Rotational Excitation of HC₅NH⁺ by He: Collision Dynamics and Astrophysical Applications

Reliable collisional rate coefficients are crucial for interpreting the rotational emission spectra of molecules in interstellar clouds. In this work, we construct a two-dimensional potential energy surface (PES) for the HC₅NH⁺--He system at the CCSD(T)-F12B/cc-pVTZ-F12 level of theory. Rotationally inelastic cross sections are calculated using the quantum close-coupling (CC) method, and the corresponding collisional rate coefficients are obtained by thermal averaging over a Maxwell--Boltzmann distribution. We use these collisional data in a non-local thermodynamic equilibrium (non-LTE) radiative transfer model to investigate the excitation of HC₅NH⁺ in the cold dark cloud TMC-1. A global χ² minimization analysis of seven observed lines yields best-fitting values of n(H₂)=1.63×10⁵\,cm⁻³ and N(H₂)=5.09×10¹¹\,cm⁻², with reduced χ²ₘᵢₙ=0.87. The modelled line intensities are in good agreement with the observations. These results provide insight into the collisional excitation and radiative properties of HC₅NH⁺ under the physical conditions prevailing in TMC-1.