============ 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= 0.010 0.700 CELL 1.00000 1.00000 1.00000 90.000 90.000 90.000 1.00000 ATOM GROUP INPUT COORDINATES AND THEIR S.U. C1 1 0.25670 0.72780 -1.25640 0.00000 0.00000 0.00000 C2 1 -0.25670 -0.72420 -1.25840 0.00000 0.00000 0.00000 C3 1 0.25670 -1.45190 -0.00210 0.00000 0.00000 0.00000 C4 1 -0.25670 -0.72780 1.25640 0.00000 0.00000 0.00000 C5 1 0.25670 0.72420 1.25840 0.00000 0.00000 0.00000 C6 1 -0.25670 1.45190 0.00210 0.00000 0.00000 0.00000 H11 -1 1.25670 0.72780 -1.35640 0.00000 0.00000 0.00000 H12 -1 -0.07670 1.20030 -2.37220 0.00000 0.00000 0.00000 H21 -1 -1.25670 -0.72420 -1.35840 0.00000 0.00000 0.00000 H22 -1 0.07670 -1.19440 -2.37560 0.00000 0.00000 0.00000 H31 -1 1.25670 -1.45190 -0.30210 0.00000 0.00000 0.00000 H32 -1 -0.07670 -2.39470 -0.30340 0.00000 0.00000 0.00000 H41 -1 -1.25670 -0.72780 1.35640 0.00000 0.00000 0.00000 H42 -1 0.07670 -1.20030 2.07220 0.00000 0.00000 0.00000 H51 -1 1.25670 0.72420 1.35840 0.00000 0.00000 0.00000 H52 -1 -0.07670 1.19440 2.37560 0.00000 0.00000 0.00000 H61 -1 -1.25670 1.45190 0.30210 0.00000 0.00000 0.00000 H62 -1 0.07670 2.39470 0.30340 0.00000 0.00000 0.00000 C1 2 0.25670 0.72780 -1.25640 0.00000 0.00000 0.00000 C2 2 -0.25670 -0.72420 -1.25840 0.00000 0.00000 0.00000 C3 2 0.25670 -1.45190 -0.00210 0.00000 0.00000 0.00000 C4 2 -0.25670 -0.72780 1.25640 0.00000 0.00000 0.00000 C5 2 0.25670 0.72420 1.25840 0.00000 0.00000 0.00000 C6 2 -0.25670 1.45190 0.00210 0.00000 0.00000 0.00000 H11 -2 1.25670 0.72780 -1.35640 0.00000 0.00000 0.00000 H12 -2 -0.07670 1.20030 -2.37220 0.00000 0.00000 0.00000 H21 -2 -1.25670 -0.72420 -1.35840 0.00000 0.00000 0.00000 H22 -2 0.07670 -1.19440 -2.37560 0.00000 0.00000 0.00000 H31 -2 1.25670 -1.45190 -0.30210 0.00000 0.00000 0.00000 H32 -2 -0.07670 -2.39470 -0.30340 0.00000 0.00000 0.00000 H41 -2 -1.25670 -0.72780 1.35640 0.00000 0.00000 0.00000 H42 -2 0.07670 -1.20030 2.07220 0.00000 0.00000 0.00000 H51 -2 1.25670 0.72420 1.35840 0.00000 0.00000 0.00000 H52 -2 -0.07670 1.19440 2.37560 0.00000 0.00000 0.00000 H61 -2 -1.25670 1.45190 0.30210 0.00000 0.00000 0.00000 H62 -2 0.07670 4.39470 0.30340 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 151.92 80.71 80.71 2 ORTHOGONALIZATION MATRIX 0.000009 0.001432 -0.999999 0.000009 0.999999 0.001432 1.000000 -0.000009 0.000009 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C1 1.25744 0.72600 0.25668 -0.00004 -0.00004 0.00002 C2 1.25736 -0.72600 -0.25670 0.00005 0.00004 0.00000 C3 0.00002 -1.45190 0.25671 -0.00002 -0.00003 -0.00001 C4 -1.25744 -0.72600 -0.25668 0.00004 0.00004 -0.00002 C5 -1.25736 0.72600 0.25670 -0.00005 -0.00004 0.00000 C6 -0.00002 1.45190 -0.25671 0.00002 0.00003 0.00001 H11 1.35745 0.72587 1.25668 -0.04992 0.02903 0.00002 H12 2.37392 1.19690 -0.07673 -0.18737 0.06550 0.00003 H21 1.35735 -0.72615 -1.25671 -0.04982 -0.02875 0.00001 H22 2.37389 -1.19780 0.07669 -0.18735 -0.06460 0.00001 H31 0.30003 -1.45232 1.25671 -0.30003 -0.05749 -0.00001 H32 0.29997 -2.39513 -0.07668 -0.29997 -0.12967 -0.00002 H41 -1.35745 -0.72587 -1.25668 0.04992 -0.02903 -0.00002 H42 -2.07392 -1.19733 0.07673 -0.11263 -0.06507 -0.00003 H51 -1.35735 0.72615 1.25671 0.04982 0.02875 -0.00001 H52 -2.37389 1.19780 -0.07669 0.18735 0.06460 -0.00001 H61 -0.30003 1.45232 -1.25671 0.30003 0.05749 0.00001 H62 -0.29997 2.39513 0.07668 0.29997 0.12967 0.00002 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C1 1 1.25741 0.72596 0.25670 0.00004 0.00004 0.00001 * C2 1 1.25741 -0.72596 -0.25670 0.00004 0.00004 0.00001 C3 1 0.00000 -1.45193 0.25670 0.00004 0.00004 0.00001 C4 1 -1.25741 -0.72596 -0.25670 0.00004 0.00004 0.00001 C5 1 -1.25741 0.72596 0.25670 0.00004 0.00004 0.00001 C6 1 0.00000 1.45193 -0.25670 0.00004 0.00004 0.00001 H11 -1 1.30753 0.75490 1.25670 # * H12 -1 2.18654 1.26240 -0.07670 # * H21 -1 1.30753 -0.75490 -1.25670 # H22 -1 2.18654 -1.26240 0.07670 # H31 -1 0.00000 -1.50981 1.25670 # H32 -1 0.00000 -2.52480 -0.07670 # H41 -1 -1.30753 -0.75490 -1.25670 # H42 -1 -2.18654 -1.26240 0.07670 # H51 -1 -1.30753 0.75490 1.25670 # H52 -1 -2.18654 1.26240 -0.07670 # H61 -1 0.00000 1.50981 -1.25670 # H62 -1 0.00000 2.52480 0.07670 # * 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 0.00004 0.00004 0.00001 0.00005 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.00005 0.00004 0.00002 0.00006 DUE TO THE ATOMS C2 C1 C4 C2 Bond lengths and bond angles after symmetrization C1 -C2 1.5400 C1 -C6 1.5400 C1 -H11 1.0017 C1 -H12 1.1235 C2 -C1 -C6 109.469 C2 -C1 -H11 111.103 C2 -C1 -H12 110.563 C6 -C1 -H11 111.103 C6 -C1 -H12 110.563 H11 -C1 -H12 103.950 Schoenflies symbol = D3d CSM = 0.0000 Molecular RMS = 0.0001 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 C3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 3 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 4 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 5 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 TYPE Ci -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 6 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 7 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE Cs 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 C2 -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 9 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S6 0.5000000000 0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 10 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 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)=0.0000 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 12 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S6 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) [C3 ] -y,x-y,z 0.0000 0.0001 3) [Cs ] -x+y,y,z 0.0000 0.0000 4) [C2 ] x-y,-y,-z 0.0000 0.0000 5) [Ci ] -x,-y,-z 0.0000 0.0000 6) [C3 ] -x+y,-x,z 0.0000 0.0001 7) [Cs ] -y,-x,z 0.0000 0.0001 8) [C2 ] y,x,-z 0.0000 0.0001 9) [S6 ] y,-x+y,-z 0.0000 0.0001 10) [Cs ] x,x-y,z 0.0000 0.0000 11) [C2 ] -x,-x+y,-z 0.0000 0.0000 12) [S6 ] x-y,x,-z 0.0000 0.0001 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C1 1.67654 0.83827 0.25670 C2 0.83827 -0.83827 -0.25670 C3 -0.83827 -1.67654 0.25670 C4 -1.67654 -0.83827 -0.25670 C5 -0.83827 0.83827 0.25670 C6 0.83827 1.67654 -0.25670 H11 1.74337 0.87169 1.25670 H12 2.91539 1.45769 -0.07670 H21 0.87169 -0.87169 -1.25670 H22 1.45769 -1.45769 0.07670 H31 -0.87169 -1.74337 1.25670 H32 -1.45769 -2.91539 -0.07670 H41 -1.74337 -0.87169 -1.25670 H42 -2.91539 -1.45769 0.07670 H51 -0.87169 0.87169 1.25670 H52 -1.45769 1.45769 -0.07670 H61 0.87169 1.74337 -1.25670 H62 1.45769 2.91539 0.07670 SYMMETRIZATION OF GROUP NR. 2 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 151.92 80.71 80.71 2 ORTHOGONALIZATION MATRIX 0.000009 0.001432 -0.999999 0.000009 0.999999 0.001432 1.000000 -0.000009 0.000009 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C1 1.25744 0.72600 0.25668 -0.00004 -0.00004 0.00002 C2 1.25736 -0.72600 -0.25670 0.00005 0.00004 0.00000 C3 0.00002 -1.45190 0.25671 -0.00002 -0.00003 -0.00001 C4 -1.25744 -0.72600 -0.25668 0.00004 0.00004 -0.00002 C5 -1.25736 0.72600 0.25670 -0.00005 -0.00004 0.00000 C6 -0.00002 1.45190 -0.25671 0.00002 0.00003 0.00001 H11 1.35745 0.72587 1.25668 -0.04992 0.02903 0.00002 H12 2.37392 1.19690 -0.07673 0.00000 0.00000 0.00000 H21 1.35735 -0.72615 -1.25671 -0.04982 -0.02875 0.00001 H22 2.37389 -1.19780 0.07669 0.00000 0.00000 0.00000 H31 0.30003 -1.45232 1.25671 -0.30003 -0.05749 -0.00001 H32 0.29997 -2.39513 -0.07668 0.00000 0.00000 0.00000 H41 -1.35745 -0.72587 -1.25668 0.04992 -0.02903 -0.00002 H42 -2.07392 -1.19733 0.07673 0.00000 0.00000 0.00000 H51 -1.35735 0.72615 1.25671 0.04982 0.02875 -0.00001 H52 -2.37389 1.19780 -0.07669 0.00000 0.00000 0.00000 H61 -0.30003 1.45232 -1.25671 0.30003 0.05749 0.00001 H62 -0.29711 4.39513 0.07666 0.00000 0.00000 0.00000 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C1 2 1.25741 0.72596 0.25670 0.00004 0.00004 0.00001 * C2 2 1.25741 -0.72596 -0.25670 0.00004 0.00004 0.00001 C3 2 0.00000 -1.45193 0.25670 0.00004 0.00004 0.00001 C4 2 -1.25741 -0.72596 -0.25670 0.00004 0.00004 0.00001 C5 2 -1.25741 0.72596 0.25670 0.00004 0.00004 0.00001 C6 2 0.00000 1.45193 -0.25670 0.00004 0.00004 0.00001 H11 -2 1.30753 0.75490 1.25670 # * H12 -2 2.37392 1.19690 -0.07673 $ H21 -2 1.30753 -0.75490 -1.25670 # H22 -2 2.37389 -1.19780 0.07669 $ H31 -2 0.00000 -1.50981 1.25670 # H32 -2 0.29997 -2.39513 -0.07668 $ H41 -2 -1.30753 -0.75490 -1.25670 # H42 -2 -2.07392 -1.19733 0.07673 $ H51 -2 -1.30753 0.75490 1.25670 # H52 -2 -2.37389 1.19780 -0.07669 $ H61 -2 0.00000 1.50981 -1.25670 # H62 -2 -0.29711 4.39513 0.07666 $ * 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. $ It was IMPOSSIBLE to symmetrize this atom according to the found symmetry group and within the given tolerance. AVERAGE DIFFERENCE ON X,Y,Z,D 0.00004 0.00004 0.00001 0.00005 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.00005 0.00004 0.00002 0.00006 DUE TO THE ATOMS C2 C1 C4 C2 Bond lengths and bond angles after symmetrization C1 -C2 1.5400 C1 -C6 1.5400 C1 -H11 1.0017 C2 -C1 -C6 109.469 C2 -C1 -H11 111.103 C6 -C1 -H11 111.103 Schoenflies symbol = D3d CSM = 0.0000 Molecular RMS = 0.0001 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 C3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 3 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 4 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 5 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 TYPE Ci -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 6 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 7 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE Cs 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 C2 -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 9 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S6 0.5000000000 0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 10 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0000 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)=0.0000 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 12 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0001 TYPE S6 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) [C3 ] -y,x-y,z 0.0000 0.0001 3) [Cs ] -x+y,y,z 0.0000 0.0000 4) [C2 ] x-y,-y,-z 0.0000 0.0000 5) [Ci ] -x,-y,-z 0.0000 0.0000 6) [C3 ] -x+y,-x,z 0.0000 0.0001 7) [Cs ] -y,-x,z 0.0000 0.0001 8) [C2 ] y,x,-z 0.0000 0.0001 9) [S6 ] y,-x+y,-z 0.0000 0.0001 10) [Cs ] x,x-y,z 0.0000 0.0000 11) [C2 ] -x,-x+y,-z 0.0000 0.0000 12) [S6 ] x-y,x,-z 0.0000 0.0001 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C1 1.67654 0.83827 0.25670 C2 0.83827 -0.83827 -0.25670 C3 -0.83827 -1.67654 0.25670 C4 -1.67654 -0.83827 -0.25670 C5 -0.83827 0.83827 0.25670 C6 0.83827 1.67654 -0.25670 H11 1.74337 0.87169 1.25670 H12 3.06495 1.38206 -0.07673 H21 0.87169 -0.87169 -1.25670 H22 1.68234 -1.38310 0.07669 H31 -0.87169 -1.74337 1.25670 H32 -1.08286 -2.76566 -0.07668 H41 -1.74337 -0.87169 -1.25670 H42 -2.76520 -1.38256 0.07673 H51 -0.87169 0.87169 1.25670 H52 -1.68234 1.38310 -0.07669 H61 0.87169 1.74337 -1.25670 H62 2.24042 5.07506 0.07666