Periodic Bootstrap Embedding

TL;DR

This paper extends bootstrap embedding to periodic systems, enabling accurate treatment of electron correlation in solids and surfaces using fragment-based methods with minimal basis sets, demonstrated on polymers relevant to solar cells.

Contribution

The paper introduces periodic bootstrap embedding, allowing traditional electronic structure codes to be applied to periodic systems without explicit reciprocal space dependence.

Findings

Achieves ~99.9% recovery of correlation energy with CCSD-in-HF

Demonstrates feasibility for complex donor-acceptor polymers

Enables application of molecular electronic structure tools to solids

Abstract

Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented in periodic boundary conditions using reciprocal space sums (i.e. $k$-point sampling). The major benefit of this approach is that the resulting fragment Hamiltonians carry no explicit dependence on the reciprocal space sums, allowing one to apply traditional non-periodic electronic structure codes to the fragments even though the entire system requires careful consideration of periodic boundary conditions. Using coupled cluster singles and doubles (CCSD) as an example method to solve the fragment Hamiltonians, we present minimal basis set CCSD-in-HF results on 1D conducting polymers. We show that periodic BE-CCSD can typically recover $\sim$99.9% of the electron correlation energy. We further demonstrate that periodic BE-CCSD is feasible even for complex donor-acceptor polymers of interest to organic solar cells - despite the fact that the monomers are sufficiently large that even a $\Gamma-$point periodic CCSD calculation is prohibitive. We conclude that BE is a promising new tool for applying molecular electronic structure tools to solids and interfaces.