论文标题
Moreau-Yosida正则化的密度接触式反转
Density-potential inversion from Moreau-Yosida regularization
论文作者
论文摘要
对于量子力学多电子系统，在密度下，Zhao-Morrison-Parr方法允许计算精确产生该密度的有效电位。在这项工作中，我们演示了这种和类似的反转程序在数学上如何与Banach空间上密度函数的Moreau-Yosida正则化有关。结果表明，随着正则化参数接近零，这些反转过程实际上可以理解为极限过程。这给出了对莫罗 - 尤西达正则化在密度功能理论中的作用的新见解，并允许系统地改善密度电势反演。我们的结果适用于具有分数职业的Kohn-Sham设置，该设置决定了有效的一身潜力，进而决定相互作用的密度。
For a quantum-mechanical many-electron system, given a density, the Zhao-Morrison-Parr method allows to compute the effective potential that yields precisely that density. In this work, we demonstrate how this and similar inversion procedures mathematically relate to the Moreau-Yosida regularization of density functionals on Banach spaces. It is shown that these inversion procedures can in fact be understood as a limit process as the regularization parameter approaches zero. This sheds new insight on the role of Moreau-Yosida regularization in density-functional theory and allows to systematically improve density-potential inversion. Our results apply to the Kohn-Sham setting with fractional occupation that determines an effective one-body potential that in turn reproduces an interacting density.
