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American Mineralogist Volume 61 pages 287 294 1976 A molecularorbital study of shared edgedistortions in linked polyhedra J A TossslrDepartmentof Chemistry Uniuersityof Maryland CollegePark Maryland 20742 nNo G V Gress Departmentof GeologicalSciences Virginia PolytechnicInstitute and State Uniuersity Blacksburg Virginia 2406I Abstract Molecular orbital results obtained using an approximate self consistent fieldmethod are presented for two systems one consisting of two silicate tetrahedra sharing a common edge and saturated with hydrogens at their periphery sirosH4 and the other consisting of a silicate tetrahedron sharing an edge with a Mg containing octahedron and saturated with hydrogens SiMgOrHr For both systemsthe O6 Si O6 angle opposite the shared edge has been varied while all distancesand anglesnot involved in the shared edge have been held fixed For SirOuHr an energy minimum is found at an O6 Si O6 angle of about 85 this is significantly less than the undistorted value of 109 5 but in fairly good agreement with the observed Ob Si Ob angle 93 in silica W and SirOz The energy stabilization at this minimum is about 100 kcal SirOuHounit For SiMgO H o the minimum energy obtains when Ob Si Ob 103 in good agreementwith the observed data for forsterite For the Si Mg cluster the energystabilizationat the minimum is only 4 kcallSiMgOrH o unit An important determinant of total energy is found to be the covalent overlap repulsion between the metal atoms manifested in large negative bond overlap populations Decreases in M O bond overlap populations and charge redistribution from M to the exterior of the bridging oxygen atoms also contribute significantly to total energy changes Introduction Pauling 1929 statedthat The presenceof shared edges and particularly of shared faces in a coordinated structure decreasesits stability this effect is large for cations with large valence and small coordination number and is especiallylarge in case the radius ratio approachesthe lower



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