The three-center two-positron bond

Abstract

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.

Fig. 1. Panel (a) shows the coordinates for the molecules with three atomic centers. The other panels illustrate relevant particular cases: (b) equilateral triangle (D_3h symmetry), (c) isosceles triangle (C_2v symmetry), and (d) collinear geometry (D_∞h symmetry).

Fig. 2. Potential energy surfaces for the singlet (a) and triplet (b) positronic states of the 2e⁺[H₃³⁻] system. The energies were computed at the MP2 level using the aug-cc-pVTZ/PSX-TZ combination of electronic and positronic basis sets centered at the hydrogen nuclei. The dashed lines correspond to constant R₃ paths obtained for C_2v conformations.

Fig. 3. Potential energy curves for the 2e⁺[H₃³⁻] system and the vertical detachment channels (10a–10d). The energies were computed with the DMC method as functions of the R coordinate in the D_3h symmetry (a) and of the θ coordinate in the C_2v symmetry (b) fixing R = 6.1 bohr. We employed the lowest energies obtained from variational calculations for Ps⁻ and Ps₂, and the exact value for Ps (−0.25 E_h).

Fig. 4. 1D cuts of the electronic density of [H₃³⁻] (black line) and the electronic (blue) and positronic (red) densities of 2e⁺[H₃³⁻]. The inset panel displays the electronic density difference, Δρ_e⁻, between 2e⁺[H₃³⁻] and [H₃³⁻] (violet). The density of the unstable [H₃³⁻] system was constructed as the sum of the densities of three H⁻ anions at the equilibrium positions of 2e⁺[H₃³⁻]. The densities were obtained as histograms of the number of particles inside voxels (width = 0.08 bohr) disposed along an internuclear axis.

Fig. 5. Comparison of three-center two-particle bonding densities. Electronic density of H₃⁺ (a), electronic bonding density of Li₃⁺ (b), and positronic bonding density of 2e⁺[H₃³⁻] (c). The densities were obtained with the DMC method as histograms of the number of particles inside voxels (width = 0.08 bohr) disposed along the molecular plane. In all panels, the atomic nuclei are represented as black dots.