Absolutely Localized Projection-Based Embedding for Excited States

We present a quantum embedding method that allows for
calculation
of local excited states embedded in a Kohn–Sham density functional
theory (DFT) environment. Projection-based quantum embedding methodologies
provide a rigorous framework for performing DFT-in-DFT and wave function
in DFT (WF-in-DFT) calculations. The use of absolute localization,
where the density of each subsystem is expanded in only the basis
functions associated with the atoms of that subsystem, provide improved
computationally efficiency for WF-in-DFT calculations by reducing
the number of orbitals in the WF calculation. In this work, we extend
absolutely localized projection-based quantum embedding to study localized
excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding
results are highly accurate compared to the corresponding canonical
EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently
more accurate than canonical TDDFT. The absolute localization method
is shown to eliminate the spurious low-lying excitation energies for
charge-transfer states and prevent overdelocalization of excited states.
Additionally, we attempt to recover the environment response caused
by the electronic excitations in the high-level subsystem using different
schemes and compare their accuracy. Finally, we apply this method
to the calculation of the excited-state energy of green fluorescent
protein and show that we systematically converge to the full system
results. Here we demonstrate how this method can be useful in understanding
excited states, specifically which chemical moieties polarize to the
excitation. This work shows absolutely localized projection-based
quantum embedding can treat local electronic excitations accurately
and make computationally expensive WF methods applicable to systems
beyond current computational limits.

本研究提出一种量子嵌入方法，可实现在科恩-沈吕九密度泛函理论（Kohn–Sham density functional theory，以下简称DFT）环境下对局域激发态的计算。基于投影的量子嵌入方法为开展DFT内嵌DFT（DFT-in-DFT）以及DFT内嵌波函数（WF-in-DFT）计算提供了严谨的理论框架。绝对定域化方法仅将每个子系统的密度展开于该子系统关联原子对应的基函数中，通过缩减波函数计算中的轨道数量，提升了WF-in-DFT计算的计算效率。本工作将基于绝对定域化的投影式量子嵌入方法拓展至结合运动方程耦合簇单双（EOM-CCSD）内嵌DFT与含时密度泛函理论（TDDFT）内嵌DFT，以研究局域激发态。相较于全体系下的标准EOM-CCSD与TDDFT计算结果，该嵌入方法所得结果精度极高；其中TDDFT-in-DFT的计算精度通常优于标准TDDFT。研究表明，绝对定域化方法可消除电荷转移态的虚假低激发能，并抑制激发态的过度离域化。此外，本研究尝试通过多种方案还原高级别子系统中电子激发所引发的环境响应，并对比了各方案的精度。最后，我们将该方法应用于绿色荧光蛋白的激发态能量计算，结果表明我们的计算可系统收敛至全体系计算结果。本研究展示了该方法在理解激发态特性方面的应用价值，具体而言，可揭示哪些化学基团会在激发过程中发生极化。本工作证实，基于绝对定域化的投影式量子嵌入方法可精准处理局域电子激发态，并将计算成本高昂的波函数方法拓展至当前计算极限以外的体系。