Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom.
J Chem Phys. 2012 Jan 21;136(3):034101. doi: 10.1063/1.3676722.
Correlated electron densities, experimental ionisation potentials, and experimental electron affinities are used to investigate the homogeneity of the exchange-correlation and non-interacting kinetic energy functionals of Kohn-Sham density functional theory under density scaling. Results are presented for atoms and small molecules, paying attention to the influence of the integer discontinuity and the choice of the electron affinity. For the exchange-correlation functional, effective homogeneities are highly system-dependent on either side of the integer discontinuity. By contrast, the average homogeneity-associated with the potential that averages over the discontinuity-is generally close to 4/3 when the discontinuity is computed using positive affinities for systems that do bind an excess electron and negative affinities for those that do not. The proximity to 4/3 becomes increasingly pronounced with increasing atomic number. Evaluating the discontinuity using a zero affinity in systems that do not bind an excess electron instead leads to effective homogeneities on the electron abundant side that are close to 4/3. For the non-interacting kinetic energy functional, the effective homogeneities are less system-dependent and the effect of the integer discontinuity is less pronounced. Average values are uniformly below 5/3. The study provides information that may aid the development of improved exchange-correlation and non-interacting kinetic energy functionals.
相关电子密度、实验电离能和实验电子亲合能被用于研究在密度标度下 Kohn-Sham 密度泛函理论的交换相关和非相互作用动能泛函的均匀性。研究结果针对原子和小分子，特别关注整数不连续性和电子亲合能选择的影响。对于交换相关泛函，有效均匀性在整数不连续性的两侧高度依赖于体系。相比之下，对于那些结合额外电子的体系使用正电子亲合能，对于那些不结合额外电子的体系使用负电子亲合能来计算不连续性时，与平均势相关的平均均匀性通常接近 4/3。随着原子序数的增加，接近 4/3 的程度变得越来越显著。在不结合额外电子的体系中使用零电子亲合能来评估不连续性，会导致在电子丰富的一侧有效均匀性接近 4/3。对于非相互作用的动能泛函，有效均匀性的体系依赖性较小，整数不连续性的影响也不那么显著。平均值普遍低于 5/3。该研究提供了可能有助于改进交换相关和非相互作用动能泛函的信息。
