Chemistry and physics of positrons interacting with atoms, molecules, and fields

The positron is the antiparticle of the electron, possesing the same mass and obeying the same spin statistics but with an opposite charge. When a positron and an electron collide, both annihilate within a few nanoseconds, emitting two or three photons. However, positrons can also form energetically metastable states with atoms and molecules before the pair annihilation. The relatively long positronic lifetime, on a nanosecond time scale, allows a positron to interfere with the faster molecular vibrational motions or with molecular reactions, which are typically in the range between femto- and picoseconds. Therefore, such positronic systems expand the field of physical chemistry, which is still vastly unexplored theoretically and experimentally, and it could lead to new and exciting applications. In recent decades, significant efforts have been made in the development of theoretical methods to accurately describe the interactions of positrons with matter, which often requires explicit many-body correlation effects, posing a substantial challenge for quantum-chemical methods based on single-particle atomic orbitals. Despite many creative and accurate approaches, most of them are extremely computationally expensive. Therefore, their application is limited to small and highly polar molecular systems, where the binding is mainly driven by the strong attractive electrostatic interaction. This thesis aims to attain a robust understanding of positrons interacting with molecular systems, starting from first principles of quantum mechanics. To this end, new variational electron-positron wave function ansatzes are proposed and discussed, which are based on a combination of electron-positron geminal orbitals and a Jastrow factor that explicitly includes three- and four-body electron-positron correlations in the field of the nuclei, that is fully optimized within the framework of the Variational Monte Carlo (VMC) method. The performance of this approach is validated in combination with the Diffusion Monte Carlo (DMC) method by calculating total energies and binding energies of a set of positronic atomic and molecular systems, demonstrating that a representation in terms of electron-positron orbitals for the fermionic and Jastrow wave functions is an accurate and efficient approach for studying the interactions of positrons with matter. Moreover, the developed methodology is applied here to study electronic and positronic response properties such as dipole polarizabilities, annihilation lifetimes, and expectation values of interparticle distances as a function of an external electric field, aiming to gain further physical insights into the electron-positron wave function structure. Through the Quantum Monte Carlo (QMC) method, non-trivial variations of the polarizabilities with respect to the interatomic length were unveiled. A further decomposition of the polarizability into electronic and positronic contributions revealed that the positronic cloud in the outer regions is highly polarizable and screens the response of the electrons to the same external electric field. Furthermore, the QMC methodology was employed to investigate the stability of a system consisting of two positrons and three hydride anions, discovering the formation of a three-center two-positron bond, analogous to the well-known three-center two-electron counterpart in Li$_3^+$, thus extending the concept of positron-bonded molecules, in which two or more repelling anions are stabilized by one or more positrons. The final section is dedicated to the exploration of using positron-bonded diatomic systems as an alternative approach for estimating interacting atomic sizes, in which it was found that their equilibrium distance is connected to the sum of van der Waals radii of the corresponding neutral atoms, and to a lesser extent to the sum of anionic radii. Overall, this thesis presents the development of a computational methodology based on QMC techniques to compute and analyze the wave function of positrons interacting with atoms, molecules, and external electric fields. The methods and analysis developed in the presented work will pave the way for further study of complex positronic systems of physical and chemical interest, encouraging new theoretical and experimental investigations in the field of positron-matter interactions.Positrons Interacting with Molecules and positronic chemistr

Correlated Wave Functions for Electron–Positron Interactions in Atoms and Molecules

The positron, as the antiparticle of the electron, can form metastable states with atoms and molecules before its annihilation with an electron. Such metastable matter–positron complexes are stabilized by a variety of mechanisms, which can have both covalent and noncovalent character. Specifically, electron–positron binding often involves strong many-body correlation effects, posing a substantial challenge for quantum-chemical methods based on atomic orbitals. Here we propose an accurate, efficient, and transferable variational ansatz based on a combination of electron–positron geminal orbitals and a Jastrow factor that explicitly includes the electron–positron correlations in the field of the nuclei, which are optimized at the level of variational Monte Carlo (VMC). We apply this approach in combination with diffusion Monte Carlo (DMC) to calculate binding energies for a positron e+ and a positronium Ps (the pseudoatomic electron–positron pair), bound to a set of atomic systems (H–, Li+, Li, Li–, Be+, Be, B–, C–, O– and F–). For PsB, PsC, PsO, and PsF, our VMC and DMC total energies are lower than that from previous calculations; hence, we redefine the state of the art for these systems. To assess our approach for molecules, we study the potential-energy surfaces (PES) of two hydrogen anions H– mediated by a positron (e+H22–), for which we calculate accurate spectroscopic properties by using a dense interpolation of the PES. We demonstrate the reliability and transferability of our correlated wave functions for electron–positron interactions with respect to state-of-the-art calculations reported in the literature

Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems

Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $\alpha$, rely on different scaling laws $\alpha \propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of single-particle quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $\alpha = C (4 \mu q^2/\hbar^2)L^4$, where $\mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless excitation-energy ratio, and the characteristic length $L$ is defined via the $\mathcal{L}^2$-norm of the position operator. %The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules. This unified formula is also applicable to many-particle systems, as shown by} accurately predicting the dipole polarizability of 36 atoms, 1641 small organic \rrr{molecules, and Bloch electrons in periodic systems.Comment: 3 figures are include

The three-center two-positron bond

Computational studies have shown that one or more positrons can stabilize two repelling atomic anions through the formation of two-center positronic bonds. In the present work, we study the energetic stability of a system containing two positrons and three hydride anions, namely 2e+[H3-3]. To this aim, we performed a preliminary scan of the potential energy surface of the system with both electrons and positron in a spin singlet state, with a multi-component MP2 method, that was further refined with variational and diffusion Monte Carlo calculations, and confirmed an equilibrium geometry with D3h symmetry. The local stability of 2e+[H3-3] is demonstrated by analyzing the vertical detachment and adiabatic energy dissociation channels. Bonding properties of the positronic compound, such as the equilibrium interatomic distances, force constants, dissociation energies, and bonding densities are compared with those of the purely electronic H+3 and Li+3 systems. Through this analysis, we find compelling similarities between the 2e+[H3-3] compound and the trilithium cation. Our results strongly point out the formation of a non-electronic three-center two-positron bond, analogous to the well-known three-center two-electron counterparts, which is fundamentally distinct from the two-center two-positron bond [D. Bressanini, J. Chem. Phys.155, 054306 (2021)], thus extending the concept of positron bonded molecules

Multicomponent Quantum Mechanics/Molecular Mechanics Study of Hydrated Positronium

We propose a model for solvated positronium (Ps) atoms in water, based on the sequential quantum mechanics/molecular mechanics (s-QM/MM) protocol. We developed a Lennard-Jones force field to account for Ps–water interactions in the MM step. The repulsive term was obtained from a previously reported model for the solvated electron, while the dispersion constant was derived from the Slater–Kirkwood formula. The force field was employed in classical Monte Carlo (MC) simulations to generate Ps–solvent configurations in the NpT ensemble, while the quantum properties were computed with the any-particle molecular orbital method in the subsequent QM step. Our approach is general, as it can be applied to other liquids and materials. One basically needs to describe the solvated electron in the environment of interest to obtain the Ps solvation model. The thermodynamical properties computed from the MC simulations point out similarities between the solvation of Ps and noble gas atoms, hydrophobic solutes that form clathrate structures. We performed convergence tests for the QM step, with particular attention to the choice of basis set and expansion centers for the positronic and electronic subsystems. Our largest model was composed of the Ps atom and 22 water molecules in the QM region, corresponding to the first solvation shell, surrounded by 128 molecules described as point charges. The mean electronic and positronic vertical detachment energies were (4.73 ± 0.04) eV and (5.33 ± 0.04) eV, respectively. The latter estimates were computed with Koopmans’ theorem corrected by second-order self-energies, for a set of statistically uncorrelated MC configurations. While the Hartree–Fock wave functions do not properly account for the annihilation rates, they were useful for numerical tests, pointing out that annihilation is more sensitive to the choice of basis sets and expansion centers than the detachment energies. We further explored a model with reduced solute cavity size by changing the Ps–solvent force field. Although the pick-off annihilation lifetimes were affected by the cavity size, essentially the same conclusions were drawn from both models