Section of Theoretical Chemistry, VU University, Amsterdam, The Netherlands.
J Chem Phys. 2012 Nov 28;137(20):204117. doi: 10.1063/1.4767774.
Whereas a density functional that incorporates dispersion interaction has remained elusive to date, we demonstrate that in principle the dispersion energy can be obtained from a density matrix functional. In density matrix functional theory one tries to find suitable approximations to the two-particle reduced density matrix (2RDM) in terms of natural orbitals (NOs) and natural orbital occupation numbers (ONs). The total energy is then given as a function(al) of the NOs and ONs, i.e., as an implicit functional of the 1RDM. The left-right correlation in a (dissociating) bond, as well as various types of dynamical correlation, can be described accurately with a NO functional employing only J and K integrals (JK-only functional). We give a detailed analysis of the full CI wavefunction of the He(2) dimer, from which the dispersion part of the two-particle density matrix is obtained. It emerges that the entirely different physics embodied in the dispersion interaction leads to an essentially different type of exchange-correlation orbital functional for the dispersion energy (non-JK). The distinct NO functionals for the different types of correlation imply that they can be used in conjunction without problems of double counting. Requirements on the (primitive) basis set for Van der Waals bonding appear to be more modest than for other types of correlation.
尽管到目前为止还难以找到一种包含色散相互作用的密度泛函，但我们证明，原则上可以从密度矩阵泛函中获得色散能。在密度矩阵泛函理论中，人们试图根据自然轨道（NOs）和自然轨道占据数（ONs）来找到合适的二体约化密度矩阵（2RDM）的近似。然后，总能量被表示为自然轨道（NOs）和自然轨道占据数（ONs）的函数（al），即作为 1RDM 的隐函数。通过使用仅包含 J 和 K 积分（仅 JK 泛函）的 NO 泛函，可以准确描述（离解）键中的左右相关以及各种类型的动力学相关。我们对 He(2)二聚体的完全组态相互作用波函数进行了详细分析，从中得到了双粒子密度矩阵的色散部分。结果表明，色散相互作用中包含的完全不同的物理性质导致了色散能的本质上不同的交换相关轨道泛函（非 JK）。不同类型相关的不同 NO 泛函意味着它们可以毫不费力地结合使用，而不会出现重复计算的问题。范德华键的（原始）基组的要求似乎比其他类型的相关要低。
