Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the ε-I relations between the Kohn-Sham orbital energies and the ionization potentials
Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the ε-I relations between the Kohn-Sham orbital energies and the ionization potentials
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DOI：
10.1063/1.1582839
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发表时间：
2003-07-22
影响因子：
4.4
通讯作者：
Baerends, EJ
中科院分区：
文献类型：
--
作者：
Gritsenko, OV;Braïda, B;Baerends, EJ
从理论和数值上研究了Kohn-Sham轨道能量ε（i）和弛豫垂直电离势（VIPs）I-j之间的ε-I关系，它提供了密度泛函理论中Koopmans定理的一个模拟。Kohn-Sham轨道能量以-n（i）I（i）-Sigma作为主导项（j是Ω的元素）（i）n（j）I（j），其中I-i是电离的初级VIP（phi（i））（-1），具有光谱因子（与光电子谱中的强度成比例）n（i）接近1，并且集合Ω（s）（i）包含VIP I-j，其是（phi（i））（-1）电离的卫星，具有小但不可忽略的n（j）。除了这种“平均光谱结构”的电子（i）有一个电子壳层的台阶结构的贡献的响应电位v（resp）。精确的KS计算原型第二和第三行闭壳层分子产生价轨道能量-ε（i），这与实验VIP密切对应，平均偏差为0.08 eV。在计算H-2分子和CO、HF、H_2O、HCN分子的ε-I关系式中，对理论关系式进行了数值研究。ε-I关系式的推导使用了戴森轨道（n（i）是它们的范数）。一个连接之间的KS和戴森轨道理论，允许自旋不受限制的KS xc潜力，以表示与统计平均的个别xc潜力的戴森自旋轨道作为主导项。附加项是由于相关动力学效应引起的校正v（c，kin，sigma），以及由于与参考电子的相关性引起的与对（N-1）个电子的能量的校正相关的“响应”v（resp，sigma）（C）2003 American Institute of Physics。
Theoretical and numerical insight is gained into the epsilon-I relations between the Kohn-Sham orbital energies epsilon(i) and relaxed vertical ionization potentials (VIPs) I-j, which provide an analog of Koopmans' theorem for density functional theory. The Kohn-Sham orbital energy epsilon(i) has as leading term -n(i)I(i)-Sigma(jis an element ofOmegas)(i)n(j)I(j), where I-i is the primary VIP for ionization (phi(i))(-1) with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) n(i) close to 1, and the set Omega(s)(i) contains the VIPs I-j that are satellites to the (phi(i))(-1) ionization, with small but non-negligible n(j). In addition to this "average spectroscopic structure" of the epsilon(i) there is an electron-shell step structure in epsilon(i) from the contribution of the response potential v(resp). Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence orbital energies -epsilon(i), which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in calculations of the components of the epsilon-I relations for the H-2 molecule, and for the molecules CO, HF, H2O, HCN. The derivation of the epsilon-I relations employs the Dyson orbitals (the n(i) are their norms). A connection is made between the KS and Dyson orbital theories, allowing the spin-unrestricted KS xc potential to be expressed with a statistical average of individual xc potentials for the Dyson spin-orbitals as leading term. Additional terms are the correction v(c,kin,sigma) due to the correlation kinetic effect, and the "response" v(resp,sigma), related to the correction to the energy of (N-1) electrons due to the correlation with the reference electron. (C) 2003 American Institute of Physics.