Embedded Mean-Field Theory

We
introduce embedded mean-field theory (EMFT), an approach that
flexibly allows for the embedding of one mean-field theory in another
without the need to specify or fix the number of particles in each
subsystem. EMFT is simple, is well-defined without recourse to parameters,
and inherits the simple gradient theory of the parent mean-field theories.
In this paper, we report extensive benchmarking of EMFT for the case
where the subsystems are treated using different levels of Kohn–Sham
theory, using PBE or B3LYP/6-31G* in the high-level subsystem and
LDA/STO-3G in the low-level subsystem; we also investigate different
levels of density fitting in the two subsystems. Over a wide range
of chemical problems, we find EMFT to perform accurately and stably,
smoothly converging to the high-level of theory as the active subsystem
becomes larger. In most cases, the performance is at least as good
as that of ONIOM, but the advantages of EMFT are highlighted by examples
that involve partitions across multiple bonds or through aromatic
systems and by examples that involve more complicated electronic structure.
EMFT is simple and parameter free, and based on the tests provided
here, it offers an appealing new approach to a multiscale electronic
structure.

本文提出嵌入式平均场理论（embedded mean-field theory），该方法可灵活实现不同平均场理论的嵌套，无需指定或固定各子系统内的粒子数目。EMFT形式简洁，无需借助额外参数即可明确定义，且继承了母平均场理论的简易梯度理论。
本文针对子系统采用不同层级科恩-沈吕九理论（Kohn–Sham theory）的场景开展了大规模基准测试：高等级子系统使用PBE或B3LYP/6-31G*泛函与基组，低等级子系统则采用LDA/STO-3G泛函与基组；同时还研究了两个子系统中不同层级的密度拟合方案。
在广泛的化学问题测试中，我们发现EMFT表现准确且稳定，随着活性子系统规模扩大，其计算结果可平滑收敛至高等级理论的结果。在多数场景下，EMFT的性能至少与ONIOM相当；而针对涉及多键分区或芳香体系分区、以及复杂电子结构的测试案例，EMFT的优势则更为显著。
EMFT形式简洁且无参数依赖，结合本文提供的测试结果，该方法为多尺度电子结构计算提供了一种极具吸引力的全新方案。