Many-body theory of positron binding in polyatomic molecules

Abstract

Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. 1 Whilst positron binding energies have been measured via resonant annihilation spectra for ∼ 80 molecules in the past two decades, [2][3][4][5][6][7][8][9][10][11][12] an accurate ab initio theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, standard quantum chemistry approaches have proved severely deficient, agreeing with experiment to at best 25% accuracy for polar molecules, and failing to predict binding in non-polar molecules. The theoretical difficulty lies in the need to accurately account for positron-molecule correlations including polarisation of the electron cloud, screening of the positron-molecule Coulomb interaction by molecular electrons, and the unique non-perturbative process of virtual-positronium formation (where a molecular electron temporarily tunnels to the positron). Their roles in positron-molecule binding have yet to be elucidated. Here, we develop a diagrammatic many-body description of positron-molecule interactions that takes ab initio account of the correlations, applying it to calculate positron binding energies for the molecules for which both theory and experimental results exist. Delineating the effects of the correlations, we find that in particular, virtual-positronium formation dramatically enhances binding in organic polar molecules, and can be essential to support binding in non-polar molecules. Overall, we find the best agreement with experiment to date (in some cases to within a few percent). The approach can be extended to provide predictive calculations of positron scattering and annihilation γ spectra in molecules and condensed matter. The fundamental insight provided by such capability is required to, e.g., develop antimatter-based technologies including positron traps, beams and positron emission tomography, properly interpret materials science diagnostic techniques, 13,14 and understand positrons in the galaxy. 15 Moreover, the positron-matter problem provides an unforgiving testbed for the development of computational methods to tackle the quantum many-body problem, for which our results can serve as benchmarks.Pioneering technological developments have enabled the trapping, accumulation and delivery 14,16,17 of positrons for study of their fundamental interactions with atoms and molecules, 1, 18 and the formation, exploitation and interrogation of more complicated antimatter, namely positronium (Ps), 19,20 and antihydrogen. 21 The ability of positrons to annihilate with atomic electrons forming characteristic γ rays make them a unique probe over vast length scales, giving them important use in e.g., materials science for ultra-sensitive diagnostics of industrially important materials and surface processes, 13, 14 positron emission tomography (PET) for functional medical imaging, 22 and in astrophysics. 15 Proper interpretation of the difficult and costly antimatter experiments and ma...

Influence of geometry on positron binding to molecules

“…These calculations showed that more compact molecular structures generally have higher ε B values. The ab initio many-body calculations of reference [4] observe a similar dependence on the shape of the molecule. In the framework of reference [4], the 'geometrical effect' described here also has contributions due to the differences in the individual molecular orbitals, including their individual ionization energies and other properties such as the anisotropic polarizability.…”

“…It was hypothesized that this could be due to virtual positronium. The important role of virtual positronium has also been quantitatively determined in recent ab initio many-body calculations of positron-molecule binding energy [4]. In the latter description, many-body techniques are used to calculate the positron-electron correlation energy, including the effect of virtual positronium.…”

“…This can be reconciled by the results of the papers discussed above that argue for the importance of virtual positronium in determining ε B . The manybody calculations show that, although virtual-positronium is important, it is not the value of E i (set by the weakest bound molecular electron) that determines the scale of enhancement, but rather interaction of the positron with all the possible molecular orbitals [4].…”

“…Although results from ab initio calculations are often quite dependent on the exact technique used, there have been several recent calculations for molecules with large dipole moments have been able to predict binding energies to within 30% of the measurements [2,3]. Further, a new many-body approach to calculate the positron-molecule correlation energies has resulted in unprecedented agreement (∼1%) with measured binding energies for several molecules [4]. It also provides new insights into the effect of virtual positronium formation and identifies the role of specific molecular orbitals in determining binding energies.…”

“…For the typical polar molecule, the negative end of the molecular dipole is at the outer edge of the molecule, and the positron can get closer to the attractive dipole potential. In addition, new ab initio calculations [4] give the best support to date that the short-range positron molecule correlation potential is much stronger than the corresponding electron-molecule potential.…”