σ-SCF: A direct energy-targeting method to mean-field excited states.
σ-SCF: A direct energy-targeting method to mean-field excited states.
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σ-SCF：平均场激发态的直接能量靶向方法。
DOI：
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发表时间：
2016
影响因子：
4.4
通讯作者：
T. Van Voorhis
中科院分区：
文献类型：
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作者：
H. Ye;Matthew Welborn;Nathan D. Ricke;T. Van Voorhis
电子激发态的平均场解比基态（如Hartree-Fock）解更难接近。基于能量的激发态优化方法，如Δ-SCF（自洽场），倾向于陷入与给定对称性一致的最低解——一个被称为“变分坍缩”的问题。在这项工作中，我们结合了直接能量目标和基于方差的优化思想，以便在平均场水平上描述激发态。所得方法σ-SCF有几个优点。首先，它允许人们通过指定单个参数来确定任何期望的激发态：对该状态能量的猜测。因此，原则上它可以找到所有的激发态。其次，它通过使用基于方差的无约束局部最小化来避免变分崩溃。因此，所有状态——基态或激发态——都被平等对待。第三，它提供了一种替代方法来定位Δ-SCF解决方案，否则通常的非aufbau配置初始猜测很难访问这些解决方案。我们给出了小原子（He, Be）和分子（H2， HF）的新方法的结果。我们发现σ-SCF在定位激发态方面非常有效，包括在密集的激发态流形中单个的高能量激发态。与所有的单行列式方法一样，σ-SCF在开壳态上表现出明显的自旋对称性破缺，我们的结果表明，该方法可以通过自旋投影进一步改进。
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry-a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states-ground or excited-are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.