线性标度密度泛函理论的Daubechies波
Daubechies Wavelets for Linear Scaling Density Functional Theory
摘要：
我们证明，Daubechies小波可以用来构建一个最小的优化的本地化收缩基函数，其中的Kohn-Sham轨道可以表示与任意高的，可控的精度。基态能量和作用在离子上的力可以在此基础上计算，具有与直接在Daubechies小波基础上计算相同的精度，只要这些收缩的基函数的振幅在局部化区域的表面上足够小，这是由本工作中描述的优化过程保证的。这种方法降低了DFT计算的计算成本，并且可以与稀疏矩阵代数相结合，以获得相对于系统中电子数量的线性缩放。因此，在具有适度计算资源的系统基组中，对10，000个或更多原子的系统的计算变得可行。进一步的计算节省可以通过利用紧密相关环境的收缩基函数的相似性来实现，例如在中性和带电系统的几何优化或组合计算中。
英文摘要：
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of DFT calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the contracted basis functions for closely related environments, e.g. in geometry optimizations or combined calculations of neutral and charged systems.
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