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tokens: fit all transtions with K ′′ a up to 20 (excluding lines of K ′′ a = 18, which showed a clear trend in residuals between 197.48 and 221.45 GHz) for frequencies below 251 GHz. But in the range 310–506 GHz, the assignments appeared difficult in spite of larger intensities. As for other vibrational states of g - n -PrCN, the oblate pairing consisting of a -type and b -type transitions facilitated the assignments. However, the increasing separation of paired transitions with increase in quantum numbers made assignments more difficult combined with the blending and broadening in the high frequency range and the possible splits caused by internal rotations. Therefore very secure assignments with K ′′ a up to 4 or 5 (for each sub-branch) were first made. Even after the improvement of the parameters several lines at each K ′′ a could not be correctly fitted showing systematic residuals. All these lines are in the ranges of J ′′ from 68 to 73 and from 89 to 93. We attributed this as due coupling with other vibrational states. Finally 935 R -branch a -type transitions were identified in all four frequency ranges. The assignment of b -type transitions was not easy due to low intensities at low frequencies and blending and broadening at high frequencies. The confidently assigned b -type transitions at high frequency were all oblate paired with intense a -type transitions with K ′′ a less than 6. Totally, 487 b -type transitions were fitted. Q -branch b -type transitions were useful to correctly determine the parameter D K . We identified internal rotation causing splits (with the components separated by around 0.6 MHz) at frequencies between 89.25–126.75 GHz, in transitions with large J ′′. In this range, Q -branch b -type transitions have K ′′ a less than 11 and those that could be securely assigned have J ′′ less than 45. For Q -branch b -type transitions with K ′′ a between 13 and 18 in the range 171–251 GHz, only prolate pairs were assigned. These transitions have low J ′′ and hence are not affected by internal rotation. Finally 466 Q -branch b -type transitions were correctly fitted. Moreover, 110 hyperfine split transitions were fitted with fixed hyperfine parameters from v 30 = 1. These are R -branch a -type transitions with J ′′ approaching K ′′ a (less than 11), b -type transitions (both R -branch and Q -branch) with K ′′ a less than 4 at frequencies below 70 GHz. The derived parameters are shown in Table 6 . The fitted transitions are in Table 18 (available at the CDS), and those confidently assigned but not correctly fitted with systematic residuals are separated in Table 19 (available at the CDS). Using the newly derived molecular parameters, confident predictions of a -type transitions can be made up to J ′′ = 68 for K ′′ a ≤ 5 below 380 GHz, and J ′′ = 41 for K ′′ a ≤ 41 below 251 GHz (excluding lines of K ′′ a = 18 that show residuals that cannot be fitted). For b -type transitions, all R -branch predictions with K ′′ a ≤ 11 below 251 GHz