论文标题
First-Principles Hubbard U和Hund的J校正了近似密度功能理论，预测了金红石和剖腹酶TiO2的准确差距
First-principles Hubbard U and Hund's J corrected approximate density-functional theory predicts an accurate fundamental gap in rutile and anatase TiO2
论文作者
论文摘要
二氧化钛（Tio $ _2 $）提出了长期以来对近似Kohn-Sham密度功能理论（KS-DFT）的挑战，以及其Hubbard校正的扩展，DFT+$ U $。我们发现，先前提议的第一原则DFT+$ U $的扩展为结合了hund的$ j $校正，称为DFT+$ u $+$+$ j $，结合使用最近提出的线性响应理论计算出的参数，预测基本的频段隙准确地在实验中，可以在实验中列入rutile the rutile the rutile the rutile interiment in rutile tio $ $ ________________2。我们的方法建立在既定的发现，即对钛$ 3D $和氧$ 2p $ 2p $ $ _2 $的子空间的校正，象征性地给出了DFT+$ u^{d，p} $，对于使用DFT+$ u $实现可接受的频带胶是必要的。当包括第一原则的$ J $时，此要求仍然存在。我们还发现，即使使用特定于子空间的第一原理$ u $和$ j $参数，计算出的差距也取决于相关的子空间定义。使用最简单的合理相关子空间定义和基础功能，即局部密度近似，我们表明，使用相对简单的DFT+$ u $+$+$ j $ junctional的形式相对简单而产生的高精度。对于诸如TIO $ _2 $之类的封闭系统，我们描述了如何使用适当修改的参数将各种DFT+$+$ j $ j $函数减少到DFT+$ u $，因此可以针对Rutile和Anatase计算可靠的频段差距，而无需修改对于传统的DFT+$ u $ $ $ $。
Titanium dioxide (TiO$_2$) presents a long-standing challenge for approximate Kohn-Sham density-functional theory (KS-DFT), as well as to its Hubbard-corrected extension, DFT+$U$. We find that a previously proposed extension of first-principles DFT+$U$ to incorporate a Hund's $J$ correction, termed DFT+$U$+$J$, in combination with parameters calculated using a recently proposed linear-response theory, predicts fundamental band-gaps accurate to well within the experimental uncertainty in rutile and anatase TiO$_2$. Our approach builds upon established findings that Hubbard correction to both titanium $3d$ and oxygen $2p$ subspaces in TiO$_2$, symbolically giving DFT+$U^{d,p}$, is necessary to achieve acceptable band-gaps using DFT+$U$. This requirement remains when the first-principles Hund's $J$ is included. We also find that the calculated gap depends on the correlated subspace definition even when using subspace-specific first-principles $U$ and $J$ parameters. Using the simplest reasonable correlated subspace definition and underlying functional, the local density approximation, we show that high accuracy results from using a relatively uncomplicated form of the DFT+$U$+$J$ functional. For closed-shell systems such as TiO$_2$, we describe how various DFT+$U$+$J$ functionals reduce to DFT+$U$ with suitably modified parameters, so that reliable band gaps can be calculated for rutile and anatase with no modifications to a conventional DFT+$U$ code.
