============ SYMMOL A PROGRAM FOR THE SYMMETRIZATION OF GROUPS OF ATOMS By Tullio Pilati and Alessandra Forni Version November 4th 2002 =================================================== INDWGH=1 ===> WEIGHTS AS ATOMIC MASS INDTOL=1 ===> TOLERANCE=CONSTANT CONSTANTS OF TOLERANCE= 0.800 1.000 CELL 1.00000 1.00000 1.00000 90.000 90.000 90.000 1.00000 ATOM GROUP INPUT COORDINATES AND THEIR S.U. Ir1 1 1.42000 -1.80760 -0.12816 0.00000 0.00000 0.00000 Ir2 1 1.42600 1.00837 -1.59734 0.00000 0.00000 0.00000 Ir3 1 1.42000 0.79922 1.72550 0.00000 0.00000 0.00000 Ir4 1 -1.42000 -1.80760 -0.12816 0.00000 0.00000 0.00000 Ir5 1 -1.42000 1.00837 -1.59734 0.00000 0.00000 0.00000 Ir6 1 -1.42600 0.79922 1.72550 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 4463.94 4224.78 4024.34 3 ********************** WARNING ********************** INCREASING THE TOLERANCE COULD BE USEFUL ***************************************************** *********************************************************** WARNING: the degeneration degree is 3 but no cubic or icosahedral group can be found. IF YOU SUSPECT THE EXISTENCE OF ONE OF THEM, PLEASE CHANGE: 1) the weighting scheme OR 2) put MOL<0 to the atoms farest from the baricenter OR 3) enlarge DCM *********************************************************** ORTHOGONALIZATION MATRIX 0.000000 -0.420288 -0.907391 0.000000 0.907391 -0.420288 1.000000 0.000000 0.000000 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP Ir1 0.87600 -1.58633 1.42000 0.05767 -0.03083 0.00251 Ir2 1.02560 1.58633 1.42600 -0.09194 0.03083 -0.00349 Ir3 -1.90161 0.00000 1.42000 0.03427 0.00000 0.00251 Ir4 0.87600 -1.58633 -1.42000 0.05767 -0.03083 -0.00251 Ir5 1.02560 1.58633 -1.42000 -0.09194 0.03083 -0.00251 Ir6 -1.90161 0.00000 -1.42600 0.03427 0.00000 0.00349 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. Ir1 1 0.93367 -1.61716 1.42251 0.05424 0.04483 0.00287 * Ir2 1 0.93367 1.61716 1.42251 0.05424 0.04483 0.00287 Ir3 1 -1.86734 0.00000 1.42251 0.03928 0.05838 0.00287 Ir4 1 0.93367 -1.61716 -1.42251 0.05424 0.04483 0.00287 Ir5 1 0.93367 1.61716 -1.42251 0.05424 0.04483 0.00287 Ir6 1 -1.86734 0.00000 -1.42251 0.03928 0.05838 0.00287 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.06129 0.02055 0.00284 0.06562 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.09194 0.03083 0.00349 0.09703 DUE TO THE ATOMS Ir2 Ir4 Ir2 Ir2 Bond lengths and bond angles after symmetrization Ir1 -Ir4 2.8450 Schoenflies symbol = D3h CSM = 0.4959 Molecular RMS = 0.0704 CSM,see: Zabrodsky et al. (1993) JACS, 115, 8278-8298 SYMMETRY GROUP MATRICES 1 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 TYPE E 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 2 CSM = 0.31 MAX. DIFF. (Angstrom)=0.0559 TYPE S3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 3 CSM = 0.37 MAX. DIFF. (Angstrom)=0.0753 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 4 CSM = 0.31 MAX. DIFF. (Angstrom)=0.0559 TYPE C3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 5 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0030 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 6 CSM = 0.37 MAX. DIFF. (Angstrom)=0.0753 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 7 CSM = 0.19 MAX. DIFF. (Angstrom)=0.0482 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 8 CSM = 0.31 MAX. DIFF. (Angstrom)=0.0559 TYPE C3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 9 CSM = 0.19 MAX. DIFF. (Angstrom)=0.0483 TYPE Cs -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 10 CSM = 0.46 MAX. DIFF. (Angstrom)=0.0951 TYPE Cs -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 11 CSM = 0.31 MAX. DIFF. (Angstrom)=0.0559 TYPE S3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 12 CSM = 0.46 MAX. DIFF. (Angstrom)=0.0951 TYPE C2 -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 SYMMETRY OPERATIONS IN HEXAGONAL COORDINATES Symmetry element its CSM and Max.Diff. Symmetry element its CSM and Max.Diff. 1) [E ] x,y,z 0.0000 0.0000 2) [S3 ] -x+y,-x,-z 0.3094 0.0559 3) [Cs ] x-y,-y,z 0.3734 0.0753 4) [C3 ] -y,x-y,z 0.3094 0.0559 5) [Cs ] x,y,-z 0.0006 0.0030 6) [C2 ] x-y,-y,-z 0.3737 0.0753 7) [C2 ] -x,-x+y,-z 0.1940 0.0482 8) [C3 ] -x+y,-x,z 0.3094 0.0559 9) [Cs ] -x,-x+y,z 0.1946 0.0483 10) [Cs ] y,x,z 0.4557 0.0951 11) [S3 ] -y,x-y,-z 0.3094 0.0559 12) [C2 ] y,x,-z 0.4560 0.0951 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) Ir1 0.00000 -1.86734 1.42251 Ir2 1.86734 1.86734 1.42251 Ir3 -1.86734 0.00000 1.42251 Ir4 0.00000 -1.86734 -1.42251 Ir5 1.86734 1.86734 -1.42251 Ir6 -1.86734 0.00000 -1.42251