Cubane - A Detailed Example

The standard example for illustrating the use of ORTEP is the novel compound cubane (C8H8), whose carbon-carbon bonds lie along the edges of a cube within experimental error. The structure was published in 1964 by E. B. Fleischer (Journal of the American Chemical Society, Vol. 86, p.3889). The compound crystallizes with the trigonal symmetry of space group R. The axis lies along a body diagonal of the molecule, and as a result the compound contains only four unique atoms. These are one carbon and its attached hydrogen in general positions off the axis (C1 and H1) and one carbon and its hydrogen in special positions on the axis (C2 and H2). Anisotropic temperature factor coefficients were fitted to the carbon atoms during the least-squares refinement of the structure, and isotropic temperature factors were used for the hydrogen atoms. The anisotropic temperature factors given for the carbon atoms are of the type called 0 in ORTEP.

To draw the structure the following information is needed:

The first line of input is a job title.
 CUBANE  E.B.FLEISCHER   1964  J.A.C.S.  86, 3889

Cell parameters are provided on the second line. The "1" in the first column signals the format of the symmetry information that follows.
1    5.34     5.34     5.34    72.26    72.26    72.26

The symmetry operators of the space group begin on line 3 of the input. The last of these has a "1" in column 1.
  x, y, z
  z, x, y
  y, z, x
  -x, -y, -z
  -z, -x, -y
1 -y, -z, -x

Two lines provide the atomic parameters for each atom. The first gives the atom's positional parameters, and the second provides its thermal parameters. The last atom has a "1" in column 1 of its thermal parameter card. Atoms are referenced in the instructions by their numeric position within this list.

Atoms 1 and 2 are entered with positional parameter type 0 and anisotropic temperature factor type 0.

  C1                         -.18711   .19519   .10706        0
0  .04100   .04250   .04500  -.00420  -.01420  -.00510        0
  C2                          .11546   .11546   .11546        0
0  .04680   .04680   .04680  -.01430  -.01430  -.01430        0
Atoms 3 and 4 are entered with positional parameter type 0 and with dummy sphere temperature factors (type 7) with a radius of 0.1 Å before scaling.
  H1                         -.32460   .34680   .18480        0
0     .10                                                     7
  H2                          .21000   .21000   .21000        0
0     .10                                                     7
A dummy atom (atom 5) at the cell origin is also included with a blank card dummy sphere. This could also be entered with type 7 as were atoms 3 and 4.
 ORGN                              0        0        0        0
1                                                             0

The 100 instructions are neither associated with nor required for producing an illustration. They are shown here to demonstrate how they are used.

A 101 instruction is used to obtain a tabulation of the atoms surrounding one atom or a series of several designated atoms. For example, to obtain a list of all atoms (hydrogen and carbon atoms) out to a distance of 3.61 Å about the two carbons C1 and C2, the following 101 instruction would be used.

      101   155501        2        1        4     3.61
           |_______________|      |__________|   |____|
                  (a)                  (b)         (c)
where the parts designate:

A 102 instruction gives both interatomic distances and interatomic angles. The following instruction could be used to find all covalent bonds and bond angles about the two carbons.

      102   155501        2        1        4      1.8
In this case a smaller Dmax was used so that only the distances and angles of immediate interest would be computed since there are n(n - 1)/2 angles for n interatomic vectors about an atom.
Plotting is initialized with a 201 instruction.

The two plot boundary dimensions can be equal for the present illustration since the cubane molecule is a cube. A 5 5 inch boundary is specified with a 0.5 inch margin to give a 4 4 inch square working area. A 15 inch view distance might be reasonable to use in viewing a model of this size. These are set with the 301 instruction.
      301      5.0      5.0      15.      0.5

The subject of the illustration is a single complete cubane molecule. Since all the atoms of the molecule were not provided in the input atoms list, the "missing" atoms may be found by using the 402 instruction to specify a sphere of enclosure, centered on the dummy atom 5, which is at the center of a cubane molecule. A radius of 3.2 Å should be adequate to find all the atoms and isolate a single molecule.
      402   555501        5        1        4      3.2
	   |_______________|      |__________|    |___|				
                  (a)                  (b)         (c)
where the parts designate:

The 501 instruction is used to establish a coordinate system in order to orient the molecule. In this case, the coordinate system is defined along the edges of the cubane cube. The origin will be positioned on the dummy atom 5. The desired coordinate system orientation will be defined by specifying two vectors from the special position atom 255501 to the two symmetry-related general-position atoms 155501 and 155502.
      501   555501   255501   155501   255501   155502        0        0

The 502 instruction is used to rotate the molecule relative to the established coordinate system to optimize the appearance of the illustration. A rotation of 25o about the y axis (axis 2) followed by a rotation of 28o about the x axis (axis 1) will produce a satisfactory view of the molecule.
      502        2      25.        1      28.

To position and scale the subject for projection onto the "drawing board" and to utilize all available space, a 604 instruction is used, which will automatically set X0, Y0, and SCALl. However, the ellipsoid scale factor ratio SCAL2 must be specified independently. A value of -50 will provide thermal ellipsoids corresponding to 50% probability as ORTEP sets the value of SCAL2 to 1.54. (If the value supplied is positive, ORTEP interprets the value as SCAL2. If the value is negative, ORTEP interprets the value as a probability and sets the appropriate value of SCAL2 automatically.)
      604                                 -50

The stereoscopic rotation for the left eye can be done at this point with the 503 instruction. A rotation of 2.7o about the y axis (axis 2) is used for the left-eye view. Later in the program, a -2.7o rotation about the same axis will be made for the right-eye view to give a total interocular angle of 5.4o.
      503        2      2.7

Since the structure will be drawn twice, once for each eye, the save sequence feature can be used to shorten the program. Note that the instructions between the start (1101) and end (1102) instructions are both executed and saved the first time through. They can then be re-executed as many times as desired by using the "execute save sequence" instruction 1103.

The 1101 instruction starts the save sequence.


The 1001 instruction (or 511) stores the information needed for the overlap hidden-line correction (i.e., as a projected boundary ellipse for each atom and a quadrangle approximation for each bond). The bonds are specified with a Format No. 2 trailer card identical to that used in the 812 instruction described below.
  2  1001        
           1  4  1  4  4   0.9   1.6   .04

The ATOMS array currently contains all the atom designators for one cubane molecule. The molecule is drawn in two separate steps so that the hydrogen and carbon atoms can be given different graphical representations. To draw the carbon atoms (ANR = 1,2), a standard model produced with the new 706/716 instruction is used. [This model is the same as that produced with a 705/715 instruction that (a) draws the three principal-plane forward traces and the boundary-plane trace (NPLANE = 4), (b) omits the reverse sides of the principal planes (NDOT = 0), (c) draws the forward principal axes without additional shading (NLINE = 1), and (d) omits the reverse principal axes (NDASH = 0).] In addition, chemical symbols are drawn with letters 0.12 in. high (before projection) and displaced from the atomic center by 0.3 in. horizontally and 0.4 in. vertically.
  1   716                                          .12      .30      .40
                                   1        2
The 716 instruction is used, rather than 706, to shorten the output listing of the example. A 706 instruction would provide a listing of all coordinates.

The hydrogen atoms (ANR = 3, 4) are to be drawn with a different standard model (instruction 702/712) than the carbon atoms. Chemical symbols are 0.12 in. high and offset 0.25 in. horizontally and vertically.

  1   712                                          .12      .25      .25
                                   3        4

The most convenient procedure for drawing bonds is to use the implicit bond instruction 812. All other information can be entered with a single Format No. 2 trailer card.
  2   812
           1  4  1  4  4   0.9   1.6   .04
          |____||____||_| |_________| |___|
            (a)   (b) (c)     (d)      (e)
where the parts designate:

The remaining fields on the card can be blank, since a complete set of bond distance labels is not desired.

The last feature of the illustration is the labeling with 900 instructions. Because of the symmetry, there are only two different C-C bond lengths in cubane. These are C1-C1 and C1-C2. One example of each of these bonds will be labeled. For variety, one will be labeled with a normal bond-length label and the other with a perspective label. The two bonds that can be labeled most advantageously are 155504-155503 and 255504-155505. The labels will be 0.12 in. high and displaced vertically from the bond center by -0.4 in.
      906   155504   155503                        .12        0      -.4
      916   255504   155505                        .12        0      -.4
Finally, a caption for the illustration is drawn. This can conveniently be positioned by "hanging" it from the dummy atom 555501 and "bouncing" it 3 in. from the left x boundary and 0.5 in. from the lower y boundary. The caption is 0.2 in. high.
  3   902   555501               3.0      0.5      .20        0        0

The save sequence is now terminated.

The plotting origin is then shifted 4 in. along x with a 202 instruction in preparation for the right-eye view.
      202      4.0

The stereo rotation of -2.7o about axis 2 is now performed for the right-eye view with a 503 instruction. (Note that this rotation starts with the reference orientation, not the previous working orientation.)
      503        2     -2.7

The save sequence can now be repeated for the right eye. (Note that the ATOMS array now contains the same information that it did when the first view was drawn.)

Plotting is terminated with a 202 instruction with no parameters.

Finally, a -1 instruction terminates the program.


Page last revised: Wednesday, 24-Jun-1998 12:52:19 EDT