============ 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 -1.49460 -0.11806 0.31368 0.00000 0.00000 0.00000 IR2 1 1.51356 0.12370 1.30401 0.00000 0.00000 0.00000 IR3 1 0.71235 0.57288 -1.89620 0.00000 0.00000 0.00000 P1 1 -0.41381 -0.34568 2.41404 0.00000 0.00000 0.00000 P2 1 2.68977 0.32890 -0.68577 0.00000 0.00000 0.00000 P3 1 -1.57718 0.37333 -2.01070 0.00000 0.00000 0.00000 C1 1 -3.19069 -0.58199 0.70192 0.00000 0.00000 0.00000 C2 1 -1.60175 1.76086 0.67824 0.00000 0.00000 0.00000 C3 1 -1.06373 -1.97558 -0.15058 0.00000 0.00000 0.00000 IR1 -2 -1.49460 -0.11806 0.31368 0.00000 0.00000 0.00000 IR2 2 1.51356 0.12370 1.30401 0.00000 0.00000 0.00000 IR3 2 0.71235 0.57288 -1.89620 0.00000 0.00000 0.00000 P1 2 -0.41381 -0.34568 2.41404 0.00000 0.00000 0.00000 P2 2 2.68977 0.32890 -0.68577 0.00000 0.00000 0.00000 P3 2 -1.57718 0.37333 -2.01070 0.00000 0.00000 0.00000 C1 2 -3.19069 -0.58199 0.70192 0.00000 0.00000 0.00000 C2 2 -1.60175 1.76086 0.67824 0.00000 0.00000 0.00000 C3 2 -1.06373 -1.97558 -0.15058 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 2852.03 1547.75 1489.08 2 ORTHOGONALIZATION MATRIX -0.924828 -0.171398 0.339583 0.361342 -0.116925 0.925073 -0.118850 0.978239 0.170068 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP IR1 1.67966 -0.20217 -0.01380 0.00006 -0.00001 0.01380 IR2 -0.80751 1.77267 0.03361 -0.00012 0.00026 -0.03361 IR3 -1.23025 -1.52979 0.02398 -0.00009 -0.00011 -0.02398 P1 1.43238 2.15797 -0.00771 0.00001 0.00001 0.00771 P2 -2.60616 0.33300 -0.24385 -0.01120 0.00143 0.24385 P3 0.88249 -2.43968 0.08141 0.00043 -0.00120 -0.08141 C1 3.45961 -0.40164 -0.20002 0.00570 -0.00066 0.20002 C2 1.58051 -0.12333 1.89897 -0.06803 -0.06787 0.03267 C3 1.44190 -0.25876 -1.96106 0.07058 0.06755 0.02942 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. IR1 1 1.67972 -0.20217 0.00000 0.00006 0.00001 0.01380 * IR2 1 -0.80763 1.77293 0.00000 0.00012 0.00026 0.03361 * IR3 1 -1.23034 -1.52991 0.00000 0.00009 0.00011 0.02398 * P1 1 1.43238 2.15798 0.00000 0.00001 0.00001 0.00771 * P2 1 -2.61736 0.33443 0.00000 0.01120 0.00143 0.24385 * P3 1 0.88293 -2.44089 0.00000 0.00043 0.00120 0.08141 * C1 1 3.46531 -0.40230 0.00000 0.00570 0.00066 0.20002 * C2 1 1.51248 -0.19121 1.93164 0.06932 0.06771 0.03109 * C3 1 1.51248 -0.19121 -1.93164 0.06932 0.06771 0.03109 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.01736 0.01546 0.07405 0.08981 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.07058 0.06787 0.24385 0.24411 DUE TO THE ATOMS C3 C2 P2 P2 Bond lengths and bond angles after symmetrization IR1 -P1 2.3731 IR1 -P3 2.3763 IR1 -C1 1.7968 IR1 -C2 1.9389 IR1 -C3 1.9389 IR2 -P1 2.2729 IR2 -P2 2.3118 IR3 -P2 2.3237 IR3 -P3 2.3013 P1 -IR1 2.3731 P1 -IR2 2.2729 P2 -IR2 2.3118 P2 -IR3 2.3237 P3 -IR1 2.3763 P3 -IR3 2.3013 C1 -IR1 1.7968 C2 -IR1 1.9389 P1 -IR1 -P3 154.426 P1 -IR1 -C1 102.378 P1 -IR1 -C2 89.163 P1 -IR1 -C3 89.163 P3 -IR1 -C1 103.196 P3 -IR1 -C2 88.648 P3 -IR1 -C3 88.648 C1 -IR1 -C2 94.954 C1 -IR1 -C3 94.954 C2 -IR1 -C3 170.082 P1 -IR2 -P2 151.273 P2 -IR3 -P3 149.968 IR1 -P1 -IR2 86.229 IR2 -P2 -IR3 91.832 IR1 -P3 -IR3 86.272 Schoenflies symbol = Cs CSM = 1.4325 Molecular RMS = 0.1197 CSM,see: Zabrodsky et al. (1993) JACS, 115, 8278-8298 Symmetry element its CSM and Max.Diff. Symmetry element its CSM and Max.Diff. 1) [E ] x,y,z 0.0000 0.0000 2) [Cs ] x,y,-z 1.4325 0.2441 SYMMETRIZATION OF GROUP NR. 2 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 2095.95 1489.87 790.65 1 ORTHOGONALIZATION MATRIX -0.109050 0.979770 0.167806 -0.238648 0.138071 -0.961241 -0.964964 -0.144870 0.218763 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP IR2 0.03240 -1.65960 -0.39636 -0.03240 -0.00533 0.00393 IR3 0.02285 1.66979 -0.38839 -0.02285 -0.00486 -0.00404 P1 -0.03104 -2.33145 1.77431 0.03104 0.01597 0.02556 P2 -0.22872 0.00069 -1.99638 0.22872 -0.00069 -0.01306 P3 0.05779 2.29870 1.82479 -0.05779 0.01679 -0.02492 C1 -0.24705 -0.05563 4.11359 0.24705 0.05563 0.00779 C2 1.87115 -0.08858 2.23573 0.05990 0.08858 -0.07763 C3 -1.98745 0.06382 2.07654 0.05639 -0.06382 0.08156 IR1 -0.04262 -0.02315 2.32478 0.04262 0.02315 0.00000 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. IR2 2 0.00000 -1.66493 -0.39243 0.02803 0.00510 0.00399 * IR3 2 0.00000 1.66493 -0.39243 0.02803 0.00510 0.00399 P1 2 0.00000 -2.31549 1.79987 0.04639 0.01638 0.02524 * P2 2 0.00000 0.00000 -2.00944 0.22872 0.00069 0.01306 * P3 2 0.00000 2.31549 1.79987 0.04639 0.01638 0.02524 C1 2 0.00000 0.00000 4.12137 0.24705 0.05563 0.00779 * C2 2 1.93106 0.00000 2.15809 0.05817 0.07720 0.07962 * C3 2 -1.93106 0.00000 2.15809 0.05817 0.07720 0.07962 IR1 -2 0.00000 0.00000 2.32478 # * * Atom defining the asymmetric unit for the found symmetry group. # This atom was symmetrized but NOT used to find the symmetry group and to calculate CMS, RMS and so on. AVERAGE DIFFERENCE ON X,Y,Z,D 0.09202 0.03146 0.02981 0.11221 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.24705 0.08858 0.08156 0.25336 DUE TO THE ATOMS C1 C2 C3 C1 Bond lengths and bond angles after symmetrization IR2 -P1 2.2868 IR2 -P2 2.3209 P1 -IR2 2.2868 P1 -IR1 2.3742 P2 -IR2 2.3209 P2 -IR3 2.3209 C1 -IR1 1.7966 P1 -IR2 -P2 150.692 IR2 -P1 -IR1 86.245 IR2 -P2 -IR3 91.673 Schoenflies symbol = C2v CSM = 1.9476 Molecular RMS = 0.1396 CSM,see: Zabrodsky et al. (1993) JACS, 115, 8278-8298 Symmetry element its CSM and Max.Diff. Symmetry element its CSM and Max.Diff. 1) [E ] x,y,z 0.0000 0.0000 2) [C2 ] -x,-y,z 1.7524 0.2534 3) [Cs ] x,-y,z 0.2613 0.0886 4) [Cs ] -x,y,z 1.8813 0.2472