发表机构
Research Center for Crystal Materials; CAS Key Laboratory of Functional Materials and Devices for Special Environmental Conditions; Xinjiang Key Laboratory of Functional Crystal Materials; Xinjiang Technical Institute of Physics and Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences（中国科学院新疆理化技术研究所; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将ACKS2$\omega$扩展到含精确交换的参考态，推导交换贡献并验证，使长程关联能可通过原子电荷涨落准确评估。
AI 中文摘要
长程电子关联可以用原子电荷和高阶多极子的耦合涨落来表示，这促使人们采用超越局域偶极极化的密度响应描述，特别是在低维、导电和小带隙系统中，集体电子涨落变得重要。我们将频率依赖的极化力场ACKS2$\omega$扩展到包含精确交换的电子结构参考态，通过推导静态和额外的频率依赖交换贡献，特别关注HFsrPBE，它结合了长程Hartree--Fock交换与短程PBE交换和关联。使用偶极极化率和TS27集合中27个分子的$C_6$色散系数，以HF、PBE、B3LYP和HFsrPBE作为底层电子结构参考态，对ACKS2$\omega$进行的数值验证表明，包含交换贡献并丰富响应基组可以改善与相应轨道空间线性响应计算的一致性，尽管有限响应基组误差仍依赖于分子。通过绝热连接涨落-耗散定理使用ACKS2$\omega$参数评估的长程关联能，在所选轨道基组内使响应基组完备时，能够重现小测试分子相应的HFsrPBE轨道空间结果，而局域多极子分解将有限基组能量分解为单极-单极、混合、偶极-偶极和剩余的高阶多极子贡献，为在原子凝聚模型中用电荷涨落评估长程关联能提供了一条途径。
英文摘要
Long-range electronic correlation can be represented in terms of coupled fluctuations of atomic charges and higher multipoles, motivating a density-response description beyond local dipolar polarization, particularly in low-dimensional, conducting, and small-gap systems where collective electronic fluctuations become important. We extend the frequency-dependent polarizable force field ACKS2$ω$ to electronic-structure references containing exact exchange by deriving both the static and additional frequency-dependent exchange contributions, with particular attention to HFsrPBE, which combines long-range Hartree--Fock exchange with short-range PBE exchange and correlation. Numerical validation of ACKS2$ω$ using dipole polarizabilities and $C_6$ dispersion coefficients for the 27 molecules of the TS27 set, with HF, PBE, B3LYP, and HFsrPBE as the underlying electronic-structure references, shows that including the exchange contributions and enriching the response basis improve agreement with the corresponding orbital-space linear-response calculations, although finite-response-basis errors remain molecule dependent. Long-range correlation energies evaluated through the adiabatic-connection fluctuation-dissipation theorem using the ACKS2$ω$ parameters reproduce the corresponding HFsrPBE orbital-space results for small test molecules when the response basis is made complete within the chosen orbital basis, while a local multipole decomposition resolves the finite-basis energies into monopole--monopole, mixed, dipole--dipole, and remaining higher-multipole contributions, providing a route to evaluating long-range correlation energies in terms of charge fluctuations within atom-condensed models.
