Issue Date: February 9, 2004
BETTER THAN FOURIER?
In chemistry these days, calculations are a ubiquitous companion to experimental results. Whether used for predicting the structure of a protein or the nuclear magnetic resonance spectrum of a molecule, calculations are indispensable for verifying experiments and generating unexpected insight.
Those who use vibrational spectroscopy to study molecules now have a new addition to the computational toolbox: Chemistry professor Ralph A. Wheeler and his colleagues at the University of Oklahoma have adapted an established statistical method to make the task of calculating vibrational spectra of molecules such as water quicker and more accurate [ChemPhysChem, 4, 1227 (2003)].
Known as principal component analysis, or PCA, the method has been used by statistical mechanicians for years to study low-frequency modes in proteins or to analyze molecular descriptors for drug design. Harnessed for spectroscopic calculations, PCA yields not only the frequencies and intensity of spectral lines but also the fundamental vibrational modes of the system.
Traditionally, chemists have turned to that decades-old workhorse, the fast Fourier transform (FFT), to compute the intensity of vibrational spectral lines in condensed-phase systems or proteins. FFT, however, is usually unwieldy, creating huge data sets that can tax even modern computers. And, Wheeler notes, it doesn't compute vibrational modes.
That's an important distinction for spectroscopists like Roger Frech, a chemistry professor at Oklahoma, whose research on polymers in the condensed phase provided the inspiration for Wheeler's work.
"We wanted to know what modes gave rise to the frequencies he measures," Wheeler says. "So we started looking at problems very closely related to this one and found some engineering literature on signal processing."
Wheeler's group, including graduate student Haitao Dong and research assistant Scott E. Boesch, used PCA to calculate the vibrational spectra of an isolated water molecule and liquid water more accurately than FFT and another popular tool known as the maximum entropy method [ChemPhysChem, 4, 382, (2003)].
"It's certainly something to put in a bag of tricks and consider," says University of California, Berkeley, chemistry professor David Chandler, a statistical mechanician who studies liquids.
The computational process starts with a dynamics simulation, which can include both quantum mechanical and classical molecular mechanical methods, and which calculates the motions of all the atoms.
THEN COMES THE MATTER of turning this motion information into spectral information. FFT calculates how the motions of atoms are correlated in time--that is, how the motion of an atom in a molecule at a previous time influences the motion at a future time. The result is a giant matrix whose solutions are the intensities and frequencies of the molecule's vibrations.
In contrast, PCA asks how the motion of one atom correlates with the motion of the other atoms. The resulting matrices are much smaller, even though their solutions are more accurate than their corresponding FFT matrices.
This lack of time dependence could also be useful with other non-time-dependent statistical computational methods, such as Monte Carlo methods.
So far, the group has used the method only to calculate vibrations of small molecules such as ammonia, ethane, and cyclopropane in solvent, in which the motion of the atoms is nearly harmonic."This is a situation where PCA is likely to work well, but it's also a very common situation in the physical sciences," Wheeler tells C&EN.
Wheeler and his colleagues plan to package the refashioned method in a program that they'll make available to other scientists. Wheeler retreats from the idea of marketing PCA for profit. "I'd just as soon give away software," he says with a laugh. "I'd just be happy if people use it."
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