周期系统的虚时含时密度泛函理论
Imaginary-time time-dependent density functional theory for periodic systems
摘要：
虚时含时密度泛函理论（it-TDDFT）作为一种在密度泛函理论（DFT）中获得基态的方法被提出，它避免了自洽场（SCF）迭代方法在收敛方面遇到的困难。它-TDDFT以前被应用到原子簇，它被证明在选择的情况下，SCF有困难的收敛。在目前的工作中，我们实现了它的TDDFT传播{ \it周期系统}通过修改量子ESTERO包，它使用一个平面波基与多个$\boldsymbol{k}$点，并有选择的非共线和DFT+U计算使用超软或范数守恒的赝势。我们证明了我们的实现多个$\boldsymbol{k}$点的it-TDDFT传播是正确的DFT+U非共线计算和DFT+U计算与超软赝势。我们的实施IT-TDDFT传播收敛到确切的SCF能量（高达双精度保证的小数），但在所有情况下，它收敛到比SCF稍低的值，这表明一个有用的替代系统，SCF有困难达到科恩-沙姆基态。此外，我们证明了快速收敛，可以实现，如果我们使用自适应大小的时间步长为不同的动能平面波。
英文摘要：
Imaginary-time time-dependent Density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was previously applied to clusters of atoms where it was demonstrated to converge in select cases where SCF had difficulty with convergence. In the present work we implement it-TDDFT propagation for {\it periodic systems} by modifying the Quantum ESPRESSO package, which uses a plane-wave basis with multiple $\boldsymbol{k}$ points, and has the options of non-collinear and DFT+U calculations using ultra-soft or norm-conserving pseudo potentials. We demonstrate that our implementation of it-TDDFT propagation with multiple $\boldsymbol{k}$ points is correct for DFT+U non-collinear calculations and for DFT+U calculations with ultra-soft pseudo potentials. Our implementation of it-TDDFT propagation converges to the exact SCF energy (up to the decimal guaranteed by double precision) in all but one case where it converged to a slightly lower value than SCF, suggesting a useful alternative for systems where SCF has difficulty to reach the Kohn-Sham ground state. In addition, we demonstrate that rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.
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