EXCHANGE AND CORRELATION IN ATOMS, MOLECULES, AND SOLIDS BY SPIN-DENSITY FUNCTIONAL FORMALISM
EXCHANGE AND CORRELATION IN ATOMS, MOLECULES, AND SOLIDS BY SPIN-DENSITY FUNCTIONAL FORMALISM
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DOI：
10.1103/physrevb.13.4274
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发表时间：
1976-01-01
影响因子：
3.7
通讯作者：
LUNDQVIST, BI
中科院分区：
文献类型：
--
作者：
GUNNARSSON, O;LUNDQVIST, BI
本文的目的是提倡自旋密度泛函(SDF)形式主义的有用性。在其热力学版本中给出了Hohenberg-Kohn-Sham格式和SDF形式的推广。将基态形式推广到更一般的哈密顿量和每个对称性的最低激发态。导出了交换关联泛函和对关联函数之间的关系。它被用来解释该理论的近似版本，特别是局域自旋密度(LSD)近似，该近似仅在密度的慢和弱空间变化极限下形式上有效。然而，结果表明，在相当不均匀的情况下也能很好地解释交换关联能量，因为只有交换关联空穴的球面平均影响该能量，并且因为它满足该空穴应该只包含一个电荷单位的求和规则。LSD近似的另一个优点是它可以被系统地改进。报道了均匀自旋极化电子液体的计算结果。这些计算以交换关联能量和势的内插公式的形式提供数据，以用于LSD近似。基态性质是从Galitskii-Migdal公式得到的，该公式将总能量与单电子能谱联系起来，用动态自能得到。自能是在电子-等离子体激元模型中计算的，其中假定电子耦合到一个单模。通过识别光谱中的准粒子峰，得到了激发态势。与Hartree-Fock近似下的结果相比，关联显著地减弱了势的自旋依赖性。在长波极限下计算了电荷和自旋响应函数。关联对于涉及自旋偏振变化的性质来说是非常重要的。对于原子、分子和固体，讨论了SDF形式的有用性。为了探讨LSD近似的适用范围，在存在精确解的系统上进行了几个应用。计算的原子电离势、亲合势和激发能表明，价电子被很好地描述，电离能的典型误差是1/2 eV。讨论了两电子离子的交换相关空穴。使用最小基组对氢分子的应用表明，与自旋无关的局域近似相比，LSD近似对所研究的所有分离度的能量曲线都有很好的结果。特别是结合能误差仅为0.1 eV，并对键断裂进行了较好的描述。对于固体，SDF形式为磁性的带模型提供了一个框架。对铁磁过渡金属自旋向上和向下能带分裂的估计表明，LSD近似给出了对已发表的Xα结果的正确符号和量级的修正。为了促进SDF形式在LSD近似中的进一步应用，本文是自给自足的，描述了位势所需的公式和输入数据。
The aim of this paper is to advocate the usefulness of the spin-density-functional (SDF) formalism. The generalization of the Hohenberg-Kohn-Sham scheme to and SDF formalism is presented in its thermodynamic version. The ground-state formalism is extended to more general Hamiltonians and to the lowest excited state of each symmetry. A relation between the exchange-correlation functional and the pair correlation function is derived. It is used for the interpretation of approximate versions of the theory, in particular the local-spin-density (LSD) approximation, which is formally valid only in the limit of slow and weak spatial variation in the density. It is shown, however, to give good account for the exchange-correlation energy also in rather inhomogeneous situations, because only the spherical average of the exchange-correlation hole influences this energy, and because it fulfills the sum rule stating that this hole should contain only one charge unit. A further advantage of the LSD approximation is that it can be systematically improved. Calculations on the homogeneous spin-polarized electron liquid are reported on. These calculations provide data in the form of interpolation formulas for the exchange-correlation energy and potentials, to be used in the LSD approximation. The ground-state properties are obtained from the Galitskii-Migdal formula, which relates the total energy to the one-electron spectrum, obtained with a dynamical self-energy. The self-energy is calculated in an electron-plasmon model where the electron is assumed to couple to one single mode. The potential for excited states is obtained by identifying the quasiparticle peak in the spectrum. Correlation is found to significantly weaken the spin dependence of the potentials, compared with the result in the Hartree-Fock approximation. Charge and spin response functions are calculated in the long-wavelength limit. Correlation is found to be very important for properties which involve a change in the spinpolarization. For atoms, molecules, and solids the usefulness of the SDF formalism is discussed. In order to explore the range of applicability, a few applications of the LSD approximation are made on systems for which accurate solutions exist. The calculated ionization potentials, affinities, and excitation energies for atoms propose that the valence electrons are fairly well described, a typical error in the ionization energy being 1/2 eV. The exchange-correlation holes of two-electron ions are discussed. An application to the hydrogen molecule, using a minimum basis set, shows that the LSD approximation gives good results for the energy curve for all separations studied, in contrast to the spin-independent local approximation. In particular, the error in the binding energy is only 0.1 eV, and bond breaking is properly described. For solids, the SDF formalism provides a framework for band models of magnetism. An estimate of the splitting between spin-up and spin-down energy bands of a ferromagnetic transition metal shows that the LSD approximation gives a correction of the correct sign and order of magnitude to published X α results. To stimulate further use of the SDF formalism in the LSD approximation, the paper is self-contained and describes the necessary formulas and input data for the potentials.