然而， DFT不能給出激發(fā)態(tài)，或者更一般地說，不能用于處理與時(shí)間相關(guān)的外部場(chǎng)響應(yīng)，外部場(chǎng)無論是弱還是強(qiáng)。在絕大多數(shù)情況下，TDDFT用于處理線性響應(yīng)機(jī)制，在頻域中表示基態(tài)的弱擾動(dòng)提供了激發(fā)譜和振子強(qiáng)度。通過嵌入方法和隨機(jī)軌道的使用，進(jìn)一步增強(qiáng)了TDDFT有利的系統(tǒng)尺寸。這些計(jì)算的關(guān)鍵要素之一是交換關(guān)聯(lián)勢(shì)，這是未知的、且需要進(jìn)行近似。此外，精確的交換關(guān)聯(lián)勢(shì)具有內(nèi)存的依賴性。自從TDDFT方法被開發(fā)以來，研究人員一直在努力構(gòu)建包括這種內(nèi)存依賴性的近似方法。

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.

來自美國羅格斯大學(xué)物理系的Neepa T. Maitra教授等，回顧了這些年來在這方面的努力及其成果，分析了為什么它們沒有被廣泛使用的原因，并討論了未來發(fā)展的前景。在這之前，他們將使用了一個(gè)精確可解的模型系統(tǒng)，演示了內(nèi)存依賴性對(duì)于動(dòng)力學(xué)和激發(fā)態(tài)的影響，并討論與內(nèi)存依賴性相關(guān)的一些確切條件。

作者指出，尋找精確和實(shí)用的非絕熱近似是一個(gè)具有挑戰(zhàn)性的問題，最近發(fā)展的幾個(gè)新方向也還處于非常初步階段，如耦合常數(shù)積分轉(zhuǎn)換、使用密度的二階導(dǎo)數(shù)作為基本變量來鑄造TDDFT、擴(kuò)展連接器理論到時(shí)域等，這些方向是否會(huì)產(chǎn)生靈丹妙藥還有待觀察，但即使不能，它們也可以揭示有關(guān)電子關(guān)聯(lián)動(dòng)力學(xué)的有趣物理。該文近期發(fā)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及其翻譯

Non-adiabatic approximations in time-dependent density functional theory: progress and prospects (含時(shí)密度泛函理論中的非絕熱近似：進(jìn)展與展望)

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.

摘要含時(shí)密度泛函理論持續(xù)吸引著廣泛領(lǐng)域的眾多用戶，探索涉及電子光譜和動(dòng)力學(xué)的多樣化應(yīng)用。盡管從原理上來說是精確的，但計(jì)算的可預(yù)測(cè)性受限于交換相關(guān)泛函的可用近似。特別是，已知精確的交換相關(guān)泛函具有內(nèi)存依賴性，但在實(shí)踐中通常使用絕熱近似，這就忽略了這一點(diǎn)。在這里，我們回顧了非絕熱泛函近似的發(fā)展，它們對(duì)計(jì)算的影響，以及在開發(fā)通用目的的實(shí)用性和準(zhǔn)確的內(nèi)存依賴性泛函方面的挑戰(zhàn)。