============ 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= 0.120 0.220 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 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 C2 1 -1.34000 0.76000 0.00000 0.00000 0.00000 0.00000 C3 1 -1.34000 -0.76000 0.00000 0.00000 0.00000 0.00000 H11 -1 0.57000 0.10000 0.81650 0.00000 0.00000 0.00000 H12 -1 0.57000 0.10000 -0.81650 0.00000 0.00000 0.00000 H21 -1 -1.65000 1.30000 0.81650 0.00000 0.00000 0.00000 H22 -1 -1.65000 1.30000 -0.81650 0.00000 0.00000 0.00000 H31 -1 -1.55000 -1.30000 0.81650 0.00000 0.00000 0.00000 H32 -1 -1.55000 -1.30000 -0.81650 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 28.25 14.38 13.88 2 ORTHOGONALIZATION MATRIX 0.506690 0.862129 0.000000 -0.862129 0.506690 0.000000 0.000000 0.000000 1.000000 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C1 0.45264 -0.77017 0.00000 -0.00991 0.00333 0.00000 C2 0.42890 0.77017 0.00000 0.01384 -0.00333 0.00000 C3 -0.88154 0.00000 0.00000 -0.00393 0.00000 0.00000 H11 0.82767 -1.21091 0.81650 -0.09099 -0.06506 0.00000 H12 0.82767 -1.21091 -0.81650 -0.09099 -0.06506 0.00000 H21 0.73737 1.31104 0.81650 -0.00069 -0.03507 0.00000 H22 0.73737 1.31104 -0.81650 -0.00069 -0.03507 0.00000 H31 -1.45349 -0.09257 0.81650 -0.01987 0.09257 0.00000 H32 -1.45349 -0.09257 -0.81650 -0.01987 0.09257 0.00000 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C1 1 0.44274 -0.76684 0.00000 0.00814 0.00654 0.00000 * C2 1 0.44274 0.76684 0.00000 0.00814 0.00654 0.00000 C3 1 -0.88547 0.00000 0.00000 0.00557 0.00883 0.00000 H11 -1 0.73668 -1.27597 0.81650 # * H12 -1 0.73668 -1.27597 -0.81650 # H21 -1 0.73668 1.27597 0.81650 # H22 -1 0.73668 1.27597 -0.81650 # H31 -1 -1.47336 0.00000 0.81650 # H32 -1 -1.47336 0.00000 -0.81650 # * 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 0.00923 0.00222 0.00000 0.00954 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.01384 0.00333 0.00000 0.01423 DUE TO THE ATOMS C2 C2 C1 C2 Bond lengths and bond angles after symmetrization C1 - C2 1.5337 C1 - C3 1.5337 C1 - H11 1.0061 C1 - H12 1.0061 C2 - C1 - C3 60.000 C2 - C1 - H11 120.400 C2 - C1 - H12 120.400 C3 - C1 - H11 120.400 C3 - C1 - H12 120.400 H11 - C1 - H12 108.491 Schoenflies symbol = D3h CSM = 0.0109 Molecular RMS = 0.0104 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 = 0.01 MAX. DIFF. (Angstrom)=0.0079 TYPE S3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 3 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0119 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 4 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0079 TYPE C3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 5 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 6 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0119 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 7 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0069 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 8 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0079 TYPE C3 -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)=0.0069 TYPE Cs -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 10 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0136 TYPE Cs -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 11 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0079 TYPE S3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 12 CSM = 0.01 MAX. DIFF. (Angstrom)=0.0136 TYPE C2 -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) [S3 ] -x+y,-x,-z 0.0062 0.0079 3) [Cs ] x-y,-y,z 0.0094 0.0119 4) [C3 ] -y,x-y,z 0.0062 0.0079 5) [Cs ] x,y,-z 0.0000 0.0000 6) [C2 ] x-y,-y,-z 0.0094 0.0119 7) [C2 ] -x,-x+y,-z 0.0047 0.0069 8) [C3 ] -x+y,-x,z 0.0062 0.0079 9) [Cs ] -x,-x+y,z 0.0047 0.0069 10) [Cs ] y,x,z 0.0093 0.0136 11) [S3 ] -y,x-y,-z 0.0062 0.0079 12) [C2 ] y,x,-z 0.0093 0.0136 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C1 0.00000 -0.88547 0.00000 C2 0.88547 0.88547 0.00000 C3 -0.88547 0.00000 0.00000 H11 0.00000 -1.47336 0.81650 H12 0.00000 -1.47336 -0.81650 H21 1.47336 1.47336 0.81650 H22 1.47336 1.47336 -0.81650 H31 -1.47336 0.00000 0.81650 H32 -1.47336 0.00000 -0.81650