============ 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 0.300 CELL 1.00000 1.00000 1.00000 90.000 90.000 90.000 1.00000 ATOM GROUP INPUT COORDINATES AND THEIR S.U. c 1 0.00000 -1.61294 0.00000 0.00000 0.00000 0.00000 c 1 -1.20003 -0.90199 0.00000 0.00000 0.00000 0.00000 c 1 -1.18751 0.48167 0.00000 0.00000 0.00000 0.00000 c 1 0.00000 1.17367 0.00000 0.00000 0.00000 0.00000 c 1 1.18751 0.48167 0.00000 0.00000 0.00000 0.00000 c 1 1.20003 -0.90199 0.00000 0.00000 0.00000 0.00000 h 1 -2.02929 -1.37546 -0.02000 0.00000 0.00000 0.00000 h 1 -2.00875 0.95868 -0.02000 0.00000 0.00000 0.00000 h 1 2.00875 0.95868 0.02000 0.00000 0.00000 0.00000 f 1 2.02929 -1.37546 0.00000 0.00000 0.00000 0.00000 h 1 0.00000 2.11346 0.02000 0.00000 0.00000 0.00000 C1 2 1.28330 0.00000 0.00000 0.00000 0.00000 0.00000 C2 2 0.77000 1.45190 0.00000 0.00000 0.00000 0.00000 C3 2 -0.77000 1.45190 0.00000 0.00000 0.00000 0.00000 C4 2 -1.28330 0.72590 1.25740 0.00000 0.00000 0.00000 C5 2 -0.77000 -0.72600 1.25740 0.00000 0.00000 0.00000 C6 2 0.77000 -0.72600 1.25740 0.00000 0.00000 0.00000 H11 -2 2.28330 0.30001 -0.00002 0.00000 0.00000 0.00000 H12 -2 0.94995 -0.37139 -0.51650 0.00000 0.00000 0.00000 H21 -2 1.10334 1.92330 -0.51650 0.00000 0.00000 0.00000 H22 -2 1.10334 1.92330 0.81650 0.00000 0.00000 0.00000 H31 -2 -1.10334 0.98051 -0.81650 0.00000 0.00000 0.00000 H32 -2 -1.10334 2.39471 0.00003 0.00000 0.00000 0.00000 H41 -2 -2.28330 0.72591 1.25742 0.00000 0.00000 0.00000 H42 -2 -0.94995 1.19729 2.07390 0.00000 0.00000 0.00000 H51 -2 -1.10334 -1.19740 0.44090 0.00000 0.00000 0.00000 H52 -2 -1.10334 -1.19740 2.07390 0.00000 0.00000 0.00000 H61 -2 1.10334 -0.25461 2.07390 0.00000 0.00000 0.00000 H62 -2 1.10334 -1.66881 1.25737 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 246.24 164.64 81.59 1 ORTHOGONALIZATION MATRIX -0.001104 -0.001079 0.999999 0.486655 0.873593 0.001480 -0.873594 0.486656 -0.000439 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP c 0.00172 -1.23919 -0.25087 -0.00172 0.00000 0.00000 c 0.00228 -1.20211 1.14346 -0.00228 0.00000 0.00000 c 0.00077 0.01274 1.80589 -0.00077 0.00000 0.00000 c -0.00128 1.19517 1.10525 0.00128 0.00000 0.00000 c -0.00185 1.16855 -0.26891 0.00185 0.00000 0.00000 c -0.00037 -0.03411 -0.95322 0.00037 0.00000 0.00000 h -0.01629 -2.01932 1.63749 0.01629 -0.00004 0.00003 h -0.01883 0.02976 2.75547 0.01883 0.00000 0.00006 h 0.01673 1.98496 -0.75421 -0.01673 0.00006 -0.00002 f -0.00077 -0.04417 -1.90807 0.00077 0.00000 0.00000 h 0.01770 2.01620 1.56260 -0.01770 0.00005 0.00004 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. c 1 0.00000 -1.23919 -0.25087 0.00172 0.00000 0.00000 * c 1 0.00000 -1.20211 1.14346 0.00228 0.00000 0.00000 * c 1 0.00000 0.01274 1.80589 0.00077 0.00000 0.00000 * c 1 0.00000 1.19517 1.10525 0.00128 0.00000 0.00000 * c 1 0.00000 1.16855 -0.26891 0.00185 0.00000 0.00000 * c 1 0.00000 -0.03411 -0.95322 0.00037 0.00000 0.00000 * h 1 0.00000 -2.01936 1.63752 0.01629 0.00004 0.00003 * h 1 0.00000 0.02976 2.75553 0.01883 0.00000 0.00006 * h 1 0.00000 1.98502 -0.75424 0.01673 0.00006 0.00002 * f 1 0.00000 -0.04417 -1.90807 0.00077 0.00000 0.00000 * h 1 0.00000 2.01624 1.56264 0.01770 0.00005 0.00004 * * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.00715 0.00001 0.00001 0.00715 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.01883 0.00006 0.00006 0.01883 DUE TO THE ATOMS h h h h Bond lengths and bond angles after symmetrization c - c 1.3948 c - c 1.3948 c - c 1.3948 c - c 1.3837 c - h 0.9550 c - c 1.3837 c - c 1.3744 c - h 0.9498 c - c 1.3744 c - c 1.3744 c - h 0.9399 c - c 1.3744 c - c 1.3837 c - h 0.9498 c - c 1.3948 c - c 1.3837 c - f 0.9549 h - c 0.9550 h - c 0.9498 h - c 0.9498 f - c 0.9549 h - c 0.9399 c - c - c 118.711 c - c - c 120.126 c - c - h 119.631 c - c - h 120.243 c - c - c 120.749 c - c - h 119.630 c - c - h 119.621 c - c - c 119.539 c - c - h 120.231 c - c - h 120.230 c - c - c 120.749 c - c - h 119.618 c - c - h 119.632 c - c - c 120.126 c - c - f 119.631 c - c - f 120.243 Schoenflies symbol = Cs CSM = 0.0112 Molecular RMS = 0.0106 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 0.0112 0.0188 SYMMETRIZATION OF GROUP NR. 2 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 151.92 80.71 80.71 2 ORTHOGONALIZATION MATRIX 0.816490 0.288693 -0.500000 -0.471420 0.833327 -0.288667 0.333328 0.471404 0.816499 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C1 1.25737 -0.72594 -0.25667 0.00002 -0.00001 0.00000 C2 1.25742 0.72594 0.25666 -0.00002 0.00001 0.00000 C3 0.00002 1.45193 -0.25666 -0.00002 -0.00001 -0.00001 C4 -1.25737 0.72594 0.25667 -0.00002 0.00001 0.00000 C5 -1.25742 -0.72594 -0.25666 0.00002 -0.00001 0.00000 C6 -0.00002 -1.45193 0.25666 0.00002 0.00001 0.00001 H11 2.16048 -0.94735 0.21807 -0.11880 -0.23141 -0.15865 H12 1.13623 -0.72919 -0.96458 0.10626 0.01184 -0.24340 H21 1.92393 1.11073 0.16827 0.11775 0.06803 -0.22769 H22 1.25743 0.72593 1.25667 -0.01494 -0.00858 -0.04868 H31 0.00002 1.45195 -1.25666 -0.00002 -0.01724 0.04867 H32 0.00002 2.39473 0.07670 -0.00002 -0.03721 -0.01728 H41 -2.07387 1.19737 -0.07664 0.03219 -0.01860 0.01722 H42 -1.25736 0.72592 1.25667 0.01487 -0.00857 -0.04869 H51 -1.25743 -0.72593 -1.25667 0.01494 0.00858 0.04868 H52 -2.07393 -1.19733 0.07668 0.03225 0.01857 -0.01726 H61 -0.00002 -1.45195 1.25666 0.00002 0.01724 -0.04867 H62 -0.00002 -2.39473 -0.07670 0.00002 0.03721 0.01728 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C1 2 1.25740 -0.72596 -0.25666 0.00002 0.00002 0.00000 * C2 2 1.25740 0.72596 0.25666 0.00002 0.00002 0.00000 C3 2 0.00000 1.45192 -0.25666 0.00002 0.00002 0.00000 C4 2 -1.25740 0.72596 0.25666 0.00002 0.00002 0.00000 C5 2 -1.25740 -0.72596 -0.25666 0.00002 0.00002 0.00000 C6 2 0.00000 -1.45192 0.25666 0.00002 0.00002 0.00000 H11 -2 2.04168 -1.17876 0.05942 # * H12 -2 1.24249 -0.71735 -1.20798 # * H21 -2 2.04168 1.17876 -0.05942 # H22 -2 1.24249 0.71735 1.20798 # H31 -2 0.00000 1.43470 -1.20798 # H32 -2 0.00000 2.35753 0.05942 # H41 -2 -2.04168 1.17876 -0.05942 # H42 -2 -1.24249 0.71735 1.20798 # H51 -2 -1.24249 -0.71735 -1.20798 # H52 -2 -2.04168 -1.17876 0.05942 # H61 -2 0.00000 -1.43470 1.20798 # H62 -2 0.00000 -2.35753 -0.05942 # * 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 0.00002 0.00001 0.00000 0.00003 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.00002 0.00001 0.00001 0.00003 DUE TO THE ATOMS C3 C3 C6 C3 Bond lengths and bond angles after symmetrization C1 -C2 1.5400 C1 -C6 1.5400 C1 -H11 0.9592 C1 -H12 0.9515 C2 -C1 -C6 109.471 C2 -C1 -H11 109.587 C2 -C1 -H12 108.950 C6 -C1 -H11 109.587 C6 -C1 -H12 108.950 H11 -C1 -H12 110.277 Schoenflies symbol = D3d CSM = 0.0000 Molecular RMS = 0.0000 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)=0.0000 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)=0.0000 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)=0.0000 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)=0.0000 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)=0.0000 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)=0.0000 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 0.0000 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 0.0000 7) [Cs ] -y,-x,z 0.0000 0.0000 8) [C2 ] y,x,-z 0.0000 0.0000 9) [S6 ] y,-x+y,-z 0.0000 0.0000 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 0.0000 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C1 0.83826 -0.83826 -0.25666 C2 1.67653 0.83826 0.25666 C3 0.83826 1.67653 -0.25666 C4 -0.83826 0.83826 0.25666 C5 -1.67653 -0.83826 -0.25666 C6 -0.83826 -1.67653 0.25666 H11 1.36112 -1.36112 0.05942 H12 0.82833 -0.82833 -1.20798 H21 2.72224 1.36112 -0.05942 H22 1.65665 0.82833 1.20798 H31 0.82833 1.65665 -1.20798 H32 1.36112 2.72224 0.05942 H41 -1.36112 1.36112 -0.05942 H42 -0.82833 0.82833 1.20798 H51 -1.65665 -0.82833 -1.20798 H52 -2.72224 -1.36112 0.05942 H61 -0.82833 -1.65665 1.20798 H62 -1.36112 -2.72224 -0.05942