possible variety of methods for constructing approximate solutions to the Schrödinger equation, not focus simply on developing, or trying to develop, scalable implementations of what we have now.

Paul Messina: Peter, I remember from a few years ago working with a colleague at Caltech, the chemist Aron Kupperman, that when we were able to provide him a substantially bigger computing environment, he quickly found that the basis set that he was using was, in fact, not adequate, and he had to come up with a more nearly orthogonal basis set to be able to get any type of accuracy. So, would you include in the new methods examination the need to look also at those aspects where now you have a much bigger system and consequently would have to worry more about the capability of the methods?

Peter Taylor: Oh, yes. I think there is no question about that. This is just another aspect of the sorts of improvements we need to try.

Thom Dunning, Pacific Northwest National Laboratory: I think just in general, to make very concrete the kind of suggestion Peter is making, that it has become painfully clear over the past decade how slowly basis-set expansions converge. Yes, we can approach the full solution of the Schrödinger equation with the basis-set technology that we have, but it is a very painful process and it gives rise to some of this very horrible scaling that Peter is talking about. Plus, it gives rise in schemes like what John is talking about, G2 and G3, to some of those large deviations that are observed just because in the basis sets that are used, the convergence is not there for that type of molecule.

John Pople: Yes, there are worries all the time that all the technology we are using, which is based very much on Gaussian functions, may not be the best approach when we come to very large systems and very new technology.

One such possibility to be looked at by chemists is the matter of plane wave expansions that solid state physicists use quite a lot. It is more appropriate for them, perhaps, because a crystal is a periodic system. But nonetheless, one can ask whether you can do better with all the modern techniques of fast Fourier transforms and so forth by taking the molecule in the middle of an empty box and proceed to expand everything in plane waves. That technology could conceivably be a new approach that would possibly eliminate some of the difficulties we have at present.

Evelyn Goldfield, Wayne State University: One of the things that I would like to address was in Peter Taylor's talk when he divided the field into three: electronic structure, reaction dynamics, and molecular dynamics. It seems that one of the hurdles to actually using these codes effectively is that there is a step between electronic structure, when you calculate points, and having a usable potential energy surface. Someone has to laboriously fit a potential, which may or may not be an accurate reflection of the ab initio surface. And then another community, the dynamics community, uses that potential and makes some predictions that may or may not compare to experiment. Among the most challenging things that could be produced are codes that actually integrate these three parts of the problem so that the fitting steps are bypassed. Such efforts are actually a hot topic right now. To deal with realistic and interesting systems is really going to be incredibly computationally intensive and I think could effectively make use of any number of processors.

Peter Taylor: I agree. I think this is a defect in what we currently have—that we do not have enough integration between these steps. While there are, for example, dynamics programs that basically call for the electronic energy or something like the gradient of the potential surface on the fly, we do not have

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