============ 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= 1.000 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. CO1 1 0.33956 0.82438 -1.31446 0.00000 0.00000 0.00000 CO2 1 0.37942 -1.43432 -0.26540 0.00000 0.00000 0.00000 O1 1 1.15491 2.31803 -3.54423 0.00000 0.00000 0.00000 O2 1 0.54638 -4.25148 -0.70472 0.00000 0.00000 0.00000 N1 1 0.76213 1.69778 -2.64375 0.00000 0.00000 0.00000 N2 1 0.60149 -3.11768 -0.53782 0.00000 0.00000 0.00000 N3 1 1.68723 -0.14539 -0.35030 0.00000 0.00000 0.00000 N4 1 -0.94269 -0.54052 -1.30642 0.00000 0.00000 0.00000 C1 1 3.13878 -0.25326 -0.64291 0.00000 0.00000 0.00000 C2 1 3.79187 -1.18071 0.37091 0.00000 0.00000 0.00000 C3 1 3.29004 -0.81958 -2.03381 0.00000 0.00000 0.00000 C4 1 3.74497 1.12443 -0.61406 0.00000 0.00000 0.00000 C5 1 -1.78923 -1.06815 -2.40678 0.00000 0.00000 0.00000 C6 1 -2.52908 0.06331 -3.06617 0.00000 0.00000 0.00000 C7 1 -0.88758 -1.71771 -3.44944 0.00000 0.00000 0.00000 C8 1 -2.76241 -2.09526 -1.84011 0.00000 0.00000 0.00000 H1 1 3.68751 -0.79965 1.28788 0.00000 0.00000 0.00000 H2 1 3.36390 -2.08353 0.31939 0.00000 0.00000 0.00000 H3 1 4.76387 -1.26161 0.15043 0.00000 0.00000 0.00000 H4 1 2.85856 -0.20284 -2.69320 0.00000 0.00000 0.00000 H5 1 2.89021 -1.73530 -2.06678 0.00000 0.00000 0.00000 H6 1 4.27025 -0.87468 -2.22545 0.00000 0.00000 0.00000 H7 1 3.29121 1.70364 -1.29200 0.00000 0.00000 0.00000 H8 1 3.65117 1.51135 0.30291 0.00000 0.00000 0.00000 H9 1 4.71462 1.04235 -0.84279 0.00000 0.00000 0.00000 H10 1 -3.12940 0.50300 -2.39854 0.00000 0.00000 0.00000 H11 1 -1.87248 0.72461 -3.43090 0.00000 0.00000 0.00000 H12 1 -3.07898 -0.30720 -3.81417 0.00000 0.00000 0.00000 H13 1 -0.38223 -2.47397 -3.03114 0.00000 0.00000 0.00000 H14 1 -0.25209 -1.03414 -3.81417 0.00000 0.00000 0.00000 H15 1 -1.45859 -2.06712 -4.19126 0.00000 0.00000 0.00000 H16 1 -2.25120 -2.83862 -1.40739 0.00000 0.00000 0.00000 H17 1 -3.34983 -1.65791 -1.15806 0.00000 0.00000 0.00000 H18 1 -3.32873 -2.46577 -2.57781 0.00000 0.00000 0.00000 N5 1 -0.14539 1.68723 0.35030 0.00000 0.00000 0.00000 CO3 1 0.82438 0.33956 1.31446 0.00000 0.00000 0.00000 N6 1 -0.54052 -0.94269 1.30642 0.00000 0.00000 0.00000 CO4 1 -1.43432 0.37942 0.26541 0.00000 0.00000 0.00000 C9 1 -0.25326 3.13878 0.64291 0.00000 0.00000 0.00000 N7 1 1.69778 0.76213 2.64375 0.00000 0.00000 0.00000 C10 1 -1.06815 -1.78923 2.40678 0.00000 0.00000 0.00000 N8 1 -3.11768 0.60149 0.53782 0.00000 0.00000 0.00000 C11 1 -1.18071 3.79187 -0.37091 0.00000 0.00000 0.00000 C12 1 -0.81958 3.29004 2.03381 0.00000 0.00000 0.00000 C13 1 1.12443 3.74497 0.61406 0.00000 0.00000 0.00000 O3 1 2.31803 1.15491 3.54423 0.00000 0.00000 0.00000 C14 1 0.06331 -2.52908 3.06617 0.00000 0.00000 0.00000 C15 1 -1.71771 -0.88758 3.44945 0.00000 0.00000 0.00000 C16 1 -2.09526 -2.76241 1.84012 0.00000 0.00000 0.00000 O4 1 -4.25148 0.54638 0.70473 0.00000 0.00000 0.00000 H19 1 -0.79965 3.68751 -1.28787 0.00000 0.00000 0.00000 H20 1 -2.08353 3.36390 -0.31939 0.00000 0.00000 0.00000 H21 1 -1.26161 4.76387 -0.15042 0.00000 0.00000 0.00000 H22 1 -0.20284 2.85856 2.69321 0.00000 0.00000 0.00000 H23 1 -1.73530 2.89021 2.06678 0.00000 0.00000 0.00000 H24 1 -0.87468 4.27025 2.22545 0.00000 0.00000 0.00000 H25 1 1.70364 3.29121 1.29200 0.00000 0.00000 0.00000 H26 1 1.51135 3.65117 -0.30291 0.00000 0.00000 0.00000 H27 1 1.04235 4.71462 0.84279 0.00000 0.00000 0.00000 H28 1 0.50300 -3.12940 2.39854 0.00000 0.00000 0.00000 H29 1 0.72461 -1.87248 3.43090 0.00000 0.00000 0.00000 H30 1 -0.30720 -3.07898 3.81417 0.00000 0.00000 0.00000 H31 1 -2.47397 -0.38223 3.03114 0.00000 0.00000 0.00000 H32 1 -1.03414 -0.25209 3.81417 0.00000 0.00000 0.00000 H33 1 -2.06712 -1.45859 4.19126 0.00000 0.00000 0.00000 H34 1 -2.83862 -2.25120 1.40739 0.00000 0.00000 0.00000 H35 1 -1.65791 -3.34983 1.15806 0.00000 0.00000 0.00000 H36 1 -2.46577 -3.32873 2.57781 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 4076.79 4002.30 3825.12 3 ORTHOGONALIZATION MATRIX 0.707107 0.707107 0.000000 0.590950 -0.590950 0.549141 0.388302 -0.388301 -0.835730 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP CO1 0.81547 -1.00833 0.91028 0.07808 0.11478 -0.01672 CO2 -0.75348 0.92609 0.92608 -0.14007 -0.03253 -0.03253 O1 2.44818 -2.63363 2.51038 0.07309 0.11236 0.01089 O2 -2.62746 2.44830 2.45197 0.10619 0.07297 0.06930 N1 1.73186 -2.00472 1.84615 0.13113 0.14173 0.01684 N2 -1.78677 1.90250 1.89363 -0.07622 -0.03951 -0.03064 N3 1.08269 0.89062 1.00437 -0.09296 0.09911 -0.01463 N4 -1.05635 -0.95507 0.93565 0.06661 -0.03466 0.05408 C1 2.03281 1.65148 1.85443 -0.18602 0.19532 -0.00764 C2 1.83881 3.14223 1.62088 -0.29231 0.15809 -0.07438 C3 1.73932 1.31173 3.29549 -0.19282 0.23477 0.00483 C4 3.43563 1.21140 1.53075 -0.13531 0.33510 0.01575 C5 -2.02803 -1.74779 1.73142 0.18124 -0.09901 0.11537 C6 -1.75112 -3.21573 1.55586 0.20462 -0.08458 -0.00936 C7 -1.84978 -1.40367 3.20514 0.30328 -0.14283 0.09518 C8 -3.44245 -1.40473 1.27878 0.14213 -0.14176 0.26772 H1 2.03447 3.35891 0.66605 -0.28701 0.13218 -0.08042 H2 0.89780 3.39455 1.84832 -0.31217 0.09655 -0.10086 H3 2.46891 3.64336 2.21399 -0.34190 0.22726 -0.08697 H4 1.87032 0.33019 3.43953 -0.12286 0.25544 0.05156 H5 0.80909 1.59849 3.52336 -0.22346 0.14897 -0.03226 H6 2.39347 1.81831 3.85766 -0.26645 0.30871 0.01296 H7 3.52434 0.22868 1.69622 -0.03324 0.35695 0.05124 H8 3.64290 1.43087 0.57775 -0.15180 0.31660 0.00788 H9 4.06324 1.70732 2.13029 -0.19262 0.41970 -0.00328 H10 -1.86470 -3.46370 0.59407 0.11724 -0.02739 -0.00843 H11 -0.81922 -3.41880 1.85885 0.23359 -0.07230 -0.11139 H12 -2.40195 -3.73250 2.11133 0.27493 -0.13812 0.01569 H13 -2.02720 -0.42841 3.34544 0.27973 -0.15722 0.14566 H14 -0.91706 -1.63237 3.49129 0.33143 -0.11510 -0.00019 H15 -2.50061 -1.94198 3.73905 0.37359 -0.18503 0.13157 H16 -3.60660 -0.42572 1.40429 0.11550 -0.15991 0.34317 H17 -3.54856 -1.63578 0.31085 0.05747 -0.11168 0.27478 H18 -4.10489 -1.92555 1.81926 0.23427 -0.20147 0.30775 N5 1.08269 -0.89062 -1.00436 -0.09296 -0.09911 0.01463 CO3 0.81547 1.00833 -0.91028 0.07808 -0.11477 0.01672 N6 -1.05634 0.95507 -0.93565 0.06661 0.03466 -0.05408 CO4 -0.75348 -0.92608 -0.92609 -0.14007 0.03253 0.03253 C9 2.03281 -1.65148 -1.85443 -0.18602 -0.19532 0.00764 N7 1.73186 2.00471 -1.84614 0.13113 -0.14172 -0.01685 C10 -2.02803 1.74778 -1.73142 0.18124 0.09901 -0.11537 N8 -1.78677 -1.90250 -1.89363 -0.07622 0.03952 0.03064 C11 1.83881 -3.14223 -1.62088 -0.29231 -0.15809 0.07438 C12 1.73932 -1.31173 -3.29549 -0.19282 -0.23477 -0.00483 C13 3.43563 -1.21140 -1.53075 -0.13531 -0.33509 -0.01575 O3 2.44818 2.63363 -2.51037 0.07309 -0.11236 -0.01090 C14 -1.75112 3.21573 -1.55586 0.20462 0.08459 0.00936 C15 -1.84977 1.40367 -3.20515 0.30328 0.14283 -0.09517 C16 -3.44245 1.40474 -1.27879 0.14213 0.14176 -0.26771 O4 -2.62746 -2.44830 -2.45198 0.10619 -0.07297 -0.06929 H19 2.03447 -3.35891 -0.66606 -0.28701 -0.13219 0.08043 H20 0.89780 -3.39455 -1.84832 -0.31217 -0.09655 0.10086 H21 2.46891 -3.64336 -2.21399 -0.34190 -0.22726 0.08697 H22 1.87032 -0.33018 -3.43954 -0.12286 -0.25545 -0.05156 H23 0.80909 -1.59849 -3.52336 -0.22346 -0.14897 0.03226 H24 2.39347 -1.81831 -3.85766 -0.26646 -0.30871 -0.01296 H25 3.52434 -0.22869 -1.69622 -0.03324 -0.35694 -0.05125 H26 3.64290 -1.43087 -0.57774 -0.15180 -0.31659 -0.00789 H27 4.06324 -1.70732 -2.13029 -0.19262 -0.41970 0.00327 H28 -1.86470 3.46370 -0.59406 0.11724 0.02740 0.00843 H29 -0.81922 3.41880 -1.85885 0.23359 0.07230 0.11139 H30 -2.40195 3.73250 -2.11133 0.27493 0.13812 -0.01569 H31 -2.02719 0.42841 -3.34544 0.27973 0.15722 -0.14566 H32 -0.91706 1.63237 -3.49128 0.33143 0.11510 0.00019 H33 -2.50061 1.94198 -3.73905 0.37359 0.18504 -0.13157 H34 -3.60660 0.42572 -1.40429 0.11550 0.15991 -0.34317 H35 -3.54856 1.63578 -0.31085 0.05746 0.11168 -0.27478 H36 -4.10489 1.92555 -1.81926 0.23427 0.20147 -0.30776 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. CO1 1 0.89355 -0.89355 0.89355 0.08295 0.08295 0.08295 * CO2 1 -0.89355 0.89355 0.89355 0.08295 0.08295 0.08295 O1 1 2.52127 -2.52127 2.52127 0.08112 0.08112 0.08112 * O2 1 -2.52127 2.52127 2.52127 0.08112 0.08112 0.08112 N1 1 1.86299 -1.86299 1.86299 0.08744 0.08744 0.08744 * N2 1 -1.86299 1.86299 1.86299 0.08744 0.08744 0.08744 N3 1 0.98973 0.98973 0.98973 0.06738 0.06738 0.06738 * N4 1 -0.98973 -0.98973 0.98973 0.06738 0.06738 0.06738 C1 1 1.84679 1.84679 1.84679 0.14650 0.14650 0.14650 * C2 1 1.54650 3.30032 1.54650 0.21251 0.11528 0.21251 * C3 1 1.54650 1.54650 3.30032 0.21251 0.21251 0.11528 C4 1 3.30032 1.54650 1.54650 0.11528 0.21251 0.21251 C5 1 -1.84679 -1.84679 1.84679 0.14650 0.14650 0.14650 C6 1 -1.54650 -3.30032 1.54650 0.21251 0.11528 0.21251 C7 1 -1.54650 -1.54650 3.30032 0.21251 0.21251 0.11528 C8 1 -3.30032 -1.54650 1.54650 0.11528 0.21251 0.21251 H1 1 1.74746 3.49110 0.58563 0.20012 0.09059 0.23037 * H2 1 0.58563 3.49110 1.74746 0.23037 0.09059 0.20012 H3 1 2.12702 3.87062 2.12702 0.26644 0.17329 0.26644 * H4 1 1.74746 0.58563 3.49110 0.20012 0.23037 0.09059 H5 1 0.58563 1.74746 3.49110 0.23037 0.20012 0.09059 H6 1 2.12702 2.12702 3.87062 0.26644 0.26644 0.17329 H7 1 3.49110 0.58563 1.74746 0.09059 0.23037 0.20012 H8 1 3.49110 1.74746 0.58563 0.09059 0.20012 0.23037 H9 1 3.87062 2.12702 2.12702 0.17329 0.26644 0.26644 H10 1 -1.74746 -3.49110 0.58563 0.20012 0.09059 0.23037 H11 1 -0.58563 -3.49110 1.74746 0.23037 0.09059 0.20012 H12 1 -2.12702 -3.87062 2.12702 0.26644 0.17329 0.26644 H13 1 -1.74746 -0.58563 3.49110 0.20012 0.23037 0.09059 H14 1 -0.58563 -1.74746 3.49110 0.23037 0.20012 0.09059 H15 1 -2.12702 -2.12702 3.87062 0.26644 0.26644 0.17329 H16 1 -3.49110 -0.58563 1.74746 0.09059 0.23037 0.20012 H17 1 -3.49110 -1.74746 0.58563 0.09059 0.20012 0.23037 H18 1 -3.87062 -2.12702 2.12702 0.17329 0.26644 0.26644 N5 1 0.98973 -0.98973 -0.98973 0.06738 0.06738 0.06738 CO3 1 0.89355 0.89355 -0.89355 0.08295 0.08295 0.08295 N6 1 -0.98973 0.98973 -0.98973 0.06738 0.06738 0.06738 CO4 1 -0.89355 -0.89355 -0.89355 0.08295 0.08295 0.08295 C9 1 1.84679 -1.84679 -1.84679 0.14650 0.14650 0.14650 N7 1 1.86299 1.86299 -1.86299 0.08744 0.08744 0.08744 C10 1 -1.84679 1.84679 -1.84679 0.14650 0.14650 0.14650 N8 1 -1.86299 -1.86299 -1.86299 0.08744 0.08744 0.08744 C11 1 1.54650 -3.30032 -1.54650 0.21251 0.11528 0.21251 C12 1 1.54650 -1.54650 -3.30032 0.21251 0.21251 0.11528 C13 1 3.30032 -1.54650 -1.54650 0.11528 0.21251 0.21251 O3 1 2.52127 2.52127 -2.52127 0.08112 0.08112 0.08112 C14 1 -1.54650 3.30032 -1.54650 0.21251 0.11528 0.21251 C15 1 -1.54650 1.54650 -3.30032 0.21251 0.21251 0.11528 C16 1 -3.30032 1.54650 -1.54650 0.11528 0.21251 0.21251 O4 1 -2.52127 -2.52127 -2.52127 0.08112 0.08112 0.08112 H19 1 1.74746 -3.49110 -0.58563 0.20012 0.09059 0.23037 H20 1 0.58563 -3.49110 -1.74746 0.23037 0.09059 0.20012 H21 1 2.12702 -3.87062 -2.12702 0.26644 0.17329 0.26644 H22 1 1.74746 -0.58563 -3.49110 0.20012 0.23037 0.09059 H23 1 0.58563 -1.74746 -3.49110 0.23037 0.20012 0.09059 H24 1 2.12702 -2.12702 -3.87062 0.26644 0.26644 0.17329 H25 1 3.49110 -0.58563 -1.74746 0.09059 0.23037 0.20012 H26 1 3.49110 -1.74746 -0.58563 0.09059 0.20012 0.23037 H27 1 3.87062 -2.12702 -2.12702 0.17329 0.26644 0.26644 H28 1 -1.74746 3.49110 -0.58563 0.20012 0.09059 0.23037 H29 1 -0.58563 3.49110 -1.74746 0.23037 0.09059 0.20012 H30 1 -2.12702 3.87062 -2.12702 0.26644 0.17329 0.26644 H31 1 -1.74746 0.58563 -3.49110 0.20012 0.23037 0.09059 H32 1 -0.58563 1.74746 -3.49110 0.23037 0.20012 0.09059 H33 1 -2.12702 2.12702 -3.87062 0.26644 0.26644 0.17329 H34 1 -3.49110 0.58563 -1.74746 0.09059 0.23037 0.20012 H35 1 -3.49110 1.74746 -0.58563 0.09059 0.20012 0.23037 H36 1 -3.87062 2.12702 -2.12702 0.17329 0.26644 0.26644 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.18680 0.16087 0.07653 0.28532 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.37359 0.41970 0.34317 0.46180 DUE TO THE ATOMS H15 H9 H34 H9 Bond lengths and bond angles after symmetrization CO1 -CO2 2.5274 CO1 - N1 1.6791 CO1 - N3 1.8882 CO1 - N4 1.8882 CO1 - N5 1.8882 CO1 -CO3 2.5274 CO1 -CO4 2.5274 O1 - N1 1.1402 N1 -CO1 1.6791 N1 - O1 1.1402 N3 -CO1 1.8882 N3 -CO2 1.8882 N3 - C1 1.4845 N3 -CO3 1.8882 C1 - N3 1.4845 C1 - C2 1.5143 C1 - C3 1.5143 C1 - C4 1.5143 C2 - C1 1.5143 C2 - H1 1.0000 C2 - H2 1.0000 C2 - H3 0.9996 H1 - C2 1.0000 H3 - C2 0.9996 CO2 -CO1 - N1 144.736 CO2 -CO1 - N3 47.991 CO2 -CO1 - N4 47.991 CO2 -CO1 - N5 94.131 CO2 -CO1 -CO3 60.000 CO2 -CO1 -CO4 60.000 N1 -CO1 - N3 121.133 N1 -CO1 - N4 121.133 N1 -CO1 - N5 121.133 N1 -CO1 -CO3 144.736 N1 -CO1 -CO4 144.736 N3 -CO1 - N4 95.682 N3 -CO1 - N5 95.682 N3 -CO1 -CO3 47.991 N3 -CO1 -CO4 94.131 N4 -CO1 - N5 95.682 N4 -CO1 -CO3 94.131 N4 -CO1 -CO4 47.991 N5 -CO1 -CO3 47.991 N5 -CO1 -CO4 47.991 CO3 -CO1 -CO4 60.000 CO1 - N1 - O1 180.000 CO1 - N3 -CO2 84.019 CO1 - N3 - C1 129.395 CO1 - N3 -CO3 84.019 CO2 - N3 - C1 129.395 CO2 - N3 -CO3 84.019 C1 - N3 -CO3 129.395 N3 - C1 - C2 108.977 N3 - C1 - C3 108.977 N3 - C1 - C4 108.977 C2 - C1 - C3 109.961 C2 - C1 - C4 109.961 C3 - C1 - C4 109.961 C1 - C2 - H1 109.500 C1 - C2 - H2 109.500 C1 - C2 - H3 108.499 H1 - C2 - H2 110.474 H1 - C2 - H3 109.418 H2 - C2 - H3 109.418 Schoenflies symbol = Td CSM = 9.2714 Molecular RMS = 0.3045 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 8.7441 0.4758 3) [C2 ] -x,-y,z 1.2492 0.1912 4) [S4 ] -x,-z,y 1.1758 0.1596 5) [C2 ] x,-y,-z 0.0000 0.0000 6) [C2 ] -x,y,-z 1.2492 0.1912 7) [C3 ] z,x,y 8.7441 0.4758 8) [C3 ] -y,z,-x 8.7441 0.4758 9) [Cs ] -z,y,-x 4.0350 0.3873 10) [C3 ] -y,-z,x 8.7441 0.5029 11) [C3 ] y,-z,-x 8.7441 0.5029 12) [C3 ] z,-x,-y 8.7441 0.5029 13) [S4 ] y,-x,-z 8.9918 0.4596 14) [C3 ] -z,x,-y 8.7441 0.5029 15) [C3 ] -z,-x,y 8.7441 0.4758 16) [Cs ] x,z,y 2.1556 0.2992 17) [Cs ] z,y,x 4.0350 0.3873 18) [Cs ] y,x,z 8.3661 0.4380 19) [S4 ] z,-y,-x 4.6596 0.4320 20) [Cs ] -y,-x,z 8.3661 0.4380 21) [S4 ] -x,z,-y 1.1758 0.1596 22) [S4 ] -y,x,-z 8.9918 0.4596 23) [Cs ] x,-z,-y 2.1556 0.2992 24) [S4 ] -z,-y,x 4.6596 0.4320