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.
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.
We present here a systematic theoretical study to explore the underlying mechanisms of the H abstraction reaction from methane. Various abstracting agents have been modeled, using oxygen radicals and a set of high valence metal oxo compounds. Our calculations demonstrate that although H abstraction from CH3-H by metal oxoes can be satisfactorily fitted into the Polanyi correlation on the basis of oxygen radicals, the mechanisms behind are significantly different. The frontier orbital analyses show that there are three electrons and three active orbitals (3e, 3o) involved in H abstraction by oxygen radicals; whereas an additional orbital of pi(M-O)* is involved in H abstraction by M = O, resulting in a (4e, 4o) interaction. In terms of valence bond state correlation diagram, we find that H abstraction by a metal oxo may benefit from the contribution of ionic resonance structures, which could compensate the penalty of opening the M-O pbond. We believe that these findings can help to design more effective catalysts for the activation of light alkanes. (C) 2016 Science Press and Dalian Institute of Chemical Physics, Chinese Academy of Sciences. Published by Elsevier B. V. and Science Press. All rights reserved.
