A density functional theory study of five-, six- and seven-atom germanium clusters: distortions from ideal bipyramidal deltahedra in hypoelectronic structures

Abstract

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge_n ^z (n = 5, 6, 7; z = −2, 0, +2) starting from a variety of initial configurations. Double zeta quality LANL2DZ basis functions extended by adding one set of polarization (d) and one set of diffuse (p) functions were used. Bipyramidal global minima were found for Ge₅ ²⁻ and Ge₇ ²⁻. These bipyramids were computed to become oblate (i.e., compressed along a major axis) without reduction in symmetry upon loss of two electrons to form the corresponding neutral species. For the six-vertex Ge₆ ²⁻/Ge₆ system our computations indicate that the oblate tetragonal bipyramid structure previously found for the 12-skeletal electron In₆ ⁶⁻ undergoes further distortion to give a less symmetrical C_s structure best regarded as an edge-capped trigonal bipyramid. Further removal of electrons from the neutral Ge_n clusters to give the dications Ge_n ²⁺ having 2n − 2 skeletal electrons was found to lead to more complicated structural changes. Thus for Ge₅ ²⁺ the lowest energy structure is a completely unsymmetrical (C₁) array of three fused triangles whereas for Ge₆ ²⁺ the edge-capped trigonal bipyramid found for Ge₆ undergoes further distortion to give a somewhat more symmetrical looking structure best regarded as an edge-bicapped butterfly. Only for the lowest energy computed structure of Ge₇ ²⁺ does the oblate pentagonal bipyramid found for Ge₇ remain recognizable although it undergoes further distortion to an unsymmetrical prolate (elongated) bipyramid related to the prolate trigonal antiprisms previously computed for In₆ ⁴⁻ and Tl₆ ⁴⁻.