Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na, Mg, Al, Si, P, S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.