Traversing a Mountain Range

A potential-energy surface is a landscape-like topographical map that describes how the energy of a water cluster varies as individual molecules move. Jordan's computations aim at accurately surveying the peaks and valleys of these surfaces. An energy minimum occurs whenever any small displacement increases the cluster's overall energy. "It's like being in a basin surrounded by mountains," explains Jordan. "A step in any direction is uphill. The mountain range can have multiple minima, called local minima, separated by passes. The minimum that's lowest in energy on the potential-energy surface is the global minimum. In the mountain range analogy, this corresponds to the deepest basin.

"The number of minima grows rapidly as the number of waters grows," says Jordan. "We've shown that for a water cluster with eight molecules there are 120 to 130 minima, depending on the model used." Finding the global minimum out of hundreds or thousands of these local minima can be a vexing computational problem. Among the questions Jordan addressed is the cluster size at which the global minimum has three-dimensional rather than ring-like two-dimensional structures. The calculations indicate that this occurs when cluster size reaches six molecules.

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