High-resolution ro-vibrational and rotational spectroscopy of HC3O+

The ro-vibrational and pure rotational spectra of the linear ion HC3O+ have been investigated in a 4 K cryogenic ion trap instrument. For this, a novel action spectroscopic technique, called leak-out-spectroscopy (LOS, Schmid et al., J. Phys. Chem. A 2022, 126, 8111), has been utilized and characterized. In total, 45 ro-vibrational transitions within the fundamental band of the ν1 C–H stretching mode were measured with a band center at 3237.132 cm−1, as well as 34 lines from the combination band ν2 + ν4, and 41 lines tentatively identified as the combination band ν2 + ν5 + ν7, interleaved and resonant with ν1. Surprisingly, also two hot bands were detected despite the cryogenic operation temperature. Based on the novel action spectroscopy approach, a new double-resonance rotational measurement scheme was established, consisting of rotational excitation followed by vibrational excitation. Seven rotational transitions were observed between 89 and 180 GHz. Highly accurate spectroscopic parameters were extracted from a fit using all available data. In addition, a pulsed laser system has been employed to record a low resolution vibrational spectrum, in order to demonstrate the compatibility of such lasers with the LOS method.


Frequency calibration
The high-resolution results shown in Fig. 1 of the main paper have been recorded in sections of about 1.5 cm −1 , the scanning range of the OPO. Within such mode-hop-free sections, the precision of the measurement is a few 0.0001 cm −1 , but the total accuracy is only on the order of 0.001 cm −1 (see also comments below). For illustration purposes in that Figure Concerning the accuracy of our high-resolution data, it became clear during the analysis that the alignment of our wavemeter had not been optimal during the measurements and therefore showed slightly lower wavenumber readings. Therefore, the spectroscopic data were recalibrated using the 3204.730595 cm −1 line of neutral C 2 H 2 contained within an absorption cell. Using this reference line (taken from the HITRAN database 1 ), we shifted our original data up by 0.009 cm −1 . With this, we assume the accuracy of the data given in the Tables to be a few 0.001 cm −1 . The precision of the data, however, is much better than this, on the order of a few 0.0001 cm −1 .

Early ro-vibrational measurements applying LIICG
In summer 2020 we did first rovibrational measurements on HCCCO + using the LIICG method. 2 With the introduction of LOS, we continued the measurements using this novel method. The signal-to-noise ratio of LOS is superior as seen in the  Figure S1: Comparison of measurements of the ν 1 P (6) line of HCCCO + using LOS and LIICG. For LIICG, HCCCO + -He complexes are generated at 4 K in the ion trap, which are finally counted (on the order of 450, see y2-axis). If the laser is in resonance with the P (6) line of HCCCO + , the counts of HCCCO + -He decrease (dip at resonance). For LOS, on the other hand, one simply counts the HCCCO + ions which are kicked out of the ion trap at resonance (about 4000, see y1-axis). As visible, the S/N ratio of LOS is superior.

S3
3 Comparison with earlier detection of ν 1 The Figure below shows a comparison of the low-resolution measurements of ν 1 and ν 2 + ν 4 of this work (Fig. 1a) with a former measurement of tagged Ne-HCCCO + published by Thorwirth et al. 3 . Both measurements exhibit two band structures, but the Ne-tagged measurement (red trace in Fig. S2) is blue-shifted by about 11 cm −1 . As the measurements in this work are corroborated by the well-calibrated high-resolution measurements (see Fig.1 b and c), and a blueshift of 11 cm −1 caused by the Ne-tag seems highly unlikely, we suspect a calibration error in measurement of the red trace. Together with theoretical predictions, this formerly mislead us to assign the left red peak to ν 1 and only speculate about the nature of the right peak, so that the ν 2 + ν 4 band could not be assigned with confidence in that work.

Resonance System
The rotational constants listed in Table 6 of the main manuscript yield experimental rotationvibration interaction constants (α 1 =13.63(4) MHz, α 2+4 =23.07(5) MHz, α 2+5+7 =11.97(5) MHz) significantly deviating from those estimated from the calculation (see Table 1 main Although the presence of the ν 2 + ν 4 combination band might have been speculated (cf., Ref. 3 ), the appearance of a third band in close proximity to ν 1 came somewhat as a surprise. A possible explanation for this finding is the existence of a (three-level) resonance system in which an initially dark state gains intensity from its resonance partners. In our case most likely a Fermi-resonance system is observed as the ν 1 fundamental as well as the ν 2 +ν 4 combination band are both of Σ + -symmetry. Hence, the initially dark state of the Fermi-resonance system has to posses at least one component of Σ + -symmetry in order to borrow intensity from the bright states. This criterion is in general fulfilled by bands such as the ν 2 + ν 5 + ν 7 combination band (Σ + , Σ − and ∆-symmetry) due to the two involved bending motions.
Within a simple second order de-perturbation approach all appearing coupling terms between the individual resonating bands should be equal in magnitude but opposite in sign vibration interaction constants of ν 1 and the ν 2 + ν 4 combination band as given above, the initially dark state of the resonance system should exhibit a rotation-vibration interaction constant α dark = 9.1(6) MHz. A reasonable estimate for the rotation-vibration coupling S5 constant α ν 2 +ν 5 +ν 7 ,l=0 of its two ℓ = 0 (Σ + -and Σ − -symmetry) components can be estimated from the values given in Table 1 in the main manuscript. The sum of the rotationvibration coupling constants of the involved fundamentals has to be raised and lowered by the difference between the ℓ-type-doubling constants of the two bending motions yielding  Table S1). We base our tentative assignments on characteristic observables such as band intensities, rotational constants B ν (or rotation-vibration constants α ν ), doubling constants q ν , and band centers (or anharmonicity constants χ).
The line lists of these two hot bands are given below. Due to the congested character of the Q-bands, only well-separated lines are listed here. The given rotational assignment is utilized to derive the term energies of the involved states by calculating combination differences. The hereby obtained ground state term values are listed in Tables S4 and S5, respectively, while those in the upper state of the hot bands are given in Table S6. The rotational constants listed in the mentioned tables refer to a least squares fit of the term values to a standard rigid rotor Hamiltonian neglecting centrifugal distortion.
A comparison of the obtained values with the results of the quantum chemical calculations given in Table S1 leaves room for two different assignments of the involved vibrational motions. One possible assignment would be "hot1" to originate from the C-C-O bending motion ν 6 ( 1 Π), while "hot2" originates from the C-C-C bending vibration ν 7 ( 1 Π). The major argument for this assignment is that their rotational-vibrational coupling constants α ν agree in magnitude and sign with their predictions. Furthermore, the assigned ν 1 + ν 6 ← ν 6 which is comparably close to the difference between the calculated anharmonicity constants χ of these two hot-bands (0.76 cm −1 , see Table S1). Also, a close inspection of "hot1" reveals resolved ℓ-type splittings for higher rotational states (see inset in Fig. 1b) which correspond to an ℓ-type doubling constant q hot1 = 3.26(5) MHz. This value is again reasonably close to the value q 6 =3.06 MHz predicted for ν 6 . On the other side, ℓ-type doubling is not observed for "hot2" which is somewhat surprising, as the l-type coupling constant of the C-C-C bending vibration, q 7 , is calculated to be more than twice than the one of the C-C-O bending q 6 .
However, taking into account our cryogenic experimental conditions, the assignment given above is difficult to accept, as we do not expect the ν 6 bending mode (at 558 cm −1 or about 803 K) to be significantly populated at T = 12 K. Therefore, we alternatively assign the more intense band "hot1" to ν 1 + ν 7 ← ν 7 and the weaker band "hot2" to ν 1 + 2ν 7 ← 2ν 7 .
Apart from this intensity argument, this assignment is corroborated by quantum levels in "hot2" apparently only existing for J ≥ 2, which suggest an assignment to a 1 ∆ ← 1 ∆ transition (but in this case we wonder why 2ν 7 appears as ∆-state (ℓ = 2) with a missing Σ-state (ℓ = 0)). Finally, we note that α hot2 ≈ −15.96 has double the value of α hot1 ≈ −7.88, as expected for an overtone state.
In summary, we can only tentatively assign the two hot bands to ν 1 + ν 7 ← ν 7 , ν 1 + 2ν 7 ← 2ν 7 , or ν 1 + ν 6 ← ν 6 . As an additional puzzle, both suggested assignment sets given above lack an explanation of the missing ℓ-type doubling in "hot2". This requires additional future  Table S1: Fundamental vibrational wavenumbers of HC 3 O + , their rotationvibration coupling constants α ν , and doubling constants q ν , calculated on the fc-CCSD(T)/pVTZ level of theory (this work). The given anharmonicity constants χ 1ν refer to the hot-bands of the C-H stretching fundamental ν 1 .  Table S2: Term values for the vibrational ground state (ν = 0) of HCCCO + as derived from all observed transitions of the ν 1 C-H stretching fundamental and resonating combination bands (ν 2 + ν 4 , ν 2 + ν 5 + ν 7 ). Two separate networks of states are derived from the experimental data, denoted as a and b. This leads to two reference points E-D 0 = 0 that are not directly linked to each other. These sets are combined based on their y-axis intercept assuming the validity of the rigid rotor approximation. 8 Term values of C-H stretching fundamental and resonating combination bands Table S3: Term energies for the observed vibrationally excited states lying in the C-H-stretching range of HCCCO + . The given energies are calculated from the observed transitions utilizing the combined ground state term values given in Table S2. a α ν =B 0 -B ν , B 0 is taken from the combined fit in Table S2. b fc-CCSD(T)/pVTZ, this study 9 Term values derived from hot-bands Table S4: Term values for the ground state of the first hot-band (Hot 1) of HCCCO + derived from ground state combination differences. Four separate networks of states are derived from the experimental data, denoted as a,b,c and d, due to the two l-type components of the underlying motion. This leads to four reference points E-D 0 = 0 that are not directly linked to each other. These sets are combined based on their y-axis intercept assuming the validity of the rigid rotor approximation. a α ν =B 0 -B ν , B 0 is taken from the combined fit in Table S2. b fc-CCSD(T)/pVTZ, this study Table S5: Term values for the ground state of the second hot-band (Hot 2) of HCCCO + as derived from ground state combination differences. Four separate networks of states are derived from the experimental data, denoted as a,b,c and d, due to the two l-type components of the underlying bending motion. This leads to four reference points E-D 0 = 0 that are not directly linked to each other. These sets are combined based on their y-axis intercept assuming the validity of the rigid rotor approximation. a α ν =B 0 -B ν , B 0 is taken from the combined fit in Table S2. b fc-CCSD(T)/pVTZ, this study a α ν =B ν hot ,ν2 -B ν hot , the values of B ν hot are taken from the combined fits in Table S4 and S5. b fc-CCSD(T)/pVTZ, taken from ν 1 stretching fundamental