Self-Consistent Green Function Embedding for Advanced Electronic Structure Methods Based on a Dynamical Mean-Field Concept

TL;DR

This paper introduces a Green function embedding scheme based on dynamical mean-field theory for periodic systems, enabling advanced electronic-structure calculations on the unit cell while efficiently treating the surrounding bulk.

Contribution

It develops a real-space dynamical mean-field embedding method that combines high-level electronic structure methods with less demanding approaches for periodic systems.

Findings

Total energy and density of states converge rapidly with cluster size.

The scheme effectively treats the unit cell with hybrid functionals and GW methods.

Approaches approach bulk limits with increasing cluster size.

Abstract

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self- consistent manner. Our scheme is based on the concept of dynamical mean-field theory (DMFT) formulated in terms of Green functions. In contrast to the original DMFT formulation for correlated model Hamiltonians, we here consider the unit cell as local embedded cluster in a first-principles way, that includes all electronic degrees of freedom. Our real-space dynamical mean-field embedding (RDMFE) scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., unit cell) size.