Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
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DOI：
10.1103/physreva.78.052513
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发表时间：
2008-08
影响因子：
2.9
通讯作者：
J. Perdew;V. Staroverov;Jianmin Tao;G. Scuseria
中科院分区：
文献类型：
--
作者：
J. Perdew;V. Staroverov;Jianmin Tao;G. Scuseria
我们构建了一个具有完全精确交换的非局部密度泛函近似，同时保留了约束满足方法和更简单的半局部泛函的合理误差消除。这是通过在适合电子密度的两个极端区域的不同近似值之间进行插值来实现的。在“正常”区域中，电子周围的确切交换相关空穴密度是半局域的，因为其空间范围因相关性而减小，并且因为它在狭窄的范围内积分到$\ensuremath{-}1$。这些区域可以通过流行的半局部近似（其中许多是非经验构造的）很好地描述，因为缓慢变化的密度具有适当的精度，或者因为交换和相关之间的误差抵消。 “异常”区域，即非局域性被揭示的区域，包括那些交换可以主导相关性的区域（单电子、不均匀的高密度和快速变化的极限），以及那些电子数波动的开放子系统，在这些子系统上，精确的交换相关性空穴积分的值大于$\ensuremath{-}1$。这些极端之间的区域由局部精确和半局部交换能量密度的混合函数来描述，即混合分数是位置 $\mathbf{r}$ 的函数和密度的函数。因为我们的混合分数在高密度极限下趋向于 1，所以我们根据任何交换相关能量泛函的交换分量的严格定义采用完全精确交换。使用完全精确交换可以满足许多精确约束，但交换的非局域性也需要相关性的平衡非局域性。我们发现这种非局域性至少需要五个经验参数，大致对应于四种异常区域。我们的局部混合泛函可能是第一个精确的第四级密度泛函或超广义梯度近似，具有完全精确的交换，即与更简单的泛函一样大小一致。它满足其他已知的精确约束，包括所有单电子密度的精确性，并且非常适合 G3/99 组的 223 个分子形成焓和 BH42/03 组的 42 个反应势垒高度，从而比大多数半局域泛函和全局杂化都改进了两者（尤其是后者）。精确的约束、物理见解和范式示例有望抑制“过度拟合”。
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a ``normal'' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to $\ensuremath{-}1$. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly varying density or because of error cancellation between exchange and correlation. ``Abnormal'' regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high density, and rapidly varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than $\ensuremath{-}1$. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally, i.e., with a mixing fraction that is a function of position $\mathbf{r}$ and a functional of the density. Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters, corresponding roughly to the four kinds of abnormal regions. Our local hybrid functional is perhaps the first accurate fourth-rung density functional or hyper-generalized gradient approximation, with full exact exchange, that is size-consistent in the way that simpler functionals are. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress ``overfitting.''