使用平面波基的多体波函数展开的收敛性：从均匀电子气到固态
Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state
摘要：
使用有限模拟单元均匀电子气（HEG）作为一个模型，我们调查的收敛性的相关能量的完全基组（CBS）限制的方法，利用平面波波函数展开。二阶Møller-Plesset理论（MP2）的简单分析和数值结果表明，基组不完整性误差的衰减为1/M，其中M是计算中使用的平面波的数量，允许直接外推到CBS极限。正如我们将要展示的，在构造多电子波函数时基组截断的选择并不明显，这里我们提出了几种基于动量传递矢量的替代方案，它们大大提高了收敛速度。这是证明了各种波函数的方法，从MP2耦合团簇双打理论（CCD）和随机相位近似加上二阶屏蔽交换（RPA+SOSEX）。有限的基础上设置的能量，这些方法和准确的基准比较。变换可以将一般固态系统的轨道映射到HEG平面波基础上，从而允许将这些方法应用于更现实的物理问题。
英文摘要：
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane wave basis and thereby allow application of these methods to more realistic physical problems.
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