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

杜克大学化学系的杨伟涛教授 由理论与计算化学基金会资助 美国国家科学基金会研究大系统电子结构的计划。 这些研究涉及分而治之的方法， 由杨教授开创。D C电子方式 结构将一个大系统分成许多小系统， 每个系统的电子密度被分别确定。的密度和 整个系统的性质是通过适当地组合 子系统的结果。DC方法提供了一种强大的方法， 使用密度泛函理论来确定能量和其他 大系统的性质，凝聚态以及孤立的 分子。这项赠款支持的工作重点之一是加强 推广了DC法中的数学方法。在 特别是，正在计算能量梯度，以便允许 这些大型系统的稳定几何结构的有效计算。 也有人致力于将量子力学和 分子力学采用精确的量子力学处理方法， 来描述系统中存在重要化学物质的区域 方面的影响.另一方面，更近似的分子力学 处理被用来描述这些区域的环境。的 这项补助金支持的第二个工作重点是应用D C 研究固体的体积和表面性质的方法。一个 DC的优点是它可以直接用于 处理没有平移对称的系统;因此， 原子和分子在表面上的吸附或化学吸附， 接受治疗 精确理论处理大分子的一个主要限制 系统一直是计算工作量的指数增长， 所研究的系统的大小。类似的评论适用于 固体的重复单元或晶胞的大小。对于大型系统，它 可以将计算工作量的缩放与 系统中包含的原子数N。从头算方法规模. N的四次或更高次幂和标准密度泛函 方法按N的三次幂缩放。然而，D C方法 密度泛函方法与N线性缩放;这种线性缩放 可以使精确的治疗成为可能，对于相当大的系统。如果 这项赠款支持的努力取得成功，将取得重大突破， 已经被制造出来了。

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.