The analog of Koopmans' theorem for virtual Kohn-Sham orbital energies
The analog of Koopmans' theorem for virtual Kohn-Sham orbital energies
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DOI：
10.1139/v09-088
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发表时间：
2009-10-01
影响因子：
1.1
通讯作者：
Baerends, Evert Jan
中科院分区：
文献类型：
--
作者：
Gritsenko, Oleg;Baerends, Evert Jan
根据KS理论在原则上不仅提供精确的电子密度，而且提供精确的电子响应的要求，对虚Kohn-Sham （KS）分子轨道（MOs）的能量epsilon a给出了一个类似于Koopmans定理的公式。起点是Koopmans定理的Kohn-Sham类比，将垂直电离能i -i与已占据MOs的能量epsilon(i)联系起来（Chong， D. P.; Gritsenko， O.V.; Baerends， E.J. J. Chem）。物理学报，2002,116,1760)。结合时间依赖密度泛函理论（TDDFT）的耦合摄动方程，得到了虚拟KS MOs的能量epsilon(a)与激发能omega（ia）和垂直电离能VIPs （I-i）之间的精确关系。在TDDFT的耦合矩阵K的小矩阵近似中，考虑了这些关系的两种极限情况。在可忽略的矩阵元素K-ia，K- ia的极限下，能量，epsilon(a)，可以解释为（减去）从(i) -> (a)激发态产生的电离能，epsilon(a)近似于-i -a，其中-i -a是由i -i = (ia) + i -a定义的。这种关系在特殊情况下就失效了，比如电荷转移跃迁和解离电子对键（也具有电荷转移特征）的HOMO-LUMO（最高占据分子轨道-最低未占据分子轨道）跃迁。目前的结果突出了Kohn-Sham模型（epsilon(a)近似于-I-a）和Hartree-Fock模型(epsilon（a)近似于-A(a)）中的虚拟轨道能量之间的重要差异。Kohn-Sham差值epsilon(a) - epsilon(i)近似激发能omega(ia)，而hartri - fock差值epsilon(HF)(a)近似于epsilon(HF)(i)不近似激发能，但近似电离能和电子亲和能的差值i -i - a(a)。
An analog of Koopmans' theorem is formulated for the energies, epsilon a, of virtual Kohn-Sham (KS) molecular orbitals (MOs) from the requirement that the KS theory provides, in principle, not only the exact electron density, but also its exact response. The starting point is the Kohn-Sham analog of Koopmans' theorem, relating the vertical ionization energies, I-i, to the energies, epsilon(i), of the occupied MOs (Chong, D. P.; Gritsenko, O.V.; Baerends, E.J. J. Chem. Phys. 2002, 116, 1760). Combining this with the coupled-perturbed equations of time-dependent density functional theory (TDDFT), exact relations between the energies, epsilon(a), of virtual KS MOs and the excitation energies, omega(ia), and vertical ionization energies (VIPs), I-i, are obtained. In the small matrix approximation for the coupling matrix K of TDDFT, two limiting cases of these relations are considered. In the limit of a negligible matrix element, K-ia,K- ia, the energy, epsilon(a), can be interpreted as (minus) the energy of ionization from the phi(i) -> phi(a) excited state, epsilon(a) approximate to -I-a, where -I-a is defined from the relation I-i = omega(ia) + I-a. This relation breaks down in special cases, such as charge-transfer transitions and the HOMO-LUMO (highest occupied molecular orbital - lowest unoccupied molecular orbital) transition of a dissociating electron-pair bond (also of charge-transfer character). The present results highlight the important difference between virtual orbital energies in the Kohn-Sham model (epsilon(a) approximate to -I-a) and in the Hartree-Fock model (epsilon(a) approximate to -A(a)). Kohn-Sham differences epsilon(a) - epsilon(i) approximate the excitation energy, omega(ia), while Hartree-Fock differences epsilon(HF)(a) approximate to epsilon(HF)(i) do not approximate excitation energies but approximate the difference of an ionization energy and an electron affinity, I-i - A(a).