Champagne Benoît, Bulat Felipe A, Yang Weitao, Bonness Sean, Kirtman Bernard
Laboratoire de Chimie Théorique Appliquée, Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles 61, B-5000 Namur, Belgium.
J Chem Phys. 2006 Nov 21;125(19):194114. doi: 10.1063/1.2388262.
The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.
利用Yang和Wu [《物理评论快报》89, 143002 (2002)] 开发的精确交换优化有效势 (OEP-EXX) 方法，对越来越大的聚二乙炔和聚丁三烯 (PBT) 链的静态极化率和二阶超极化率进行了评估，其中有效势的未知部分表示为高斯函数的线性组合。各种传统原子轨道基组被用于交换势 (X基组) 以及Kohn-Sham轨道 [分子轨道 (MO) 基组]。我们的结果与耦合微扰Hartree-Fock (CPHF) 计算结果以及在不同近似水平下获得的从头算相关值进行了比较。结果表明：(a) 一般来说，小的传统基组对于X基组是不令人满意的；(b) 给定X基组的性能取决于MO基组，并且在使用更大的MO基组时通常会得到改善；(c) 与极化率相比，二阶超极化率的这些效应被放大了；(d) 除了PBT链的二阶超极化率外，对于所有MO基组，使用6-311++G**作为X基组与CPHF结果给出了合理的一致性；(e) 我们的结果表明，在完整X基组的极限情况下，OEP-EXX值可能接近CPHF数据；以及(f) 一般来说，给定传统X基组的质量随着低聚物长度的增加而下降，这与X基组函数的数量占精确再现有限基组Hartree-Fock能量所需数量的比例变小这一事实相关。线性尤其是非线性电场响应构成了评估泛函和势质量的非常严格的测试；需要适当定制的基组来描述后者。最后，这项研究进一步强调了电子相关效应在线性和非线性响应中的重要性，对于这些效应需要使用带有OEP的相关泛函。
