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.