查看“︁非共價作用力指數”︁的源代码

'''非共價作用力指數'''一般來說是根據{{le|電子密度|Electron density}}（ρ）以及簡化密度梯度（s）來使[[非共價作用力]]（NCI）具體化的數值。由實證研究得知非共價作用力在低電子密度下與低簡化密度梯度區域相關聯。量子化學中，非共價作用力指數在三維空間下可以被用來具體化非共價交互作用。<ref name=":0">Pastorczak, E. and Corminboeuf, C. (2017) ‘Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions’, The Journal of Chemical Physics. AIP Publishing LLC , 146(12), p. 120901. doi: 10.1063/1.4978951.</ref>

其具體化是藉由不同著色深淺度（強度）來表現簡化密度梯度的等值曲面。其深淺度通常透過電子密度以及各個在等值曲面其[[黑塞矩陣|黑塞]]電子密度的第二特徵值 (λ<sub>H</sub>) 來量測，吸引或是排斥的特性則由λ<sub>H</sub>的正負號決定。因此可以直接在三維空間中展現非共價作用力以及其特性，如氫鍵和空間位阻。<ref name=":1">Contreras-García, J., Yang, W. and Johnson, E. R. (2011) ‘Analysis of Hydrogen-Bond Interaction Potentials from the Electron Density: Integration of Noncovalent Interaction Regions’, The Journal of Physical Chemistry A. American Chemical Society, 115(45), pp. 12983–12990. doi: 10.1021/jp204278k.</ref><ref name=":2">Johnson, E. R. et al. (2010) ‘Revealing Noncovalent Interactions’, Journal of the American Chemical Society. American Chemical Society, 132(18), pp. 6498–6506. doi: 10.1021/ja100936w.</ref>基於電子密度和導出的純量場，非共價作用力指數不會因[[分子軌域]]的轉化而改變。此外，一系統的電子密度可以藉由[[X光散射技术|X光繞射]]實驗以及理論波函數計算來推算。<ref name=":3">Saleh , G. et al. (2012) ‘Revealing Non-covalent Interactions in Molecular Crystals through Their Experimental Electron Densities’, Chemistry - A European Journal, 18(48), pp. 15523–15536. doi: 10.1002/chem.201201290.</ref>

簡化密度梯度（s）為一電子密度的純量場（ρ），其可表示如下:

<math>s(r) = {\mid\nabla\rho(r)\mid\over 2(3\pi^2)^\frac{1}{3}\rho(r)^\left ( \frac{4}{3} \right )}</math>

在[[密度泛函理論]]框架中，簡化密度梯度起源於廣義密度梯度近似（GGA）的交換泛函<ref name=":4">{{cite journal|last1 = Perdew|first1 = J. P.|last2 = Burke|first2 =  K. |last3 = Ernzerhof|first3 =  M. |year = 1996|title = Generalized Gradient Approximation Made Simple|volume = 77|doi = 10.1103/PhysRevLett.77.3865 |journal = Phys. Rev. Lett. }}</ref>，最初的定義為:

<math>s(r) = {\mid\nabla\rho(r)\mid\over 2k_{F}\rho(r)}</math>

k<sub>F</sub> 在此表示{{le|自由電子氣體|Jellium}}的[[费米能|費米動量]]。<ref name=":5">Hohenberg, P. and Kohn, W. (1964) ‘Inhomogeneous Electron Gas’, Physical Review. American Physical Society, 136(3B), pp. B864–B871. doi: 10.1103/PhysRev.136.B864.</ref>

== 参考资料 ==
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[[Category:物理学术语]]
[[Category:化学术语]]