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本文回顾了现代密度泛函理论的基础,着重评述了XYG3型双杂化(XYG3 type of doubly hybrid,xDH)泛函的最新进展,解析能量梯度的实现.XYG3是首个依照绝热途径理论建立的双杂化泛函,在具体实现上具有独特的构架.该类型泛函利用常用泛函(如B3LYP或PBE0等)作母泛函来进行自洽计算,以期获得更好的密度和轨道,然后将所得到的轨道和密度信息带入到xDH泛函中以得到最终能量.由于自洽泛函和最终能量泛函不同,因而在计算解析能量梯度时需要求解耦合微扰Kohn-Sham方程.在此基础上,还评述了xDH泛函在能量,尤其是构型优化方面的具体表现.测试的构型集包括以共价键键合的分子和非键相互作用体系的平衡结构,以及反应过渡态结构.结果表明,xDH双杂化泛函总体上给出了比母泛函更好的能量和几何构型.
In this paper, the basis of modern density functional theory is reviewed, and the recent progress of XYG3 type of doubly hybrid (xDH) functionalization is reviewed and the realization of energy gradient is analyzed. XYG3 is the first one based on adiabatic pathway theory Two-hybrid functional, which has a unique framework in the concrete realization, is a self-consistent calculation using common functional (such as B3LYP or PBE0) as mother function, in order to obtain better density and orbit, and then The resulting orbital and density information is introduced into the xDH functional to obtain the final energy. Since the self-consistent functional and the final energy functional are different, it is necessary to solve the coupled perturbation Kohn-Sham equation in the calculation of analytical energy gradient. In addition, the specific performance of xDH functionalities in terms of energy, especially configuration optimization, is also reviewed.The test configuration set includes the equilibrium structure of covalently bonded molecules and non-bond interaction systems, and the reaction transition State structure.The results show that xDH two-hybrid functional general gives better energy and geometry than the functional matrix.