Traore Diata, Giner Emmanuel, Toulouse Julien
Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France.
J Chem Phys. 2022 Jan 28;156(4):044113. doi: 10.1063/5.0076128.
We re-examine the recently introduced basis-set correction theory based on density-functional theory, which consists of correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions, which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction, which has the advantage of being suited to the development of an adapted local-density approximation. We show, indeed, how to develop a local-density approximation for the basis-set correction functional, which is automatically adapted to the basis set employed, without resorting to range-separated density-functional theory as in previous studies, but using instead a finite uniform electron gas whose electron-electron interaction is projected on the basis set. The work puts the basis-set correction theory on firmer ground and provides an interesting strategy for the improvement of this approach.
我们重新审视了最近基于密度泛函理论引入的基组校正理论，该理论包括使用密度泛函校正波函数方法的基组不完备误差。我们使用具有δ势相互作用的一维模型哈密顿量，其优点是与三维库仑系统相比，更容易进行更系统的分析，同时保留波函数方法基组收敛缓慢问题的本质。我们提供了该理论的一些数学细节，并提出了一种新的基组校正变体，其优点是适合于发展自适应局域密度近似。事实上，我们展示了如何为基组校正泛函发展一种局域密度近似，该近似能自动适应所使用的基组，无需像先前研究那样借助范围分离密度泛函理论，而是使用有限均匀电子气，其电子-电子相互作用投影到基组上。这项工作为基组校正理论奠定了更坚实的基础，并为改进该方法提供了一个有趣的策略。
