Herman-Wallis factor for a molecule of type HCN

•Rovibrational interactions affect the line intensities.•The theory for the first Herman-Wallis factor is renewed.•Numerical values for the HCN Herman-Wallis factors are given. [Display omitted] We suggest a novel theoretical approach to calculate Herman-Wallis factors in rovibrational spectra of non-centrosymmetric linear molecules possessing a permanent dipole. A fresh glance allowed to extend the theory recently formulated in [K.V. Kazakov and A.A. Vigasin, Phys. Rev. A, 104, 042805 (2021)]. Our obtained expressions for the first Herman-Wallis correction factors result in evaluation of the rovibrational interaction impact on the line intensities belonging to fundamental modes ν1,ν2, and ν3 for H12C14N, H13C14N, H12C15N, D12C14N, D13C14N, and D12C15N. As an auxiliary outcome, the sum rule for the Coriolis constants is generally derived in detail.