Classifying interactions is key in the physical sciences, and bonding mechanisms in matter-antimatter systems remain particularly enigmatic. Here we focus on a paradigmatic example of positronium hydride (PsH) dimer composed of two protons, two positrons, and four electrons, whose bonding nature has been previously described as either ionic, covalent, or van der Waals-like. Accurate quantum Monte Carlo calculations show that the two positrons occupy a delocalized molecular orbital that envelopes the two hydrogen anions and responds as a collective dipole to an applied electric field. This positronic bonding stems from quantum correlations that resemble a single covalent bond formed between negatively charged pseudo-nuclei, but with a bond strength commensurate with the traditional van der Waals interaction. Our findings suggest that the ability to form delocalized proto-bonds is a more general property of quantum systems, and could be present in a broader class of particles, antiparticles, and quasi-particles interacting with matter.

We present the first open access version of the QMeCha (Quantum MeCha /'mεkə/) code, a quantum Monte Carlo package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. QMeCha is now available under a CC BY-NC-ND license through the repository github.com/QMeCha. The present code has been developed to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g., electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes geminal functions, such as the Pfaffian, and presents different types of explicit correlation terms in Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational Ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystems. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.

Predicting the binding affinity of ligands to protein pockets is key in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a range of attractive and repulsive electronic interactions during binding. Accurately accounting for all interactions requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. Additionally, disagreement between "gold standard" Coupled Cluster (CC) and Quantum Monte Carlo (QMC) methods casts doubt on many benchmarks for larger non-covalent systems. We introduce the "QUantum Interacting Dimer" (QUID) benchmark framework containing 170 non-covalent (non-)equilibrium systems modeling chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic contributions. Robust binding energies are obtained using complementary CC and QMC methods, achieving agreement of 0.5 kcal/mol. The benchmark data analysis reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though their atomic van der Waals forces differ in magnitude and orientation. Contrarily, semiempirical methods and empirical force fields require improvements in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of NCIs, highly accurate interaction energies, and analysis of molecular properties take QUID beyond the "gold standard" for QM benchmarks of ligand-protein systems.

In a recent study [Angew. Chem., Int. Ed.62, e202312078 (2023)], it was suggested that the maxima of the dipole polarizability along the bond dissociation coordinate can be used to define chemical bond cleavage. In this work, we systematically analyze this hypothesis by performing a spatial partitioning of the local derivatives of the electronic densities and dipole moments with respect to the external field along the bond axis, considering a set of chemically bonded and non-covalently bonded systems. Through this decomposition, we associate the behaviours of the polarizability and bond stretching with the intra- and/or extra-bond remodulations of the charge and of the fragments' local dipole. In particular, the remodulations are used to characterize the three interaction regions: (I) the bonded region, where the system responds to the field as a single molecular entity; (II) the bond-breaking region, characterized by the additional formation of a dipole moment, in between the atoms participating in the bond, that opposes the total molecular dipole; and (III) the dissociated state, corresponding to the sum of independent dipoles. Furthermore, our decomposition allows us to identify one critical point that might be used to roughly mark the transition between regions (II) and (III) and provides a more exhaustive understanding of the second region within a first principles framework, unravelling the nature of a bond by its electronic response properties, rather than by analyzing the hybridization of the electronic structure. Finally, we complemented this discussion by comparing the polarizability curve against standard methodologies to characterise chemical bonds, finding an alignment between the inflection points of bond order curves with the maxima of the molecular polarizability for covalent bonded systems, thus confirming the start of the bond-breaking.

Positronium (Ps) atoms are highly sensitive probes of condensed-phase structure and dynamics, yet their theoretical description in complex molecular environments remains challenging. We present an extension of our QM/MM protocol to investigate Ps in methanol and ethanol, building on our earlier study in water. Classical Monte Carlo simulations employing newly parametrized Ps-solvent force fields reveal well-defined cavity structures, whose sizes are consistent with hydrated Ps and systematically smaller than those predicted by empirical bubble models. Multicomponent quantum calculations employing the Any Particle Molecular Orbital (APMO) method have identified physically meaningful cavity states, characterized by substantial electron-positron overlap, and have ruled out spurious surface states as artifacts of the QM region truncation. While vertical detachment energies are insensitive primarily to solvent structure, computed pick-off annihilation lifetimes showed a marked dependence on cavity size. Employing orbital-dependent enhancement factors, our results achieve good agreement with experimental PALS data for both solvents. This study demonstrates the transferability and predictive power of our QM/MM protocol for Ps, providing a framework that can be systematically extended to more complex solvents and biological environments, thereby advancing the theoretical interpretation of Ps annihilation in complex systems.

Positrons, the antiparticles of electrons, serve as unique probes for fundamental interactions and are crucial in diverse applications. We present a new mechanism in chemical bonding: the formation of a positron-driven bond that fundamentally alters electronic bonding interactions. Investigating the Be2 dimer with Quantum Monte Carlo (QMC) simulations, we construct the potential energy curve of e+:Be2. Our analysis reveals a significant energetic stabilization of the Be-Be bond upon positron attachment, a result that challenges conventional understanding. We show this stabilization arises from a novel, two-stage mechanism: at longer distances, a positron bond forms via internuclear positron accumulation, similar to that in positron-anion systems. However, as the atoms approach equilibrium, the positron density undergoes a unique redistribution, moving out of the internuclear region to accumulate in the outer molecular vicinity. This distinct positron localization, combined with an otherwise repulsive electronic component, leads to overall system stabilization as the electron density dynamically follows the positron. This work expands our understanding of chemical bonding by strongly suggesting how an antiparticle can profoundly influence molecular stability.

This study explores the energetic stability and physical properties of Ps 2 XY ${{\rm{Ps}}_2 {\rm{XY}}}$ complexes formed by two halide anions (X-, Y-=F-, X-, Br-), and two positrons (Ps: positron-electron pair). We combine electronic coupled cluster (CCSD(T)) calculations with positronic multicomponent renormalized partial third-order propagator (MC-REN-PP3) calculations to effectively recover correlation energies. Analysis of potential energy curves confirms the energetic stability of these positronic molecules, with optimized structures identified as global minima. Further investigation of electron and positron densities reveals stabilization owing to the formation of two-positron bonds. The global stability of the Ps 2 XY ${{\rm{Ps}}_2 {\rm{XY}}}$ complexes contrasts with the metastable two-positron-bonded (PsH)2, which energetically favors the emission of Ps2. Comparative analysis of one- and two-positron dihalides indicates that the addition of a positron to PsXY- generally results in shorter bond distances, higher force constants, and lower dissociation energies, with exceptions due to differences in positron affinities of PsXY- and Y-. We explore the analogy between two-positron-bonded dihalide systems Ps 2 XY ${{\rm{Ps}}_2 {\rm{XY}}}$ and two-electron-bonded dialkali molecules AB, (A, B=Na, K, Rb). The bonding properties in two-positron dihalides and their electronic dialkali analogs are comparable, displaying identical periodic trends. However, compared to their isoelectronic AB counterparts, the positron bonds in Ps 2 XY ${{\rm{Ps}}_2 {\rm{XY}}}$ have shorter bond lengths, higher force constants, and higher bond energies.

Positronium (Ps) exhibits the ability to form energetically stable complexes with atoms and molecules before annihilation occurs. In particular, F, a halogen, shows the highest reported positronium binding energy (2.95 eV) in the periodic table. Superhalogens are defined as molecules with electron affinities exceeding that of Cl (3.61 eV), the atom with the highest electron affinity. Building upon the concept of superhalogens, we can define Ps-superhalogens as molecules with Ps binding energies surpassing that of F. This study explores structural and energetic aspects of positronium and positron binding to neutral and anionic superhalogen molecules of the MXk+1 family (M = Li, Na, Be, Mg, B, Al, Si, P; X = F, Cl, Br), respectively and where k represents the highest formal valence of M. We perform multicomponent MP2 calculations for positron systems, which reveal how positron affinities vary with the type and number of halogen atoms present. The analysis of the results emphasizes the predominant role of electrostatic interactions in determining the positron affinity, with negligible effects of electronic and geometric relaxation upon positron attachment. We predict the energetic stability of 22 of the 24 PsMXk+1 complexes with respect to the chemically relevant dissociation channels: e+ emission, Ps emission and M-X bond breaking. Our findings reveal six MFk+1 systems that qualify as Ps-superhalogens, showing a positronium binding energy exceeding 2.95 eV. Of these, AlF4 stands out by setting a new record for the highest positronium binding energy among neutral molecules, reaching 4.36 eV. Positronium (Ps) exhibits the ability to form energetically stable complexes with atoms and molecules before annihilation occurs.

Reliable numerical values of van der Waals (vdW) radii are required for constructing empirical force fields, vdW-inclusive density functional and quantum-chemical methods, as well as for implicit solvent models. However, multiple definitions exist for vdW radii, involving either equilibrium or closest contact distances between free or bonded atoms within molecules or crystals. For the paradigmatic case of hydrogen atom, its reported vdW radius fluctuates between 2.15 and 3.70 Bohr depending on the definition, leading to a high uncertainty in calculations and different conceptual interpretations of non-covalent interactions. In this work, we systematically review different definitions and methodologies to establish the free and bonded vdW radii for hydrogen, based on equilibrium vdW distances in non-covalently bonded molecules, enveloping electron density cutoffs, non-covalent positron bonds in hydrogen anion dimer, vacuum virtual photon cloud caused by the hydrogen atom, and atomic dipole polarizability. By doing so, we show that the vdW radius of free hydrogen atom is 3.16$\pm0.06$ Bohr. By employing the most general and elegant definition of atomic vdW radius as a function of the atomic polarizability, we tabulate consistent values of vdW radii for all atoms in the periodic table up to $Z=118$.

We performed a computational study of positron attachment to hydrated amino acids, namely glycine, alanine, and proline in the zwitterionic form. We combined the sequential quantum mechanics/molecular mechanics (s-QM/MM) method with various levels of any particle molecular orbital (APMO) calculations. Consistent with previous studies, our calculations indicate the formation of energetically stable states for the isolated and microsolvated amino acids, in which the positron localizes around the carboxylate group. However, for the larger clusters, composed of 7 to 40 water molecules, hydrogen bonding between the solute and solvent molecules disfavors positron attachment to the amino acids, giving rise to surface states in which the positron is located around the water-vacuum interface. The analysis of positron binding energies, positronic orbitals, radial probability distributions, and annihilation rates consistently pointed out the change from positron-solute to positron-solvent states. Even with the inclusion of an electrostatic embedding around the aggregates, the positrons did not localize around the solute. Positron attachment to molecules in the gas phase is a well-established fact. The existence of hydrated positronic molecules could also be expected from the analogy with transient anion states, which are believed to participate in radiation damage. Our results indicate that positron attachment to hydrated biomolecules, even to zwitterions with negatively charged carboxylated groups, would not take place. For the larger clusters, in which positron-water interactions are favored, the calculations indicate an unexpectedly large contribution of the core orbitals to the annihilation rates, between 15 and 20%. Finally, we explored correlations between positron binding energies (PBEs) and dipole moments, as well as annihilation rates and PBEs, consistent with previous studies for smaller clusters.

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.

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 positrons 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 D 3h 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 H3 + and Li3 + 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., 2021, 155, 054306], thus extending the concept of positron bonded molecules.

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, α, rely on different scaling laws α∝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 α=C(4μq^{2}/ℏ^{2})L^{4}, where μ 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 L^{2} norm of the position operator. This unified formula is also applicable to many-particle systems, as shown by accurately predicting the dipole polarizability of 36 atoms, 1641 small organic molecules, and Bloch electrons in periodic systems.

We report a computational study on homo- and heteronuclear e+[X-Y-] compounds formed by two halide anions (X-, Y- = F-, Cl-, Br-) and one positron. Our results indicate the formation of energetically stable positronic molecules in all cases. Analysis of the electron and positron densities points out that the formation of positron covalent bonds underlies the stabilization of the otherwise repelling dihalides, revealing that positronic bonding can reach far beyond the previously addressed e+[H-H-] molecule [J. Charry, M. T. do N. Varella and A. Reyes, Angew. Chem. Int. Ed., 2018, 57, 8859-8864.]. To a significant extent, the properties of the positron dihalides are similar to those of the purely electronic analogs, e-[A+B+], molecular cations with isoelectronic atomic cores (A+, B+ = Na+, K+, Rb+) bound by one electron. The positron bonds in the e+[X-Y-] complexes are however stronger than those in the isoelectronic e-[A+B+] counterparts, as the former have shorter bond lengths and higher bond energies. While an energy decomposition analysis points out that both electronic and positronic bonds essentially arise from electrostatic interactions, the more stable positron bonds are partly due to the higher polarizabilities of the dihalide anions, and partly to more significant contributions from correlation and relaxation effects.

The any particle molecular orbital (APMO) approach extends regular electronic structure methods to study atomic and molecular systems in which electrons and other particles are treated simultaneously as quantum waves. A number of electronic structure methodologies have been extended under the APMO framework and applied to investigate nuclear quantum effects including isotope effects and nuclear delocalization and to calculate proton binding energies and affinities. In addition, APMO methodologies have been employed to analyze physical and chemical properties of atomic and molecular systems containing exotic subatomic particles.

We report sufficient theoretical evidence of the energy stability of the e+ ⋅H22- 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+ ⋅H22- 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.

In this work we propose schemes based on the extended Koopmans' theorem for quantum nuclei (eKT), in the framework of the any particle molecular orbital approach (APMO/KT), for the quantitative prediction of gas phase proton affinities (PAs). The performance of these schemes has been tested on a set of 300 organic molecules containing diverse functional groups. The APMO/KT scheme scaled by functional group (APMO/KT-SC-FG) displays an overall mean absolute error of 1.1 kcal mol-1 with respect to experimental data. Its performance in PA calculations is similar to that of post-Hartree-Fock composite methods or that of the APMO second order proton propagator (APMO/PP2) approach. The APMO/KT-SC-FG scheme is also employed to predict PAs of polyfunctional molecules such as the Nerve Agent VX and the 20 common α-amino acids, finding excellent agreement with available theoretical and/or experimental data. The accuracy of the predictions demonstrates that the APMO/KT-SC-FG scheme is a low-cost alternative to adiabatic methods for the calculation of accurate PAs. One of the most appealing features of the APMO/KT-SC-FG scheme, is that PAs can be derived from one single-point APMO Hartree-Fock calculation.

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

We discuss the connection between the Feshbach Projection Operator approach to resonant positron annihilation on molecules and the Any-Particle Molecular Orbital Method to positronic molecules. This combination of formal and computational tools is a promising approach to the ab initio description of vibrationally-enhanced annihilation in molecular gases.