k空间的离散化实际上对应的就是对布洛赫波函数施加周期性边界条件
The discretization of k space amounts to imposing periodic boundary conditions on the Bloch wave functions over a supercell in real space.
如果考虑的系统可以用LDA交换关联势计算的很好，那它的交换关联势对自冾势的贡献就是短程的。
If the system under consideration can be described by the localdensity approximation to density-functional theory, the exchange-correlation contribution to the self-consistent potential is short ranged,
《Electron-phonon interaction using Wannier functions》
在金属中，静电相互作用在几个键长范围内就被屏蔽了
In metals, the electrostatic interactions are efficiently screened within a few bond lengths
《Electron-phonon interaction using Wannier functions》
在某些情况下，费米面的拓扑性会导致Kohn异常，这就对应于长程力常数沿着异常波矢方向传播的情况。
In some cases, the topology of the Fermi surface gives rise to Kohn anomalies, which correspond to long ranged force constants propagating along the wave vector associated with the anomaly.
在极化绝缘体中，波恩动力学电荷是非零的，力常数也是长程的由于极化相互作用。
In polar insulators, the Born dynamical charges are nonvanishing, and the force constants are long ranged due to their dipolar interactions
声子频率与声子自能的实部相关，声子线宽与声子自能虚部相关。力常数的虚部和声子屏蔽(damping)相关
More specifically, within the Born-Oppenheimer approximation, the determination of phonon frequencies, that are
related to the real part of the phonon self-energy, requires the calculation, in a self-consistent manner, of the variation in
the Kohn-Sham potentialwith respect to a static ionic displacement
, namely
As the displacement of the ions is static, the obtainedis real. Conversely, the phonon linewidth, related to the imaginary part of the phonon self-energy, is obtained in a nonself-consistent procedure using the electron charge density and the previously determined
《Adiabatic and nonadiabatic phonon dispersion in a Wannier function approach》
计算自冾势对微扰
能带里面的平带对应的就是实空间中的局域态，因为能带的斜率就是准粒子激发的有效质量，而平带意味着有效质量无穷大，也就意味着粒子无法hopping到紧邻的site上去，也就对应的局域态。
K点取样对于结构优化的影响
最近在尝试重新计算TiSe2里面的CDW的时候遇到一个奇怪的事，就是不管怎么做结构优化都没有CDW，结构全部自动优化到高温相。难道之前算的都是错的？一番检查测试之后发现事K点取样导致的问题，K点取样如果没有六方对称性，那么很有可能会导致结构优化不到势能面极值点上去，不仅如此，根据这样的k点抽样画出来的势能面也是不对的，做结构优化的时候务必注意。
