do, and to simulate-all should be part of a n integral approach for science teaching. Acknowledgment This work was supported in part by the UNAM-DGAPA 51.53.418.01 educational project. The author wishes to thank Glinda Irazoque for showing him those incredible Liesegang rings, and to Maria Eugenia Costas for helpful comments on the manuscript. Literature Cited 1. Pngogne, I; Stengers, I. O d e r out of Chaos; Bantam:USA. 1988. 2. N i c o l i s , G . I n T ~ N ~ u P h y ~ i i i ; D i v l v l v l , P ~ , E d : C a n ,
.1..W 9 3. Boyer, W H. A ndbrnk of CoNold Chamisfry, 2nd ed.; John Wliey and Sons: USA. 1956: p 320. 4. Ksi, 5.; Muller S. C.; Ross,J. J Cham Phw. 1982,76,1392-1406. 5. ShaWlashi", B. 2. Chemical Demonlmlions; University of Wismnlin: USA. 1985:
v", l . .... -. 6. Sehibeci, R. A,; Cerlsen, C. J. J. C h m . Educ. 1888.65.356366,
7. Sharbaugh. 111, A. H.: Sharbaugh, JI, A. H. J Chem. Educ. 1989,66,58(L594.
8.Prager.S. J. Chem. Educ. 1956.25.279-284.
9. FkkerM:Ross. J. J. Chem. Phvs 1974.60.3458-3465.
Models of 2-Butanone: Using Graphics To Illustrate Complementary Approaches to Molecular Structure and Reactivity T. W. Hanks Furrnan University Greenville, SC 29613
An eloquent case for the introduction of compnter-based molecular modeling into the undergraduate curriculum has been made in recent issues of this Journal (Id).Computer modeling is not only a n active area of chemical research but also a n increasingly routine t w l in industrial settings. From a purely practical viewpoint, students need to be exposed to modeling because it is a tool that many will use throughout their professional careers. Additionally, the very features that make this technology useful in research also make modeling valuable in education. The wav chemists think about the ~hvsicaluniverse is by building mental "pictures" or models of the system under consideration. To be useful, the model must be simple enough to manipulate but complete enough to enable accurate predictions about the svstem. Aside from the mechanical aspects of laboratory te&niques, chemical education consists largelv of helping students develop their own models of the &cr&copic LnGerse. Computer-based molecular models can emphasize or conceal details of a chemical system in a n extraordinarily flexible way, permitting a particular system to be viewed from many different perspectives. The result is a tool for interpreting experimental results in terms of critical chemical concepts and for making predictions about the properties of new systems. Advantage of Using Graphics with Computational Techniques The basic computational methods for molecular modeling have been available for a number of years, including empirical force field methods and quantum mechanical methods, both semiempirical and ab initio (6).As computer technology has progressed, the complexity of the molecules t h a t may be treated by a given method has rapidly increased. Simultaneously, the computational programs
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have moved from mainframes to desktop and laboratory class computers. These developments, though important and exciting, are only part of the picture. As long a s the models produced by these methods consisted primarily of quantitative detail (columns of numbers). thev were inaccessible to lower level students-and many fatuity a s well! Even interpretations of data by experts suffered because the overall view was sometimes obscured by the multitude of detail. The key to widespread use of computer molecular models in the undergraduate curriculum is the same a s that for industry: graphics. The conversion of tabulated output into three-diminsional figures vastly improves accessibility to the computational models available. Although graphics workstations are not currentlv available to most undergraduate institutions, they soon will be. In both price and graphics capabilities. the high end of the MS-DOS and ~ a i i n t o s hcbmputers'(7) nowoverlaps the low end of the Unix workstations, such a s the Silicon Graphics Indigo series. Along with this is fierce competitionamong vendors of molecular modeling packages to improve user interfaces while expanding capabilities. I n this article, we explore ways i n which a graphics workstation can be used to illustrate various concepts of molecular structure. Throughout, a simple organic molecule will be used a s a n example. Comments will also be made concerning possible application of particular modeling techniques to more complex molecular systems. Experimental Basic Equipment This article was prepared on a CAChe (Computer-Aided Chemistrs, Molecular Modcline svstem1and printed on an Apple ~ a i e r ~ r i t IIg e r laser priiter. The graphics were ~roducedbv mapping the color disdav information onto a &ay scale Buitabie for printing onAtheLaserwriter. Color output can be achieved with a n appropriate color printer. The CAChe modeling system comes in a variety of configurations. The minimum system consists of a n Apple Macintosh I1 computer or compatible, a CAChe 3D trackball, and three soRware modules. Software CAChe Molecular Editor, which permits meation of moleeular structure files from a fraement librarv or a "oeriodic table" of atom types Files mnv also be imported from rrwrallogrnphir dntnhn;w ur other sonware psckagci 'The hlolecular Mechanlrs package, which ia b a d un rhe 31M2 force field in w i ~ hoaditionnl panrnrtcrlzstwm for nonstandard arum types, lncludmg trmairlon metals 'The Visualizer package, which is a viewer for the data generated in other modules, enabling near realtime rotation and translation of models in three dimensions (All figuresin this article were printed directly from it.) Additional Equipment Additional software modules include Extended Hiickel, MOPAC, and ZINDO semiempirical computational methods, a molecular mechanics-based ~ ~ n a m ipackage, cs and Tabulator, which converts output from the semiempirical packages into graphical images. Both the Extended Hiickel and ZINDO packages contain extended parameterization that allow calculations to be made for molecules that contain many elements in the periodic table, including a number of transition metals. These packages require additional computational hardware. This may be either a coprocessor card that fits into the back of the Macintosh or a n IBM RISC 6000 computer. 'CAChe Scientific, P.O. Box 500 MIS 13-400, Beaverion, OR 97077.
Visualization can be greatly enhanced with a Tektronix video card and stereo monitor. The monitor displays one image with left circularly polarized light and a second stereo image with right circularly polarized light. Thus, viewing of the screen through polarizing lenses results in fullcolor, three-dimensional figures. What Does PButanone "Look Like? This is a deceptively simple question because the answer depends on how one chooses to "look" a t the molecule. Often the translation of classroom knowledge to practical chemical problem solving is also a matter of "looking" a t the molecule in a n appropriate way. Visual inspection of 2-hutanone reveals a colorless liquid that is less dense and less viscous than water. A chemist, however, is likely to be more interested in the molecular structure of 2-butanone than in the bulk liquid. Because we are unable to view a single molecule directly, we use a combination of indirect methods and theory to construct models of the molecule. Elemental analvsis. for example, reveals that 2-butanone "looks" like "&H~w. Mass spectral analysis indicates that this ratio of elements in the bulk material is also the ratio of elements in the individual molecule. Through the use of NMR and IR spectroscopy, we get a somewhat different and more detailedview ofthe molecule in which atom connectivitv is s~ecified:CH2C(O)CH9CHQ. " " The structures shown in Figure 1 are the type typically drawn in introductory organic chemistry courses. These pictures of 2-butanone arise from simple Lewis theory as well as spectroscopy. s
Figure
2. Balland stickmodel of 2.butanone,
.
Figure 3. Space-filling model of 2-butanone.
Figure 1 . Simple representations of 2-butanone. The structures in Figure 1 are useful because they are easy to draw and manipulate with ordinary pen and paper. Experienced organic chemists have no trouble mentally translating wedges and dashes into qualitative three-dimensional structures, but beginning students do not yet have the mental models needed to feel comfortable with this. Even the more advanced students can become baffled when confronted with the idea that the carbonyl carbon has two sterwtopically different faces! The Molecular Mechanics Model Minimum-Energy Configurations from Force Field Computations
One convenient solution to this problem is to view the molecule a s "seen" by neutrons. Neutrons are dim-acted by the nuclear centers of molecules and can lead to a "tinker toy" view of a molecule, a s shown in Figure 2. As with a physical model, the computer model permits the structure to be rotated and viewed from different angles. This effect is particularly dramatic with a stereo monitor. The way in which the atoms are drawn can be adjusted as well. Figure 3 shows a space-filling model of 2-hutanone with the atoms drawn to 70% of their Van der Waals radii. Our student's first exposure to computer molecular models comes in their first introductory chemistry course. We find it valuable to augment discussions of molecular shape by having students build physical "hall and stick" models
of simple compounds. They also examine computer models because Firmres 2 and 3 contain more detail than a tinker These structures are the minimum-energy configurations a s found by MM2 force field calculations. With a few clicks of a mouse button, the computer can be made to display bond lengths, angles, and through-space atom distances. Additionally, very accurate estimates of the heat of formation may be calculated for many molecules. The computer model delivers the basic message--that molecules are, in fact, three-dimensional-and it simultaneously provides quantitative details to reinforce and expand upon that concept. Topics in Stereochemistry
The more advanced students also benefit from molecular mechanics based computer models. Topics in stereochemistry are more readily understood when isomers can be constructed. comoared, and suoerimoosed. An organic chemistry st"denr'may bc asked Lo pro\ycthat nucleophilic attack on 2-lrutanone 1c;ids t o dimerent enantiomers dcpending on the face attacked, whereas a biochemistry student might be asked to examine the steric interactions in docking; small molecule to a fragment of DNA. The students need not be burdened with the details of the calculations a t this point-aside from a few caveats about potential pitfalls in the methodology. Conformation and Molecular Energy
Central to all of these themes is the relationship between structure and molecular energy. Computational methods Volume 71
Number 1 January 1994
63
Flgure 4 Potential energy map of the rotatlon about the C& of 2-butanone
The Quantum Mechanical Model Electronic Structure and Reactivity
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Journal of Chemical Education
I
-1 80
bond
allow a graphical display of energy versus the change in some parameter, such a s the distance between two atoms, a bond lenfi, or a bond angle. Fimre 4 shows the variation in ene&on rotating th; bondbetween carbons 2 and 3 in 2-butanone. This was accomplished by defming a dihedral angle that has the value 0' when the oxygen, Cz, Cg, and Cq a11 lie in the same plane. This occurs when the oxygen and C4 a n eclipsed when looking down the Cz-Ca axis. Likewise, the two atoms are in a n anti configuration when the dihedral angle is 18W.The dihedral angle was varied from -180~to 18W in 1W increments. At each point, the steric energy2 was calculated by molecular mechanics. The black dot on the e n e m diamam in Figure 4 corresponds to the conformation ghownlfor the stGcture a t the top of the figure. With the CAChe system, i t is possible to automatically step through the various conformations and see how the overall energy changes a s the bond rotates. The concepts of local minima and rotational energy barriers are clearly illustrated. I t is also possible to plot energy versus two different structural features, giving a "topographical" map of conformations and further establishing the idea of a multidimensional energy "surface". Figure 5 shows such a map. The rotation about the CzC3 bond is plotted along the x axis, and rotation about the CrC4 bond is plotted on they axis. Energy is plotted along the z axis. Again, energies were calculated by molecular mechanics force field computation. Potential energy diagrams, such a s those shown in Figures 4 and 5, are not limited to conformational changes within a sinele molecule. Reaction ~ a t h w a v scan be explored in diagrams of energy versus the distance between particular atoms in two reacting molecules. However, molecular mechanics is not suitable for looking a t bond making and breaking processes. For this, we need a model that considers electrons. Indeed, many important descriptions of 2-butanone r e w i r e that we beein with a more sophisticated treatment.
-
X
DlhednlAngle (Degrees) 1801
Dihedral Angle (Degrees)
-90 CC ;,
I
0
I
90
I
180
Dlhedral Angle (Degrees)
Figure 5. Potential energy surface of the rotation about the C2-C3 and C3-G bonds of 2-butanone. The molecular mechanics model of molecules is useful, h u t it has severe conceptual and practical limitations. Clearly, nuclear centers are not large spheres a s depicted, and bonds are not sticks or springs that hold the nuclear centers rigidly in place. A more comprehensive model of 2-butanone requires that we consider the spacial positioning and energetics of the electrons in the molecule. This in turn, requires consideration of the Schrodinger equation. There are many ways of including the affect of electrons in the computations and models. The optimal method depends upon several factors: size of the molecule
available computational resources parameters (if any) upon which the method is based information desired from the calculation A comparison of these methods is beyond the scope of this article (61, hut for simple organic molecules, most of them work verv well.3 A major advantage of the current generation of computational packages is that they can be used without detailed knowledge of t h e computational methodology itself, though a t least some discussion of limitations should be included. The graphical output can be very meaningful to students who are trying to learn molecular structure and reactivity-even before they fully understand the origin of the models. ZSrer~c energy s an energy express on the sLm of tne varloJs polent a energy fJnn ons Lsed n a mo ecu ar mecnan cs force fteo (e.g.,bond lengths, bond angles). It is not the same as free energy, strain energy, or heat of formation,though it can be related to the latter through a simple expression (6).~Lcausewe are interested in the difference in enerav ". between conformations. a discussion of stero energy is s~Hlcen1 lor oJr pJrposes 'Tne rema n ng f gJres in rh~sarl CIC arise fromthe PM3 r9, merhoa as lmplemenleo n !he MOPAC 6 0 cornpLlarlona pacnage
Figure 7. Electron density cross section of 2-butanone. Contours at 0.001-0.064 au show a doubling of the value. relatively simple molecules) to the appropriate level of detail required to discuss the issue a t hand. Using a computer model. an instructor can help students build these connections between models more rapidly Also, orbital arm m e n t s can be used to illustrate lecture topics more readily l~rceusrthe instructor&can gcncrete molecul;ir orbital drpicti(~nsfor any numt~erof examples needed. Firmre 6 alone doesnot allow for accurate nredictions of chemical reactivity; important questions cannot be answered using this model alone.
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'For example, why do electrophiles interact with the oxygen atom when the HOMO has substantial amplitude in C-C o-bondinginteractions around the carhanyl carhon? 'Similarly, why do nucleophiles attack the carbonyl carbon exclusively when the LUMO has substantial amplitude on theoxygen? These questions arise due to the rather artificial portrayal of the HOMO and LUMO a s isolated entities. Other meaningful models can be created by manipulating the information calculated in order to plot the molecular orbitals. Models Based on Electron Density
Figure 6. HOMO (top)and LUMO (bottom)of Pbutanone
Frontier Orbitals Semiempirical methodologies use linear combinations of valence atomic orbitals to construct molecular orbitals (MO's). The most important MO's to consider for grasping chemical reactivity are the highest energy occupied orbitals (HOMO'S) and the lowest energy unoccupied orbitals (LUMO's), t h a t is, virtual orbitals. Figure 6 shows the HOMO and LUMO of 2-butanoue drawn a t the 0.1-au contour. I n a sense, the HOMO is a good model for showing the way 2-butanone "looks" to a n incoming electrophile because eood orbital overlao is necessarv for reaction to ~ a n indication of how the occur. Likewise, the L U M gives molecule looks to a nucleophile. The location, shape, and energy of these frontier orbitals is critical to molecular reactivitv. and all of this information is readilv available from MO calculations.
The Isosurface If we consider the "shape" of a molecule to be the volume occupied by the electrons of that molecule, it is useful to draw a n electron densitv isosurface." This descrintion of molecular shape is attractive because it is similar to the space-filling model (Fig. 3) and is useful for understanding steric interactions. The electron density isosurface also has some physical basis. Because X-rays are scattered by electrons, this view of a molecule is related to that 'seen" in a n X-rav diffraction exoeriment. A simpie electron density isosurface is a useful method of visualizing steric interactions, but it is not a complete representation of the electron density. Even if we consider the electron density of the lowest energy conformation a s on avcragc of a n cnscmblc oismtcs, an ~
