Symmetry Breaking and the Generation of Spin Ordered Magnetic States in Density Functional Theory Due to Dirac Exchange for a Hydrogen Molecule
Symmetry Breaking and the Generation of Spin Ordered Magnetic States in Density Functional Theory Due to Dirac Exchange for a Hydrogen Molecule
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DOI：
10.1007/s00332-022-09845-2
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发表时间：
2022-09
影响因子：
3
通讯作者：
M. Holst;Houdong Hu;Jianfeng Lu;J. Marzuola;D. Song;J. Weare
中科院分区：
文献类型：
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作者：
M. Holst;Houdong Hu;Jianfeng Lu;J. Marzuola;D. Song;J. Weare
我们研究对称性破缺的平均场解的电子结构问题的2电子氢分子内的KohnSham（KS）局域自旋密度泛函理论与狄拉克交换（XLDA模型）。这个简化的模型显示了与（KS）自旋密度泛函理论（SDFT）在凝聚态和分子系统中的预测相关的行为。受约束的SDFT变分问题的KS解决方案进行自发对称性破缺，导致形成自旋有序态的非凸交换项的相对强度增加。数值上，我们观察到，随着核间键长的增加，分子基态的变化从顺磁状态（自旋离域）的反铁磁（自旋局域化）基态和对称的离域（自旋离域）激发态。我们进一步刻画了交换项的强度趋于无穷大时的极小化的极限行为的解析和数值。这导致进一步的分叉和高度本地化的状态，具有不同的字符。有限元数值计算结果为形式化描述提供了支持。各种解决方案类被发现是数值稳定的。然而，在theR参数的变化，数值海森计算表明，这些是固定的，但不稳定的解决方案。
We study symmetry breaking in the mean field solutions to the electronic structure problem for the 2 electron hydrogen molecule within the Kohn Sham (KS) local spin density functional theory with Dirac exchange (the XLDA model). This simplified model shows behavior related to that of the (KS) spin density functional theory (SDFT) predictions in condensed matter and molecular systems. The KS solutions to the constrained SDFT variation problem undergo spontaneous symmetry breaking leading to the formation of spin ordered states as the relative strength of the non-convex exchange term increases. Numerically, we observe that with increases in the internuclear bond length, the molecular ground state changes from a paramagnetic state (spin delocalized) to an antiferromagnetic (spin localized) ground state and a symmetric delocalized (spin delocalized) excited state. We further characterize the limiting behavior of the minimizer when the strength of the exchange term goes to infinity both analytically and numerically. This leads to further bifurcations and highly localized states with varying character. Finite element numerical results provide support for the formal conjectures. Various solution classes are found to be numerically stable. However, for changes in theRparameter, numerical Hessian calculations demonstrate that these are stationary but not stable solutions.