将记忆纳入单电子约化密度矩阵的传播
Incorporating Memory into Propagation of 1-Electron Reduced Density Matrices
AI总结：
针对单电子约化密度矩阵在TDCI中的记忆依赖性性质不明问题，推导了封闭时滞线性系统及保持对称性的传播方法，通过H₂和HeH⁺数值测试验证了大时滞下的高精度，且推导适用于任意TDCI系统。
摘要：
对于任何由可逆传播子控制的非约化动力学线性系统，我们推导了一个封闭的、时滞的线性系统，用于研究感兴趣的降维量。该方法不针对降维：相反，它有助于阐明单电子约化密度矩阵在含时组态相互作用（TDCI，一种求解分子中电子关联动力学的方案）中的记忆依赖性。尽管含时密度泛函理论已证实单电子约化密度具有记忆依赖性，但其记忆依赖性的精确性质尚未被理解。我们推导了一种保持对称性/约束的方法来传播约化TDCI电子密度矩阵。在两个模型系统（H₂和HeH⁺）的数值测试中，我们表明，当时间延迟（或记忆依赖性）足够大时，我们的方法能以高定量精度传播约化TDCI密度矩阵。我们研究了结果对时间步长和基组的依赖性。为实现该方法，我们推导了关联约化与完整TDCI密度矩阵的4-指标张量。我们的推导适用于任何TDCI系统，无论基组、电子数或波函数中Slater行列式的选择如何。
英文摘要：
For any linear system with unreduced dynamics governed by invertible propagators, we derive a closed, time-delayed, linear system for a reduced-dimensional quantity of interest. This method does not target dimensionality reduction: rather, this method helps shed light on the memory-dependence of $1$-electron reduced density matrices in time-dependent configuration interaction (TDCI), a scheme to solve for the correlated dynamics of electrons in molecules. Though time-dependent density functional theory has established that the $1$-electron reduced density possesses memory-dependence, the precise nature of this memory-dependence has not been understood. We derive a symmetry/constraint-preserving method to propagate reduced TDCI electron density matrices. In numerical tests on two model systems ($\text{H}_2$ and $\text{HeH}^+$), we show that with sufficiently large time-delay (or memory-dependence), our method propagates reduced TDCI density matrices with high quantitative accuracy. We study the dependence of our results on time step and basis set. To implement our method, we derive the $4$-index tensor that relates reduced and full TDCI density matrices. Our derivation applies to any TDCI system, regardless of basis set, number of electrons, or choice of Slater determinants in the wave function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
