Symmetric tensor decomposition-configuration interaction study of BeH$_2$

The configuration interaction (CI) is a straightforward approach to describing interacting fermions. However, its application is hampered by the non-polynomially increasing computational time and memory requirements with the system size. To overcome this problem, we have been developing a variational method based on the canonical decomposition of the full-CI coefficients, which we call the symmetric tensor decomposition (STD)-CI [1]. The applicability of STD-CI was tested for simple molecular systems, but here we test it using a stringent benchmark system, i.e., the insertion of Be into H$_2$. The Be + H$_2$ system is known for strong configurational degeneracy along the insertion pathway, and has been used for assessing a method's capability to treat correlated systems. We obtained errors compared to full CI results of $\sim$10 mHartrees when using a rank 2 decomposition of the full CI coefficients. This is a huge improvement over Hartree-Fock results having errors of up to $\sim$100 mHartrees in worst cases, although not as good as, e.g., CAS-CCSD with errors less than 1 mHartree [2].\\[4pt] [1] Uemura and Sugino, Phys. Rev. Lett. 109, 253001 (2013).\\[0pt] [2] Lyakh et al., Theor. Chem. Acc. 116, 427 (2006).