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Size extensivity, defined as the correct scaling of energy with system size,is a desirable property for any many-body method. Traditional CI methods arenot size extensive hence the error increases as the system gets larger. Coupledelectron pair approximation (CEPA) methods can be constructed as simpleextensions of truncated configuration interaction (CI) that ensures sizeextensivity. One of the major issues with the CEPA and its variants is thatsingularities arise in the amplitude equations when the system starts to bestrongly correlated. In this work, we extend the traditional Slaterdeterminant-based coupled electron pair approaches like CEPA-0, averagedcoupled-pair functional (ACPF) and average quadratic coupled-cluster (AQCC) toa new formulation based on tensor product states (TPS). We show that a TPSbasis can often be chosen such that it removes the singularities that commonlydestroy the accuracy of CEPA-based methods. A suitable TPS representation canbe formed by partitioning the system into separate disjoint clusters andforming the final wavefunction as the tensor product of the many body states ofthese clusters. We demonstrate the application of these methods on simple bondbreaking systems such as CH$_4$ and F$_2$ where determinant based CEPA methodsfail. We further apply the TPS-CEPA approach to stillbene isomerization and fewplanar $\pi-$conjugated systems. Overall the results show that the TPS-CEPAmethod can remove the singularities and provide improved numerical resultscompared to common electronic structure methods.

Coupled electron pair-type approximations for tensor product state wavefunctions