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For several years now, quantum Monte Carlo (QMC) has been like an
actor awaiting his big break. This unconventional "stochastic," or
statistical, approach for predicting the behavior of subatomic particles has
successfully described a few systems, such as electron gas and small
molecules, but it hasn't found a blockbuster application that will propel this
relative newcomer into mainstream methodologies. Scarcely 10 percent
of physicists and chemists who investigate quantum mechanics -- the
science that examines the world of protons, electrons, and other subatomic
particles -- apply QMC to their problems.
Until recently, they had no reason to change. At the heart of quantum mechanics is a partial differential equation called the Schrödinger equation. Its solution, a wavefunction, fully captures the wavelike and particular behavior displayed by matter at this level. Theoretically, one could predict atomic structures, even chemical reactions, by solving the Schrödinger equation, but the physics underlying it lead to equations too complicated to solve for systems of more than a few atoms. Consequently, scientists have been trying to simplify the equation since it was first proposed in 1926 by Austrian physicist Erwin Schrödinger. Some approaches emphasize accuracy; others strive for size. None have achieved both. This past year, QMC was nudged into the scientific spotlight as word spread about how researchers in NCSA's Condensed Matter Physics Group and at AT&T had stumbled upon a structural problem QMC could solve better than could any of the existing theoretical approaches -- for systems of up to 50-100 atoms. And that number of atoms is an order of magnitude larger than traditional approaches that try to exactly solve Schrödinger. It didn't hurt that the system in question was closely related to the provocative buckyball.
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