应用自洽$α$方法改进模型交换势的性能
Application of self-consistent $α$ method to improve the performance of model exchange potentials
摘要：
自相互作用误差是密度泛函理论中的一个重要问题。为了在保持计算效率的前提下修正这一误差，最近提出了一些近似的精确交换方法。我们提出了一个关键的比较模型交换势通过应用渐近调整自洽$α$，AASC $α$，方法和BJ有效交换势先进的[A. D. Becke和E.R. Johnson，J.Chem.Phys.124，221101（2006）]和[V.N. Staroverov，J.Chem.Phys.129，134103（2008）]。特别是，我们讨论了他们遵守坐标标度，维里和功能性衍生物的条件。讨论了AASC $α$方法在AA-BJ势生成中的应用。数值比较是通过实施一个完全数值的双原子分子代码产生分子维里能量和电离势近似的HOMO轨道的能量。结果表明，这些模型的潜力，如不遵守Levy-Perdew维里关系的一些缺点，可以消除乘一个轨道相关的功能$α$，它可以简化为一个常数确定的过程中的自洽（自洽$α$）的响应项。
英文摘要：
Self interaction error remains an impotrant problem in density functional theory. A number of approximations to exact exchange aimed to correct for this error while retainining computational efficiency had been suggested recently. We present a critical comparison between model exchange potentials generated through the application of the asymptotically-adjusted self-consistent $α$, AASC$α$, method and BJ effective exchange potential advanced in [A.D. Becke and E.R. Johnson, J. Chem. Phys. 124, 221101 (2006)] and [V.N. Staroverov, J. Chem. Phys. 129, 134103 (2008)]. In particular we discuss their compliance with coordinate-scaling, virial and functional derivative conditions. We discuss the application of the AASC$α$ method to generate the AA-BJ potential. A numerical comparison is carried out through the implementation of a fully-numerical diatomic molecule code yielding molecular virial energies and ionization potentials approximated by the energies of the HOMO orbitals. It is shown that some of the shortcomings of these model potentials, such as the non-compliance with the Levy-Perdew virial relation, may be eliminated by multiplying the response term by an orbital-dependent functional $α$, which can be simplified to a constant determined during the self-consistent procedure (self-consistent $α$).
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