Constantin Lucian A, Fabiano Eduardo, Della Sala Fabio
Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, via Barsanti, I-73010 Arnesano, Italy.
J Chem Phys. 2016 Aug 28;145(8):084110. doi: 10.1063/1.4961300.
We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.
约化哈特里参数，它在密度的均匀缩放变换下保持不变，并且代表了单电子和双电子体系的精确交换增强因子。约化哈特里参数与传统的元广义梯度近似（meta-GGA）半局部成分（即电子密度、其梯度和动能密度）一起用于构建新一代交换泛函，称为u-meta-GGA。这种u-meta-GGA泛函对于任何单电子和双电子体系的交换都是精确的，具有尺寸一致性且非经验性，满足均匀密度缩放关系，并恢复了从半经典原子理论推导的修正梯度展开。对于原子、离子、金属球和分子，它显示出良好的精度，通常优于meta-GGA交换泛函。我们的构建验证了在交换关联泛函发展中使用约化哈特里成分的合理性，为非经验密度泛函的雅各布天梯分类增添了新的一级。
