School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India.
J Chem Phys. 2018 Apr 7;148(13):134117. doi: 10.1063/1.5019251.
The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate techniques to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas. The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory, which indicates why these are suitable for two-dimensional quantum systems.
基于密度矩阵展开（DME）的泛化梯度逼近的构造被认为是二维密度泛函形式中设计半局部交换能泛函的最准确技术之一。使用 DME 建模的交换孔具有独特的特性，使其成为优越的实体。提出了基于 DME 的参数化半局部交换能泛函。使用不同形式的动量和灵活的参数是为了包含在新构造的半局部泛函中密度的不均匀效应。除了交换泛函，还通过对为 2D 均匀电子气体开发的局部相关函数进行工作来构建合适的相关函数。通过一个新构造的交换能泛函的参数形式将非局部效应引入相关函数中。所提出的泛函应用于具有不同数量的受限电子和受限强度的抛物量子点。用上述泛函得到的结果相当令人满意，这表明了为什么它们适用于二维量子系统。
