School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
J Chem Phys. 2013 Aug 7;139(5):054107. doi: 10.1063/1.4817001.
A new method for finite-temperature density functional theory calculations which significantly increases the number of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic system, described in terms of a set of non-orthogonal, localized functions which are optimized in situ using a periodic-sinc basis set, equivalent to plane waves. Most parts of the calculation, including the demanding operation of building the Hamiltonian matrix, have a computational cost that scales linearly with the number of atoms in the system. Also, this approach ensures that the Hamiltonian matrix has a minimal size, which reduces the computational overhead due to diagonalization, a cubic-scaling operation that is still required. Large basis set accuracy is retained via the optimization of the localized functions. This method allows accurate simulations of entire metallic nanostructures, demonstrated with calculations on a supercell of bulk copper with 500 atoms and on gold nanoparticles with up to 2057 atoms.
提出了一种新的有限温度密度泛函理论计算方法，该方法显著增加了可以在金属体系中模拟的原子数量。采用自洽直接最小化技术来获得电子系统的亥姆霍兹自由能，该电子系统采用一组非正交的局域函数来描述，这些局域函数可以使用周期性 sinc 基函数原位优化，该基函数等效于平面波。计算的大部分部分，包括构建哈密顿矩阵的要求操作，其计算成本与系统中的原子数量呈线性比例。此外，这种方法确保了哈密顿矩阵具有最小的大小，从而减少了由于对角化导致的计算开销，而对角化是仍然需要的三次方比例运算。通过对局部函数的优化，保留了大基集精度。该方法允许对整个金属纳米结构进行精确的模拟，通过对 500 个原子的块状铜超晶胞和多达 2057 个原子的金纳米粒子的计算证明了这一点。
