The Divide-and-Conquer Density-Functional Approach for Large Molecules and for Molecules on Surfaces

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Professor Weitao Yang at the Chemistry Department of Duke University is supported by a grant from the Theoretical and Computational Chemistry Program at NSF for studies of the electronic structure of large systems. These studies involve the divide-and-conquer, D&C, approach which has been pioneered by Professor Yang. The D&C approach to electronic structure divides a large system into many smaller systems and the electron density of each system is determined separately. The density and properties of the entire system are obtained by appropriately combining the results for the sub-systems. The D&C approach provides a powerful way to use Density Functional Theory to determine the energies and other properties of large systems, condensed matter as well as isolated molecules. One focus of the work supported by this grant is to enhance and extend the mathematical methods used in the D&C approach. In particular, energy gradients are being calculated in order to allow the efficient calculation of the stable geometries of these large systems. There is also effort directed toward combining quantum mechanics and molecular mechanics. The accurate quantum mechanical treatments are used to describe regions of the system where there are important chemical effects. On the other hand, the more approximate molecular mechanics treatments are used to describe the environment of these regions. The second focus of the work supported by this grant is to apply the D&C approach to the study of the bulk and surface properties of solids. An advantage of D&C is that it can be used in a straightforward way to treat systems without translational symmetry; thus, problems involved in the adsorption, or chemisorption, of atoms and molecules on surfaces are being treated. A major limitation for accurate theoretical treatments of large molecular systems has been the exponential increase in computational effort with the size of the system being studied. A similar comment holds for the size of the repeat unit, or unit cell, of solids. For a large system, it is possible to relate the scaling of the computational effort to the number of atoms, N, contained in the system. Ab initio methods scale at the fourth or even higher powers of N and standard Density Functional methods scale as the third power of N. However, the D&C approach to Density Functional methods scales linearly with N; this linear scaling could make accurate treatments possible for quite large systems. If the efforts supported by this grant are successful, a major breakthrough will have been made.