de Wergifosse Marc
Laboratory of Theoretical Chemistry, University of Namur , Rue de Bruxelles 61, 5000 Namur, Belgium.
Department of Chemistry, University of Southern California , 90089-0482 Los Angeles, California, United States.
J Phys Chem A. 2016 May 5;120(17):2727-36. doi: 10.1021/acs.jpca.6b02076. Epub 2016 Apr 26.
The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg's differentiation procedure is used to improve the numerical accuracy in the finite-field method. This implementation is tested in the present report for the challenging case of the evaluation of the second hyperpolarizability of the singlet ground state of p-quinodimethane (PQM) for the equilibrium geometry as well as for a stretched geometry where the diradical character of PQM is increased, and for twisted ethylene models where the diradical character changes with the dihedral angle. The application of the approximate spin-projected (ASP) scheme leads to a major improvement of the density functional theory calculations. In particular, for PQM models, BHandHLYP functional reproduces the UCCSD(T) values when the diradical character is below 0.5. The visualization of the γ-densities shows that (i) when increasing the diradical character, the amount of γ-density increases on the -CH2(•) extremities, and (ii) the ASP scheme decreases the amount of "p-like" γ-density for diradical character below 0.4, and increases it for larger diradical character. For twisted ethylene model, we show that the UCCSD(T) reference values can be reproduced by the ASP-UB3LYP method for y < 0.4 and by the ASP-UBHandHLYP method for y > 0.6. To best reproduce the UCCSD(T) reference calculations, the amount of exact exchange in hybrid functionals needs to be tuned along the range of diradical characters.
由于使用自旋非限制方法可能会受到自旋污染，因此评估双自由基物种的静态二阶超极化率（γ）是一项具有挑战性的任务。在此，我们介绍一种基于密度的微分程序的方法学方面，以评估静态极化率和超极化率。有限场计算是在自旋投影电子密度上进行的，以消除自旋污染，并且使用自动化的龙贝格微分程序来提高有限场方法的数值精度。本报告中对该实现进行了测试，用于评估对苯二醌二甲烷（PQM）单重基态在平衡几何构型以及拉伸几何构型（其中PQM的双自由基特征增加）下的二阶超极化率这一具有挑战性的情况，以及用于扭曲乙烯模型（其中双自由基特征随二面角变化）。近似自旋投影（ASP）方案的应用导致密度泛函理论计算有了重大改进。特别是对于PQM模型，当双自由基特征低于0.5时，BHandHLYP泛函能重现UCCSD(T)值。γ密度的可视化显示：（i）当增加双自由基特征时，γ密度在-CH2(•)末端增加；（ii）对于双自由基特征低于0.4的情况，ASP方案减少了“p类”γ密度的量，而对于更大的双自由基特征则增加了该量。对于扭曲乙烯模型，我们表明对于y < 0.4，ASP - UB3LYP方法可以重现UCCSD(T)参考值，对于y > 0.6，ASP - UBHandHLYP方法可以重现。为了最佳地重现UCCSD(T)参考计算，需要在双自由基特征范围内调整混合泛函中精确交换的量。
