分子Kohn-Sham能隙和虚轨道的连续修正
Continuous corrections to the molecular Kohn-Sham gap and virtual orbitals
摘要：
我们使用投影算子来修正密度泛函理论（KS-DFT）的Kohn-Sham哈密顿量，使得得到的平均场方案在有限系统中产生的虚轨道和能隙与准粒子理论预测的更好的一致性。所提出的校正项是$(\hat{I}-\hatρ)δ\hat{H}(\hat{I}-\hatρ)$形式的剪刀状算子，其中$\hat{I}$是恒等算子，$\hatρ$是N粒子系统的密度矩阵，而$δ\hat{H}$是N+1粒子和N粒子Kohn-Sham哈密顿量之间的差，或者是对它的非自洽近似。这样的项取代了$N$的Kohn-Sham虚轨道。粒子系统的HOMO和虚轨道的系统与$N+1$粒子，试图模仿一个真正的准粒子谱。使用局域密度近似（LDA），我们计算的各种小分子的间隙找到良好的协议与实验和计算更苛刻的方法。对于这些系统，我们检查这个间隙校正的物理起源，并表明，所谓的带隙不连续性，$Δ_{xc}$，包含静电的贡献，不源于交换相关电位的不连续性。校正和Hartree-Fock虚拟轨道之间的相似性被示出，并在何种程度上被认为是裸LDA虚拟轨道的改善。带隙不连续性的缺乏和存在的自相互作用的建议修正的错误进行了讨论。
英文摘要：
We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that the resulting mean-field scheme yields, in finite systems, virtual orbitals and energy gaps in better agreement with those predicted by quasiparticle theory. The proposed correction term is a scissors-like operator of the form $(\hat{I}-\hatρ)δ\hat{H}(\hat{I}-\hatρ)$, where $\hat{I}$ is the identity operator, $\hatρ$ the density matrix of the N-particle system and $δ\hat{H}$ is either the difference between the N+1- and N-particle Kohn-Sham Hamiltonians or a non-self-consistent approximation to it. Such a term replaces the Kohn-Sham virtual orbitals of the $N$-particle system by the HOMO and virtual orbitals of the system with $N+1$ particles in an attempt to mimic a true quasiparticle spectrum. Using a local density approximation (LDA) we compute the gaps of a variety of small molecules finding good agreement with experiment and computationally more demanding methods. For these systems we examine the physical origin of this gap correction and show that so-called band gap discontinuity, $Δ_{xc}$, contains electrostatic contributions that do not originate from the discontinuity in the exchange-correlation potential. The similarity between the corrected and Hartree-Fock virtual orbitals is illustrated and the extent to which the bare LDA virtual orbitals are improved is considered. The lack of band-gap discontinuity and the presence of self-interaction errors in the proposed correction are also discussed.
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