原子能量和自旋的可包合表示从头算密度泛函计算：交换相关近似的一种检验
Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations
摘要：
在密度泛函理论的交换关联能的局域自旋密度近似（LSDA）和广义梯度近似（GGA）下，计算了Z = 1-86的原子及其第一离子的总能量和自旋态.基态密度不能用纯态v-表示的原子和离子，可以用Kohn-Sham系统的分数占据来表示。一个新发展的算法，搜索整体v-可表示密度[E。Kraisler等人，Phys.Rev.A80，032115（2009）]在计算中使用。结果发现，对于许多原子的电离能与GGA得到的只是温和的改善相对于实验数据，相比，LSDA。然而，即使在那些改进是系统性的原子团中，相对于实验仍然存在不可忽略的差异。在Kohn-Sham参考系中的从头算电子构型并不总是等于在独立电子近似下从光谱项得到的构型。结果表明，使用后者的配置可以防止能量最小化过程收敛到全局最小值，例如在镧系元素。从头计算的自旋值适合大多数原子的实验，几乎不受xc-功能的选择。在不正确获得自旋的系统中，存在某些情况（例如V，Pt），发现结果相对于xc近似的小变化是稳定的。这些研究结果表明，有必要进行重大修改的交换相关功能，可能是一个非本地的性质，准确地描述这样的系统。PACS编号：31.15.A
英文摘要：
The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equal the configuration obtained from the spectroscopic term within the independent-electron approximation. It was shown that use of the latter configuration can prevent the energy-minimization process from converging to the global minimum, e.g. in lanthanides. The spin values calculated ab-initio fit the experiment for most atoms and are almost unaffected by the choice of the xc-functional. Among the systems with incorrectly obtained spin there exist some cases (e.g. V, Pt) for which the result is found to be stable with respect to small variations in the xc-approximation. These findings suggest a necessity for a significant modification of the exchange-correlation functional, probably of a non-local nature, to accurately describe such systems. PACS numbers: 31.15.A
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