Takahashi Hideaki
Department of Chemistry, Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan.
J Chem Phys. 2024 Sep 14;161(10). doi: 10.1063/5.0221906.
The inverse Kohn-Sham (inv-KS) density-functional theory for the electron density of the Hartree-Fock (HF) wave function was revisited within the context of the optimized effective potential (HF-OEP). First, we clarify the relationship between the inv-KS and the HF-OEP within the framework of the potential-functional theory. The similarities and the differences of the approaches are then discussed on the basis of their methodological details, which motivates comparisons of the wave function provided by each method. Next, the real-space grid implementations of the inv-KS and the HF-OEP are addressed for the comparisons. The total HF energies EHF[{φiinv-KS}] for the wave functions φiinv-KS on the effective potentials optimized by the inv-KS are computed for a set of small molecules. It is found that the mean absolute deviation (MAD) of EHF[{φiinv-KS}] from the HF energy is clearly smaller than the MAD of EHF[{φiOEP}], demonstrating that the inv-KS is advantageous in constructing the detailed structure of the exchange potential υx as compared with the HF-OEP. The inv-KS method is also applied to an ortho-benzyne radical known as a strongly correlated polyatomic molecule. It is revealed that the spin populations on the atomic sites computed by the UHF calculation can be faithfully reproduced by the wave functions on the inv-KS potential.
在优化有效势（HF - OEP）的背景下，重新审视了用于哈特里 - 福克（HF）波函数电子密度的逆科恩 - Sham（inv - KS）密度泛函理论。首先，我们在势函数理论框架内阐明了inv - KS与HF - OEP之间的关系。然后根据它们的方法细节讨论了这些方法的异同，这促使我们对每种方法提供的波函数进行比较。接下来，为了进行比较，讨论了inv - KS和HF - OEP在实空间网格上的实现。对于一组小分子，计算了在由inv - KS优化的有效势上波函数φiinv - KS的总HF能量EHF[{φiinv - KS}]。结果发现，EHF[{φiinv - KS}]相对于HF能量的平均绝对偏差（MAD）明显小于EHF[{φiOEP}]的MAD，这表明与HF - OEP相比，inv - KS在构建交换势υx的详细结构方面具有优势。inv - KS方法还应用于一种被称为强关联多原子分子的邻苯炔自由基。结果表明，通过UHF计算得到的原子位点上的自旋布居可以由inv - KS势上的波函数如实地再现。
