============ 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= 0.300 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. C1 1 0.00000 -1.61294 0.00000 0.00000 0.00000 0.00000 C2 1 -1.20003 -0.90199 0.00000 0.00000 0.00000 0.00000 C3 1 -1.18751 0.48167 0.00000 0.00000 0.00000 0.00000 C4 1 0.00000 1.17367 0.00000 0.00000 0.00000 0.00000 C5 1 1.18751 0.48167 0.00000 0.00000 0.00000 0.00000 C6 1 1.20003 -0.90199 0.00000 0.00000 0.00000 0.00000 H1 1 0.00000 -2.45000 0.00000 0.00000 0.00000 0.00000 H2 1 -2.02929 -1.37546 0.00000 0.00000 0.00000 0.00000 H3 1 -2.00875 0.95868 0.00000 0.00000 0.00000 0.00000 H4 1 2.00875 0.95800 0.00000 0.00000 0.00000 0.00000 H5 1 2.02929 -1.37500 0.00000 0.00000 0.00000 0.00000 H6 1 0.00000 2.11300 0.00000 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 170.52 85.62 84.90 2 ORTHOGONALIZATION MATRIX -0.512323 -0.858793 0.000000 0.858793 -0.512323 0.000000 0.000000 0.000000 1.000000 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C1 1.20319 0.71778 0.00000 -0.00438 -0.02564 0.00000 C2 1.20744 -0.67703 0.00000 -0.00862 -0.01510 0.00000 C3 0.01275 -1.37516 0.00000 -0.01275 -0.00911 0.00000 C4 -1.18993 -0.70987 0.00000 -0.00889 0.01773 0.00000 C5 -1.20403 0.66449 0.00000 0.00521 0.02765 0.00000 C6 -0.02217 1.38412 0.00000 0.02217 0.00015 0.00000 H1 1.92206 1.14663 0.00000 0.08290 0.01093 0.00000 H2 2.03890 -1.14663 0.00000 -0.03395 -0.01093 0.00000 H3 0.02384 -2.32482 0.00000 -0.02384 0.00970 0.00000 H4 -2.03384 1.12573 0.00000 0.02889 0.03183 0.00000 H5 -0.04080 2.33862 0.00000 0.04080 -0.02350 0.00000 H6 -1.99662 -1.19111 0.00000 -0.00834 0.03355 0.00000 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C1 1 1.19882 0.69214 0.00000 0.01258 0.01804 0.00000 * C2 1 1.19882 -0.69214 0.00000 0.01258 0.01804 0.00000 C3 1 0.00000 -1.38427 0.00000 0.02022 0.00863 0.00000 C4 1 -1.19882 -0.69214 0.00000 0.01258 0.01804 0.00000 C5 1 -1.19882 0.69214 0.00000 0.01258 0.01804 0.00000 C6 1 0.00000 1.38427 0.00000 0.02022 0.00863 0.00000 H1 1 2.00495 1.15756 0.00000 0.03471 0.03405 0.00000 * H2 1 2.00495 -1.15756 0.00000 0.03471 0.03405 0.00000 H3 1 0.00000 -2.31512 0.00000 0.03372 0.03503 0.00000 H4 1 -2.00495 1.15756 0.00000 0.03471 0.03405 0.00000 H5 1 0.00000 2.31512 0.00000 0.03372 0.03503 0.00000 H6 1 -2.00495 -1.15756 0.00000 0.03471 0.03405 0.00000 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.02339 0.01799 0.00000 0.03324 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.08290 0.03355 0.00000 0.08362 DUE TO THE ATOMS H1 H6 H1 H1 Bond lengths and bond angles after symmetrization C1 -C2 1.3843 C1 -C6 1.3843 C1 -H1 0.9308 H1 -C1 0.9308 C2 -C1 -C6 120.000 C2 -C1 -H1 120.000 C6 -C1 -H1 120.000 Schoenflies symbol = D6h CSM = 0.1424 Molecular RMS = 0.0377 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 = 0.07 MAX. DIFF. (Angstrom)=0.0770 TYPE C6 0.5000000000 -0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 3 CSM = 0.04 MAX. DIFF. (Angstrom)=0.0434 TYPE C2 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 4 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0571 TYPE Cs -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 5 CSM = 0.12 MAX. DIFF. (Angstrom)=0.0586 TYPE Cs 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 6 CSM = 0.05 MAX. DIFF. (Angstrom)=0.0578 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 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 8 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0571 TYPE C2 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 9 CSM = 0.12 MAX. DIFF. (Angstrom)=0.0586 TYPE C2 1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 10 CSM = 0.04 MAX. DIFF. (Angstrom)=0.0434 TYPE Ci -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 11 CSM = 0.05 MAX. DIFF. (Angstrom)=0.0578 TYPE C3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 12 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0545 TYPE Cs -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 13 CSM = 0.07 MAX. DIFF. (Angstrom)=0.0336 TYPE Cs 0.5000000000 0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 14 CSM = 0.07 MAX. DIFF. (Angstrom)=0.0770 TYPE S6 0.5000000000 -0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 15 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0545 TYPE C2 -0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 16 CSM = 0.07 MAX. DIFF. (Angstrom)=0.0336 TYPE C2 0.5000000000 0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 17 CSM = 0.05 MAX. DIFF. (Angstrom)=0.0578 TYPE S3 -0.5000000000 0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 18 CSM = 0.07 MAX. DIFF. (Angstrom)=0.0770 TYPE C6 0.5000000000 0.8660254038 0.0000000000 -0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 19 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0518 TYPE Cs 0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 20 CSM = 0.12 MAX. DIFF. (Angstrom)=0.0624 TYPE Cs -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 21 CSM = 0.05 MAX. DIFF. (Angstrom)=0.0578 TYPE S3 -0.5000000000 -0.8660254038 0.0000000000 0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 22 CSM = 0.11 MAX. DIFF. (Angstrom)=0.0518 TYPE C2 0.5000000000 -0.8660254038 0.0000000000 -0.8660254038 -0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 23 CSM = 0.12 MAX. DIFF. (Angstrom)=0.0624 TYPE C2 -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 24 CSM = 0.07 MAX. DIFF. (Angstrom)=0.0770 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) [C6 ] x-y,x,z 0.0682 0.0770 3) [C2 ] -x,-y,z 0.0377 0.0434 4) [Cs ] -x+y,y,z 0.1112 0.0571 5) [Cs ] x-y,-y,z 0.1205 0.0586 6) [C3 ] -y,x-y,z 0.0497 0.0578 7) [Cs ] x,y,-z 0.0000 0.0000 8) [C2 ] -x+y,y,-z 0.1112 0.0571 9) [C2 ] x-y,-y,-z 0.1205 0.0586 10) [Ci ] -x,-y,-z 0.0377 0.0434 11) [C3 ] -x+y,-x,z 0.0497 0.0578 12) [Cs ] -x,-x+y,z 0.1119 0.0545 13) [Cs ] x,x-y,z 0.0742 0.0336 14) [S6 ] x-y,x,-z 0.0682 0.0770 15) [C2 ] -x,-x+y,-z 0.1119 0.0545 16) [C2 ] x,x-y,-z 0.0742 0.0336 17) [S3 ] -x+y,-x,-z 0.0497 0.0578 18) [C6 ] y,-x+y,z 0.0682 0.0770 19) [Cs ] -y,-x,z 0.1116 0.0518 20) [Cs ] y,x,z 0.1202 0.0624 21) [S3 ] -y,x-y,-z 0.0497 0.0578 22) [C2 ] -y,-x,-z 0.1116 0.0518 23) [C2 ] y,x,-z 0.1202 0.0624 24) [S6 ] y,-x+y,-z 0.0682 0.0770 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C1 1.59842 0.79921 0.00000 C2 0.79921 -0.79921 0.00000 C3 -0.79921 -1.59842 0.00000 C4 -1.59842 -0.79921 0.00000 C5 -0.79921 0.79921 0.00000 C6 0.79921 1.59842 0.00000 H1 2.67327 1.33663 0.00000 H2 1.33663 -1.33663 0.00000 H3 -1.33663 -2.67327 0.00000 H4 -1.33663 1.33663 0.00000 H5 1.33663 2.67327 0.00000 H6 -2.67327 -1.33663 0.00000