symmetry is addressed next, followed by dihedral symmetry (Fig. 1). The program then moves on to molecular examples of point groups, u s i n g t h e molecules water, ammonia, t-1,2-dichloroethene, and benzene to illustrate the point groups CzDczmm,, C3" mm1. C z h (ZI~I, and D 6 h c a m ) . These modules also use a ghost image to demonstrate when the symmetry operations have been completed. Rotation axes and mirror planes fade in and out or slide through the system to depict their "imaginary" nature. From point groups, the modules continue w i t h r u l e s for t r a n s l a t i o n t h a t give rise t o plane groups. The five two-dimensional plane groups for biological systems are covered curr e n t l y i n t h e s e modules. A scalene triangle serves a s the asymmetric unit here, and the motif is some erouoine . -of triangles (15).
D2 Symmetry (222)
his system represents 0 2 ( 2 2 2 ) symmetry which 1s characterized by a 2-fold E X I S perpendicular to two 2-fold axes The axes i n this point group, shown here I n red, white, and blue, are mutually perpendicular A system with 02
symmety consists of four asymmetrlc unlts (illustrated here by a nahl hand)
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Response and Conclusions [,:: , .,. , Animation in the Macintosh "'; WTfWS ' . environment has Proven be an Figure 1. Dihedral Symmetry. The hand as asymmetric unit is indicated, followed by the principle and effective medium for illustrating 2-fold rotation axes. Rotation about each of the rotation axes is demonstrated. Ghost images of the spatial concepts. We have shown original positions of the asymmetric units are visible. the tutorial or selected modules to students a t various stages in sheets in chemical education have been described, but only their undergraduate curriculum. They have found the tua few involve direct collection of exoerimental data into a torial highly user-friendly and have been impressed by the spreadsheet (17-21). 3D color graphic display. All have appreciated the way it supplements the lecture experience and clarifies illustraDirect Communication tions in their notes and texts. Although the tutorial is directed orimarilv a t couce~tsi m ~ o r t a n to t understanding A powerful feature of modern spreadsheets that is often molecuiar strultures of biological interest and for crystal overlooked is their ability to communicate directly with exlattices. its modules can be viewed independently a s part ternal devices through the computer's communication of a n introductory chemistry course & more advanced ports using the file commands available in a spreadsheet's course in X-ray I t complements other macro programming language (22). A series of papers in . crystallopraphy. . teaching approaches, such a s l & r e s , model building, and this Journal described a number of such applications for the use of Escher drawings (16). the chemistrv laboratorv (19-21). In this reDort we deCurrently the tutorial is being expanded to include illusscribe two spreadsheet macro routines that complement this work. alloninr! direct contnd of n dirital DH mV meter trations of higher symmetry point groups (tetrahedral, octhrough serial iEterface. One program autbmates titratahedral, icosahedral), glide planes, points of inversion, screw axes, and selected three-dimensional space groups. tion data collection, while the other automates data acuuiAn archived copy of a current version of the program may sition for potentiometric analyses that require the prebaration of standard curves, such as ion-selective electrode be obtained by ftp. Please contact KAK (kantafullerton.edu) to obtain access information. analyses. The spreadsheet macros place the instrument's data directly into the appropriate spreadsheet cells. Because all instrument control and data acquisition are hanSpreadsheet-Controlled Potentiometric Analyses dled by the spreadsheet itself, there is no need to use programs in other languages to read data blocks into the Jerome Mullin and Michael Marquardt spreadsheet, a s in some previous work (23-25). The proUniversity of New England grams described here automate only the collection of the Biddeford, ME 04005 data and their placement in the worksheet, not the data reduction or plotting. Spreadsheet .roer rams runninz on microcom~utersoffer many advantages to scientists interested in a n easy, userTitration Program friendly way of exploiting the power of the microcomputer I n the titration program, the system is used to collect without the time commitment usually required for learning a programming language. A spreadsheet's capabilities pWmV data following the manual entry of buret readings a t each step of a titration as titrant is added from a buret are especially valuable for problems involving repetitive into the analyte solution. When the macro-containing calculations, graphics, large data sets, or those that inworksheet is loaded, a n autoexecuting routine displays a volve What-If queries. A number of applications of spread@
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menu with the choices Titrate. Save. End. and Help. Selecting Titrate s t a r t s the d a t a col'lecti&~routine and prompts the user to enter the initial volume reading of the buret. Once a volume is entered, the system reads the meter and ulaces the DH or potential datum in the cell adiacent to the volume-reading, moves the cursor to the next cell, and prompts for the next buret reading. At the end of the titration, signaled by entering 999 when prompted for a buret-reading entry, the menu reappears. Selecting Save automatically extracts the data to the user's floppy disk; the macro code is not saved on the data disk, thus keeping data file size to a minimum. Data files may be extracted in Lotus 1-2-3 or Quattro Pro format, a s specified by the user. Choosing Help presents brief information screens, which are also accessible during data collection by typing 911. Selecting End returns manual spreadsheet control, allowing the user to access all of the usual spreadsheet features for data reduction and graphing. The skills required to carry out a n accurate and precise wet chemical analvsis are still stressed. and students use the sprt~adnhectthemselves to carry out all data redurt i m and plotting, thus beromingproficicnt spreadsheet 11sers. Collection of Calibration-Curve Data
The macro routine for the collection of potentiometric calibration-curve data presents the menu choices Collect Data, Save, End, and Help. The user is prompted to enter the numbers of standards, samples, and replicates to be measured. A macro subroutine automatically prepares a random sampling sequence and instructs the user& insert the electrodes into the proper solution. Once the electrodes are inserted, the user preises Enter, the system pauses for 30 s to allow electrode equilibration, reads the potential, and enters it beside the solution description in the spreadsheet. After the last data point is collected the system reorders the samplelstandard list and presents the user with a menu similar to the one a t the heginning of the program. Essential error-checking routines are built into the data acauisition macros so that command echoes from the mete; will be rejected and not affect the data. A complex cleaning routine removes unwanted characters from the innut strines . . and ~ converts the strine..data from the instmment to numerical values w ~ t hthe appropriate numbers of sienificanl firmres. As a safcmx~rd.s c l e r t l n ~ T ~ t r a t eor Collect Data r e h s in a caution message warning that any existine data in the sureadsheet will be overwritten and gives the user the option of extracting the data into a separate file before continuing. We have chosen not to fully automate the analyses because we believe it to be more instructive for students to handle their own calculations and graphmg with the spreadsheet. The use of these uroerams makes the sureadsheet-controlled . appnrach UI irlsuument interfxinga simple and inexpensive means of introducinp automated data rollection into the Ink) in a manner that isreadily accessible to students. The programs have been used successfully in quantitative analysis, instrumental analysis, and biochemistry laboratory courses, as well as in oceanographic research. The macro routines have been developed and tested on a personal computer running Quattro Pro 4.0 under DOS 5.0, interfaced to a n Orion model 520ApWmV meter using the RS232-C uorts available on each device. Before loading the spreadsheet itself, the DOS MODE command is used t; confieure the comuuter's serial port. No add-in uromams or adbitional hardware other t h i n a cable are required if the instrument to be interfaced has bidirectional RS232 capability. Copies of the spreadsheet-controlled data acquisition macros described in this paper are available (with brief ~~~
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documentation) by sending a blank disk and postage-paid mailer to J. Mullin. Acknowledgment The authors wish to thank the University of New England College of Arts and Sciences Dean's Office for partial funding of this project, and Gene Yonuschot of the UNE College of Osteopathic Medicine for the loan of a computer and printer.
Where the Electrons Are Roger Earth West Chester University West Chester, PA19383, E-mail:
[email protected] Locating electrons and modeling their behavior is a t the heart of much of today's chemistry. Acursory glance a t any organic chemistry textbook shows the central role played by electrons in our view of chemical reactions. Chemists need to have a n approximate pictorial understanding of where the electrons are. For students of chemistry, an understanding of the behavior of the electron begins with atomic orbitals, in particular, with the s, p, and d orbitals of hydrogen. To most chemists, a n orbital is used as a picture, not a mathematical function. Our concern as educators should be that the correct picture be implanted in the minds of chemistry students. Methods of Representation Adesirable picture would be one that is closely related to where the electrons are. Ease of drawing and remembering would also be helpful. The best picture, in my view, is a contour surface of the probability density (26). A related, and also effective picture, is the dot-cloud diagram (27). The use of surface plots of the wavefunction has been advocated (281, but I think that students may find them less helpful in the central concern: learning where the electrons are. I n any event, the same methods used for the contour plots can be made to give surface plots. Kikuchi and Suzuki (29) have made a lucid comparison of various representations of orbitals. Methods and programs for preparing all of these representations have apneared in this Journal. Baughman's proposal, that s t u d e k s draw the contours (in twodimensions) as an exercise (301,should be given very serious consideration by teachers and textbook authors. I will describe a method for preparing two-dimensional contours using a commonly avaiiable general-purpose mathematics-engineering program. I will also demonstrate that this same method Fan be used to prepare the matrices that serve as the basis for students'own hand-drawn diagrams, a s recommended by Baughman. The Shaded Hourglass
The usual representation of a p orbital shown in general chemistry textbooks differs in nearly every detail from the contour plot of a 2p, orbital shown in Figure 2. The most popular textbook drawing is what I call a shaded hourglass, a two-dimensional version of which is shown in Figure 3. As an indication of where the electrons are, Figure 3 is not realistic. I t leaves the impression that there is significant electronic charge density a t the nucleus. The shaded hourglass is actually a graph, in spherical coordinates, of the square of the angular part of the wavefunction (y2).The distance from the origin represents the magnitude of Y'. Afew texts represent the p orbitals with a pair of tangent spheres (Fig. 4),which is a graph of the angular part (Y). It is unthinkable that anyone teaching general chemistry Volume 72 Number 5 May 1995
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