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得到了美国国家科学基金会理论和计算化学项目的资助，用于研究大系统的电子结构。这些研究涉及杨教授首创的分而治之的D&A；C方法。电子结构的D&A；C方法将一个大的系统分成许多较小的系统，每个系统的电子密度是单独确定的。整个系统的密度和性质是通过适当地组合子系统的结果来获得的。D&A；C方法提供了一种使用密度泛函理论来确定大系统、凝聚态物质以及孤立分子的能量和其他性质的有效方法。这笔赠款支持的工作重点之一是加强和推广D&A；C方法中使用的数学方法。特别是，正在计算能量梯度，以便能够有效地计算这些大系统的稳定几何结构。还有一项努力是将量子力学和分子力学结合起来。精确的量子力学处理被用来描述系统中存在重要化学效应的区域。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。这笔赠款支持的工作的第二个重点是将D&A；C方法应用于固体的体积和表面性质的研究。D&Amp；C的一个优点是，它可以直接用于处理没有平移对称性的体系；因此，涉及原子和分子在表面上的吸附或化学吸附的问题正在被处理。大分子体系精确的理论处理的一个主要限制是计算量随着所研究的体系的大小呈指数增长。对于实体的重复单位或单元格的大小，也有类似的评论。对于一个大的系统，可以将计算工作量的比例与系统中包含的原子数量N联系起来。从头算方法的标度是N的4次方甚至更高，而标准密度泛函方法的标度是N的3次方。然而，密度泛函方法的D&A；C方法随着N的线性标度；这种线性标度可以使非常大的系统的精确处理成为可能。如果这笔赠款支持的努力取得成功，将取得重大突破。

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.