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TOWARD COMPUTING CRYSTAL FORMS
by Katherine A. Caponi, NCSA Science Writer

Chemists make many compounds that can be prepared in crystal form, three- dimensional solids arranged in a repeating pattern. The physical and chemical properties of those compounds, or crystalline solids, depend on two factors: the type of molecules that they are composed of and the arrangement of those molecules.

Unfortunately, there is no accurate method for predicting the arrangement that those molecules will take, which currently makes it impossible for scientists to design crystalline solids with useful traits. This difficulty must be overcome to make synthetic organic chemistry a practical tool for materials engineering.

One much-discussed example of this problem is a type of crystal that converts laser light from one color to another. For the crystalline solid to have that ability, the arrangement of molecules within the smallest repeating unit must be asymmetrical. However, there are many possible ways the molecules may arrange themselves when forming crystals. Scientists are trying to find a way to predict what conditions must be present in order for a particular arrangement to occur so that they can produce crystal with that quality in the lab.

Bruce Hudson and a team of scientists from Syracuse University are trying to break down such barriers. Because computational methods for studying crystals have only recently become widely available, chemists have not previously studied them with these methods. The Syracuse team uses NCSA's IBM p690 and now-retired SGI Origin2000 and other supercomputers to evaluate the accuracy of solid-state quantum chemical theory in comparison to experimental methods that investigate crystals and the quantum chemical methods commonly employed to examine isolated molecules.

Hydrocarbons

Their project has several goals. The first is to see how reliable current computational methods are for certain molecules that have very weak intermolecular bonds, such as hydrocarbons. Hydrocarbons are simple compounds that contain only hydrogen and carbon. Since these molecules have weak interactions that stabilize their orientations, many of them, when surrounded by other molecules just like them, form crystals that retain the arrangement of atoms that they had as isolated molecules.

In those cases, scientists usually think of the crystalline solid as composed of molecular building blocks linked together. If the molecules don't change their structure when surrounded by other like molecules, scientists treat them as an oriented gas, a collection of molecules with fixed relative orientation, spacing, and properties. Because the arrangement of the individual molecules is not altered by strong chemical interactions with surrounding molecules, their traits will be expressed in the whole crystalline solid. Scientists can then predict the properties of the crystalline solid based on the traits of the individual building blocks by using quantum chemical methods called oriented gas approximations.

On the other hand, some molecules--even some hydrocarbons--do change their structure when surrounded with other like molecules. The properties of those crystalline solids are different than the properties of the individual molecules, and oriented gas approximations fail. In those cases, Hudson says, "the assembly of the crystalline solid with the desired properties may not be as simple as the independent packing of the building blocks but rather a cooperative process of different chemical reactions working together when each molecule interacts with the ones surrounding it."

The team found that the best way to look for failure in quantum theoretical methods like the oriented gas approximation was to experimentally test the vibrations in the molecular structure. The bonds between atoms in a molecule are a lot like springs. By exciting a molecule with energy, you can learn a lot about its structure and the strength of its bonds based on the way those springs vibrate.

Hudson's team did this by shooting a beam of neutrons into a highly symmetric hydrocarbon molecule called dodecahedrane, using an experimental method called inelastic neutron scattering (INS) spectroscopy. The intensity with which the neutrons scattered upon interaction with the nuclei of particular molecules was computed from knowledge of which atoms were moving like they normally would absent the beam of neutrons. The team then compared the results of this experimental method on both isolated crystal molecules and a sample of the crystalline solid.

Damian Allis, a graduate student working on the project, says, "Molecules feel the same physical constraints from crystal packing that someone on the subway would from other passengers. If you take that person on the subway and put them on a bumpy track, where they move and how far they move will be determined by where everyone else is. Their restricted motion on a crowded subway will look very different to an observer than their motion on a bumpy track if the car was empty of other people. We see those differences when comparing vibrational spectra of isolated molecules with crystalline solids and, therefore, learn about the environment of the molecule in the crystal."

The team found that quantum theoretical methods currently used by scientists described the vibrations observed in the isolated molecule fairly well. However, when looked at in detail, the methods used for isolated molecules did not accurately describe the molecular structure of many molecules forming a solid, showing that the arrangement of dodecahedrane atoms relative to each other changes slightly when surrounded by other like molecules. New quantum chemical methods applicable to solids correctly predict this molecular deformation.

Hydrogen-bonded crystals

Another aspect of the team's project was to study the accuracy of quantum theoretical methods when dealing with crystals that contain hydrogen bonds. "Hydrogen bonding is one of the major bonding mechanisms that lead to large- scale crystal architectures," says Hudson. "In chemistry, hydrogen bonding is like molecular Velcro--or some type of rearrangeable glue. It forms bonds that can come apart at room temperature because they have an energy that is not much larger than thermal energy."

Because hydrogen bonds can form and come apart easily, they are quite forgiving with respect to the orientation of the atoms forming them. That the bonds form easily is useful in the engineering of crystals because the hydrogen-bonding molecules will self-assemble rather than requiring a specific reaction to make each attachment between molecules. That the bonds come apart easily is also useful because they are just weak enough that when one forms incorrectly, there is a good chance that it will be jostled apart by other molecules and reformed correctly.

However, the fact that hydrogen bonds act as molecular Velcro instead of Superglue also has a downside: polymorphism. Polymorphism is a characteristic of many molecular compounds whereby they can form distinct crystals with more than one arrangement because of the forgiving nature of hydrogen bonds.

While organic chemists can produce many molecular species, they cannot yet predict which polymorphic arrangement a crystal will form. In fact, the molecules of the compound may convert from one arrangement to another in time, and one polymorphic form may disappear in favor of another form with minor changes in crystallization conditions. In some cases, different polymorphic arrangements may coexist within a batch of crystals all grown from the same solution.

The arrangement of the molecules in these polymorphic crystals will cause variances in the traits that they display--such as the rate at which the substance dissolves. This results in differences in drug diffusion rates and is therefore a problem for the pharmaceutical industry.

To learn more about the molecular arrangements of hydrogen-bonded crystals, Hudson's team performed INS spectroscopy experiments on crystalline 1,3- cyclohexanedione. INS spectroscopy proved a particularly valuable method for testing hydrogen-bonded crystals because hydrogen atoms are known to scatter the neutrons much more strongly than other atoms. This feature made it simple to find where the hydrogen bonds were located in the structure of the sample material and therefore easier to pinpoint the arrangement of the whole molecule.

The team applied standard quantum mechanical methods to both individual molecules and "cluster" models of the crystalline solid to examine how being surrounded by others of the same molecule would affect the arrangement of the atoms in the crystal-forming molecules. The major point of interest is how the molecular structure changes as the cluster chain length used to model the crystal becomes longer. From these computations, they found that hydrogen bonding between molecular units results in significant changes in molecular structure with increasing chain length. This effect is cooperative, meaning that the effect observed on bonding one molecule to another depends on whether either of those two molecules is already bonded to a third. The hydrogen bonding process is not simply additive.

The team then compared its experimental results and the known crystal structure with results from new periodic quantum theoretical computations. This assessment showed that the full three-dimensional model corresponds well to what is extrapolated for the finite chain cluster and also to what is observed for the crystal.

The vibrational spectra computed using the same methods agree very well with the observed INS spectrum, meaning that the solid-state calculations are providing a reliable description of the energy of the solid. Further to the point, the vibrational spectrum measured or calculated at a very low frequency is important in establishing the relative thermodynamic stability of two crystals, which is the first step in understanding and controlling polymorphism.

The team hopes that someday its findings will help scientists use the theoretical methods tested on NCSA supercomputers to predict what arrangement crystals will make. "One of our ultimate objectives is to be able to compute the relative free energies of crystals so as to be able to predict the relative stability of observed or proposed crystalline structures. This may permit crystal engineering in a proactive sense," Hudson states. Instead of using quantum chemistry merely as a way of describing the arrangements of the molecules in a lab, scientists may be able to predict what arrangements will form and even produce compounds with specific molecular arrangements and thus specific properties.