge with a variable mass, m = 200–10¹³ m _e, supplements the theoretical argument demonstrating unambiguously that the TC-QTAIM analysis yields reasonable results. It reveals that the contribution of the positively charged particle in the topological analysis and basin properties is non-negligible. Most importantly, it is demonstrated that by increasing the mass of the positive particle, the TC-QTAIM analysis tends toward the QTAIM analysis of the lithium hydride system considered within the clamped nucleus paradigm. This result seems to indicate that the orthodox QTAIM is just the asymptote of the TC-QTAIM, the latter encompasses the former. Thus, one may claim that the TC-QTAIM is a unified framework for the AIM analysis of vast variety of quantum systems.     

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.     

Ab initio study of the positronation of the CaO and SrO molecules including calculation of annihilation rates

Ab initio multireference single‐ and double‐excitation configuration interaction calculations have been performed to compute potential curves for ground and excited states of the CaO and SrO molecules and their positronic complexes, e⁺CaO, and e⁺SrO. The adiabatic dissociation limit for the ²Σ⁺ lowest states of the latter systems consists of the positive metal ion ground state (M⁺) and the OPs complex (e⁺O^?), although the lowest energy limit is thought to be e⁺M + O. Good agreement is found between the calculated and experimental spectroscopic constants for the neutral diatomics wherever available. The positron affinity of the closed‐shell X ¹Σ⁺ ground states of both systems is found to lie in the 0.16–0.19 eV range, less than half the corresponding values for the lighter members of the alkaline earth monoxide series, BeO and MgO. Annihilation rates (ARs) have been calculated for all four positronated systems for the first time. The variation with bond distance is generally similar to what has been found earlier for the alkali monoxide series of positronic complexes, falling off gradually from the OPs AR value at their respective dissociation limits. The e⁺SrO system shows some exceptional behavior, however, with its AR value reaching a minimum at a relatively large bond distance and then rising to more than twice the OPs value close to its equilibrium distance. © 2012 Wiley Periodicals, Inc.     

Full variational molecular orbital method: Application to the positron-molecule complexes

Optimal Gaussian-type orbital (GTO) basis sets of positron and electron in positron-molecule complexes are proposed by using the full variational treatment of molecular orbital (FVMO) method. The analytical expression for the energy gradient with respect to parameters of positronic and electronic GTO such as the orbital exponents, the orbital centers, and the linear combination of atomic orbital (LCAO) coefficients, is derived. Wave functions obtained by the FVMO method include the effect of electronic or positronic orbital relaxation explicitly and satisfy the virial and Hellmann–Feynman theorems completely. We have demonstrated the optimization of each orbital exponent in various positron-atomic and anion systems, and estimated the positron affinity (PA) as the difference between their energies. Our PA obtained with small basis set is in good agreement with the numerical Hartree–Fock result. We have calculated the OH⁻ and [OH⁻; e⁺] species as the positron-molecular system by the FVMO method. This result shows that the positronic basis set not only becomes more diffuse but also moves toward the oxygen atom. Moreover, we have applied this method to determine both the nuclear and electronic wave functions of LiH and LiD molecules simultaneously, and obtained the isotopic effect directly. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 491–501, 1998     

Solvated positron chemistry. II. The reaction of hydrated positrons with Cl−, Br− and I− ions

The reaction of the hydrated positron, e_aq⁺ with Cl^?, Br^?, and I^? ions in aqueous solutions was studied by means of positron The measured angular correlation curves for [Cl^?, e⁺], [Br^?, e⁺, and [I^?, e⁺] bound states were in good agreement with th Because of this agreement and the fact that the calculated positron wavefunctions penetrate far outside the X^? ions in the [X^?, e⁺] sta propose that a bubble is formed around the [X^?, e⁺] state, similar to the Ps bubble found in nearly all liquids. F^?ions did not react w Preliminary results showed that CN^? ions react with e_aq⁺ while OH^?ions are non reactive. The rate constants were 3.9 × 10¹⁰ M^?1 s^?1, 4.4 × 10¹⁰ M^?1 s^?1, and 6.3 × 10¹⁰ M^?1 s^?1 for Cl^?, Br^?, and I^?, respectively, at low (? 0.03 M) X^? concentrations. A 25% decrease in the rate constant caused by the addition of 1 M ethanol to the I^? solutions was i The influence of halide ions on the positronium (Ps) yields in pure water was studied by use of lifetime measurements. The Cl^?, Br^?, and I^? ions reduced the Ps yields at low concentrations (? 0.03 M), while F^? ions only reduced the Ps-yield However, the Ps yields saturated (e.g. at ≈ 21% ortho-Ps yield in the Cl^? case) at higher concentrations. This saturation and the high-concentration effects-in the angular correlation results were interpreted as caused by rather complicated spur effects, wh It is proposed that spur electrons may pick off the positron from the [X^?, e⁺ states with an efficiency which depends on the structure of the     

Simultaneous optimization of Gaussian type function exponents for electron and positron with full-CI wavefunction – application to ground and excited states of positronic compounds with multi-component molecular orbital approach

In order to obtain the best wavefunction of positronic compound with molecular orbital (MO) treatment, the full-configuration interaction (full-CI) fully variational MO (FVMO) method is proposed for multi-component systems, in which all the variational parameters in electronic and positronic wavefunctions are optimized under the full-CI scheme. We have applied the full-CI multi-component FVMO method to the ground and positronic-excited states of [H⁻;e⁺] system. Our treatment gives good improvement in the basis functions for positronic compounds owing to the extension of flexibility in the variational space, though the convergence of electron–positron correlation term is slower than that of conventional electron correlation.     

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ together with (ii) the anions F⁻, Cl⁻, Br⁻, NO₃⁻ and SO₄²⁻ with water clusters (H₂O)_n, n=1–8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.     

Formation of Superoxo Species by Interaction of O2 with Na Atoms Deposited on MgO Powders: A Combined Continuous‐Wave EPR (CW‐EPR), Hyperfine Sublevel Correlation (HYSCORE) and DFT Study

The formation of O₂^? radical anions by contact of O₂ molecules with a Na pre‐covered MgO surface is studied by a combined EPR and quantum chemical approach. Na atoms deposited on polycrystalline MgO samples are brought into contact with O₂. The typical EPR signal of isolated Na atoms disappears when the reaction with O₂ takes place and new paramagnetic species are observed, which are attributed to different surface‐stabilised O₂^? radicals. Hyperfine sublevel correlation (HYSCORE) spectroscopy allows the superhyperfine interaction tensor of O₂^?Na⁺ species to be determined, demonstrating the direct coordination of the O₂^? adsorbate to surface Na⁺ cations. DFT calculations enable the structural details of the formed species to be determined. Matrix‐isolated alkali superoxides are used as a standard to enable comparison of the formed species, revealing important and unexpected contributions of the MgO matrix in determining the electronic structure of the surface‐stabilised Na⁺? O₂^? complexes.     

Toward the multi-component quantum theory of atoms in molecules: a variational derivation

The general formalism of an extended quantum theory of atoms in molecules (QTAIM) dealing with the multi-component quantum systems, composed of various types of quantum particles, is disclosed in this contribution. This novel methodology, termed as the multi-component QTAIM (MC-QTAIM), is able to deal with non-adiabatic ab initio wavefunctions extracting atoms in molecules quantifying their properties. It can also be applied to elucidate the AIM structure of exotic species and bound quantum systems consisting of fundamental elementary particles like positrons and muons. The formalism is based on the previously disclosed density combination idea that is extended to derive the multi-component subsystem hypervirial theorem as well as the extended subsystem energy functional. Through the extended subsystem variational procedure, inspired from Schrödinger’s original variational principle, the surface terms containing the flux of the current property densities are derived. Accordingly, the extended Gamma field is introduced during this variational procedure that is used as the basic scalar field in the topological analysis yielding atoms in molecules and their real space boundaries. The Gamma field is central to the MC-QTAIM, replacing the usual one-electron density employed in the orthodox QTAIM and corresponding topological analysis. Through the multi-component hypervirial theorem, various regional theorems are derived which are then used to quantify the mechanical properties of atoms in molecules; these include the force, virial, torque, power, continuity and current theorems. In order to demonstrate the capability of the formalism, isotopically asymmetric hydrogen molecules, HD, HT and DT as well as YX systems (Y = ⁶Li, ⁷Li; X = H, D, T) composed of electrons and two different nuclei, all treated equally as quantum waves instead of clamped particles, are analyzed within context of the MC-QTAIM. The resulting computational analysis demonstrates that the MC-QTAIM is able to yield reasonable topological structures similar to those observed previously for diatomic species within context of the orthodox QTAIM. The asymmetrical nature of these species, inherent in their non-Born–Oppenhiemer wavefunctions, manifests itself clearly in the MC-QTAIM analysis yielding two distinguishable atomic basins with different properties. These differences are rationalized generally by the observed electron transfer from one basin to the other. Finally, some possible future theoretical extensions are considered briefly.     

What does shape a topological atom?

In this pedagogical communication after demonstrating the legitimacy for using the quantum theory of atoms in molecules (QTAIM) to non-Coulombic systems, Hookean H₂ ⁺/H₃ ²⁺ species are used for AIM analysis. In these systems, in contrast to their Coulombic counterparts, electron density is atom-like and instead of expected two/three topological atoms, just a single topological atom emerges. This observation is used to demonstrate that what is really “seen” by the topological analysis of electron densities is the clustering of electrons. The very trait of monotonic decay of electron density around the “centers” of clustering guarantees the appearance of topological atoms as basin of attraction of the gradient vector field of the electron density. Although observations with Hookean molecules may seem disappointing at first glance, a careful reasoning points to the fact that the QTAIM methodology is extendable to novel domains, by a knowledge of the morphology of underlying densities, beyond the typical Coulombic systems.     

Penning and associative ionizations in collisions of laser-excited Na atoms with K atoms

Collisional ionization has been observed in the collision of electronically excited sodium atoms with potassium atoms. By means of the crossed-beam and stepwise laser excitation technique and time-of-flight measurements, the folowing reactions have been investigated: Penning ionization, Na^* + K → Na + K⁺ + e^?, and associative ionization, Na^* + K → NaK⁺ + e^?.     

Ground state for two‐electron and electron‐muon three‐body atomic systems

In this article, the angular correlated configuration interaction method previously introduced by some of the authors is extended to three‐body atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct ground state wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) have only linear coefficients; and (iii) show a fast convergency rate for the energy. The efficiency of the construction is illustrated by the study of the negatively charged hydrogen‐like systems (^∞H^?, T^?, D^?, ¹H^?, and Mu^?), neutral helium‐like systems (e^?e^{? ∞}He⁺²,e^?e^{? 4}He⁺², e^?e^{? 3}He⁺², e^?μ^{? ∞}He⁺², e^?μ ^?4He⁺², and e^?μ^{? 3}He⁺²), and positively charged lithium‐like systems (e^?e^{? ∞}Li⁺³, e^?e^{? 7}Li⁺³, e^?e^{? 6}Li⁺³, e^?μ^{? ∞}Li⁺³, e^?μ^{? 7}Li⁺³, and e^?μ^{? 6}Li⁺³). The ground state energies and other mean values are compared with those given in the literature, when available. Wave functions with a moderate number of (20 maximum) linear coefficients are given explicitly; they are sufficiently simple and accurate to be used in practical calculations of atomic collision in which multidimensional integrations are involved. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

A Study of picosecond dehalogenation of chlorobenzene anions in liquids by positronium inhibition measurements

Radiation chemistry and results of Ps yields indicate that the following processes occur in the positron spur in solution of halogen-substituted hydrocarbons, RX_n: e⁺ + e^? → Ps, e^? + RX _n → (RX_n)^? → RX_n?1 + X^?, e⁺ + (RX_n)^? → Ps + RX_n, e⁺ + X^? → [X^?, e⁺]. Hence the trapped electron can form Ps only if (RX _n)^? is stable or has a lifetime that is longer than o comparable to the Ps formation time. Previous studies have shown that some of the strongly chlorinated benzenes (n = 4.5 give reasonable inhibition in benzene but not in linear hydrocarbons. The reason is very probably that the dechlorination time is much shorter in benzene than in saturated hydrocarbons because Cl^? is more strongly solvated in benzene than in non-aromatic hydrocarbons. To test those ideas further we have begun detailed studies of solutions of the possible “intermediate” inhibitors, viz. 1,2,3,5- and 1,2,4,5-C₆H₂Cl₄, in mixtures of C₆H₆/C₆H₁₄ different methyl-substituted benzene aniline, anisole, dioxane and ethylbenzene. The results are discussed and interpreted in terms of the spur model. The Ps inhibition efficiency of the two isomeric forms of tetrachlorobenzene studied, appears most probably to depend on intramolecular electron transfer with subsequent dehalogenation of the molecular anion on a picosecond timescale. The divergence in inhibitor efficiency obtained for the chlorobenzenes when dissolved in aromatic solvents compared to the same solutes when dissolved in a saturated alkane appears most probably to be caused by complex formation between the initially formed chlorobenzene anion and benzene molecules, which permits a rapid relaxation of the molecular anion with subsequent bond stretching and expulsion of the chloride anion.     

Theoretical condiserations regarding the existence of PsO and PsS+

At has been proposed from experimental studies and in analogy with hydrogen compounds that PsO may be an entity of some importance, or an intermediate, in the reaction of positronium, Ps, with aqueous oxyacid species such as H₂PO^?₄, HSO^?₄, ClO^?₄, and NO^?₃. This communication explores the stability of PsO and PsS, or [0^?: e⁺] and [S^?:e⁺], respectively, relative to dissociation into Ps and O(³P) or S(³P) on the basis of restricted Hartree-Fock calculations for the PsO and PsS systems and certain correlation correction arguments. We obtain a reasonable lower estimate of the dissociation energy to Y + Ps of ? ?0.47 eV for PsO and ? ?0.70 eV for PsS. It is suggested that a modest correlation correction to the positron affinity (PA) of O^? would very probably lead to a bound state system for PsO.     

The first two excited 1Σg+ states of Cs2

Laser-induced fluorescence Of Cs₂ molecules in the infrared region (4000–9000 cm^?1) has been observed using several exciting wavelengths from an argon-ion laser and from a ring dye laser. Accurate molecular constants for the first two excited ¹Σ_g⁺ electronic states are derived from spectra recorded at high resolution by Fourier transform spectroscopy. Main molecular constants are: (2)¹Σ_g⁺: T_c = 12114.090 cm^?1, ω_e = 23.350 cm^?1, B_c = 7.4.5 × 10^?3 cm^?1, R_c = 5.8316 Å; (3)¹Σ_g⁺: T_e = 15975.450 cm^?1, ω_e = 22.423 cm^?1 , B_e = 8.23 × 10^?3 cm^?1, R_c = 5.5569 Å.     

The scavenging of the precursors of the solvated electron from the positron lifetime spectroscopy and the doppler broadening of annihilation line shape technique

The electron scavenging properties of aqueous solutions of two series of solutes are investigated, using the positron as a probe. For a better interpretation of the data, both lifetime spectroscopy and the Doppler broadening of annihilation line shape technique are used. All solutes inhibit the positronium (Ps) formation, by the scavenging of electrons. The first series consists of the halate ions, that should follow the Hunt linear relation between the rate constant for reaction with the solvated electrons, k_(e^?aq+S), and that for its precursor(s), 1/C₃₇. The Ps inhibition constants, k, are 0.14, 1.44 and 3.45 M^?1 for ClO^?₃, BrO^?₃ and IO^?₃, respectively. This sequence is quantitatively consistent with that of the respective k_(e^?eq+S). The second series includes the SeO⁼₄, Te(OH)₆ and BrO^?₄ species, and the Ps inhibition constants are 5.62, 10.5 and 14.3 M^?1 respectively. These values are much higher than expected from the k_(e^?aq+S) constants, on basis of the Hunt relation, in agreement with previous results from pulse radiolysis experimets.