============ 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=2 ===> TOLERANCE BASED ON DISTANCES CONSTANTS OF TOLERANCE= 0.200 0.200 CELL 1.00000 1.00000 1.00000 90.000 90.000 90.000 1.00000 ATOM GROUP INPUT COORDINATES AND THEIR S.U. Mo1 1 0.00000 0.00000 -1.26160 0.00000 0.00000 0.00000 Mo2 1 0.00000 0.00000 1.26160 0.00000 0.00000 0.00000 O3 1 2.72890 0.00000 0.00000 0.00000 0.00000 0.00000 O4 1 -1.36450 2.36330 0.00000 0.00000 0.00000 0.00000 O5 1 -1.36450 -2.36330 0.00000 0.00000 0.00000 0.00000 O6 1 -2.51260 -0.04810 -2.82640 0.00000 0.00000 0.00000 O7 1 1.29790 -2.15190 -2.82640 0.00000 0.00000 0.00000 O8 1 1.21460 2.19990 -2.82640 0.00000 0.00000 0.00000 O9 1 -2.51260 -0.04810 2.82640 0.00000 0.00000 0.00000 O10 1 1.29790 -2.15190 2.82640 0.00000 0.00000 0.00000 O11 1 1.21460 2.19990 2.82640 0.00000 0.00000 0.00000 C12 1 1.56910 0.00000 0.00000 0.00000 0.00000 0.00000 C13 1 -0.78460 1.35890 0.00000 0.00000 0.00000 0.00000 C14 1 -0.78460 -1.35890 0.00000 0.00000 0.00000 0.00000 C15 1 -1.57500 -0.01850 -2.20400 0.00000 0.00000 0.00000 C16 1 -1.57500 -0.01850 2.20400 0.00000 0.00000 0.00000 C17 1 0.80350 -1.35470 -2.20400 0.00000 0.00000 0.00000 C18 1 0.77140 1.37320 -2.20400 0.00000 0.00000 0.00000 C19 1 0.80350 -1.35470 2.20400 0.00000 0.00000 0.00000 C20 1 0.77140 1.37320 2.20400 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 2037.94 2037.92 1231.18 2 ORTHOGONALIZATION MATRIX 0.499994 0.866029 0.000000 -0.866029 0.499994 0.000000 0.000000 0.000000 1.000000 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP Mo1 0.00002 -0.00001 -1.26160 -0.00002 0.00001 0.00000 Mo2 0.00002 -0.00001 1.26160 -0.00002 0.00001 0.00000 O3 1.36445 -2.36332 0.00000 0.00001 0.00001 0.00000 O4 1.36446 2.36332 0.00000 0.00000 -0.00001 0.00000 O5 -2.72891 0.00005 0.00000 -0.00001 -0.00005 0.00000 O6 -1.29792 2.15192 -2.82640 0.04155 0.02418 -0.00023 O7 -1.21465 -2.19997 -2.82640 -0.04172 0.02387 -0.00023 O8 2.51249 0.04804 -2.82640 0.00026 -0.04804 -0.00023 O9 -1.29792 2.15192 2.82640 0.04155 0.02418 0.00023 O10 -1.21465 -2.19997 2.82640 -0.04172 0.02387 0.00023 O11 2.51249 0.04804 2.82640 0.00026 -0.04804 0.00023 C12 0.78456 -1.35890 0.00000 0.00001 -0.00001 0.00000 C13 0.78457 1.35892 0.00000 0.00000 -0.00001 0.00000 C14 -1.56913 0.00003 0.00000 0.00000 -0.00003 0.00000 C15 -0.80350 1.35473 -2.20400 0.01600 0.00925 -0.00005 C16 -0.80350 1.35473 2.20400 0.01600 0.00925 0.00005 C17 -0.77145 -1.37321 -2.20400 -0.01605 0.00922 -0.00005 C18 1.57494 0.01852 -2.20400 0.00006 -0.01852 -0.00005 C19 -0.77145 -1.37321 2.20400 -0.01605 0.00922 0.00005 C20 1.57494 0.01852 2.20400 0.00006 -0.01852 0.00005 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. Mo1 1 0.00000 0.00000 -1.26160 0.00001 0.00001 0.00000 * Mo2 1 0.00000 0.00000 1.26160 0.00001 0.00001 0.00000 O3 1 1.36446 -2.36331 0.00000 0.00003 0.00002 0.00000 * O4 1 1.36446 2.36331 0.00000 0.00003 0.00002 0.00000 O5 1 -2.72892 0.00000 0.00000 0.00001 0.00003 0.00000 O6 1 -1.25637 2.17610 -2.82663 0.04162 0.02403 0.00023 * O7 1 -1.25637 -2.17610 -2.82663 0.04162 0.02403 0.00023 O8 1 2.51274 0.00000 -2.82663 0.00021 0.04806 0.00023 O9 1 -1.25637 2.17610 2.82663 0.04162 0.02403 0.00023 O10 1 -1.25637 -2.17610 2.82663 0.04162 0.02403 0.00023 O11 1 2.51274 0.00000 2.82663 0.00021 0.04806 0.00023 C12 1 0.78456 -1.35890 0.00000 0.00002 0.00001 0.00000 * C13 1 0.78456 1.35890 0.00000 0.00002 0.00001 0.00000 C14 1 -1.56913 0.00000 0.00000 0.00001 0.00002 0.00000 C15 1 -0.78750 1.36399 -2.20405 0.01603 0.00925 0.00005 * C16 1 -0.78750 1.36399 2.20405 0.01603 0.00925 0.00005 C17 1 -0.78750 -1.36399 -2.20405 0.01603 0.00925 0.00005 C18 1 1.57500 0.00000 -2.20405 0.00004 0.01851 0.00005 C19 1 -0.78750 -1.36399 2.20405 0.01603 0.00925 0.00005 C20 1 1.57500 0.00000 2.20405 0.00004 0.01851 0.00005 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.01157 0.01332 0.00008 0.01998 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.04172 0.04804 0.00023 0.04808 DUE TO THE ATOMS O10 O8 O6 O6 Bond lengths and bond angles after symmetrization Mo1 -Mo2 2.5232 Mo1 - C12 2.0134 Mo1 - C13 2.0134 Mo1 - C14 2.0134 Mo1 - C15 1.8354 Mo1 - C17 1.8354 Mo1 - C18 1.8354 O3 - C12 1.1598 O6 - C15 1.1256 C12 -Mo1 2.0134 C12 -Mo2 2.0134 C12 - O3 1.1598 C15 -Mo1 1.8354 C15 - O6 1.1256 Mo2 -Mo1 - C12 51.200 Mo2 -Mo1 - C13 51.200 Mo2 -Mo1 - C14 51.200 Mo2 -Mo1 - C15 120.896 Mo2 -Mo1 - C17 120.896 Mo2 -Mo1 - C18 120.896 C12 -Mo1 - C13 84.897 C12 -Mo1 - C14 84.897 C12 -Mo1 - C15 172.096 C12 -Mo1 - C17 89.276 C12 -Mo1 - C18 89.276 C13 -Mo1 - C14 84.897 C13 -Mo1 - C15 89.276 C13 -Mo1 - C17 172.096 C13 -Mo1 - C18 89.276 C14 -Mo1 - C15 89.276 C14 -Mo1 - C17 89.276 C14 -Mo1 - C18 172.096 C15 -Mo1 - C17 95.999 C15 -Mo1 - C18 95.999 C17 -Mo1 - C18 95.999 Mo1 - C12 -Mo2 77.600 Mo1 - C12 - O3 141.200 Mo2 - C12 - O3 141.200 Mo1 - C15 - O6 177.315 Schoenflies symbol = D3h CSM = 0.0796 Molecular RMS = 0.0282 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 = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 3 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 4 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 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)=0.0000 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 6 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 7 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 8 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE C3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 9 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 TYPE Cs -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 10 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 TYPE Cs -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 11 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 12 CSM = 0.08 MAX. DIFF. (Angstrom)=0.0481 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 0.0000 0.0001 3) [Cs ] x-y,-y,z 0.0796 0.0481 4) [C3 ] -y,x-y,z 0.0000 0.0001 5) [Cs ] x,y,-z 0.0000 0.0000 6) [C2 ] x-y,-y,-z 0.0796 0.0481 7) [C2 ] -x,-x+y,-z 0.0796 0.0481 8) [C3 ] -x+y,-x,z 0.0000 0.0001 9) [Cs ] -x,-x+y,z 0.0796 0.0481 10) [Cs ] y,x,z 0.0796 0.0481 11) [S3 ] -y,x-y,-z 0.0000 0.0001 12) [C2 ] y,x,-z 0.0796 0.0481 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) Mo1 0.00000 0.00000 -1.26160 Mo2 0.00000 0.00000 1.26160 O3 0.00000 -2.72892 0.00000 O4 2.72892 2.72892 0.00000 O5 -2.72892 0.00000 0.00000 O6 0.00000 2.51274 -2.82663 O7 -2.51274 -2.51274 -2.82663 O8 2.51274 0.00000 -2.82663 O9 0.00000 2.51274 2.82663 O10 -2.51274 -2.51274 2.82663 O11 2.51274 0.00000 2.82663 C12 0.00000 -1.56913 0.00000 C13 1.56913 1.56913 0.00000 C14 -1.56913 0.00000 0.00000 C15 0.00000 1.57500 -2.20405 C16 0.00000 1.57500 2.20405 C17 -1.57500 -1.57500 -2.20405 C18 1.57500 0.00000 -2.20405 C19 -1.57500 -1.57500 2.20405 C20 1.57500 0.00000 2.20405