Espinosa Leal L A, Karpenko A, Caro M A, Lopez-Acevedo O
COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland.
Phys Chem Chem Phys. 2015 Dec 21;17(47):31463-71. doi: 10.1039/c5cp01211b.
Because of issues with accuracy and transferability of existing orbital-free (OF) density functionals, OF functional development remains an active research area. However, due to numerical difficulties, all-electron self-consistent assessment of OF functionals is limited. Using an all-electron radial OFDFT code, we evaluate the performance of a parametrized OF functional for a wide range in parameter space. Specifically, we combine the parametrized Thomas-Fermi-Weizsäcker kinetic model (λ and γ for the fractions of Weizsäcker and Thomas-Fermi functionals, respectively) with a local density approximation (LDA) for the exchange-correlation functional. In order to obtain the converged results for λ values other than λ = 1, we use the potential scaling introduced in previous work. Because we work within a wide region in parameter space, this strategy provides an effective route towards better understanding of the parameter interplay that allows us to achieve good agreement with the Kohn-Sham (KS) model. Here, our interest lies in total energy, Euler equation eigenvalue, and electronic densities when the parameters are varied between 0.2 and 1.5. We observe that a one-to-one relation between λ and γ defines a region in parameter space that allows the atomic energies to be approximated with a very small average error (less than 3% percent for all the atoms studied) with respect to the KS reference energies. For each atom, the reference KS HOMO eigenvalue can also be reproduced with a similar error, but the one-to-one correspondence between λ and γ belongs to a different region of the same parameter space. Contrary to both properties, the atomic density behaves more smoothly and the error in reproducing the KS reference densities appears more insensitive to variation of the parameters (with mostly an average integrated difference of 0.15-0.20 |e| per electron). These results pave the way towards testing of parameter transferability and further systematic improvement of OF density functionals.
由于现有无轨道（OF）密度泛函在准确性和可转移性方面存在问题，OF泛函的开发仍然是一个活跃的研究领域。然而，由于数值困难，对OF泛函进行全电子自洽评估受到限制。我们使用全电子径向OFDFT代码，在参数空间的广泛范围内评估一种参数化OF泛函的性能。具体而言，我们将参数化的托马斯 - 费米 - 魏茨泽克动力学模型（分别用λ和γ表示魏茨泽克泛函和托马斯 - 费米泛函的分数）与用于交换关联泛函的局域密度近似（LDA）相结合。为了获得除λ = 1之外的λ值的收敛结果，我们采用了先前工作中引入的势缩放方法。由于我们在参数空间的广泛区域内进行研究，该策略为更好地理解参数相互作用提供了一条有效途径，使我们能够与科恩 - 沈（KS）模型达成良好的一致性。在这里，当参数在0.2和1.5之间变化时，我们关注的是总能量、欧拉方程本征值和电子密度。我们观察到，λ和γ之间的一一对应关系在参数空间中定义了一个区域，相对于KS参考能量，该区域允许原子能量以非常小的平均误差（对于所有研究的原子，误差小于3%）进行近似。对于每个原子，参考KS HOMO本征值也可以以类似的误差重现，但λ和γ之间的一一对应关系属于同一参数空间的不同区域。与这两个性质相反，原子密度的行为更为平滑，并且在重现KS参考密度时的误差对参数变化似乎更不敏感（每个电子的平均积分差异大多为0.15 - 0.20 |e|）。这些结果为测试参数可转移性以及进一步系统改进OF密度泛函铺平了道路。
