Xiang H J, Yang Jinlong, Hou J G, Zhu Qingshi
Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
J Chem Phys. 2007 Jun 28;126(24):244707. doi: 10.1063/1.2746322.
Linear scaling methods provide total energy, but no energy levels and canonical wave functions. From the density matrix computed through the density matrix purification methods, we propose an order-N [O(N)] method for calculating both the energies and wave functions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematically and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.
线性缩放方法能提供总能量，但无法给出能级和正则波函数。通过密度矩阵纯化方法计算得到密度矩阵后，我们提出了一种用于计算带边态能量和波函数的 $N$ 阶算法，这些带边态对光学性质和化学反应很重要。此外，我们还基于计算带边态的 $N$ 阶算法开发了一种处理掺杂半导体的 $N$ 阶算法。我们将新方法应用于氮化硼（BN）纳米管和吸附有氢原子的 BN 纳米管，以此来说明该方法的 $N$ 阶特性。系统地研究了各种 BN 纳米管的带隙，并计算了带有孤立吸附氢原子的 BN 纳米管的受主能级。我们的方法简单、稳健，特别适用于自洽场电子结构理论中的应用。
