Cioslowski Jerzy
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
J Chem Phys. 2005 Oct 22;123(16):164106. doi: 10.1063/1.2074527.
Three strict constraints upon the electron-electron repulsion energy functional of the one-electron reduced density matrix (the 1-matrix) are obtained by combining its invariance and stationary properties with the extended Koopmans' theorem. The constraints relate the quantities derived from the functional pertaining to an N-electron system with those of its (N-1)-electron congener. Together with the N-representability requirement for the 1-matrix of the congener, identities involving the electron-electron repulsion energies of the two systems and their derivatives with respect to the 1-matrices seriously narrow down the choices for potential approximate density-matrix functionals. This fact is well illustrated in the case of two-electron systems, where the validity of the new constraints is confirmed and found to originate from a nontrivial cancellation among different terms. Thus, the constraints provide a new tool for the construction and testing of new functionals that complements the previously known conditions such as the reproduction of the homogeneous gas energies and momentum distributions, convexity, and the N-representability of the associated 2-matrices.
通过将单电子约化密度矩阵（1-矩阵）的电子-电子排斥能泛函的不变性和平稳性与扩展的库普曼斯定理相结合，得到了对该泛函的三个严格约束。这些约束将从与N电子体系相关的泛函导出的量与其（N-1）电子同系物的量联系起来。连同同系物1-矩阵的N可表示性要求，涉及两个体系的电子-电子排斥能及其相对于1-矩阵的导数的恒等式，严重限制了潜在近似密度矩阵泛函的选择。这一事实在双电子体系的情况下得到了很好的说明，在该情况下，新约束的有效性得到了证实，并发现其源于不同项之间的非平凡抵消。因此，这些约束为构建和测试新泛函提供了一种新工具，补充了先前已知的条件，如均匀气体能量和动量分布再、凸性以及相关2-矩阵的N可表示性。
