周期系统中的密度拟合：应用于金刚石和氧化物中的TDHF
Density fitting in periodic systems: application to TDHF in diamond and oxides
摘要：
描述了一种基于Ewald势的两中心和三中心矩阵元计算Bloch函数上的库仑矩阵元的鲁棒密度拟合方法，并在激子码的高斯轨道基上实现。该方法进行了测试，通过比较库仑和交换能量密度拟合相应的能量SCF HF计算金刚石，氧化镁和散装氖。从强大的方法的密度拟合系数进行比较，从变分法适用于散装Ne的波函数轨道产品的系数。采用密度拟合的四中心库仑矩阵元对金刚石、氧化镁、金红石和金红石多型钛白进行了含时Hartree-Fock（TDHF）计算。相对于占据态均匀向下移动虚态，并将TDHF哈密顿量中的电子-空穴吸引项缩放0.4，这与实验和/或Bethe-Salpeter方程计算结果吻合得很好。这种方法反映了类似的“剪刀”的调整占用和虚拟的状态和引入一个缩放的电子空穴吸引力项在一些时间依赖DFT计算。
英文摘要：
A robust density fitting method for calculating Coulomb matrix elements over Bloch functions based on calculation of two- and three-center matrix elements of the Ewald potential is described and implemented in a Gaussian orbital basis in the Exciton code. The method is tested by comparing Coulomb and exchange energies from density fitting to corresponding energies from SCF HF calculations for diamond, magnesium oxide and bulk Ne. Density fitting coefficients from the robust method are compared to coefficients from a variational method applied to wave function orbital products in bulk Ne. Four center Coulomb matrix elements from density fitting are applied to time dependent Hartree-Fock (TDHF) calculations in diamond, magnesium oxide and anatase and rutile polytypes of titanium dioxide. Shifting virtual states downwards uniformly relative to occupied states and scaling the electron-hole attraction term in the TDHF Hamiltonian by 0.4 yields good agreement with either experiment and/or Bethe-Salpeter equation calculations. This approach mirrors similar 'scissors' adjustments of occupied and virtual states and introduction of a scaled electron-hole attraction term in some time dependent DFT calculations.
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