强关联或经典极限下对称破缺自相互作用修正的精确性：以谐振子为例
Exactness of Symmetry-Broken Self-Interaction Correction in the Strongly-Correlated or Classical Limit: Harmonium as a Demonstration
- Tulane University（杜兰大学）
- College of Chemistry, Beijing Normal University（北京师范大学化学学院）
- College of Chemistry and Molecular Engineering, Peking University（北京大学化学与分子工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究强关联或经典极限下对称破缺自相互作用修正的精确性，以谐振子为例，结合相关观点证明其在普朗克常数趋于零极限下精确，0到物理值间有效，且可通过球平均恢复相关密度。
AI中文摘要：
强电子关联对波函数和密度泛函理论都是重要挑战。有人认为，1981年佩德韦-宗格对任意密度泛函近似的自相互作用修正，在对称破缺后，能在强关联极限下正确描述基态能量，此时每个电子由高度局域且不重叠的单电子自旋轨道描述。也有人认为，普朗克常数趋于零的经典极限是量子力学的强关联极限，标准密度泛函在此严重失效，如谐振子（两个由球对称谐振子外势束缚的库仑相互作用电子）的精确可解问题所示。本文结合这两个观点，证明对于谐振子，对称破缺自相互作用修正在普朗克常数趋于零的极限下是精确的，且在0到物理值（原子单位下为1）之间的所有值都有有效精度。还表明，通过对破缺对称密度进行球平均可恢复依赖普朗克常数的对称基态密度。
英文摘要：
Strong electron correlation is an important challenge to both wavefunction and density functional theory. It has been argued that the Perdew-Zunger 1981 self-interaction correction to any density functional approximation, after symmetry breaking, can correctly describe the ground-state energy in the strongly-correlated limit in which each electron is described by a highly-localized and non-overlapped one-electron spin orbital. It has also been argued that the classical limit, in which Planck's constant tends to zero, is the strongly-correlated limit of quantum mechanics, where standard density functionals fail badly, as demonstrated by the exactly-solvable problem of harmonium (two Coulomb-interacting electrons bound by a spherically-symmetric harmonic-oscillator external potential). Here we combine these two ideas and demonstrate that, for harmonium, symmetry-broken self-interaction correction is exact in the limit where Planck's constant tends to zero, and usefully accurate for all values between 0 and the physical value (1 in atomic units). We also show that the Planck-constant-dependent symmetric ground-state density can be restored by spherical averaging of the broken-symmetry density.
