ICAM Themes
Susan R. Atlas
Department of Physics and Astronomy
University of New Mexico
800 Yale NE
Albuquerque, NM 87131
(505) 277-1509
The advent of nanoscale materials and interest in large molecular clusters as materials in their own right is focusing increased attention on the interface between what have traditionally been considered disparate research domains: molecular physics and materials physics. These domains share a common dependence on the quantum-mechanical behavior of their constituent electrons as the ultimate determinant of system behavior. An analogous situation obtains in biophysics, where large molecules (proteins) immersed in aqueous solution interact quantum-mechanically to create emergent system behavior (biologically-active conformations) via protein folding.
In all of these problems there are two fundamental nonlinearities at work, and both must be understood if macroscopic behavior is to be controlled and adapted through modifications to microscopic properties. The first nonlinearity is related to the venerable self-consistent field problem of electronic structure theory. Re-cast in modern terms, the challenge is to determine a strictly density-dependent effective potential that is simple in the sense of being identical for all electrons in the problem, while simultaneously preserving information on the complex underlying electronic dynamics. The existence of such a potential, guaranteed by a theorem that was the subject of this year's Nobel Prize, provides essentially no guidance on how to construct it. This is an arena where advanced techniques from nonlinear optimization theory seem likely to be able to play a role, and the first steps in this direction are being taken. Confronting the intrinsic nonlinearity head-on may also help shed light on the closely-related length-scale problem of striking a balance between localized and itinerant electronic behavior in constructing the effective potential, a specific manifestation of the molecule/material conceptual interface mentioned above.
The second essential nonlinearity is the well-known electronic/atomistic length-scale coupling problem. In macromolecular (protein) dynamics, many years have been spent refining force-field parameterizations based on empirical data and quantum-mechanical calculations, but the introduction of a single new atom type can throw the entire force-field into disarray. More generally, since materials behavior is ultimately determined by atomistic dynamics (defect diffusion, slip, etc.) the ability to abstract a governing potential from the underlying electronic interactions is essential to understanding macroscopic properties at a fundamental level. Here again, it is possible that nonlinear optimization techniques may prove useful, by providing a mechanism for weighting the quantum-mechanical energy landscape in terms of ultimate contributions to the atomistic dynamics, so that computational efforts at the quantum length-scale can be focused accordingly.