综述：含时密度泛函理论的非绝热近似

然而， DFT不能给出激发态，或者更一般地说，不能用于处理与时间相关的外部场响应，外部场无论是弱还是强。在绝大多数情况下，TDDFT用于处理线性响应机制，在频域中表示基态的弱扰动提供了激发谱和振子强度。通过嵌入方法和随机轨道的使用，进一步增强了TDDFT有利的系统尺寸。这些计算的关键要素之一是交换关联势，这是未知的、且需要进行近似。此外，精确的交换关联势具有内存的依赖性。自从TDDFT方法被开发以来，研究人员一直在努力构建包括这种内存依赖性的近似方法。

Fig. 2 Time-resolved spectroscopy in the Hubbard dimer (U = 10 case): at the times T indicated during the dynamics in the top panels of Fig. 1, the field is turned off and the system is probed to measure its absorption spectrum.

来自美国罗格斯大学物理系的Neepa T. Maitra教授等，回顾了这些年来在这方面的努力及其成果，分析了为什么它们没有被广泛使用的原因，并讨论了未来发展的前景。在这之前，他们将使用了一个精确可解的模型系统，演示了内存依赖性对于动力学和激发态的影响，并讨论与内存依赖性相关的一些确切条件。

作者指出，寻找精确和实用的非绝热近似是一个具有挑战性的问题，最近发展的几个新方向也还处于非常初步阶段，如耦合常数积分转换、使用密度的二阶导数作为基本变量来铸造TDDFT、扩展连接器理论到时域等，这些方向是否会产生灵丹妙药还有待观察，但即使不能，它们也可以揭示有关电子关联动力学的有趣物理。该文近期发布于npj Computational Materials  9: 124 (2023).

Editorial Summary

Over the past almost 40 years, time-dependent density functional theory (TDDFT) has enabled the calculation of electronic spectra and dynamics in systems that would have been otherwise out of reach to treat quantum-mechanically. While ground-state density functional theory (DFT) is the mainstay of electronic structure, being itself the most widely-used method for materials and molecules as well as the starting point of almost all other treatments of materials, it does not give excitations, or more generally the response to a time-dependent external field whether weak or strong. In the vast majority of cases, TDDFT is applied in the linear response regime, where weak perturbations of the ground state formulated in the frequency domain provide excitation spectra and oscillator strengths; the favorable system-size scaling of TDDFT has been further enhanced with the use of embedding methodsor stochastic orbitals. A key element in these calculations is the exchange-correlation potential, which is unknown and needs to be approximated. Moreover, exact exchange-correlation potential has memory-dependence. Ever since the early days of TDDFT, researchers have been striving to build approximations that include this memory-dependence.

Fig. 5 Frequency-dependence of the diagonal part of fHXC in a model system (see ref. 77) for the exact (orange) and density-matrix coupled approximation (blue).

In this work, Prof. Neepa T. Maitraet al. from the Department of Physics, Rutgers University, reviewed these efforts and their successes, reasons for why they are not widely used, and discussed prospects of future developments. Before doing so, the authors demonstrated, using an exactly-solvable model system, the implications of memory-dependence for both dynamics and excitations, and discussed some exact conditions related to memory dependence. They indicated that the search for an accurate and practical non-adiabatic approximation is a challenging one. The search is on-going and creative: several recent new directions have been proposed for time-dependent functional development which are still at a very preliminary stage, including coupling-constant integral transforms, re-casting TDDFT using the second-time-derivative of the density as basic variable, and extensions of the connector theory approach to the time-domain. Whether one of these will yield an elixir remains to be seen, but even if not, they reveal interesting physics about the dynamics of electron correlation. This article was recently published in npj Computational Materials  9: 124 (2023).

原文Abstract及其翻译

Non-adiabatic approximations in time-dependent density functional theory: progress and prospects (含时密度泛函理论中的非绝热近似：进展与展望)

Lionel Lacombe & Neepa T. Maitra 

AbstractTime-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practice adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.

摘要含时密度泛函理论持续吸引着广泛领域的众多用户，探索涉及电子光谱和动力学的多样化应用。尽管从原理上来说是精确的，但计算的可预测性受限于交换相关泛函的可用近似。特别是，已知精确的交换相关泛函具有内存依赖性，但在实践中通常使用绝热近似，这就忽略了这一点。在这里，我们回顾了非绝热泛函近似的发展，它们对计算的影响，以及在开发通用目的的实用性和准确的内存依赖性泛函方面的挑战。