collaborative and synergistic research in the mathematical sciences that can accelerate progress in theoretical and computational chemistry and their applications, and make recommendations for promoting this research." It was clear from the outset that the study could not presume to be exhaustive. However, it seemed realistic to strive for representative sampling of the two communities involved and to identify instructive examples of past collaborative successes, likely prospects for interdisciplinary synergy, and barriers to joint research that could be removed or at least lowered.

A number of fruitful collaborations between mathematical scientists and theoretical/computational chemists have occurred in the past. Noteworthy examples include the Nobel prize-winning work of Hauptman and Karle to advance the science of X-ray crystallography, now a basic tool; quantitative structure-activity relationships have led to the development of at least four commercially successful products (an antibacterial compound, two herbicides, and one fungicide); and insights into molecular structure have been gained from mathematical results in group theory and topology.

In scanning the research needs of theoretical/computational chemistry, the committee found opportunities for synergistic research with almost the entire mathematical sciences community, where that term is used in its broadest sense to include core and applied mathematicians, statisticians, operations researchers, and theoretical computer scientists. Many of the mathematical lines of research that, if reoriented, could contribute to chemistry are already being pursued in other contexts. The matrix in Figure ES.1 displays a subjective assessment of the depth of potential cross-fertilization between major challenges from theoretical and computational chemistry and relevant topics in the mathematical sciences. This matrix is based to some extent on intuition because it is an assessment of future research opportunities, not past results. An "H" in the matrix implies an overlap that appears clearly promising, while an "M" suggests that some synergy between the areas is likely. The absence of an H or an M should not be taken to imply that some clever person will not find an application of that technique to that problem at some point.

Conclusions and Recommendations

As a result of its investigations and collective evaluation of the available information, the committee has reached the following conclusions.

  • Several notable "success stories" can be identified, illustrating the value of interdisciplinary stimulation and synergistic research collaboration involving cooperation between the mathematical sciences and the theoretical/computational chemistry communities.

  • Many opportunities appear to exist for further collaborations between the mathematical and chemical sciences that could result in high-quality scholarship and research progress that would advance national interests. The productivity of applied computational chemistry would likely be enhanced as a result, which could be potentially significant for industry.

  • Active encouragement of further collaborations is warranted because it would likely result in an acceleration of such research progress.

  • Cultural differences between the mathematics and the chemistry communities, involving language, training, aesthetics, and research style, have tended to act as barriers to collaboration, even in circumstances that might otherwise suggest the benefit of cooperation.

  • Institutional structures and reward systems in the academic community have often placed significant difficulties in the way of collaborative research across traditional disciplinary boundaries, which can be especially inhibiting to those in early career stages.

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