Half-Projected σ Self-Consistent Field For Electronic Excited States
Half-Projected σ Self-Consistent Field For Electronic Excited States
复制标题
电子激发态的半投影Ï 自洽场
DOI：
10.1021/acs.jctc.8b01224
复制
发表时间：
2019
影响因子：
5.5
通讯作者：
Van Voorhis, Troy
中科院分区：
文献类型：
--
作者：
Ye, Hong-Zhou;Van Voorhis, Troy
与基态解（如Hartree-Fock）相比，电子激发态的完全自一致平均场解要难得多。其主要原因是大多数激发态都是能量鞍点，因此基于能量的优化方法（如Δ-SCF）经常会崩溃到基态。最近，本课题组开发了一种新的方法，σ-SCF [J]。化学。物理学报，2017,147,214104]，成功解决了基于能量方法的“变分崩溃”问题。尽管取得了成功，但σ-SCF解在开壳态时由于单决定性质经常受到自旋污染；随着自旋或空间对称性的自发破缺，还观察到解消失和一阶能量导数不连续等非物理行为。在这项工作中，我们通过一种称为半投影的近似自旋投影格式，部分地恢复了σ-SCF解的自旋对称性。投影波函数的轨道以投影后变化（VAP）的方式进行优化。所得到的理论，我们称之为半投影(HP) σ-SCF，对原始σ-SCF方法的单重态和三重态激励的描述有了实质性的改进。对小分子的数值模拟表明，HP σ-SCF提供了高质量的激发态解决方案，适用于具有光滑势能表面的各种几何形状。我们还证明了HP σ-SCF中的局部激励可以是尺寸密集的。
Fully self-consistent mean-field solutions of electronic excited states have been much less accessible compared to ground state solutions (e.g., Hartree–Fock). The main reason for this is that most excited states are energy saddle points, and hence energy-based optimization methods such as Δ-SCF often collapse to the ground state. Recently, our research group has developed a new method, σ-SCF [J. Chem. Phys.2017, 147, 214104], that successfully solves the “variational collapse” problem of energy-based methods. Despite the success, σ-SCF solutions are often spin-contaminated for open-shell states due to the single-determinant nature; unphysical behaviors such as disappearing solutions and discontinuous first-order energy derivatives are also observed along with the spontaneous breaking of spin or spatial symmetries. In this work, we tackle these problems by partially restoring the broken spin-symmetry of a σ-SCF solution through an approximate spin-projection scheme called half-projection. Orbitals of the projected wave function are optimized in a variation-after-projection (VAP) manner. The resulting theory, which we term half-projected (HP) σ-SCF, brings substantial improvement to the description of singlet and triplet excitations of the original σ-SCF method. Numerical simulations on small molecules suggest that HP σ-SCF delivers high-quality excited-state solutions that exist in a wide range of geometries with smooth potential energy surfaces. We also show that local excitations in HP σ-SCF can be size-intensive.