符合Koopmans的泛函及其对参考分子数据的性能
Koopmans-compliant functionals and their performance against reference molecular data
摘要：
Koopmans兼容的泛函出现自然从延长的约束分段线性的总能量作为一个函数的电子数到每个分数轨道占领。当应用于近似密度泛函理论时，这些修正引起轨道密度相关的泛函和势。我们表明，Koopmans顺从性的最简单实现提供了准粒子激发的准确估计，并且使总能量泛函几乎或完全不变，即，它们正确地描述了电子的去除或添加，但不一定改变系统内的电子电荷密度分布。然后可以构建修改势能面的附加泛函，包括例如Perdew-Zunger校正。这些泛函变得完全无单电子自相互作用，并且与所有符合库普曼的泛函一样，近似无多电子自相互作用。我们详细讨论了这些不同的配方，并提供了广泛的基准参考G2-1组中的55个分子，使用Koopmans兼容的泛函从局部密度或广义梯度近似构建。在所有情况下，我们发现优良的性能，在电子性能，可比或改进的多体微扰理论，如G $_0$ W $_0$和自洽GW，在成本的一小部分，并在一个变分的框架，也提供了能源衍生物。结构性质和原子化能量保持或略微提高了基本密度泛函近似的准确性（注：补充材料包含在源代码中）。
英文摘要：
Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional functionals can then be constructed that modify the potential energy surface, including e.g. Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G$_0$W$_0$ and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations (Note: Supplemental Material is included in the source).
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