A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si 6 ground state

Abstract

We report a critical analysis of the performance of conventional ab initio and density functional methods in the computation of the ligand-free Si 6 “magic-number” cluster ground state, structure relying on the recent advances in modern pseudo-Jahn-Teller theory. Our study focuses on the equilibrium structures that have been concluded, at one point or another, as the true ground state structure in the literature. Namely, the distorted (compressed) octahedron of D 4h ( 1A 1g) symmetry which is indirectly supported by earlier experimental studies, the edge- and face-capped trigonal bipyramids of C 2v ( 1A 1) symmetry. Geometry optimizations have been carried out, with a vast selection of basis sets with methods that are extensively used for geometry optimizations such as Hartree–Fock, Møller–Plesset perturbation theory, coupled cluster techniques and the widely used B3LYP and B3PW91 density functional methods. Our results expose that the determination of Si 6 ground state structure is extremely sensitive to basis set effects and depends on the particular capabilities of each method in the treatment of the pseudo Jahn-Teller effect (PJTE). More specifically, geometry optimizations with methods based on Møller–Plesset perturbation theory, which have been demonstrated that do not treat the PJTE, predict that the distorted octahedron of D 4h ( 1A 1g) symmetry is the ground state structure, while methods which do provide PJTE treatment suggest that the distorted octahedron is unstable and undergoes PJTE distortions.