用于电子结构理论的系统可解激子哈密顿量
Systematically Improvable Excitonic Hamiltonians for Electronic Structure Theory
摘要：
在这里，我们表明，电子系统的哈密顿量可以写在波动算子，内部相关状态之间的过渡组成片段，会计严格为片段间的电子交换和电荷转移。熟悉的电子结构方法可以应用于重整化哈密顿量。为了效率，每个碎片的基础可以被截断，从考虑中去除电子的高能局部排列，并有效地定义碎片的集体坐标。对于大量的问题（特别是对于非共价相互作用的碎片），这有可能将大部分电子相关折叠成有效的哈密顿量，它应该提供一个强大的方法来将困难的电子结构问题纳入大型系统。精确变换的哈密顿量中的项的数量形式上与系统大小成四次方，但在介观状态下，这可以减少到二次方，在任意误差容限内。最后，除了线性缩放数量的这些项之外的所有项都可以根据预先计算的转换密度的线性缩放数量之间的静电相互作用来有效地分解。在一篇配套文章中，这种形式主义适用于耦合簇理论的激子变体。
英文摘要：
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalized Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems (especially for non-covalently interacting fragments), this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory.
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