============ 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= 0.100 0.100 CELL 1.00000 1.00000 1.00000 90.000 90.000 90.000 1.00000 ATOM GROUP INPUT COORDINATES AND THEIR S.U. Mg 1 0.00010 0.00100 0.00050 0.00000 0.00000 0.00000 O1 1 2.11000 0.01000 0.00000 0.00000 0.00000 0.00000 O2 1 -2.10000 0.01000 0.00100 0.00000 0.00000 0.00000 O3 1 0.00000 2.12000 0.01000 0.00000 0.00000 0.00000 O4 1 0.00000 -2.11000 -0.01000 0.00000 0.00000 0.00000 O5 1 -0.01000 0.00000 2.12000 0.00000 0.00000 0.00000 O6 1 0.01000 0.01000 -2.11000 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 286.60 285.12 284.43 3 ORTHOGONALIZATION MATRIX -0.003996 -0.001628 0.999991 0.999988 0.002950 0.004001 -0.002956 0.999994 0.001616 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP Mg -0.00105 -0.00127 -0.00452 0.00105 0.00127 0.00452 O1 -0.01000 2.10863 -0.00176 0.01000 0.00306 0.00176 O2 0.00783 -2.10131 0.01069 -0.00783 -0.01037 -0.01069 O3 0.00500 0.00492 2.11448 -0.00500 -0.00492 -0.00280 O4 -0.00812 -0.00764 -2.11552 0.00812 0.00764 0.00384 O5 2.11847 -0.00289 -0.00207 -0.00678 0.00289 0.00207 O6 -2.11159 0.00022 0.00104 -0.00010 -0.00022 -0.00104 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. Mg 1 0.00000 0.00000 0.00000 0.00278 0.00278 0.00278 * O1 1 0.00000 2.11169 0.00000 0.00623 0.00556 0.00623 * O2 1 0.00000 -2.11169 0.00000 0.00623 0.00556 0.00623 O3 1 0.00000 0.00000 2.11169 0.00623 0.00623 0.00556 O4 1 0.00000 0.00000 -2.11169 0.00623 0.00623 0.00556 O5 1 2.11169 0.00000 0.00000 0.00556 0.00623 0.00623 O6 1 -2.11169 0.00000 0.00000 0.00556 0.00623 0.00623 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.00555 0.00434 0.00382 0.00861 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.01000 0.01037 0.01069 0.01683 DUE TO THE ATOMS O1 O2 O2 O2 Bond lengths and bond angles after symmetrization Mg -O1 2.1117 Mg -O2 2.1117 Mg -O3 2.1117 Mg -O4 2.1117 Mg -O5 2.1117 Mg -O6 2.1117 O1 -Mg 2.1117 O1 -Mg -O2 180.000 O1 -Mg -O3 90.000 O1 -Mg -O4 90.000 O1 -Mg -O5 90.000 O1 -Mg -O6 90.000 O2 -Mg -O3 90.000 O2 -Mg -O4 90.000 O2 -Mg -O5 90.000 O2 -Mg -O6 90.000 O3 -Mg -O4 180.000 O3 -Mg -O5 90.000 O3 -Mg -O6 90.000 O4 -Mg -O5 90.000 O4 -Mg -O6 90.000 O5 -Mg -O6 180.000 Schoenflies symbol = Oh CSM = 0.0096 Molecular RMS = 0.0098 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) [C3 ] y,z,x 0.0089 0.0147 3) [C2 ] -x,-y,z 0.0048 0.0111 4) [C4 ] x,z,-y 0.0065 0.0134 5) [C2 ] x,-y,-z 0.0050 0.0106 6) [C2 ] -x,y,-z 0.0059 0.0132 7) [Cs ] x,y,-z 0.0044 0.0107 8) [Ci ] -x,-y,-z 0.0018 0.0059 9) [C3 ] z,x,y 0.0089 0.0147 10) [C3 ] -y,z,-x 0.0055 0.0119 11) [C2 ] z,-y,x 0.0060 0.0120 12) [C3 ] -y,-z,x 0.0075 0.0134 13) [C3 ] y,-z,-x 0.0067 0.0125 14) [S6 ] y,-z,x 0.0058 0.0127 15) [S6 ] -y,-z,-x 0.0095 0.0160 16) [C3 ] z,-x,-y 0.0075 0.0134 17) [C4 ] -y,x,z 0.0081 0.0130 18) [C3 ] -z,x,-y 0.0067 0.0125 19) [C3 ] -z,-x,y 0.0055 0.0119 20) [S6 ] -z,x,y 0.0077 0.0141 21) [S6 ] -z,-x,-y 0.0095 0.0160 22) [C2 ] -x,-z,-y 0.0082 0.0121 23) [C2 ] -z,-y,-x 0.0031 0.0075 24) [C2 ] -y,-x,-z 0.0040 0.0099 25) [C4 ] -z,y,x 0.0063 0.0132 26) [C2 ] y,x,-z 0.0060 0.0091 27) [C4 ] x,-z,y 0.0065 0.0134 28) [S6 ] -y,z,x 0.0078 0.0157 29) [S6 ] z,x,-y 0.0058 0.0127 30) [Cs ] x,-y,z 0.0054 0.0115 31) [S6 ] y,z,-x 0.0077 0.0141 32) [S6 ] z,-x,y 0.0078 0.0157 33) [Cs ] -x,y,z 0.0044 0.0100 34) [C4 ] y,-x,z 0.0081 0.0130 35) [C2 ] -x,z,y 0.0054 0.0116 36) [C4 ] z,y,-x 0.0063 0.0132 37) [Cs ] x,-z,-y 0.0045 0.0103 38) [S4 ] -z,-y,x 0.0068 0.0138 39) [S4 ] -y,x,-z 0.0080 0.0127 40) [S4 ] -x,z,-y 0.0069 0.0124 41) [S4 ] z,-y,-x 0.0068 0.0138 42) [Cs ] -y,-x,z 0.0070 0.0111 43) [Cs ] z,y,x 0.0029 0.0063 44) [Cs ] y,x,z 0.0032 0.0080 45) [Cs ] x,z,y 0.0082 0.0141 46) [S4 ] y,-x,-z 0.0080 0.0127 47) [S4 ] -x,-z,y 0.0069 0.0124 48) [Cs ] -z,y,-x 0.0052 0.0131