论文标题

部分可观测时空混沌系统的无模型预测

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods

论文作者

Jacobson, Greta, Marmolejo-Tejada, Juan M., Mosquera, Martín A.

论文摘要

密度功能理论(DFT)为研究分子系统和材料的研究提供了方便的电子结构方法。常规的Kohn-Sham DFT计算依赖于单一转换来确定地面电子密度,基态能量和相关特性。但是,由于分子系统将分子系统分离为开放壳片段,由于大量密度功能近似中存在的自我交互误差,基于这种类型的转换的自洽过程会导致众所周知的电荷分离定位问题。为了避免这个问题,我们先前表明,可以在DFT的背景下使用耦合群集理论的群集操作员以替代方式求解和近似于基层自洽的问题。这项工作进一步研究了单打群集操作员在分子基态计算中的应用。得出和探索了两个近似值:i),一种用于确定群集幅度的二次方程的线性化方案,以及ii),在非自动矛盾的场时进行计算的效果。发现这些方法能够提高系统的能量和密度,并且在任何一种情况下都非常稳定。这项工作中讨论的理论框架可以用来描述具有较大的灵活性的量子系统,这些系统表现出具有挑战性的特征并需要扩展的理论方法。

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i), A linearized scheme of the quadratic equation used to determine the cluster amplitudes, and, ii), the effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.

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