Recommended Essay: Writing to Find Connections
Seeing the Unseeable
Atoms and molecules, even the largest molecules, are far too small for us to see directly. Chemists work out their structures by very indirect means, repeatedly solving the puzzle of structure by imagining what kinds of structures are needed to explain and agree with measurements made by methods ranging from simple lab procedures like weighing, or from complex measurements with modern instruments, as in spectroscopy and X-ray diffraction (explained below). As more structures are known, scientists discover general structural principles that guide reliable educated guesses about structure, which they then try to confirm by other measurements.
Structure from simple chemistry and weighing
We can learn a lot about the structure of simple molecules by simply learning what they are composed of. For simple organic molecules made up of a few atoms of carbon, hydrogen, and oxygen, such as the wine ingredient ethanol, there are only a few ways that a small number of atoms can be combined to make small molecules. Some weighing experiments can sometimes limit us to just one possibility.
[Aside: Well, this is vexing. After working with this website for all these weeks, I did not know that it would not allow me to make superscripts or subscripts, like the question marks in the formula of the figure below. So, we'll make do. In text, I'll have to present the formula above as C(?)H(?)O(?). So water is H(2)O. This is an awkward way to write formulas, but it will have to do for now. I am amazed to realize that we have come so far in the course without my writing a single chemical formula. Perhaps that's one reason that you are still coming to class.]
For example, to learn the structure of ethanol, we can burn it—that is, combine it with oxygen to convert it into carbon dioxide and water—to find out the ratio of carbon, hydrogen, and oxygen atoms are in each molecule. The formula C(?)H(?)O(?) in the figure means that the each molecule of the substance contains atoms of carbon, hydrogen, and oxygen, but that we do not know how many of each. That's just what we are trying to figure out.
To do this, we weigh a sample of the ethanol, then burn it and collect all of the water and carbon dioxide produced. We then weigh the water and carbon dioxide. We assume that all hydrogen atoms in the water and all carbon atoms in the carbon dioxide came from the sample, and we calculate the weights of C and H that came from the sample of ethanol. If the total weight of C and H is less than the weight of the ethanol sample, then we presume that the remaining weight of ethanol was oxygen.
From the weights of the C, H, and O, we can figure out the ratio of atoms C:H:O for ethanol. The ratio is this case turns out to be C:H:O = 2:6:1. So ethanol could be composed of molecules with composition C(2)H(6)O, C(4)H(12)O(2), C(6)H(18)O(3), or of any heavier molecules containing C, H, and O in the ratio C:H:O = 2:6:1. Other methods allow chemists to learn the weights of molecules, and in this case, the weight corresponds to C(2)H(6)O. We know from many known structures (those general structural principles mentioned above) that a carbon atom usually forms 4 bonds to other atoms, O usually forms 2, and H can form only 1. Only two structures are compatible with this information: CH(3)OCH(3) and CH(3)CH(2)OH.
We can choose between them by considering the differences in properties expected for molecules of these structures. For example, substances that contain the -O-H grouping usually mix readily with water, because they are quite water like in structure (H-O-H vs CH(3)CH(2)-O-H). We know that ethanol mixes readily with water, else it would form a separate layer in beer, wine, or spirits. So CH(3)CH(2)OH is the more likely structure.
Spectroscopy can tell us more
For more complicated molecules, we need some hints about specific structural elements, such as the
-O-H group that ethanol has, and that dimethyl ether does not have. It would help a lot to see them, but to simply illuminate objects, and see them by the light they reflect, you need light waves that are smaller then the objects themselves. Visible light waves reflect off of objects in all directions, and the small fraction of them that enter our eyes allow us to see the objects. But visible light waves are huge compared to molecules. They pass over individual molecules with no effect whatsoever, so we cannot see molecules in the way we see ordinary objects around us.
The light we can see—and see by—is but one form of electromagnetic radiation (EMR). Although visible light cannot help us to see molecules, various other types of EMR do have effects on molecules, and can reveal various aspects of molecular structure.
 |
We are constantly bathed in electromagnetic radiation (EM), in the form of waves ranging from miles long (radio waves) to smaller than atoms. We can see only the waves in the very narrow band marked "VISIBLE". Most of the EM to the right of the visible band is harmful to living organisms, and is present only in small amounts in our natural environment. (Notice that radioactivity is not on this chart, because most of it it is not electromagnetic radiation.)
|
Each of the forms of energy in the EM spectrum has different effects on molecules, and some of these effects can be revealing. Following are some of the effects of EMR on molecules:
• IR energy makes molecules vibrate. Bonded atoms act like balls joined by springs, and each bond vibrates at a slightly different energy, causing molecules to absorb IR radiation of just that energy. This principle is the basis of IR spectroscopy.
• Visible and ultraviolet energy moves electrons around in the molecules of a substance, and if some visible frequencies are absorbed or reflected more than others, that substance will be colored (UV-Visible spectroscopy)
• Microwave and radio-frequency (RF) energy makes molecules spin or move faster. Microwave ovens spin up and heat the water in food in this way, and the heated water heats everything else. (Radio spectroscopy)
• If the molecules are placed in a strong magnetic field, radio-frequency energy interacts with nuclei in atoms and reveals the number and nature of atoms near them in a molecule (the basis of NMR spectroscopy and of MRI, magnetic resonance imaging).
• X-rays are diffracted or scattered by molecules (the X-rays bounce off, sort of), in the same way that visible light bounces off of visible objects. Because X-rays waves are about the size of molecules, X-ray beams that can reveal the shapes of molecules (X-ray crystallography).
Each form of EM radiation can tell us something about molecular structures. Putting these types of information together can often help us puzzle out even the most complex structures.
To learn what EMR will tell us, we must measure precisely the wavelengths that a specific substance absorbs. This technique is called spectroscopy, and entails directing a beam of EMR through a sample and comparing the spectrum of EMR entering the sample with that which passes through.
 |
| When EM radiation of varying wavelengths passes through a sample, specific wavelengths are absorbed, and thus are missing in the spectrum measured by the detector. The missing wavelengths reveal specific details of structure. |
This form of spectroscopy can reveal specific groupings of bonded atoms. For example, the O-H bond of ethanol vibrates at, and absorbs, IR energy at a different wavelength from any other group. Ethanol absorbs this wavelength strongly, while dimethyl ether does not, which means that an IR spectrum can allow us to distinguish these two very similar molecules.
A dramatic web page (click HERE) by Dr. S. Immel of the Technische Universität Darmstadt demonstrates how specific bonds vibrate in response to IR energy. To play with vibrating molecular models, go to this site and wait for everything to load (until the Jmol symbol goes away). After the model appears, repeatedly click the small green right-arrow above the "Simulated IR Spectrum". Each time you click, a green line moves to a different dip in the spectrum (dips are called spectral lines, or more commonly, peaks), and the model vibrates in the manner that would be induced by the specific amount of energy represented by the peak. Click and drag on the model to rotate it and see just how it is vibrating.
To see models of other molecules, click on a chemical name under "3D Models for IR-Spectroscopy". Notice that the more complex the model is, the more complex its spectrum. IR spectra can be used as fingerprints to identify samples of unknown substances. Computer algorithms can match spectra of millions of compounds to a library of spectra, and thus identify the compounds.
IR spectroscopy easily distinguishes ethanol from dimethyl ether by the presence of the absorption band for the -O-H group in the spectrum of ethanol and its absence in dimethyl ether. (For the adventurous, at Dr. Immel's page, look at the spectrum of 1-butanol, and click on the small absorption band at 3669. The model will show the vibration of the -O-H bond. See if you can find a band that makes the C-O bond vibrate. Dimethyl ether would also have this band, but lack any band above 3500.)
Big molecules
For learning the structures of very large and complex molecules, such as DNA and proteins described in Unit 1, by far the most powerful method is X-ray crystallography. Although the method complicated and difficult to understand in detail, it is the method that is most like simply seeing objects in the world around us. So in a way, it is the easiest method to understand. First we need to think about how we see objects around us, and then we can compare this with how we see by X-ray crystallography.
We see objects when light bounces off them (we say that they diffract light) and then enters our eyes. Any lighted object diffracts light in all directions, and we see the object because a tiny fraction of that diffracted light passes through the lenses of our eyes and strikes the retinas at the backs of our eyeballs. An eye lens forms an image on a retina of scene before the eye, and the light-sensing cells there send electrical signals to the brain. Interpretation of those signals results in our awareness of the objects in our view (now there is a mystery!).
By considering how a lens works, we can draw analogies to explain how X-ray crystallography works.
 |
A lens can form a magnified image of an object. A second
lens, placed to the right of the image, can magnify it further.
In a microscope or telescope, the lens shown is called the
objective lens, and a second lens to magnify the image is
called the eyepiece.
|
The dotted lines in the figure show the paths of a few specific light rays, and thus reveal how the lens works its magic. 1) Light rays that pass through the lens parallel to its axis (that is, parallel to the line O-I), are bent so as to pass through a focal point (F or F'). An example is the horizontal ray that passes from the bottom of the Object through the lens, through F', and on to the (inverted) bottom of the Image. 2) Light rays that enter the lens after passing through a focal point are bent so as to emerge parallel to the lens axis (example: they ray that passes from the bottom of the Object through F and on through the lens). As a result, for an Object outside focal point F, the lens forms an inverted and enlarged Image on the opposite side.
Why not look at molecules with microscopes?
In theory, we should be able to place a molecule in the position of the Object, and see an enlarged image of it. Two problems prevent us from taking this simple approach. First, molecules are so small that visible light does not bounce off them; it simple passes right by. The molecules and the visible light do not affect each other at all. In order for light waves to bounce off of something, the waves and the something must be about the same size. Visible light waves are 100 to 1000 times larger than typical molecules.
Look again at the electromagnetic spectrum about halfway back up this page. What we need is electromagnetic radiation that has waves small enough to bounce off of—be diffracted by—molecules. Do such waves of EM exist? Yes, there is electromagnetic radiation of every imaginable wavelength, from miles long to smaller than water molecules, as shown on the spectrum.
You can see from the chart that "soft" X-rays are the closest in size to molecules. So molecules can diffract X-rays. The trouble is, we cannot see X-rays, although we can capture them on film or on a detector sort of like the one in a digital camera. But the trouble there is, there are no lenses for X-rays, so we cannot focus the diffracted rays with a lens to capture an image. Fortunately, a Frenchman named Fourier pioneered a field of mathematics that can help us. A mathematical operation called the Fourier transform allows us to calculate just what a lens would do with the diffracted rays from molecules. So we can let a computer do the job of a lens for us.
Why do we need to grow crystals?
One more problem (in crystallography, there is no end of trouble): a single molecule diffracts X-rays so weakly that the diffracted beams are too weak to detect. We solve this problem by using crystals of the molecules. In a crystal, billions of billions of identical molecules sit in nice rows and columns, facing the same way, so that all the molecules diffract in the same way (they sing in unison, so to speak), and the crystal diffracts just like a single strongly diffracting molecule. This diagram summarizes how we collect X-rays for calculation of an image by the Fourier transform.
.jpg) |
A narrow beam of X-rays strike a crystal and are diffracted into many
individual beams. The beams expose a film or a detector. The measured
intensity (darkness) and direction of each beam is fed to a computer,
where the Fourier transform calculation produces an image.
|
So the whole process is something like this: An X-ray beam is trained onto a crystal (labeled Object below). The diffracted X-rays are captured by a detector and fed to a computer, where the Fourier transform calculation produces an image of the average molecule in the crystal.
.jpg) |
The source shown here is the National Synchrotron Light Source
at Brookhaven National Laboratory in Upton, NY, one of the most
powerful sources of X-rays for crystallography. X-rays are produced
as electrons travel near the speed of light in the larger of the two red
rings (diameter, 843 feet, which is longer than two football fields).
|
Can scientists actually see the molecules?
In a word, no. As I will show in class, the image produced is not the color-coded, ball-and-stick model shown above. On a computer, the image looks like the blue netlike surface in the following figure (top panel). What X-ray diffraction "shows" us is the surface of the electron cloud surrounding the molecule. To interpret the surface, scientists build a chemical model, adhering to rules about how atoms fit together, to fit it into the surface (bottom panel).
In a word, no. As I will show in class, the image produced is not the color-coded, ball-and-stick model shown above. On a computer, the image looks like the blue netlike surface in the following figure (top panel). What X-ray diffraction "shows" us is the surface of the electron cloud surrounding the molecule. To interpret the surface, scientists build a chemical model, adhering to rules about how atoms fit together, to fit it into the surface (bottom panel).
.jpg) |
Top: Image of molecular surface calculated from crystallographic data.
Bottom: Model of molecule built to fit inside the surface. These images
are stereo pairs, like slides for a stereopticon or View Master.To learn
how to see stereo pairs in 3D, visit
|
I hope now that the first paragraph of this page means more to you than it did on first reading. Here it is again:
Seeing the Unseeable
Atoms and molecules, even the largest molecules, are far too small for us to see directly. Chemists work out their structures by very indirect means, repeatedly solving the puzzle of structure by imagining what kinds of structures are needed to explain and agree with measurements made by methods ranging from simple lab procedures like weighing, or from complex measurements with modern instruments, as in spectroscopy and X-ray diffraction (explained below). As more structures are known, scientists discover general structural principles that guide reliable educated guesses about structure, which they then try to confirm by other measurements.
