### Thursday, September 21

## IP2

The Electronic Structure of Molecules -- Theory, Algorithm, and Application

9:15 AM-10:00 AM

*New Hampshire Ballroom*

Chair: Michael T. Heath, University of Illinois, Urbana-Champaign, USA

Over the last two decades quantum chemistry has evolved from an interpretative tool, usually only able to provide qualitative results, into a predictive tool, often able to achieve accuracies comparable to or exceeding experiment. This has been achieved by the development and systematic testing of families of improved approximate solutions to the Schrödinger and Dirac equations, and the use of these has been enabled by advances in computer algorithms and hardware. So successful has been this development that in many application areas quantum chemistry has become an engineering tool.

However, despite these advances, very high precision results are still only attainable for molecules of modest size. This is a result of the cost these electronic structure calculations scaling with up to the seventh power of the number of electrons being modeled. There are also other severe dimensionality problems such as finding and connecting via reaction pathways the minimum energy structures of large, floppy molecules, or correctly describing the very large manifold of states arising from coupling even a modest number of unpaired electrons.

Many people are working to address these issues and are exploring new theoretical approximations, algorithmic formulations, and the use of new (and old) results of applied mathematics. The result is the beginning of a renaissance period in quantum chemistry.

I will briefly describe some of the many methods used to describe molecular electronic structure including some of their applications at Pacific Northwest National Laboratory. Most of my talk will focus on the origin of the scaling problems and some of the approaches being taken to remedy them. I hope to convey to you the enormous importance of applied math to computational chemistry, how the methods currently used differ sharply from those of most other disciplines, and some of the many opportunities for fruitful interaction between mathematicians and chemists.

**Robert J. Harrison**

*Pacific Northwest National Laboratory, USA*