Quantifying the effects of the self-interaction error in DFT: When do the delocalized states appear?
Quantifying the effects of the self-interaction error in DFT: When do the delocalized states appear?
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DOI：
10.1063/1.1926277
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发表时间：
2005-06-08
影响因子：
4.4
通讯作者：
Siegbahn, PEM
中科院分区：
文献类型：
--
作者：
Lundberg, M;Siegbahn, PEM
密度泛函理论中的自相互作用误差导致离域态的人为稳定，这在具有奇数电子的系统中最为明显。明显的例子是碳正离子自由基的解离，它通常会在长距离处产生离域状态，并且计算的结合能存在较大误差。另一方面，许多已知表现出价捕获的混合价过渡金属二聚体被正确预测为局部化的。为了了解自相互作用误差对这些不同系统的影响，使用 B3LYP 计算离域态和局域态之间的能量差异。在自由基在无限距离处解离成对称片段时，这种能量差等于密度泛函处理的误差。能量差随着系统尺寸的增加而减小，从 H-2(+) 的 55 kcal/mol 到 C12H26+ 的 15 kcal/mol。溶剂校正可稳定局部状态并导致较小的误差。大多数反应是不对称的，这减少了自相互作用误差的影响。在许多系统中，如果将电子从一个片段移动到另一个片段的成本为 70-80 kcal/mol (3.0-3.5 eV)，则不会发生离域。这个估计是指碎片之间的距离无限大的情况。该限制随着片段距离的减小而减小。对 Mn(III,IV) 二聚体铁磁态的 B3LYP 计算预测，正确的定域态比错误的离域态稳定 22 kcal/mol。在金属-金属距离短的情况下，预计自相互作用误差的影响很小。然而，当两个锰中心之间的距离增加到 7 A 时，二聚体开始离域，能量人为降低。在解离极限下，误差为 10 kcal/mol。这被解释为源自自交互错误的伪影。由于相对较短的金属-金属距离和不对称的配体环境，许多系统中不会遇到离域。然而，一些电荷转移络合物无法正确计算，并且离域态可能成为具有多个过渡金属络合物的酶系统大型模型中的问题。
The self-interaction error in density-functional theory leads to artificial stabilization of delocalized states, most evident in systems with an odd number of electrons. Clear examples are dissociations of carbocation radicals that often give delocalized states at long distances and large errors in computed binding energies. On the other hand, many mixed-valence transition-metal dimers known to exhibit valence trapping are correctly predicted to be localized. To understand the effects of the self-interaction error on these different systems, energy differences between delocalized and localized states are calculated with B3LYP. In the dissociation of radicals into symmetric fragments at infinite distance, this energy difference equals the error of the density-functional treatment. The energy difference decreases with increasing size of the system, from 55 kcal/mol in H-2(+) to 15 kcal/mol for C12H26+. Solvent corrections stabilize the localized state and result in smaller errors. Most reactions are asymmetric and this decreases the effect of the self-interaction error. In many systems, delocalization will not occur if the cost to move the electron from one fragment to the other is 70-80 kcal/mol (3.0-3.5 eV). This estimate refers to a situation where the distance between the fragments is infinite. The limit decreases with decreasing fragment distance. B3LYP calculations on the ferromagnetic state of a Mn(III,IV) dimer predict that the correct localized state is 22 kcal/mol more stable than the incorrect delocalized state. At short metal-metal distances the effect of the self-interaction error is predicted to be small. However, as the distance between the two manganese centers is increased to 7 A, the dimer starts to delocalize and the energy artificially decreases. In the dissociation limit, the error is 10 kcal/mol. This is interpreted as an artifact originating from the self-interaction error. Delocalization is not encountered in many systems due to relatively short metal-metal distances and asymmetric ligand environments. However, some charge-transfer complexes cannot be properly calculated and delocalized states may become a problem in large models of enzyme systems with multiple transition-metal complexes.