Role of exchange in density-functional theory for weakly interacting systems: Quantum Monte Carlo analysis of electron density and interaction energy
Role of exchange in density-functional theory for weakly interacting systems: Quantum Monte Carlo analysis of electron density and interaction energy
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交换在弱相互作用系统的密度泛函理论中的作用：电子密度和相互作用能的量子蒙特卡罗分析
DOI：
10.1103/physreva.80.032504
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Grossman
中科院分区：
文献类型：
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作者：
Y. Kanai;J. Grossman
我们分析了密度泛函理论DFT描述的弱相互作用，采用扩散和蠕动量子Monte Carlo QMC计算，为一组苯分子复合物。虽然结合能显着依赖于用于DFT计算的交换相关近似，QMC计算表明，电子密度准确地描述在DFT内，包括在约化密度梯度的定量特征。我们阐明了如何在一个大的约化密度梯度的exchangeenergy密度的增强起着至关重要的作用，在获得准确的DFT描述弱相互作用系统。弱相互作用在自然界中的许多化学，物理和生物现象中发挥着重要作用1，并且存在将弱相互作用用于各种技术应用的巨大机会，例如可再生能源的储氢和生物化学检测器的高选择性涂层2，3。我们在理论计算中准确描述这种相互作用的能力对于推进这些技术重要领域非常重要。密度泛函理论DFT 4，5是一种很有前途的方法，用于描述现实系统的电子结构，因为它适用于从分子到固体的一大类材料，在精度和计算能力方面。然而，弱相互作用系统仍然是一类具有挑战性的材料，在实践中要准确地描述DFT方法6。这一困难主要归因于非局域相关在描述弱相互作用（如货车范德华相互作用）中的主导作用，而在许多交换相关XC近似中，范德华相互作用是不存在的或被错误地解释了。已经有一些努力，无论是经验或正式包括非本地相关性的XC近似7。除此之外，由于配对交换部分，定量描述仍然具有高度挑战性，这需要进一步研究8，并且通常比相关部分大得多。在提高DFT精度的背景下，量子蒙特卡罗QMC计算在XC近似的发展中发挥了重要作用，从Ceperley和桤木关于均匀电子气的开创性工作开始。随着计算和方法的进步，QMC现在有可能为现实系统计算精确的电子密度。在这篇文章中，我们采用QMC计算分析的电子密度和结合能计算密度泛函理论，以阐明交换的XC近似描述弱相互作用的作用。尽管严重的XC近似依赖的结合能，我们的QMC结果表明，电子密度和约化密度梯度RDG的DFT描述相当准确。使用这些结果，我们表明，在大RDG值的交换能密度的增强在获得准确的结合能中起着至关重要的作用。我们表明，这种增强因子在大RDG不同的交换近似之间的发散行为导致显着差异的结合能。两者合计，这些结果表明，交换描述XC近似需要改进，如果DFT是定量和正确地描述弱相互作用系统的物理，即使有一个准确的包含非局部相关。在大RDG下为弱相互作用定制交换增强因子可能会显着改善描述，同时基本上不影响其他类型的相互作用，并避免计算昂贵的优化有效势方法来获得精确的交换。
We analyze the density-functional theory DFT description of weak interactions by employing diffusion and reptation quantum Monte Carlo QMC calculations, for a set of benzene-molecule complexes. While the binding energies depend significantly on the exchange-correlation approximation employed for DFT calculations, QMC calculations show that the electron density is accurately described within DFT, including the quantitative features in the reduced density gradient. We elucidate how the enhancement of the exchangeenergy density at a large reduced density gradient plays a critical role in obtaining accurate DFT description of weakly interacting systems. Weak interactions play an important role in numerous chemical, physical, and biological phenomena in nature 1, and vast opportunities exist for using weak interactions for various technological applications such as hydrogen storage for renewable energy and highly selective coatings for biochemical detectors 2,3. Our ability to accurately describe such interactions in theoretical calculations is important for advancing these technologically important fields. Density-functional theory DFT4,5 is a promising method for describing the electronic structure of realistic systems because of its applicability to a large class of materials ranging from molecules to solids, in terms of both accuracy and computational affordability. Weakly interacting systems, however, remain a challenging class of materials to describe accurately within the DFT approaches in practice 6. The difficulty has been attributed primarily to the dominant role of nonlocal correlation in describing weak interactions such as the van der Waals interaction, which is absent or incorrectly accounted for within many exchange-correlation XC approximations. There have been a number of efforts to either empirically or formally include nonlocal correlation in the XC approximation 7. In addition to this, a quantitative description remains highly challenging due to the pairing exchange part, which requires further investigation 8 and is in general considerably larger than the correlation part. In the context of improving the accuracy of DFT, quantum Monte Carlo QMC calculations have played an important role in the development of the XC approximation, starting with the seminal work of Ceperley and Alder on the homogeneous electron gas 9. With computational and methodological advances, it is now becoming possible for QMC to compute accurate electron densities for realistic systems. In this article, we employ QMC calculations to analyze the electron density and binding energies calculated from DFT in order to elucidate the role of exchange in the XC approximation for describing weak interactions. In spite of the severe XC approximation dependence of the binding energy, our QMC results show that both the electron density and the reduced density gradient RDG are described quite accurately by DFT. Using these results, we show that an enhancement of the exchange energy density at large RDG values plays a critical role in obtaining accurate binding energies. We demonstrate that the diverging behavior of this enhancement factor at large RDG among different exchange approximations leads to significant differences in the binding energy. Taken together, these results show that the exchange description in XC approximations needs to be improved if DFT is to describe quantitatively and correctly the physics of weakly interacting systems, even with an accurate inclusion of nonlocal correlation. Tailoring the exchange enhancement factor at large RDG for weak interactions might improve significantly the description while essentially leaving unaffected other types of interactions and avoiding the computationally expensive optimized effective potential approach to obtain the exact exchange.