Approximation Methods for Many—Electron Systems

Osvaldo Goscinski

Physical properties of many-electron systems : a study of approximation methods with emphasis on perturbation theory

Thomas Pruschke

Karan Aryanpour

D. Baeriswyl

Vibin Abraham, Nicholas J. Mayhall

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH 4 and F 2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

Chen Huang

Local correlation methods rely on the assumption that electronic correlation is nearsighted. In this work, we develop a method to alleviate this assumption. The first step is to approximately decompose the electron correlation to the nearsighted and farsighted components based on the wavelength decomposition of electron correlation by Langreth and Perdew. The nearsighted component is then calculated using the recently developed embedded cluster density approximation (ECDA) which is a local correlation method formulated in the context of density functional theory. The farsighted component is calculated based on the system’s Kohn-Sham orbitals. The accuracy of this new method depends on the quality of the decomposition. We examined the method’s accuracy by patching the random phase approximation (RPA) correlation energy in a H 24 chain in which the electron correlation is highly nonlocal. This new method predicts bond stretching energies, RPA correlation potential, and Kohn-Sham eigenvalues in good agreement with the benchmarks. Our results demonstrate the importance of including the farsighted part of electron correlation for studying systems having nonlocal correlations.