Council, 1974, 1975, 1976; Schatz, 1984; Berne, 1985). Not surprisingly, physics and engineering manifested similar experiences at the same time (National Science Foundation (NSF) Advisory Committee for Physics, 1981; Lax, 1982; NSF Working Group on Computers for Research, 1983; National Research Council, 1984).

The pervasive significance and widespread applicability of theoretical and computational chemistry may not always be immediately obvious to those not frequently concerned with this activity. Nevertheless, it is central to rational drug design, it contributes to the selection and synthesis of new materials, and it guides the design of catalysts. New quantum mechanical techniques underlie the understanding of electronic properties of materials and have advanced the level of precision at which molecules of at least moderate size can be modeled. Furthermore, computational chemistry software is a set of tools used increasingly by chemists of many persuasions. These various abilities and facilities have proved to be very important to American industry, and their advancement would generate even further industrial benefits. Engaging problems and deep challenges for mathematical scientists are posed by the needs of theoretical and computational chemists, and the products of mathematical research in these areas can have far-reaching ramifications.

The marked growth of theoretical/computational chemistry inevitably has involved a substantial national investment of skilled human resources and of expensive computing resources (both hardware and software). Both of these types of commodities are relatively scarce and are subject to competition between alternative scientific and technological disciplines. Table 1.1 shows, for instance, that software for theoretical and computational chemistry claims much of the cpu usage on the Cray Y-MP at the San Diego Supercomputer Center. Data from other NSF supercomputer centers reveals similar patterns. What Table 1.1 does not show is the heavy dependence of these chemistry codes on mathematical software such as LINPACK and EISPACK. The productivity of these computational resources, broadly construed, must be an issue for continual analysis and informed action by policymakers. In particular, the strong mathematical flavor of theoretical/computational chemistry leads to a natural examination of the efficacy of links between the mathematical and the chemical sciences, and to the past, present, and future rules of interdisciplinary research at the interface between these subjects. These issues constitute basic concerns for the present study.

The 14 chemists, biochemists, and mathematical scientists from industry, government, and academia who attended a 1991 workshop at the National Research Council (NRC) decided that the interface of the mathematical sciences and theoretical/computational chemistry was an area that deserved encouragement, and that a fuller study of the issues was warranted. Subsequently, the Board on Mathematical Sciences and the Board on Chemical Sciences and Technology of the NRC jointly proposed a study to identify research opportunities for the mathematical sciences relevant to computational chemistry, with the goal of engaging the talent of more mathematical scientists in the problems of computational chemistry, which should produce advances of benefit to both the mathematical and the chemical sciences. The phrase "computational chemistry" was to be interpreted to include those areas related to molecular structure and its determination, broadly defined; it was felt that there was less need to promote greater participation by mathematical scientists in the areas of computational chemistry on the macroscopic scale—including such topics as reaction/diffusion modeling and most of chemical engineering. On securing approval and funding for this study, a Committee on Mathematical Challenges from Computational Chemistry was selected, with its first meeting held in Washington, D.C. on March 29–30, 1994. Two subsequent meetings took place: June 910, 1994, in Washington, D.C., and September 911, 1994, in Woods Hole, Massachusetts.

The statement of task given to the Committee on Mathematical Challenges from Computational Chemistry reads as follows: "The committee will investigate and report on opportunities for 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



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