Data-Driven Chemistry: Building Models of Molecular Structure (Literally) from Electron Diffraction Data Robert M. Hanson and Sara A. Bergman St. Olaf College, 1520 St. Olaf Ave., Northfield, MN 55057-1098 Electron diffraction data can be used as the basis for becoming familiar with molecular structure. Analysis of simple electron diffraction results makes i t clear that NH3 must be pyramidal and not planar. Chemistry is an experimental science. As Albert Einstein repeatedly emphasized, Science must start with facts and end with facts,no matter what theoretical structuresit builds in between. First of all the scientist is an observer ( I ) . As such, one might expect introductory courses in chemistry to focus on the data of chemistry, teaching students how to collect and interpret it. However, a quick look a t representative entry-level chemistry texts (241,will show that this is not the case, a t least with respect to molecular structure. Rather, our traditional method of introducing students to the structure of molecules focuses almost exclusively on the theoretical aspects of chemistry (5-7). This theoretical focus is actuallv fairlv new in the historv of chemical education, and thltrendover the past tweky to thirty years toward more theory and less descriptive chemistry has We focus on this rather been assailed in this Journal (8,9). subtle problem, and we offer an example of an alternative approach to the study of molecular structure. As an example, we consider the case of ammonia, NH3. What is the H-N-H bond angle in this molecule? Is ammonia ~ l a n a ror ~vramidal?First-vear chemistw students are told the fa& and expected tdlearn them: k m o n i a is pyramidal, with a n angle closer to 109.5' than 90°, and the reason for all this has something to do with electron pair repulsion or orbital hybridization. The simple issue of how we know is not addressed. At the outset of this project we were struck by the seeming lack of hard "evidence" for molecular structure, at least in the sense of evidence as presented to introductory students. The reason became clear immediately Our detailed knowledge of molecular structure is largely based on infrared and microwave spectroscopy, two &hniques that are not particularly upen tu struightfonvnrd interpretion. The ~ a t from h raw~dGato bond distances is too c i m ~ l e xto be Lade meaningful to firsbyear students. Too maiy parameters are involved. What seems to be largely forgotten, however, is that the orieinal driving force behind theories of molecular structure was not microwave or infrared spectroscopy. Structural work on small molecules in the 1930's and 1940's was carried out almost exclusively using X-ray and electron diffraction (10). We show here how easily electron diffraction data can be presented as evidence for structure to firstyear students, thus eliciting the "why" questions that uaturally lead to a desire for theoretical explanation.
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The Electron Diffraction Method Without going into great detail about the exact method, one can easily describe electron diffraction to first-year students. More detailed accounts are available (11-13). The students a t least must be aware that electrons'can bdhave as waves and that an important wave property is dif-
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Journal of Chemical Education
fraction. Diffraction phenomena are easily demonstrated in class using a hand-held laser as described recently in this Journal (14). Electron diffraction is in many ways similar to X-ray diffractiou. X-ray diffraction is due to the interaction between light and electrons in molecules, whereas electrou diffraction is due primarily to interaction of a high-energy electron beam with the nuclei of molecules. Electrons have much shorter wavelengths than do X-ravs. that is. 0.06 x 10-1° m vs. 1x lo-" m. ~n'thkbasic electron diffraction study of small molecules, a beam of electrons, similar to the one that illuminates a computer screen or home television, is passed through a gas. The molecules of the gas diffract the electrons: Each atom-atom connection in the molecules of the gas acts as a small slit through which the electron waves must Dass. Although most of the electrons fail to interact with molecules, some do, and the resultant image of the beam appears as concentric interference rings on the detector "screen" (Fig. la). The data in Figure 1 are simulations based on reported interatomic distances in NH3 (15).The data involve only the molecular component of the diffraction after the atomic com~onentshave been subtracted. Quantitation of the i n t e n s h s of the nngs gives fluctuating data of the type shown in Figure Ib.
Figure 1. Electron diffraction interference rings (a) as might be seen on a detector screen and (b) quantified as intensity vs. angle from source. In principle these intensity data actually hold all of the information needed to reconstruct a three-dimensional model of the gas molecules because they contain information about all the possible diffracting atom-atom distances. Thus, when the intensity data are transformed by a type of Fourier analysis, the result is a curve such as the one for ammonia depicted in Figure 2 (15).These "radial distribution curves" are the actual data we propose to present to first-year students for their own analysis. (They are data in precisely the same way nuclear magnetic resonance spectra are data.) From the radial distribution curve one learns that there are two unique atom-atom distances in ammonia.
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,b
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2.0
1.0
Figure 2. Radial distribution curve for ammonia based on actual electron diffraction data. Units are in Angstroms. We emphasize that these resultant curves directly indicate nothine about the bondine in molecules. For exam~le, in NH1 the data do not lstin&ish between distances iuch as N-H that theoretically are due to bonds and distances such as H-H that presumably are not. This lstinctlon between observed structure and theoretical bonding is at the heart of what we are trying to impress upon students when we introduce data-driven chemistry. Learning to clearlv differentiate between atom-atom distance and bond le&h, students see the limitations of observation. Hopefully they will later encounter less difficulty with the concept of delocalized electrons. For example, using only the diffraction data showing CHa as tetrahedral, students cannot conclude that each C-H bond must be attributed to a oair of localized s d electrons. Thus, by making the disGnction between structure and bonding, we help students to distinguish between what Barrow (5)has called the science and the mythology of chemistry. Interpreting the Results Using Geometry
The observation of only two peaks in the data for NH3 indicates that there are only twodistinct atom-atom distances in ammonia, hi^ mles out such typical student hypotheses as rpshaped or y-shaped structures in which one H~i s-distinctlv different from the others, are onlv ~ - - - ~ two possible stkctures for ammonia, given two distinct atom-atom distances: planar and pyramidal. The relative height of the peaks is related (though not linearly) to the product of the atomic numbers of the two atoms involved in the diffraction. Thus, H-H diffraction results in small and sometimes unobservable peaks. In this case it js clear that the N-H distance in amponia is about 1.00 A, and the H-H distance is about 1.63A. These two lengths are all the information necessary to show that the structure of ammonia is pyramidal and not planar. As shown in Figure 3 for the general case in which a o b, the cosine law can be used to determine the H-N-H angle (0)in ammonia. If 0 turns out to be 120°,then NH3must be ~
~~
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planar. Any smaller angle implies a pyramidal structure. In this case we discover that cos 0 = -0.328, so 0 = 109'. An estimate of the error in the measurement is calculated by determining 0 for a range of distances around the measured values. Usinga = b = 1.01and c = 1.62, we get 0 = 107'. Using a = b = 0.99 and c = 1.64, we get 8 = 112". Thus, from the uncertainty of our crude measurement alone we have that 0 = 109 f 34 Although an uncertainty of 3' may seem unacceptable in light of the precision obtainable from microwave and infrared spectroscopy, this order of precision is completely appropriate to the question at hand. Ammonia cannot possibly be planar. Generating Three-Dimensional Scale Models From the Data Perhaps the most surprising aspect of our finding is that students can easily make three-dimensional scale models directly from their data. meway this is done is quite simple and is sketched in Figure 4 and outlined below.
Because the H-H distance is known to be 1.63 A, place one H at 0.0 on the axis and one at 1.63. 'Using a drawing compass, draw an arc around each H at a radius of 1.00. The intersection of these two ares loeates the N atom and defines the H-N-H angle. Using the compass, draw a complete circle of radius 1.00 around theN atom. The third hydrogen atommust beon this circle somewhere. With the wmpass again set at 1.63, intersect the circle with arcs around each known hydrogen position. The third hydrogen atom is both of these positions. Draw lines wnnecting all atoms. Cut out the figure, and fold along the lines. * Bring the two positions of the third H atom together and fold. Clip any exposed excess paper. Tape the model together to complete the figure. This basic technique works for more complex structures a s well, and we have made models of CH4, CH2Clz. CHCls, CFC13, PC13, PCls, and UFs, among others. For example, the folding diagram for CH2C12 is given in Figure 5. To use the diagram, photocopy (enlarge) and fold away from you on the solid lines, toward you on the dotted lines. Not only is i t fun to construct the models in this way, but the experience relates what we really mean by the geometry of chemistry. The models produced for tetrahedral molecules are unique in that they retain all of the atom-atom distances as folds or edges so that bond angles are clearly represeuted. Limitations of the Method
A few limitations to the analysis of electron diffraction data arise. There are not many published radial distribu-
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Figure 3. Cosine law for determining the H-N-H angle in ammonia.
Figure 4. Using only atomatom distances to construct a model of ammonia. Volume 71
Number 2
February 1994
151
