Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.

中文翻译：

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智能局部轨道，可在密度泛函理论及其他范围内进行高效计算

投影机增强波形式主义中的局部基集允许在密度泛函理论（DFT）中进行高效的计算。但是，要获得较高的数值精度，需要广泛的基础集，这也为解释结果带来了根本性的问题。我们提出了一种通过对哈密顿量的每个原子块进行对角线化来获得原子轨道的减基集的方法。生成的局部轨道（LO）继承了局部晶体场的信息。在本振基础上，很明显，哈密顿量几乎是块对角线，并且我们证明了有可能只保留一个相关本振的子集，以提供费米能级附近的物理学的准确描述。这在某种程度上减少了原始基础集的冗余，同时，