Quasi-infinite order vibronic coupling expansions with neural networks for linear systems: The C4H radical

We present a generic scheme for the development of coupled diabatic potential energy surfaces for Renner-Teller systems. The derived method re-expresses an infinite-order vibronic coupling expansion in terms of analytic functions of invariant coordinates, preserving the symmetry and structure of the vibronic coupling ansatz. Using feed-forward artificial neural networks as a flexible and well-established functional form, the formalism is applied to the C4H radical as a challenging (Σ+ + Π) ⊗ π system of astrochemical interest. Focusing on a 6D subspace of the most relevant modes, the neural network model is found to be in good agreement with computed ab initio data and significantly outperforms a comparable polynomial ansatz in terms of fitting error.