Density Functional Theory-based Embedding for Periodic Systems Using Gaussian Basis Functions

The high computational demand for modeling complex hybrid systems, such as solvated molecules or molecules adsorbed on a surface, has led to the development of numerous embedding techniques. We present an implementation of density functional theory (DFT)-based embedding coupled with complex electronic structure methods such as Green's function-based many-body perturbation theory (e.g., the GW approximation combined with the Bethe–Salpeter equation (GW/BSE)), wavefunction theory (WFT) methods (e.g., Møller–Plesset second-order perturbation theory (MP2) and coupled cluster theory), and real-time time-dependent DFT (RTTDDFT). Its key feature is that it allows treating both periodic and aperiodic systems on an equal footing using an all-electron direct-space representation, by employing Gaussian basis functions. This enables straightforward embedding of molecule-like clusters in periodic environments, where the cluster is treated using complex and computationally expensive methods while the environment is handled at the DFT level. The influence of the environment is captured by a DFT-based embedding potential. The effectiveness of the cluster-in-periodic embedding method is demonstrated through investigations of various ground state and excited state properties. We calculate adsorption energies, excitation energies, optical gaps, and high harmonic generation spectra to showcase the method's broad applicability and accuracy.