Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, United Kingdom.
J Chem Phys. 2011 Oct 28;135(16):164110. doi: 10.1063/1.3653980.
Dispersion, static correlation, and delocalisation errors in density functional theory are considered from the unconventional perspective of the force on a nucleus in a stretched diatomic molecule. The electrostatic theorem of Feynman is used to relate errors in the forces to errors in the electron density distortions, which in turn are related to erroneous terms in the Kohn-Sham equations. For H(2), the exact dispersion force arises from a subtle density distortion; the static correlation error leads to an overestimated force due to an exaggerated distortion. For H(2)(+), the exact force arises from a delicate balance between attractive and repulsive components; the delocalisation error leads to an underestimated force due to an underestimated distortion. The net force in H(2)(+) can become repulsive, giving the characteristic barrier in the potential energy curve. Increasing the fraction of long-range exact orbital exchange increases the distortion, reducing delocalisation error but increasing static correlation error.
从拉伸双原子分子中原子核受力的非常规角度出发，考虑了密度泛函理论中的弥散、静态相关和离域误差。范曼的静电定理被用来将力的误差与电子密度变形的误差联系起来，而电子密度变形的误差又与 Kohn-Sham 方程中的错误项有关。对于 H(2)，精确的弥散力来自于微妙的密度变形；静态相关误差导致力的高估，这是由于过度夸张的变形。对于 H(2)(+)，精确的力来自于吸引力和排斥力之间的微妙平衡；离域误差导致力的低估，这是由于变形的低估。H(2)(+)中的净力可能会变得排斥，从而在势能曲线上产生特征势垒。增加长程精确轨道交换的分数会增加变形，从而减少离域误差，但增加静态相关误差。
