Pérez-Becerra Kevin O, Pedroza-Montero Jesús N, Pederson Mark R, Hernández-Segura Luis I, Köster Andreas M
Departamento de Química, Cinvestav, Mexico.
Physics Department, Central Michigan University, Mt. Pleasant, Michigan, USA.
J Comput Chem. 2025 Sep 5;46(23):e70210. doi: 10.1002/jcc.70210.
A hybrid diagonal approximation (HDA) for time-dependent auxiliary density functional theory (TD-ADFT) is presented. This newly implemented method allows the use of global and range-separated hybrid functionals in TD-ADFT for the calculation of vertical excitation energies and corresponding oscillator strengths. To preserve the exceptional computational efficiency and low-order scaling of TD-ADFT, only the diagonal elements of exact exchange are included in the TD-ADFT matrices. For singlet excitations, this approximation reaches accuracies comparable to four-center electron repulsion integral (ERI) implementations, albeit with a fraction of the computational cost. For triplet excitations, larger deviations are found with the HDA. Despite additional integral calculations, the low-order scaling of TD-ADFT is preserved with the HDA. We explain this by the intact index alignment between the ERIs and the excitation vectors, which remains unaltered in TD-ADFT with the HDA.
提出了一种用于含时辅助密度泛函理论（TD-ADFT）的混合对角近似（HDA）。这种新实现的方法允许在TD-ADFT中使用全局和范围分离的混合泛函来计算垂直激发能和相应的振子强度。为了保持TD-ADFT卓越的计算效率和低阶标度，TD-ADFT矩阵中仅包含精确交换的对角元素。对于单重态激发，这种近似达到了与四中心电子排斥积分（ERI）实现相当的精度，尽管计算成本仅为其一小部分。对于三重态激发，HDA存在较大偏差。尽管进行了额外的积分计算，但HDA仍保持了TD-ADFT的低阶标度。我们通过ERI与激发向量之间完整的索引对齐来解释这一点，在采用HDA的TD-ADFT中，这种对齐保持不变。
