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arXiv:2605.15099

Two Protons, Two Positrons, and Four Electrons: Covalent Bond with van der Waals Characteristics

Jorge Charry, Alexandre Tkatchenko

physics.chem-phquant-phSubmitted May 14, 2026• Announced May 15, 2026• Revised Jun 30, 2026 (v2)
v1 · May 14, 2026v2 · Jun 30, 2026
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Abstract

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.

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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 report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
Calculations are reported for positronium (Ps) scattering by atomic hydrogen (H) in the energy range 0--6.5 eV in a coupled-pseudostate approximation in which excitation and ionization channels of both the Ps and the H are taken into account. The approximation contains an accurate representation of the van der Waals coefficient. Results are presented for phase shifts, scattering lengths, effective ranges, and various cross sections including partial wave, total, and ortho-para conversion cross sections. An analysis of the possible spin transitions is provided and the energy of the positronium hydride (PsH) bound state is determined. Substantial differences are found from earlier work within the frozen target approximation, now clearly confirming the importance of target excitation channels. Good agreement is obtained with recent calculations of S-wave phase shifts and scattering lengths using the stabilization method. Convergence to the exact binding energy for PsH appears to be slow. Resonances corresponding to unstable states of the positron orbiting ${\mathrm{H}}^{\ensuremath{-}}$ are seen in the electronic spin singlet partial waves. The importance of the ${\mathrm{H}}^{\ensuremath{-}}$ formation channel is discussed.
Abstract We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding.
The present manuscript revisits one of the earliest approaches to treating molecular systems within the Schrödinger formalism of quantum mechanics: the Heitler-London (HL) model. Originally proposed in 1927 and based on a linear combination of atomic orbitals, the HL model provided a foundational description of covalent bonds and has served as the basis for numerous variational methods. Focusing on the hydrogen molecule, we begin by revisiting the analytical calculations of the original HL model, from which the qualitative physics of bonding and antibonding states can be obtained. Subsequently, we propose including electronic screening effects directly in the original HL wave function. We then compare our proposal with variational quantum Monte Carlo (VQMC) calculations, whose trial wave function allows us to optimize the electronic screening potential as a function of the inter-proton distance. We obtain the bond length, binding energy, and vibrational frequency of the H2_22​ molecule. Beyond revisiting this foundational approach in quantum mechanics, our proposal can serve as improved input for constructing new, but still analytically simple, variational wave functions to describe dissociation or bond formation.
A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of H2 molecule. This is achieved by starting from analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (\textit{atomicity}) in an unequivocal manner. The presence the of atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atomic correspondant is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved by combining the single--particle wave function readjustment with a simultaneous determination of two-particle states in the particle (second--quantization) representation