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Continuity of nearly degenerate X1Σg+ and A1Πu states of C2 at large bond lengths in transferable DeepQMC

Determine whether a geometrically transferable deep-learning variational Monte Carlo wave function that employs dynamic state ordering and shared parameters across electronic states can maintain continuity of the adiabatic wave functions for the X1Σg+ and A1Πu electronic states of the carbon dimer (C2) at large internuclear separations greater than 1.6 Å, where these two states are nearly degenerate.

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Background

The carbon dimer presents a challenging electronic structure problem with strong static and dynamic correlation and several low-lying states that approach degeneracy along dissociation. The authors introduce a transferable DeepQMC framework with dynamic state ordering and partial parameter sharing to promote continuity of state representations across geometries, particularly near level crossings and conical intersections.

While the approach successfully models multiple singlet and triplet states and preserves continuity at certain crossings (e.g., a3Πu and c3Σu+), the authors report an inability to maintain continuity for the X1Σg+ and A1Πu states at larger bond lengths (>1.6 Å), where these states are nearly degenerate. Resolving this continuity issue would strengthen the method’s robustness in highly challenging near-degenerate regimes.

References

Even with dynamic state ordering and sharing of network parameters across states, we did not succeed in keeping the continuity of the $X1\Sigma+_g$ and $A1\Pi_u$ states at large bond lengths, where they are very nearly degenerate ($>1.6$ \AA).

— Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlo (2503.19847 - Schätzle et al., 25 Mar 2025) in Section “Efficiently simulating challenging electronic structures” (Carbon dimer)