Irreducible Representations as Multireference Indicators for Diradicaloid Systems

Multireference behavior in molecules often arises when a small gap between frontier orbitals results in mixing of closed and open-shell configurations.

Standard multireference diagnostics of this regime usually rely on correlated wavefunctions, natural-orbital occupations, or reduced density matrices.

Here, we examine a complementary, symmetry-based criterion for a model system.

For a time-reversal-invariant Hamiltonian, a symmetry-preserving, closed-shell Slater determinant must transform as the trivial irreducible representation of its point group.

Therefore, a nontrivial, many-electron irreducible representation excludes such a description.

We compare two pathways within the same model to demonstrate this.

Along the control pathway, the frontier orbitals remain separated and the ground state retains a trivial irreducible representation over the weak-to-intermediate interaction regime.

Along the obstructed pathway, a high-symmetry point produces a frontier-orbital degeneracy, resulting in a singlet ground state with two-configuration character and a nontrivial irreducible representation.

Exact diagonalization, a two-state effective model, and the Frobenius norm of the two-particle cumulant provide a consistent picture in this regime, demonstrating that irreducible representations can serve as a low-cost diagnostic of multireference character in diradicaloid models.

While symmetry is not a quantitative measure of correlation strength, it does offer a computationally inexpensive screening tool to identify obstructions to a single-reference description.