电子结构计算的量子化学方法
Electronic Structure Calculations Using the Thomas-Fermi Model
摘要：
利用Wentzel-Kramers-Brillouin方法，我们导出了一种修正的电子密度近似。这一新的结果使我们能够计算的自洽离子核的细节，以及第一个s-轨道绑定到第III，IV和V族元素的闭壳层离子核的电离势。接下来，我们展示了一种从价电子密度中分离核心电子密度的方法。当我们计算价动能密度时，我们发现它分为两项：第一项恰好抵消了核心区域中离子核心的势能;第二项表示由价密度单独产生的剩余动能密度。此外，我们表明，动力学抵消和剩余动能可以从一个缓慢变化的包络近似的核心区域的价轨道。这种动力学取消在核心区域和剩余价动能项允许我们写一个功能的总价能依赖于一个低的空间频率价密度。在极限情况下，当我们可以冻结闭壳层离子核的电势时，假设它们不受价电子重新调整的影响很大，我们可以最小化相对于价密度自由度的总价能。价态总能量方程的变分为大量的原子、分子和固态电子结构问题提供了出发点。在这里，我们用它来计算能带结构所产生的自洽的价密度和潜在的锌石榴石和金刚石晶格。我们给能带结构的结果，为大多数的第III-V族，以及第IV族，材料。
英文摘要：
Using the Wentzel-Kramers-Brillouin method, we derive a modified form of the Thomas-Fermi approximation to electron density. This new result enables us to calculate the details of the self-consistent ion cores, as well as the ionization potentials for the first s-orbital bound to the closed-shell ion core of the Group III, IV and V elements. Next, we demonstrate a method for separating core electron densities from valence electron densities. When we calculate the valence kinetic energy density, we show that it separates into two terms: the first exactly cancels the potential energy of the ion core in the core region; the second represents the residual kinetic energy density resulting from the valence density alone. Furthermore, we show that the kinetic cancellation and the residual kinetic energy can be derived from a slowly varying envelope approximation for the valence orbitals in the core region. This kinetic cancellation in the core region and the residual valence kinetic energy term allow us to write a functional for the total valence energy dependant only on a low spatial frequency valence density. In the limit, when we can freeze the potential of the closed-shell ion cores, assuming that they are not greatly influenced by the readjustment of the valence electrons, we can minimize the total valence energy with respect to the valence density degrees of freedom. The variation of the valence total energy equation provides the starting point for a large number of atomic, molecular and solid-state electronic structure problems. Here, we use it to calculate the band structures resulting from the self-consistent valence density and potential on the zinc-blende and diamond lattices. We give band structure results for most of the Group III-V, as well as Group IV, materials.
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