An optimized full-configuration-interaction nuclear orbital approach to a “hard-core” interaction problem: Application to $(H3e)N–Cl2(B)$ clusters $(N≤4)$

An efficient full-configuration-interaction nuclear orbital treatment has been recently developed as a benchmark quantum-chemistry-like method to calculate ground and excited “solvent” energies and wave functions in small doped $ΔEest$ clusters $(N≤4)$ [M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, and A. O. Mitrushchenkov, J. Chem. Phys. 125, 221101 (2006)]. Additional methodological and computational details of the implementation, which uses an iterative Jacobi–Davidson diagonalization algorithm to properly address the inherent “hard-core” He–He interaction problem, are described here. The convergence of total energies, average pair He–He interaction energies, and relevant one- and two-body properties upon increasing the angular part of the one-particle basis set (expanded in spherical harmonics) has been analyzed, considering $Cl2$ as the dopant and a semiempirical model (T-shaped) $He–Cl2(B)$ potential. Converged results are used to analyze global energetic and structural aspects as well as the configuration makeup of the wave functions, associated with the ground and low-lying “solvent” excited states. Our study reveals that besides the fermionic nature of $H3e$ atoms, key roles in determining total binding energies and wave-function structures are played by the strong repulsive core of the He–He potential as well as its very weak attractive region, the most stable arrangement somehow departing from the one of $N$ He atoms equally spaced on equatorial “ring” around the dopant. The present results for $N=4$ fermions indicates the structural “pairing” of two $H3e$ atoms at opposite sides on a broad “belt” around the dopant, executing a sort of asymmetric umbrella motion. This pairing is a compromise between maximizing the $H3e–H3e$ and the He-dopant attractions, and suppressing at the same time the “hard-core” repulsion. Although the He–He attractive interaction is rather weak, its contribution to the total energy is found to scale as a power of three and it thus increasingly affects the pair density distributions as the cluster grows in size.