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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 termedλ‐ECDA, whereλindicates the wavelength decomposition. The performance ofλ‐ECDA is examined on a one‐dimensional model system: aH₂₄chain, 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 (1.2e) are assigned to the pseudo‐H atoms. Bond stretching energies, RPA correlation potentials, and Kohn‐Sham eigenvalues predicted byλ‐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.

 

A kernel polynomial method is developed to calculate the random phase approximation (RPA) correlation energy. In the method, the RPA correlation energy is formulated in terms of the matrix that is the product of the Coulomb potential and the density linear response functions. The integration over the matrix's eigenvalues is calculated by expanding the density of states of the matrix in terms of the Chebyshev polynomials. The coefficients in the expansion are obtained through stochastic sampling. Since it is often the energy difference between two systems that is of much interest in practice, another focus of this work is to develop a correlated sampling scheme to accelerate the convergence of the stochastic calculations of the RPA correlation energy difference between two similar systems. The scheme is termed the atom-based correlated sampling (ACS). The performance of ACS is examined by calculating the isomerization energy of acetone to 2-propenol and the energy of the water–gas shift reaction. Using ACS, the convergences of these two examples are accelerated by 3.6 and 4.5 times, respectively. The methods developed in this work are expected to be useful for calculating RPA-level reaction energies for the reactions that take place in local regions, such as calculating the adsorption energies of molecules on transition metal surfaces for modeling surface catalysis.