Establish whether SS-CASSCF(2,2) with 6-31G can yield meaningful ethylene excited-state surfaces

Establish whether state-specific CASSCF(2,2) using the 6-31G basis set can produce physically meaningful potential energy surfaces for the singly excited π→π* and doubly excited (π)²→(π*)² states of ethylene, or characterize the conditions under which such solutions cannot be obtained within this approximation.

Background

Diffuse basis functions are known to be important for describing Rydberg character in ethylene excitations. Using 6-31G, the authors report an inability to find meaningful SS-CASSCF(2,2) solutions for key excitations, linking this to incorrect state ordering and symmetry-broken/coalescing solutions.

Clarifying whether meaningful surfaces can be achieved with SS-CASSCF(2,2) and 6-31G (and under what modifications, if any) would help delineate the role of basis-set diffuseness and the limitations of state-specific approximations for ethylene and similar systems.

References

While the ground state exhibited a global minimum and four-fold degenerate local minima that are directly analogous to the aug-cc-pVDZ basis, we were unable to find any physically meaningful approximations to the singly excited \uppi \rightarrow \uppi* or the doubly excited (\uppi)2 \rightarrow (\uppi*)2 energy surfaces.

— Excited state-specific CASSCF theory for the torsion of ethylene  (2402.13046 - Saade et al., 2024) in Section 3.4 (Consequences of a non-diffuse basis set)