============ 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 0.100 CELL 15.61340 15.61340 35.20610 90.000 90.000 120.000 7432.64725 ATOM GROUP INPUT COORDINATES AND THEIR S.U. C8 1 0.57676 0.33333 0.08333 0.00000 0.00000 0.00000 C9 1 0.57751 0.24417 0.08333 0.00000 0.00000 0.00000 C82 1 0.66667 0.24342 0.08333 0.00000 0.00000 0.00000 C92 1 0.75583 0.33330 0.08333 0.00000 0.00000 0.00000 C83 1 0.75658 0.42324 0.08333 0.00000 0.00000 0.00000 C93 1 0.66670 0.42249 0.08333 0.00000 0.00000 0.00000 C4 1 0.48169 0.33333 0.08333 0.00000 0.00000 0.00000 C42 1 0.66667 0.14835 0.08333 0.00000 0.00000 0.00000 C43 1 0.85165 0.51831 0.08333 0.00000 0.00000 0.00000 C3 1 0.40548 0.27194 0.10828 0.00000 0.00000 0.00000 C36 1 0.46690 0.39473 0.05839 0.00000 0.00000 0.00000 C32 1 0.72806 0.13350 0.10828 0.00000 0.00000 0.00000 C34 1 0.60527 0.07215 0.05839 0.00000 0.00000 0.00000 C33 1 0.86650 0.59452 0.10828 0.00000 0.00000 0.00000 C35 1 0.92785 0.53310 0.05839 0.00000 0.00000 0.00000 SYMMETRIZATION OF GROUP NR. 1 PRINCIPAL INERTIA MOMENTS and DEGENERATION DEGREE 1424.41 767.78 767.78 2 ORTHOGONALIZATION MATRIX -7.807882 -7.805518 0.000000 13.520919 -13.522283 0.000306 -0.000117 0.000117 35.206100 ATOM ORTHOGONAL COORDINATES VECTORS TO MAKE SYMMETRICAL THE GROUP C8 0.70201 -1.21579 -0.00006 -0.00011 0.00006 0.00006 C9 1.39209 0.00000 -0.00007 0.00000 0.00000 0.00007 C82 0.70179 1.21566 -0.00008 0.00011 0.00006 0.00008 C92 -0.69592 1.20580 -0.00008 -0.00013 -0.00022 0.00008 C83 -1.40380 -0.00025 -0.00007 0.00000 0.00025 0.00007 C93 -0.69617 -1.20537 -0.00006 0.00013 -0.00022 0.00006 C4 1.44430 -2.50123 -0.00005 -0.00022 0.00000 0.00005 C42 1.44386 2.50123 -0.00009 0.00022 0.00000 0.00009 C43 -2.88817 -0.00038 -0.00007 0.00000 0.00038 0.00007 C3 2.51852 -2.70151 0.87835 -0.00024 -0.00006 -0.00013 C36 1.08052 -3.53148 -0.87808 -0.00004 -0.00021 -0.00014 C32 1.08045 3.53209 0.87829 0.00004 -0.00040 -0.00007 C34 2.51805 2.70143 -0.87813 0.00024 0.00014 -0.00008 C33 -3.59897 -0.83012 0.87833 0.00020 0.00000 -0.00011 C35 -3.59857 0.82991 -0.87812 -0.00020 0.00020 -0.00010 SYMMETRIZED ORTHOGONAL COORDINATES ATOMIC R.M.S. C8 1 0.70190 -1.21573 0.00000 0.00014 0.00011 0.00007 * C9 1 1.39209 0.00000 0.00000 0.00010 0.00018 0.00007 * C82 1 0.70190 1.21573 0.00000 0.00014 0.00011 0.00007 C92 1 -0.69605 1.20559 0.00000 0.00016 0.00013 0.00007 C83 1 -1.40380 0.00000 0.00000 0.00009 0.00015 0.00007 C93 1 -0.69605 -1.20559 0.00000 0.00016 0.00013 0.00007 C4 1 1.44408 -2.50123 0.00000 0.00024 0.00015 0.00007 * C42 1 1.44408 2.50123 0.00000 0.00024 0.00015 0.00007 C43 1 -2.88817 0.00000 0.00000 0.00009 0.00027 0.00007 C3 1 2.51829 -2.70157 0.87822 0.00025 0.00012 0.00011 * C36 1 1.08049 -3.53168 -0.87822 0.00009 0.00026 0.00011 C32 1 1.08049 3.53168 0.87822 0.00009 0.00026 0.00011 C34 1 2.51829 2.70157 -0.87822 0.00025 0.00012 0.00011 C33 1 -3.59877 -0.83011 0.87822 0.00022 0.00018 0.00011 C35 1 -3.59877 0.83011 -0.87822 0.00022 0.00018 0.00011 * Atom defining the asymmetric unit for the found symmetry group. AVERAGE DIFFERENCE ON X,Y,Z,D 0.00012 0.00015 0.00008 0.00025 MAXIMUM DIFFERENCE ON X,Y,Z,D 0.00024 0.00040 0.00014 0.00041 DUE TO THE ATOMS C34 C32 C36 C32 Bond lengths and bond angles after symmetrization C8 -C9 1.3980 C8 -C93 1.3980 C8 -C4 1.4844 C9 -C8 1.3980 C9 -C82 1.3980 C4 -C8 1.4844 C4 -C3 1.4019 C4 -C36 1.4019 C3 -C4 1.4019 C9 -C8 -C93 119.169 C9 -C8 -C4 120.416 C93 -C8 -C4 120.416 C8 -C9 -C82 120.831 C8 -C4 -C3 120.457 C8 -C4 -C36 120.457 C3 -C4 -C36 119.086 SYMMETRIZED FRACTIONAL COORDINATES C8 1 0.57677 0.33333 0.08333 0.00000 0.00000 0.00000 C9 1 0.57751 0.24417 0.08333 0.00000 0.00000 0.00000 C82 1 0.66667 0.24341 0.08333 0.00000 0.00000 0.00000 C92 1 0.75583 0.33332 0.08333 0.00000 0.00000 0.00000 C83 1 0.75659 0.42323 0.08333 0.00000 0.00000 0.00000 C93 1 0.66668 0.42249 0.08333 0.00000 0.00000 0.00000 C4 1 0.48170 0.33334 0.08333 0.00000 0.00000 0.00000 C42 1 0.66666 0.14834 0.08333 0.00000 0.00000 0.00000 C43 1 0.85166 0.51830 0.08333 0.00000 0.00000 0.00000 C3 1 0.40549 0.27196 0.10828 0.00000 0.00000 0.00000 C36 1 0.46689 0.39474 0.05839 0.00000 0.00000 0.00000 C32 1 0.72804 0.13351 0.10828 0.00000 0.00000 0.00000 C34 1 0.60526 0.07213 0.05839 0.00000 0.00000 0.00000 C33 1 0.86649 0.59451 0.10828 0.00000 0.00000 0.00000 C35 1 0.92787 0.53311 0.05839 0.00000 0.00000 0.00000 Schoenflies symbol = D3 CSM = 0.0000 Molecular RMS = 0.0003 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)=0.0002 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)=0.0004 TYPE C2 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)=0.0002 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)=0.0003 TYPE C2 -0.5000000000 0.8660254038 0.0000000000 0.8660254038 0.5000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 6 CSM = 0.00 MAX. DIFF. (Angstrom)=0.0004 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) [C3 ] -y,x-y,z 0.0000 0.0002 3) [C2 ] x-y,-y,-z 0.0000 0.0004 4) [C3 ] -x+y,-x,z 0.0000 0.0002 5) [C2 ] y,x,-z 0.0000 0.0003 6) [C2 ] -x,-x+y,-z 0.0000 0.0004 OBLIQUE COORDINATES (HEXAGONAL SYSTEM) C8 0.00000 -1.40380 0.00000 C9 1.39209 0.00000 0.00000 C82 1.40380 1.40380 0.00000 C92 0.00000 1.39209 0.00000 C83 -1.40380 0.00000 0.00000 C93 -1.39209 -1.39209 0.00000 C4 0.00000 -2.88817 0.00000 C42 2.88817 2.88817 0.00000 C43 -2.88817 0.00000 0.00000 C3 0.95853 -3.11951 0.87822 C36 -0.95853 -4.07804 -0.87822 C32 3.11951 4.07804 0.87822 C34 4.07804 3.11951 -0.87822 C33 -4.07804 -0.95853 0.87822 C35 -3.11951 0.95853 -0.87822