Izmaylov Artur F, Scuseria Gustavo E
Department of Chemistry, Rice University, Houston, Texas 77005, USA.
J Chem Phys. 2008 Jul 21;129(3):034101. doi: 10.1063/1.2953701.
We examine the time-dependent density functional theory (TD-DFT) equations for calculating excitation energies in solids with Gaussian orbitals and analytically show that for semilocal functionals, their lowest eigenvalue collapses to the minimum band orbital energy difference. With the introduction of nonlocal Hartree-Fock-type exchange (as in hybrid functionals), this result is no longer valid, and the lowest TD-DFT eigenvalue reflects the appearance of excitonic effects. Previously reported "charge-transfer" problems with semilocal TD-DFT excitations in molecules can be deduced from our analysis by taking the limit to infinite lattice constant.
我们研究了用于计算固体中激发能的含时密度泛函理论（TD-DFT）方程，该方程采用高斯轨道，并通过分析表明，对于半局域泛函，其最低本征值会收敛到最小带轨道能量差。随着非局域哈特里 - 福克型交换（如在杂化泛函中）的引入，这一结果不再成立，且TD-DFT的最低本征值反映了激子效应的出现。先前报道的分子中半局域TD-DFT激发的“电荷转移”问题可通过取无限晶格常数的极限从我们的分析中推导得出。
