Basic Research Needs for Geosciences - Energetics Meetings and ...

GRAND CHALLENGE: COMPUTATIONAL THERMODYNAMICS OF COMPLEX FLUIDS AND SOLIDSsystem is given in Figure 24. In this problem, DFT calculations (Figure 24a) yield a completelydelocalized spin density (incorrect), in contrast to the predictions of an exchange localized spindensity when self-interactions are taken into account (Figure 24b; correct). The proper inclusionof exchange may have a dramatic effect on the reactivity of surface defects. Scalable algorithmsthat include exact exchange need to be developed for first-principles dynamics.A more difficult problem with the DFT method is that long-range non-bonded (van der Waals)interactions are not included formally in the theory. These interactions dominate many problemsof interest to subsurface modeling. The inclusion of exact self-consistent exchange as above isnot sufficient to improve the accuracy for these problems. They can be treated by using highaccuracy molecular orbital-based methods, e.g., MP2, or CCSD(T) (Bartlett 2005), or QuantumMonte Carlo methods (Grossman et al. 2001). However, these methods are currently too costly.New techniques may broaden their applications to much more complex systems (Kowalski andValiev 2006; Valiev and Kowalski 2006). A critical research area is the development of higherlevels of approximation for the electronic Schrödinger equation that can be used with dynamicmethods in a computationally efficient manner.Significant improvements in algorithm performance, scalability and implementation are requiredto treat important energy applications using any level of solution to the Schrödinger equation.For example, currently an ab initio molecular dynamics simulation of 128 water molecules for0.1 picosecond (ps) requires about 1000 CPU hours, 30 ps about 34 CPU years! The projectedsize of the next generation supercomputers (10,000–100,000 processors) suggests that simulationtimes and particle size limitations could be overcome by brute force increases in computer size.However, there is a substantial problem in the parallelization of the Fast Fourier Transform(FFT) method that is critical to solving the electronic motion problem with plane wave DFT.Available implementations of present methods do not scale much beyond 1000 processors. Thereare fundamental reasons for this limitation which are difficult to overcome. The question ofproper approximation in terms of discretization and the (separate) question of proper choice ofiterative methods need to be addressed. More efficient and/or better scaling methods could bebased on the use of completely unstructured simplex finite element or wavelet techniques(Harrison et al. 2004) built adaptively (Bank and Holst 2003) using a multilevel solve-estimaterefineiteration. Scaling can also be improved by finding methods to hide the latency in thecalculation (Sorenson and Baden 2006).The third problem demands new methods of upscaling both in number of particles tracked andtime. The particle numbers included in a calculation can often be greatly increased by dividingthe problem into a region in which quantum chemistry is required and a region in which a muchmore efficient molecular mechanics description of the forces is adequate, referred to as QM/MM(Quantum Mechanics/Molecular Mechanics) approaches (Field et al. 1990; Eichinger et al.1999). These methods need to be made more efficient by coupling to faster solvers of theelectronic Schrödinger equation. A promising way to upscale time is the introduction of rareevent strategies. These approaches recognize that the important dynamics of a system—thosethat dramatically change the structure of the system as in a chemical reaction—occur rarely (seeFigure 25). There are a number of ways to search for rare events. However, most of these havebeen designed for problems with only a few degrees of freedom. One class of methodsaccelerates or makes more efficient the exploration of phase space either by using higher72 Basic Research Needs for Geosciences: Facilitating 21 st Century Energy Systems