Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge n z (n = 5, 6, 7; z = Ϫ2, 0, ϩ2) 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 Ge 5 2Ϫ and Ge 7 2Ϫ . 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 Ge 6 2Ϫ /Ge 6 system our computations indicate that the oblate tetragonal bipyramid structure previously found for the 12-skeletal electron In 6 6Ϫ 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 2ϩ having 2n Ϫ 2 skeletal electrons was found to lead to more complicated structural changes. Thus for Ge 5 2ϩ the lowest energy structure is a completely unsymmetrical (C 1 ) array of three fused triangles whereas for Ge 6 2ϩ the edge-capped trigonal bipyramid found for Ge 6 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 Ge 7 2ϩ does the oblate pentagonal bipyramid found for Ge 7 remain recognizable although it undergoes further distortion to an unsymmetrical prolate (elongated) bipyramid related to the prolate trigonal antiprisms previously computed for In 6 4Ϫ and Tl 6 4Ϫ .
Geometry optimization results are reported for secondary structural elements of small proteins and polypeptides. Emphasis is placed on how well molecular mechanics as well as semiempirical, ab initio, and density functional methods describe α-helical and related structures in purely theoretical models (Gly10, Ile10) as well as in realistic models (an α-helical region of calmodulin, and the complete structure of a small protein). Many of the methods examined here were found to provide unsatisfactory descriptions of the hydrogen-bonding interactions within polypeptide-type structures, as the α-helical canonical secondary structure motif was not reproduced accurately. Ab initio and DFT methods provided reasonable results only when solvation models were included, although Hartree-Fock failed even with solvation in one of the test cases; among the semiempirical methods, one of the PM6 implementations performed very well.
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