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.
Technically, when dealing with a perfect crystal, methods in k-(reciprocal) space that impose periodic boundary conditions(PBC) in conjunction with plane-wave basis sets are widely used. Chemists, however, tend to think of a solid as a giant molecule, which offers a molecular way to describe a solid by using a finite cluster model(FCM). However, FCM may fail to simulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space information of a perfect crystalline solid out of a reduced real space(RRS) of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.
