Linear Scaling Algorithms For Daubechies Wavelet Density Functional Theory

Electronic structure calculations based on density functional theory calculations traditionally suffering from an inherent cubic scaling with respect to the size of the system can't satisfy the current study and it needs urgently to develop a method that computational time and memory with system size can increase linearly, which is called the linear scaling algorithm. The background of physical for linear scaling algorithm is quantum mechanics locality due to the locality and orthogonal of Daubechies wavelet in real space and Fourier space. It has become a powerful system of electronic structure calculations basis set. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementation offering such a linear complexity either yielding only a limited accuracy or require a tedious fine tuning of many parameters. This is the most important weakness of this method.In this paper, we have studied the latest international conduct linear scaling algorithm which use Daubechies wavelets to construct a minimal set of localized adaptively contracted basis functions. After analysis we found that algorithm using the BigDFT package in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Through strictly localized basis of research,we define this approach reduces the complexity of density functional theory calculations, and can be combined with sparse matrix algebra to obtain a linear scaling with respect to the number of electrons in the system. With actual numerical experiments, we found that under the conditions of moderate computational resources, it is feasible to achieve the millennium atoms or more computing.Research work of this paper is as follows.(1) Through the research literature Daubechies wavelet density functional theory calculations related aspects of home and abroad, we summed up the latest research about the dynamics of the DFT algorithm, in particular the principles density functional calculations advances in linear scaling algorithm;(2) we detailed description of the calculation method based on density functional Daubechies wavelet, as well as the corresponding linear scale to achieve;(3)we analyze the degree of linear scaling BigDFT specific application performance and gave the linear scale of density functional calculations examples of cases considered, through BigDFT1.7.1 scheduling software installation and use on the high-performance computing platform.