H. J. G. Hayman The Hebrew University Jerusalem, Israel
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Stereoscopic Diagrams Prepared by a Desk Calculator and Plotter
be eminently suitable for this purpose; in particular, with appropriate programming, the three-line display proved invaluable both when entering data and when running the drawing programs. The partirular calculator used had 111 storage registers (the maximum available); 30 of these were needed for carrying out the calculations, leaving 81 registers for storing molecular data. Registers 11-91 were reserved for this purpose and since each such register sufficed for storing the data for a sinale atom (three Cartesian coordinates together with an a&ropriate'radius), the calculator could be used for drawina stereosconic diagrams of molecules havine up to 81 displayeh atoms, these atoms being numbered serial6 from 11 onwards. As explained later, different programs were used for different purposes such as entering data, drawing bond-lines and so on. The programs were recorded on magnetic cards and loaded into the calculator as required. These programs were specifically tailored for the calculator used (Model 10 with 500 Presented at the 25th IUPAC Congress, Jerusalem, July 1975. program steps) and will be referred to collectively as HUSTEP (Hebrew University Stereoscopic Programs). The standard programs give the perspective required when using a stereoscope having a viewing distance of 12.5 crn hut can easily he adapted to give perspectives suitable for other viewing conditions such as those encountered in stereoscopic projection. In the standard programs, the difference between the two perspective drawings of the stereopair corresponds to a rotation of 6" of the three-dimensional model depicted. This method DECRLIN LC157 D E C A L I N LC151 of obtaining the difference between the two diagrams is Figure 1. HUSTEP drawing of cisdecalin. The coordinates were evaluated assuming tetrahedral valence angles correct provided the line of throughout. (Drawing time 1 1 min.) sight of each eye is perpendicular to the paper; this will usually be the case since the two diagrams are customarily drawn with their centers separated by the average interocular distance. It has recently been painted out ( 3 , 4 )that if the two perspective diagrams are mounted with their centers separated by a distance less than the interocular distance so as to obtain the correct convergence angle, the two diagrams should he obtained hy applying a translation rather than a rotation to the threedimensional model; in practice C Y C L O H E X R N E CTWIST-BORT3 C Y C L O H E X R N E CTWIST-BURT3 however this refinement has Figure 2. HUSTEP drawing of the twist-boat form of cyclahexane. The coordinates were evaluated assuming tetbeen found to make little difrahedral valence angles and the dihedral angles given by Hendrickson (10). (Drawing time 9 min.) ference. In the author's opinStereoscopic diagrams for illustrating molecular structure are usually produced with the help of a large computer using a program such as ORTEP ( I ) , though recently Curtin ( 2 ) has shown that bond-line stereoscopic diagrams can be drawn by a programmable desk calculator and plotter; the main emphasis in Curtin's paper is however on crystal structure and symmetry operations rather than on molecular structure. We describe here the use of a Hewlett-Packard Model 9810A oroerammable desk calculator (commonlv referred to as " ~ o d e l 1 0 " )with plotter for drawing "halland line" stereoairs (Figs. 1 and 2) as well as three-dimensional structural &rmulas(~igs.3 and 4), the latter being particularly suitable for teaching stereochemical principles and molecular structure. Although the Model 10 calculator was originally chosen merely because it happened to he available, it turned out to
Volume 54, Number 1, Januarv 1977 / 31
ion, the advantages of this method are usually outweighed by the somewhat smaller size of the perspective diagrams used. The standard programs can he modified to give rotations of 4", 2 O , or lo. Whereas a rotation of 6" is appropriate for direct observation with or without a stereoscope, it leads to greatly exaggerated depth perception if used for stereoscopic projection, except for an TRRNS-IX, p-DICYRNOSTILBENE TRRNS-IX, p-DICYRNU5TILBENE observer situated extremely Figure 3. HUSTEP drawing of bans-n.@dicyanostilbene. me ~rystellographicdata used were those of Wailwork close to the screen. Stereopairs (11).(Drawingtime 6 min.) corresponding to an angular rotation of 2 O have been found highly satisfactory for projection in a seminar room or small lecture hall; stereopairs corresponding to an angular rotation of only lo have also been used and would possibly be a more appropriate choice for a larger lecture hall. The drawing programs were designed for semiautomatic operation as illustrated by the following examples. The standard bond-line program is operated by entering the serial numbers of two atoms in turn !X-METHYL-D-GRLACTUSIDE X-METHYL-D-GRLRCTOSIDE into the calculator. If the first 6-EROMUHYDRIN 6-EROMOHYDRIN of these is (say) 16 and the second 20, the calculator will Figure 4. HUSTEP drawing of a-melhyl-D-galactosideE-bromohydrin. The crystallographic data used were those of Robertson and Sheldrick ( 12).(Drawing time 8 m i n ) draw a sequence of four hondlines. 16-11. 17-18. 18-19. and 19-20. On ihe otlier hadd, if the first serial number is 20 lographic coordinates x , y, and z, together with the feeding and the second is 16, on1y.a single bond-line, 20.16, will he program corresponding to the particular crystal system condrawn. The standard sphere program is operated in a similar cerned. In this case the parameters defining the size and shape manner: if the first serial number is 16 and the second 20. the of the unit cell are entered first, followed by the crystallocalculat'or will draw five spheres corresponding to atom; 16, graphic coordinates of each atom in turn. The calculator stores 17.. 18.. 19.. and 20. The hidden-line orohlem is solved hv using these data in the form of Cartesian coordinates, rounded to special programs and entering the serial numbers of all atoms the nearest 0.01 A. In symmetrical molecules the crystallo(uv to a maximum of six a t anv one time), susoected of obgraphic coordinates are usually not listed for all atoms; the sc&ing part of the particular bond-line or sphere to be drawn. missing atoms occupy positions equivalent to those whose The semiautomatic nature of the Droarams facilitates the coordinates are eiven. The vroarams can evaluate and store production of three-dimensional s t r u c t u d formulas since the the coordinates of a set of sich atoms in positions equivalent component parts of such formulas can he drawn in turn in to those whose coordinates are already stored, hut the calcutheir appropriate places as desired. lator must he instructed which particular set of equivalent positions is required. Figures 3 and 5 were prepared in this Entering.Molecular Data way. A third method which is sometimes useful is to build up the 'I'hr I'lrst itage in using HIJSTEI' is to feed the molecular molecule atom by atom by entering the appropriate data into dntn m;rnually mtaj the cnlt:ulator. 'Phis can he done in thwe the calculator; in general, for each atom, the data required diffw6mt woya hut i n all r n s c i a printout of rhe data entertd consist of the serial number of an earlier atom to which the is otrtai~wdand a sinll,lt, r eavailat~lefur intrwiucin~ . -p r o ~ e d ~ tI> . atom is bonded, the length of the corresponding bond, and a changes and corrections. valence angle and dihedral angle defining the direction of this If the Cartesian coordinates X, Y, and Z of each atom of the bond with respect to the rest of the molecule. The program molecule are known or easily evaluated, the simplest feeding used in this method stores the above data in the calculator and program can he used. In this program, the maximum and then evaluates and stores the Cartesian coordinates of each minimum values of X, Y, and Z are entered first, followed by atom, rounded to the nearest 0.01 A. This procedure was used the Cartesian coordinates and an appropriate radius for each for preparing Figure 2. In this and the previous method a atom in turn; this radius is usually chosen proportional to the further program is required for normalizing the Cartesian Van der Waals radius1of the atom concerned (15%of the Van der Waals radius when drawing ball and line diagrams and 20% when drawing three-dimensional structural formulas) though occasionallv. as in Fipure 4, a constant radius for all atoms is more satisfactory. his procedure was used for pre' The Van der Wads radii were taken from Pauling, L., "The Naparing Figures 1 and 4. tureofthe Chemical Rand," 3rd Ed, Cornell University Press, Ithaea, If the Cartesian coordinates X, Y , and Z of the atoms are N.Y., 1960, p. 260. The Van der Wads radius olthe carbon atom was not known, the usual procedure is to use the relative crystaltaken as 1.7 A. 32 / Journal of Chemical Education
After selecting a suitable orientation, the final detailed stereoscopic diagram can he drawn. Ball and line stereopairs can he drawn in which the spheres representing the atoms are drawn either in outline only or together with auxiliary lines for increased depth perception as shown in Figures 1and 2. Atoms can he labeled using a labeling program as shown in Figure 1; the label can he positioned in any one of eight positions arranged symmetrically round the sphere or in a ninth position inside the sphere which is then drawn in outline only. Figure 2 illustrates the use of the special hidden-line programs. As an alternative to ball and line stereopairs, three-dimensional structural formulas can he drawn. In such formulas, the symbols representing atoms are supposed to he situated well inside imaginary transparent spheres of appropriate radii on whose surfaces the various hond-lines terminate. Although no 2-RMlNO-3-METHYLBENZOIC RClD 2-RMlNO-3-METHYLEENZOIC RClD hidden-line problem arises in such Fioure 5. HUSTEP drawincl of the unit cell of 2-amino-3methylbenroic acid. The crystallographicdata used were formulas. it is hiehlv " .desirable to those of Brown and Marsh ( 13). (Drawing time 25 min.) choose a molecular orientation such that no two symbols overlap in either of the diagrams forming the stereopair. Figure 3 illustrates the use of programs for drawing double and triple bonds and for indicating the arocoordinates and for entering and storing the appropriate ramatic character of rings. Figure 4 illustrates the possibility of dius of each atom. using ordinary formulas for groups (e.g. CHd as part of a Drawing Procedure three-dimensional structural formula. Prior to drawing the final detailed stereoscopic diagram a HUSTEP can also he used for showing the distribution of suitahle orientation must he found for the molecule; this is molecules in the crystallographic unit cell; this is illustrated usually done by trial and error using apreliminary program by Figure 5 which also shows the use of broken lines to repdesigned for the rapid drawing of perspective hond-line diresent hydrogen bonds and of arrows to indicate the directions agrams, i.e. of stereoscopic diagrams consisting entirely of of the x and z axes of the unit cell. Since, in general, the unit hond-lines drawn from atom center to atom center. Such dicell contains several molecules, the restriction to 81 atoms agrams are often sufficient for selecting a suitahle orientation presents a serious limitation to this use of the programs. (The hut if necessary the ahove preliminary program can he used programs can in fact he used for drawing molecules or unit also for drawing atoms in the form of disks and hence for incells of any size by dividing the atoms into sets of rather less dicating which atoms (if any) will be responsible for hidden than 81 atoms each and storing the data corresponding to each lines in a hall and line diagram. The number of such hidden set on a series of magnetic cards; however, the necessity to use lines should be kept to a minimum since they detract from the these cards for changing the data in the calculator a t frequent general appearance of the final stereoscopic diagram. A change intervals renders the method so laborious and time-consuming of orientation corresponding to rotations 81,82, and 8s about that i t is not recommended for general use.) thex and v axes of the nlot& and about the t (oeroendicular) The final diagrams are usually drawn first for direct steaxis, respectively, is obtained using the preliminary program reoscopic observation using a 12.5 X 12.5-cm plotting area. by entering 8,, 02 and 01 in turn into the calculator; this reLarger diagrams suitahle for photographic reduction for reorientation of the molecule can he repeated as often as desired production purposes can he drawn by using a larger plotting without loss of accuracy. area (up to a maximum of 25 X 25 cm). Still larger diagrams The preliminary program is used with a 12.5 X 12.5-cm (up to three times the usual size for direct stereoscopic oholottine" area corresoondine to 6.25 cm between the centers servation) can he drawn using a minor modification of the 'of the left- and right-hand diagrams of the stereopair which drawing programs; in this case, the left- and right-hand dican therefore he seen stereoscopically a t all stages of its proagrams must he drawn separately hut this can be done on the duction. The time required for drawing such a stereopair is same sheet of paper with the two diagrams in their correct on the average 8 s per bond line and a further 6 s for each atom relative positions. shown as a disk. After deciding on a suitahle molecular oriStereoscopic Projection entation, the scale of the stereopair can often he increased hy This is best accomplished by projecting images of the two changing the scaling paramete; stored in the calculator so as members of a stereopair onto a metallized screen using two to make maximum use of the drawing area available. beams of light, polarized in directions which are mutually The search for a suitahle molecular orientation can someperpendicular. The stereopair is observed through appropriate times he shortened by using one or other of two automatic polarizing glasses such that each eye sees only one of the two orienting and scaling programs. The first of these orients the images on the screen. Apart from the use of a special double molecule so that the bisector of any desired valence angle slide projector, two matched projectors can he used, mounted points vertically upwards; the second orients the molecule in side by side (5)or one ahove the other (6); other projection accordance with its principal axes of rotation (assuming all methods include a prism attachment for an ordinary slide atoms to have e q u a l ~ a s s ) s othat it has essentially its maxiprojector (7) and an anaglyph technique for use with an mum width and minimum depth.
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overhead projector (8). We have recentlv modified an ordinaw overhead oroiedor . . hy equipping it with n double head for stereoscopic projection and helleve that this method of projection has certain advantiryes over those usually used. The standard head of this projector con.;ists of H fixed horizontal lens together with an ~nrlinahleupper part made up o f a mirror and a serond (vertical1 Irni, the effective focal length of the lens systrm heing 14 in. The unuer nnrt ~ rthGdm~ble f head nmsistr ofthe uouer parts of twd ;tankard heads bolted together with a common horizontal axis so that the two mirrors are in the same plane, the distance between the centers of the two (vertical) lenses h e ~ n g11.3 cm. Polaroid filters were fitted in front of these lenses, the planes of polarization heing f45' to the vertical (9).The lower part of the double head contains the two horizontal lenses arranged so that the distance between their centers can he chaneed continuouslv from 10.0-13.3 cm: this adjustment serves for adjusting the position of the stereoscopic image with respect to the screen. The ordinary Fresnel lens was replaced by a douhle-centered Fresnel lens (obtained by cutting down two standard Fresnel lenses), the distance between the two centers heing 3.8 cm. This douhle-centered Fresnel lens serves to concentrate the light from the left- and right-hand sides of the projector stage onto the corresponding horizontal lens of the double head. The transparencies consist of stereopairs in which the distance between the centers of the two drawings is 12.5 cm; since the heightsof the transparencies are always appreciably smaller than their width (25 em), a mask was placed on the projector stage to eliminate unnecessarv light. The movahle horizontal lenses of the double head enahTed-the projector to function satisfactorily for screens situated between 2 and 6m from the nroiector. . . corresnondine to stereoscopic images having widths between 60 and 200 cm. The advantages of this method of stereoprojection are threefold 1) The transparencies can be drawn directly by the computer plotter using a 25 X 2 k m plotting area. For this purpose the usual plotter Den is reolaced bv a standard oen for transnaren~ies.~ cut down I . . r, 1.1 h n l h cff >3,.tu t o l u ~ c ritsrtnlrr 8 t maiit, snu held
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