============ 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= 0.500 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 1.49000 -1.80760 -0.12816 0.00000 0.00000 0.00000 Ir2 1 1.49600 1.00837 -1.59734 0.00000 0.00000 0.00000 Ir3 1 1.49000 0.79922 1.72550 0.00000 0.00000 0.00000 Ir4 1 -1.49000 -1.80760 -0.12816 0.00000 0.00000 0.00000 Ir5 1 -1.49000 1.00837 -1.59734 0.00000 0.00000 0.00000 Ir6 1 -1.49600 0.79922 1.72550 0.00000 0.00000 0.00000 P1 1 0.00000 2.63688 -2.70556 0.00000 0.00000 0.00000 P2 1 0.00000 0.84600 3.70396 0.00000 0.00000 0.00000 P3 1 0.00000 -3.58145 -1.00118 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 5382.48 5342.00 5094.15 3 ********************** WARNING ********************** INCREASING THE TOLERANCE COULD BE USEFUL ***************************************************** Weights are changed PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 1902.89 1427.07 1280.98 2 ORTHOGONALIZATION MATRIX -0.702412 -0.008009 0.711726 0.711769 -0.010314 0.702338 0.001716 0.999915 0.012945 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP Ir1 1.26484 -1.38687 -1.48981 0.01788 0.02833 -0.00318 Ir2 -1.79922 -0.55037 -1.49179 -0.01867 0.11877 -0.00120 Ir3 0.61281 1.74465 -1.49427 -0.07764 0.04549 0.00127 Ir4 1.27022 -1.38151 1.49018 0.01250 0.02297 0.00282 Ir5 -1.79383 -0.54501 1.49420 -0.02406 0.11341 -0.00121 Ir6 0.61820 1.75002 1.49172 -0.08303 0.04012 0.00127 P1 -3.74426 -0.25358 0.00719 -0.02110 0.15480 -0.00719 P2 1.92600 3.23025 -0.00930 -0.12886 0.08004 0.00930 P3 1.97518 -3.23025 0.00222 -0.00695 0.01874 -0.00222 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. Ir1 1 1.28272 -1.35854 -1.49299 0.06902 0.05434 0.00201 * Ir2 1 -1.81789 -0.43160 -1.49299 0.01529 0.08651 0.00201 Ir3 1 0.53517 1.79014 -1.49299 0.08111 0.03375 0.00201 Ir4 1 1.28272 -1.35854 1.49299 0.06902 0.05434 0.00201 Ir5 1 -1.81789 -0.43160 1.49299 0.01529 0.08651 0.00201 Ir6 1 0.53517 1.79014 1.49299 0.08111 0.03375 0.00201 P1 1 -3.76536 -0.09878 0.00000 0.01691 0.12512 0.00691 * P2 1 1.79714 3.31029 0.00000 0.11207 0.05813 0.00691 P3 1 1.96823 -3.21151 0.00000 0.10518 0.06983 0.00691 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.04341 0.06919 0.00330 0.08965 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.12886 0.15480 0.00930 0.15640 DUE TO THE ATOMS P2 P1 P2 P1 Bond lengths and bond angles after symmetrization Ir1 -Ir4 2.9860 Ir1 -P3 2.4764 P1 -Ir2 2.4764 P1 -Ir5 2.4764 Ir4 -Ir1 -P3 52.923 Ir2 -P1 -Ir5 74.155 Schoenflies symbol = C3h CSM = 1.0477 Molecular RMS = 0.1024 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 = 1.05 MAX. DIFF. (Angstrom)=0.1564 TYPE S3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 3 CSM = 1.05 MAX. DIFF. (Angstrom)=0.1564 TYPE C3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 4 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0093 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 5 CSM = 1.05 MAX. DIFF. (Angstrom)=0.1564 TYPE C3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 6 CSM = 1.05 MAX. DIFF. (Angstrom)=0.1564 TYPE S3 -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 1.0477 0.1564 3) [C3 ] -y,x-y,z 1.0477 0.1564 4) [Cs ] x,y,-z 0.0026 0.0093 5) [C3 ] -x+y,-x,z 1.0477 0.1564 6) [S3 ] -y,x-y,-z 1.0477 0.1564 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) Ir1 0.49837 -1.56871 -1.49299 Ir2 -2.06707 -0.49837 -1.49299 Ir3 1.56871 2.06707 -1.49299 Ir4 0.49837 -1.56871 1.49299 Ir5 -2.06707 -0.49837 1.49299 Ir6 1.56871 2.06707 1.49299 P1 -3.82239 -0.11406 0.00000 P2 3.70833 3.82239 0.00000 P3 0.11406 -3.70833 0.00000