The strong boundary normalized condition of wavefunction for fully occupied semicore 3d orbitals leads the linear response DFT+U on such metal oxide to have an insurmountable obstacle in Hubbard U determination. We treated the orbital self-energy and orbital relaxation as components of eigenvalues with respective orbital occupation number that follows the Fermi-Dirac distribution. By self-consistently solving the second partial deviation of total energy based on the most simple local density formalism with Hubbard U correction, we found the local density exchange-correlation potential functional can only give a minimized residue of the self-energy and orbital relaxation on the focus orbital if the Janak theorem maintained. Such residue turns to well counteracted in the fully occupied orbitals and non-zero the partially occupied orbitals. With keeping the validation of Janak theorem on localized orbitals, the self-consistent cycle by local density functional with Hubbard U correction cannot find out a set of orbital occupation that simultaneously offsets the orbital self-energy and relaxations in the empty and partially filled shell, but returns a unique set of the occupation for fully occupied shell. The band gap calculations on fully occupied orbital based compounds are thus improved and the relaxed lattices are also shown based on minimization of the self-energy error, which shows a possible route for accurate excited state studies.
Orbital-Order Driven Ferroelectricity and Dipolar Relaxation Dynamics in Multiferroic GaMo$_4$S$_8$
我们提出的宽带介电谱的GaMo $_4$ S $_8$，一个空洞的尖晶石系统，最近被证明表现出非典型的，轨道驱动的铁电性的结果。我们的研究揭示了这种多铁性材料的复杂的弛豫动力学，在T $_{\textrm{JT}}=47$ K的Jahn-Teller转变之上和之下。在T $_{\textrm{JT}}$以上，两种类型的偶极-轨道动力学似乎在竞争：在具有短程极序的团簇状区域内的弛豫，如弛豫铁电体和仅弱相互作用偶极的临界涨落，后者类似于有序-无序型铁电体的典型动力学。在Jahn-Teller转变下，轨道有序的开始驱动系统进入长程铁电有序，并且观察到铁电畴内的偶极动力学。耦合偶极和轨道弛豫行为的GaMo $_4$ S $_8$以上的Jahn-Teller转变显着不同的skyrmion主机的GaV $_4$ S $_8$，这似乎是链接到两个系统的结构畸变的差异上的晶胞水平。
Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy
