Construction of strongly orthogonal geminals and group functions with general spinorbitals

Ab initio variational treatment of the antisymmetrized product of strongly orthogonal geminals (APSG) allowing for full mixing of singlet and triplet geminals, presented in our previous study [Nakatani and Sato, J. Chem. Phys. 158, 211104 (2023)], was reformulated and extended according to the group function model. A key feature of the reformulation lies in the construction of strongly orthogonal geminals or group functions using general spinorbitals, which allows us to describe strong correlation through breaking both Ŝ2 and Ŝz symmetries while maintaining the simplicity of the trial wave functions and variational equations. Numerical analysis of correlated hydrogen clusters suggested that a noncollinear spin state cannot be the ground state in the APSG model. In some cases, when group functions for an odd number of electrons are used, on the other hand, symmetry breaking was observed for a spin-unrestricted, collinear state, and an obtained ground state was noncollinear. The present framework clearly detects instabilities of geminals and group functions and also provides effective reference states for the strongly correlated regime.