Luo Ji, Xue Zeng Quan, Liu Wei Min, Wu Jin Lei, Yang Zhong Qin
Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, China.
J Phys Chem A. 2006 Nov 2;110(43):12005-9. doi: 10.1021/jp063669m.
It is shown that in density functional theory (DFT), Koopmans' theorem for a large molecular system can be stated as follows: The ionization energy of the system equals the negative of the highest occupied molecular orbital (HOMO) energy plus the Coulomb electrostatic energy of removing an electron from the system, or equivalently, the ionization energy of an N-electron system is the negative of the arithmetic average of the HOMO energy of this system and the lowest unoccupied molecular orbital (LUMO) energy of the (N - 1)-electron system. Relations between this DFT Koopmans' theorem and its existing counterparts in the literature are discussed. Some of the previous results are generalized and some are simplified. DFT calculation results of a fullerene molecule, a finite single-walled carbon nanotube and a finite boron nitride nanotube are presented, indicating that this Koopmans' theorem approximately holds, even if the orbital relaxation is taken into consideration.
结果表明，在密度泛函理论（DFT）中，大分子体系的库普曼斯定理可表述如下：体系的电离能等于最高占据分子轨道（HOMO）能量的负值加上从体系中移除一个电子的库仑静电能，或者等效地，N电子体系的电离能是该体系HOMO能量与（N - 1）电子体系最低未占据分子轨道（LUMO）能量算术平均值的负值。讨论了此DFT库普曼斯定理与文献中现有对应定理之间的关系。对一些先前的结果进行了推广，一些进行了简化。给出了富勒烯分子、有限单壁碳纳米管和有限氮化硼纳米管的DFT计算结果，表明即使考虑了轨道弛豫，该库普曼斯定理也近似成立。
