论文标题
部分可观测时空混沌系统的无模型预测
One-electron self-interaction error and its relationship to geometry and higher orbital occupation
论文作者
论文摘要
密度功能理论（DFT）认为在计算化学和物理学中的显着用途，但是由于自我交互误差（SIE）引起的问题提出了额外的挑战，可以获得定性正确的结果。电子的非物理能量自身施加，SIE会影响最实用的DFT计算。我们对单电子SIE进行了深入的分析，在该分析中，我们复制了用于简单几何形状的定居效应。我们提出了这种效果的简单可视化，这可能有助于对单电子SIE的未来定性分析。通过在线性排列中增加核的数量，SIE急剧增加。我们还展示了分子形状如何影响SIE。二维形状和三维形状显示出更大的SIE，主要源于交换功能，并从一电子误差中获得了一些误差补偿，我们以前定义了该误差[phys。化学化学物理。 22，15805（2020）]。大多数测试的几何形状受功能误差的影响，而有些则遭受密度误差的影响。对于后者，我们建立了通过DFT方法不平等地将电子定位的潜在联系。我们还展示了如果电子占据上林的原子轨道，SIE如何增加；在兴奋的状态下，看似单电子的SIE方法不再是无sie的，这对于某些流行的，非经验的DFA来说是一个重要的见解。我们得出的结论是，即使在最简单的几何形状中，SIE的行为不稳定，表明需要强大的密度功能近似值。我们的测试系统可以用作未来的基准或为DFT开发做出贡献。
Density Functional Theory (DFT) sees prominent use in computational chemistry and physics, however, problems due to the self-interaction error (SIE) pose additional challenges to obtaining qualitatively correct results. An unphysical energy an electron exerts on itself, the SIE impacts most practical DFT calculations. We conduct an in-depth analysis of the one-electron SIE in which we replicate delocalization effects for simple geometries. We present a simple visualization of such effects, which may help in future qualitative analysis of the one-electron SIE. By increasing the number of nuclei in a linear arrangement, the SIE increases dramatically. We also show how molecular shape impacts the SIE. Two and three dimensional shapes show an even greater SIE stemming mainly from the exchange functional with some error compensation from the one-electron error, which we previously defined [Phys. Chem. Chem. Phys. 22, 15805 (2020)]. Most tested geometries are affected by the functional error, while some suffer from the density error. For the latter we establish a potential connection with electrons being unequally delocalized by the DFT methods. We also show how the the SIE increases if electrons occupy higher-lying atomic orbitals; seemingly one-electron SIE free methods in a ground are no longer SIE free in excited states, which is an important insight for some popular, non-empirical DFAs. We conclude that the erratic behavior of the SIE in even the simplest geometries shows that robust density functional approximations are needed. Our test systems can be used as a future benchmark or contribute towards DFT development.
