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首页> 外文期刊>International Journal of Quantum Chemistry >Time-dependent density functional theory as a foundation for a firmer understanding of sum-over-states density functional perturbation theory: 'Loc.3' approximation
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Time-dependent density functional theory as a foundation for a firmer understanding of sum-over-states density functional perturbation theory: 'Loc.3' approximation

机译：与时间有关的密度泛函理论为更牢固地理解和态密度函数泛函理论的基础：“ Loc.3”近似

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摘要

Sum-over-states density functional perturbation theory (SOS-DFPT) (Malkin, V.G.; Malkina, O.L.; Casida, M.E.; Salahub, D.R.J Am Chem Soc 1994, 116,5898) has been successful as a method for calculating nuclear magnetic resonance (NMR) chemical shfits. The key to this success is the introduction of an ad hoc correction to the excitation energies represented by simple orbital energy differences in uncoupled density functional theory. It has been suggested (Jamorski, C.; Casida, M.E.; Salahub, D.R.J.Chem Phys 1996, 104, 5134) that the good performance of this methodology could be partly explained by the resemblance of the corrected excitation energy to the orbital energy difference given by time-dependent density functional theory (TDDFT). In fact, according to exact (wave function) time-dependent perturbation theory, both magnetic and electric perturbations may be described using essentially the same simple SOS expression. However in adiabatic TDDFT, with no explicit relativistic or current density functional dependence, the functional is approximate and so the magnetic and electric SOS expressions are different. Because TDDFT (neglecting relativistic and current density functional dependence) is formally exact for electric perturbations but not magnetic perturbations and because the two SOS expressions should have the same form, we propose that the SOS expression for electric perturbations should also be used for magnetic perturbations. We then go on to realize our theory by deriving a "Loc.3" approximation that is explicity designed by applying the electric field SOS expression to magnetic fields within the two-level model and Tamm-Dancoff approximation. Test results for 13 small organic and inorganic molecules show that the Loc.3 approximation performs at least as well as the "Loc.1" and "Loc.2" approximations of SOS-DFPT.
机译：状态总和密度泛函微扰理论（SOS-DFPT）（Malkin，VG; Malkina，OL; Casida，ME; Salahub，DRJ Am Chem Soc 1994，116,5898）已成功作为计算核磁共振的方法（NMR）化学碎片。成功的关键是对非耦合密度泛函理论中由简单轨道能量差表示的激发能进行特别校正。已经提出（Jamorski，C。; Casida，ME; Salahub，DRJChem Phys 1996，104，5134），该方法的良好性能可以部分地通过校正的激发能与给定的轨道能量差的相似性来解释。通过时变密度泛函理论（TDDFT）。实际上，根据精确的（波动函数）随时间变化的扰动理论，可以使用基本相同的简单SOS表达式来描述磁扰动和电扰动。但是，在绝热TDDFT中，由于没有显式的相对论或电流密度函数依赖性，其函数是近似的，因此SOS的磁表达和电表达都不同。由于TDDFT（忽略相对论和电流密度函数的依赖关系）在形式上对于电扰动是精确的，而对于磁扰动却不是，并且由于两个SOS表达式应具有相同的形式，因此我们建议对于电扰动的SOS表达式也应用于磁扰动。然后，我们通过推导“ Loc.3”近似来实现我们的理论，该近似是通过将电场SOS表达式应用于两层模型中的磁场和Tamm-Dancoff近似来明确设计的。对13个有机和无机小分子的测试结果表明，Loc.3近似至少与SOS-DFPT的“ Loc.1”和“ Loc.2”近似相同。

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