传统的利用变分原理求解Schrfidinger方程获得原子激发态波函数的方法是基于HUM理论(HylleraasUndheim and MacDonald theorem),在有限的N维Hilbert空间中,通过求解久期方程的高阶根获得激发态的近似波函数.在我们前期的工作中已指出,由于HUM方法的几个内禀缺陷限制,它将导致在相同的函数空间中,由传统变分法得到的激发态波函数的‘质量’远差于足够好的基态波函数.进一步地,为了避免基于HUM方法的变分缺陷,本文提出了新的变分函数,并证明其试探激发态波函数在其本征态处具有局域极小值,因而可以通过变分极小无限制的逼近该本征态.在此基础上,利用广义的Laguerre类型轨道(GLTO)在组态相互作用的框架下,分别编写了基于传统HUM理论和新变分函数的关于求解原子近似波函数的计算程序,并且利用该程序计算了氦原子(He)在1S(e),1P(o)态下相应的基态及激发态近似波函数及对应的能量值和径向平均值,并与已有文献中结果进行比较,计算结果显示了HUM理论的缺陷及新变分函数优越性,并就进一步提高激发态的精度指明了方向.
The SAPO-34 catalyst was fine-tuned with zinc cations through a straightforward template-assisted ion incorporation (TH) process, without the necessary template pre-removal and the preparation of NH4- SAPO-34 intermediate, which is more facile, efficient and cost-effective than the conventional ion exchange process. The template-assisted zinc cations incorporated SAPO-34 catalysts were characterized by XRD, XRF, N2 adsorption-desorption, XPS, SEM, EDX,NMR, respectively. Enhanced selectivity to ethylene and ratio of ethylene to propylene in MTO reaction are observed over the zinc cations modified SAPO-34 catalysts, due to the facilitated formation of lower methylbenzenes that favour the ethylene gen eration, as well as the increased diffusion hindrance originated from the zinc cations incorporation and the facil让ated generation of aromatics compound.
Jiawei ZhongJingfeng HanYingxu WeiShutao XuTantan SunXinwen GuoChunshan SongZhongmin Liu
The AEI cavity of SAPO-18 catalyst was modified with zinc cations with the conventional ion exchange procedure.The cavity modification effectively tunes the product selectivity,and shifts the products from mainly propylene to comparable production of ethylene and propylene in methanol to olefin(MTO)reaction.The incorporation of zinc ions and the generation of bicyclic aromatic species in the AEI cavity of SAPO-18 catalysts introduce additional diffusion hindrance that exert greater influence on the relatively bulky products(e.g.propylene and higher olefins),which increase the selectivity to small-sized products(e.g.ethylene).It appears that the incorporated zinc cations facilitate the generation of lower methylbenzenes which promote the generation of ethylene.The cavity modification via incorporating zinc ions effectively tunes the product selectivity over SAPO molecular sieves with relatively larger cavity,which provides a novel strategy to develop the potential alternative to SAPO-34 catalysts for industrial MTO reaction.
Jiawei ZhongJingfeng HanYingxu WeiShutao XuTantan SunShu ZengXinwen GuoChunshan SongZhongmin Liu
