Helium cluster ions: coherent charge sharing and the general trimerization trend

The coupled-monomers model views any molecular system as a coherent network of interacting monomers. Developed as a self-consistent density-matrix adaptation of the Hückel MO theory, it has been applied to various X^± cluster ions, where X is an inert (closed-shell) neutral monomer. Rather than keeping the bond integrals constant, the model considers their variation with the bond orders χ using a bonding function β(χ). In this work, high-level ab initio data are used to obtain the bonding function for He⁺. As the simplest inert species, helium is used to illustrate the general X^± bonding trends, using the most elementary example. Two alternative approaches to the bonding function are described. One is based on the He₂⁺ potential, the other on the "multicluster" training points obtained by analysing several special He⁺ structures. Each approach is tested in two regimes: by considering only the local bonds, and by including both local and remote pairwise interactions. The remote forces in He⁺, n ≥ 3 are destabilising and account for approximately -5% of total covalent energy. Each model variation yields similar structural results, indicating a general trend for trimer-ion formation. In the absence of geometric constraints, this appears to be a universal feature of the X^± covalent networks, resulting from the enthalpy-driven competition between charge sharing and localisation. Therefore, many currently unknown trimer-ions are likely to be found in cold environments, such as exoplanetary atmospheres and outer space.