Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity.
Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity.
复制标题
密度泛函理论中的轨道能量和负电子亲和势：来自整数不连续性的见解。
作者：
A. M. Teale;F. de Proft;D. Tozer
研究了Kohn-Sham密度泛函理论(DFT)中的轨道能量，考虑了整数间断在精确交换相关势中的作用。我们考虑了一系列封闭壳分子，包括一些垂直结合多余电子的分子和一些不垂直结合多余电子的分子。高水平从头算电子密度被用来计算最低未占据分子轨道(LUMO)和最高占据分子轨道(HOMO)之间的精确轨道能量差Deltavarepsilon，对两者使用相同的势。它们与精确的垂直电离势I(0)和电子亲合势A(0)相结合，可以确定准确的“平均”轨道能量。这些是与交换关联势有关的轨道能量，它在精确势的恒定跳跃上取平均值，如不连续分析所给出的量级为Delta(Xc)=(I(0)-A(0))-Deltavarepsilon。局域泛函HOMO能几乎比-I(0)更接近这些平均值一个数量级，典型的偏差仅为0.02A.U。对于不结合过剩电子的体系，只有当A(0)设置为等于来自电子透射谱(ETS)的负实验亲和力时，才能达到这种一致性水平；当改为使用零基态亲和力时，A(0)显著退化。对于局域泛函LUMO能量也进行了类似的观察，尽管对于ETS值非常负的系统来说，使用ETS亲和力的必要性不那么明显。渐近修正的应用恢复了偏好，导致这些系统的LUMO能量为正(但束缚轨道)，与平均能量的行为一致。渐近校正的LUMO能量通常与平均值一致，在0.02aU以内，与HOMO观测到的结果相当。这项研究为局部泛函表现出基于幅度增量(XC)的恒定跳跃的近平均行为的观点提供了数值支持。它解释了为什么最近提出的包含局域函数前线轨道能量和电离势的密度泛函表达式给出了对负ETS亲和势的合理估计，并且与早期关于电荷转移激发态密度泛函失效的工作是一致的。对于选定的系统，明确地说明了交换关联势的近平均行为。文中还提到了杂化轨道能的性质，并讨论了电子能量随电子数变化的研究结果。DFT轨道能量的性质在化学上具有重要意义，这一研究有助于理解这些量。
Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital energy differences, Deltavarepsilon, between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), using the same potential for both. They are combined with accurate vertical ionization potentials, I(0), and electron affinities, A(0), to determine accurate "average" orbital energies. These are the orbital energies associated with an exchange-correlation potential that averages over a constant jump in the accurate potential, of magnitude Delta(XC)=(I(0)-A(0))-Deltavarepsilon, as given by the discontinuity analysis. Local functional HOMO energies are shown to be almost an order of magnitude closer to these average values than to -I(0), with typical discrepancies of just 0.02 a.u. For systems that do not bind an excess electron, this level of agreement is only achieved when A(0) is set equal to the negative experimental affinity from electron transmission spectroscopy (ETS); it degrades notably when the zero ground state affinity is instead used. Analogous observations are made for the local functional LUMO energies, although the need to use the ETS affinities is less pronounced for systems where the ETS values are very negative. The application of an asymptotic correction recovers the preference, leading to positive LUMO energies (but bound orbitals) for these systems, consistent with the behavior of the average energies. The asymptotically corrected LUMO energies typically agree with the average values to within 0.02 a.u., comparable to that observed with the HOMOs. The study provides numerical support for the view that local functionals exhibit a near-average behavior based on a constant jump of magnitude Delta(XC). It illustrates why a recently proposed DFT expression involving local functional frontier orbital energies and ionization potential yields reasonable estimates of negative ETS affinities and is consistent with earlier work on the failure of DFT for charge-transfer excited states. The near-average behavior of the exchange-correlation potential is explicitly illustrated for selected systems. The nature of hybrid functional orbital energies is also mentioned, and the results of the study are discussed in terms of the variation in electronic energy as a function of electron number. The nature of DFT orbital energies is of great importance in chemistry; this study contributes to the understanding of these quantities.