Convergence of direct space exchange lattice sums in polymer band structure calculations
Convergence of direct space exchange lattice sums in polymer band structure calculations
复制标题
聚合物能带结构计算中直接空间交换晶格和的收敛
DOI：
10.1063/1.451671
复制
发表时间：
1986
影响因子：
4.4
通讯作者：
J. Calais
中科院分区：
文献类型：
--
作者：
J. Delhalle;J. Calais
一个研究的收敛性与直接晶格求和的交换贡献的聚合物的限制Hartree-Fock计算中所需的数量，导致详细分析的分析和渐近性质的Fock-Dirac密度矩阵的LCAO表示。简单地通过傅里叶分析获得的结果提供了应用于链式系统的限制Hartree-Fock方法的重要特征。作为一个副产品，我们得到了一个一般性的证明，在直接空间中，一个部分填充的带，这极大地影响了倒易空间中密度矩阵的解析性质，导致费米能级上轨道能量的几何发散导数。这反过来又给出了在该水平上消失的态密度。这个结果，众所周知的电子气模型，因此是一个固有的属性限制哈特里-福克近似。
A study of the convergence properties associated with direct lattice summations of the exchange contributions to the quantities needed in a restricted Hartree–Fock calculation for a polymer, leads to a detailed analysis of the analytic and asymptotic properties of the Fock–Dirac density matrix in the LCAO representation. The results, obtained simply by means of Fourier analysis, provide an important characterization of the restricted Hartree–Fock method as applied to chain‐like systems. As a by‐product we obtain a general proof in direct space that a partially filled band, which influences drastically the analyticity properties of the density matrix in reciprocal space, leads to a logarithmically diverging derivative of the orbital energy at the Fermi level. This in turn gives a vanishing density of states at that level. This result, well known for the electron gas model, is thus an inherent property of the restricted Hartree–Fock approximation.