Constructing potential energy surface for carbon-chain containing systems using the radial angular network with gradual expansion method.

Investigating molecular excitation induced by collisions requires the prior determination of accurate analytical potential energy surfaces for the colliding partners. For carbon-chain molecules, such as cyanopolyynes, this has been a longstanding challenge, resulting in the absence of rate coefficients for HC5N, HC7N, HC9N, and others, induced by collisions with He. To overcome this bottleneck, we introduce a new approach: the Radial Angular Network with Gradual Expansion (RANGE). This method jointly connects the construction of ab initio interaction potentials with the determination of their analytical forms. We use the HC3N-He molecular complex as a reference to assess the reliability of our method, given that its analytical potential has been derived using various methods. Additionally, we apply the RANGE approach to construct the analytical representation of the interaction potential for HC5N-He and HC7N-He. The analysis of the analytical potentials reveals three systematic trends: (i) the anisotropy increases with the length of the carbon chain, (ii) the number of local minima correlates with the number of carbon atoms, and (iii) the shallowest local minimum is consistently located at ∼30 cm-1 below the dissociation limit of the complex. Using the time-independent quantum mechanical close-coupling formalism, we briefly estimate the propensity rules governing the excitation of HC3N, HC5N, and HC7N induced by collisions with He. Consequently, the three collisional systems exhibit the same propensity rule, favoring Δj = 2 transitions.