Wavelength‐decomposition‐based embedded cluster density approximation for systems with nonlocal electron correlation. Issue 21 (4th July 2020) - Huang, Chen
Abstract: Local correlation methods rely on the assumption that electron correlation is nearsighted. In this work, we develop a method to alleviate this assumption. This new method is demonstrated by calculating the random phase approximation (RPA) correlation energies in several one‐dimensional model systems. In this new method, the first step is to approximately decompose the RPA correlation energy to the nearsighted and farsighted components based on the wavelength decomposition of electron correlation developed by Langreth and Perdew. The short‐wavelength (SW) component of the RPA correlation energy is then considered to be nearsighted, and the long‐wavelength (LW) component of the RPA correlation energy is considered to be farsighted. The SW RPA correlation energy is calculated using a recently developed local correlation method: the embedded cluster density approximation (ECDA). The LW RPA correlation energy is calculated globally based on the system's Kohn‐Sham orbitals. This new method is termed λ ‐ECDA, where λ indicates the wavelength decomposition. The performance of λ ‐ECDA is examined on a one‐dimensional model system: a H24 chain, in which the RPA correlation energy is highly nonlocal. In this model system, a softened Coulomb interaction is used to describe the electron‐electron and electron‐ion interactions, and slightly stronger nuclear charges (1.2 e ) are assigned to the pseudo‐H atoms. Bond stretching energies, RPA correlation potentials, and Kohn‐Sham eigenvalues predicted by λ ‐ECDA are in good agreement with the benchmarks when the clusters are made reasonably large. We find that the LW RPA correlation energy is critical for obtaining accurate prediction of the RPA correlation potential, even though the LW RPA correlation energy contributes to only a few percent of the total RPA correlation energy. Abstract : Local correlation methods cannot be applied to systems having highly nonlocal electron correlations. A methodology for overcoming this limitation is developed in this work. The electron correlation is partitioned to the nearsighted and farsighted contributions based on its wavelength decomposition. The nearsighted part is then treated using a local correlation method, while the farsighted contribution is calculated explicitly. This new methodology is tested and found to perform well on strongly correlated one‐dimensional H chains.