Vibrational Predissociation Spectra of C_{2}N^{−} and C_{3}N^{−}: Bending and Stretching Vibrations
Graphical Abstract
Infrared predissociation spectra of C_{2}N^{−}(H_{2}) and C_{3}N^{−}(H_{2}) is reported using a cryogenic ion trap at the FELIX Laboratory, thus allowing the detection of lowlying bending and stretching vibrations of both anions simultaneously. Vibrational configuration interaction calculations validate the assignment. The recorded spectra can be used as a proxy for the vibrational spectra of the bare anions since the tag does not significantly affect the mode position.
Abstract
We present infrared predissociation spectra of C_{2}N^{−}(H_{2}) and C _{3}N^{−}(H_{2}) in the 300–1850 cm^{−1} range. Measurements were performed using the FELion cryogenic ion trap end user station at the Free Electron Lasers for Infrared eXperiments (FELIX) laboratory. For C_{2}N^{−}(H_{2}), we detected the CCN bending and CC−N stretching vibrations. For the C_{3}N^{−}(H_{2}) system, we detected the CCN bending, the CC−CN stretching, and multiple overtones and/or combination bands. The assignment and interpretation of the presented experimental spectra is validated by calculations of anharmonic spectra within the vibrational configuration interaction (VCI) approach, based on potential energy surfaces calculated at explicitly correlated coupled cluster theory (CCSD(T)F12/ccpVTZ−F12). The H_{2} tag acts as an innocent spectator, not significantly affecting the C_{2,3}N^{−} bending and stretching mode positions. The recorded infrared predissociation spectra can thus be used as a proxy for the vibrational spectra of the bare anions.
Introduction
The linear carbon chains of the type C_{n}N^{−} attracted much interest in theoretical and experimental studies over recent years,^{1} encouraged by the discoveries of CN^{−}, C_{3}N^{−}, C_{5}N^{−}, and very recently C_{7}N^{−} in the circumstellar envelope of the latetype star IRC+10216 with highresolution radio spectroscopy in combination with laboratory data or highlevel abinitio calculations.^{26} C_{3}N^{−} and C_{5}N^{−} were recently also detected in the cold molecular cloud TMC1,^{7} whereas only an upper limit was found for CN^{−} in this source.^{3} The observed abundances hint towards efficient formation pathways via reaction of nitrogen atoms with longer carbon chain anions rather than via direct radiative attachment. In contrast, no member of the C_{2n}N^{−} group has been detected in space, even though they are predicted to play a role in the chemical pathways of the interstellar medium (ISM).^{8, 9} This is likely due to their open shell electronic ground states ( ) leading to increased reactivity but also larger rotational partition functions, hampering not only radioastronomical detection but also their laboratory spectroscopic characterization.
The neutral C_{2}N ( ) radical has been characterized in a variety of electronic states by means of electronic absorption and vibrational emission spectroscopy,^{1012} laserinduced fluorescence spectroscopy^{13} and infrared (IR) spectroscopy and farinfrared laser magnetic resonance for selected bands.^{14, 15} Through matrix isolation infrared spectroscopy,^{1618} the C_{2}N radical has been observed as a byproduct in the degradation of various carbonnitrogen species, such as acetonitrile (CH_{3}CN),^{16, 18} or cyanogen (NCCN).^{17} C_{2}N is also well studied from a theoretical point of view.^{19, 20} For the C_{n}N^{−} anion, the cases have been investigated at several levels of theory by Pascoli et al.^{21} and rotational statechanging dynamics for C_{2}N^{−} have been reported by Franz et al.^{22} Experimentally, high resolution photoelectron spectra for C_{2}N^{−}, C_{4}N^{−}, and C_{6}N^{−} have been detected by slow electron velocity map imaging.^{23} For C_{2}N^{−} the authors assigned the fundamental bending vibration. Up to now, further spectroscopic signatures were only theoretically predicted by Rocha and Linnartz.^{24} They performed extensive anharmonic calculations for C_{2}N^{−} and CNC^{−} using vibrational perturbation theory of second order (VPT2) to solve the threeatom rovibrational Hamiltonian by discrete variable representation (DVR3D).^{25} As the C_{2}N^{−} is a triplet (or biradical) in its electronic ground state,^{24} its high reactivity poses experimental challenges for its production. This has led to a lack of gasphase vibrational measurements, e. g., using infrared predissociation (IRPD) spectroscopy, so far. To our knowledge, no previous measurements of the vibrational predissociation spectra of tagged C_{2}N^{−} anions exist.
Oddnumbered C_{n}N species are less reactive than the evennumbered species due to their closed shell ^{1}Σ electronic ground states,^{26, 27} and are thus easier to isolate in experiments. Vibrational bands of C_{3}N^{−} were identified using krypton, argon and neonmatrix IR isolation spectroscopy, supported by anharmonic VPT2 frequency calculations based on cubic force fields at the coupled cluster level of theory by Kołos et al..^{28} This leads to the assignment of the C_{3}N^{−} absorption feature around 2180 cm^{−1} to be the C−N stretching.^{29, 30} The C−CCN stretching band at ∼1944 cm^{−1} was also detected in a krypton, and argon matrix.^{28} Fourier transform microwave spectroscopy was used to measure the rotational spectra of C_{3}N^{−} in the vibrational ground state with high spectral resolution.^{2, 31} Yen et al.^{32} extracted the vibrational frequencies of the cis and trans bending modes of C_{3}N^{−} with photoelectron spectroscopy using slow electron velocitymap imaging (SEVI). Cryogenic IRPD spectra of C_{3}N^{−} were obtained by StancaKaposta et al.^{33} in the spectral range of the C−N and C−CCN stretching bond (1850–2400 cm^{−1}) with D_{2} as messenger tag. The bands were assigned based on scaled harmonic frequencies at CCSD(T) level of theory. As far as we know, there are no experimental records available for the vibrational predissociation spectrum of C_{3}N^{−} using any tagging agent at frequencies lower than 1850 cm^{−1}.
The advent of cryogenic multipole radiofrequency ion traps and buffergas cooling has contributed to investigate weaklybound ionic complexes by IRPD spectroscopy.^{3439} Here, we extend our studies on CI^{−}(H_{2})^{40, 41} and CI^{−}(H_{2})^{42} and present the vibrational spectra of dihydrogen polycyanides C_{n}N^{−}(H_{2}), and 3 using the same experimental approach, i. e., cryogenic infrared predissociation spectroscopy. Two stable conformers (C_{2}N^{−}(H_{2}) or (H_{2})C_{2}N^{−} and C_{3}N^{−}(H_{2}) or (H_{2})C_{3}N^{−}, respectively) can be formed. In contrast to CN^{−}(H_{2}), where we studied the lowlying intermonomer vibrations, we focus here on the vibrational modes of the C_{2}N^{−} and C_{3}N^{−} anionic core. To aid the assignment and interpretation of the experimental spectra, we provide anharmonic frequency calculations suited for calculation of these species. Additionally, previous theoretical studies and similar experimental studies are used for comparison. For C_{3}N^{−} with H_{2} the potential energy surface (PES) has been developed and the rovibrational bound states have been calculated by LaraMoreno et al.^{43} Rocha and Linnartz^{24} and Kołos et al.^{28} have shown that accurate prediction of the vibrational structure of the C_{2}N^{−} and C_{3}N^{−} species can be achieved based on Taylor series expansions of the PES. It was shown that vibrational perturbation theory of second order (VPT2) is a viable way to calculate the spectroscopic features of these species^{24, 28}. In the present work, we extend and support these theoretical predictions with an alternative approach. We calculate multimode expansions of the PES at explicitly correlated coupled cluster theory, and perform anharmonic calculations using a variational approach, i. e., vibrational configuration interaction (VCI).^{44} In contrast to the variational DVR3D approach^{25} used by Rocha and Linnartz,^{24} we are not limited to threeatomic systems, making it possible to calculate both C_{2}N^{−} and C_{3}N^{−} with the same accuracy. Even though substancial differences between the vibrational spectra of the para and ortho nuclear spin isomers have to be expected, we focus on the intramolecular bending and stretching vibrations, not on the intermolecular vibrations including the H_{2} tag. The reason is that the theoretical treatment of this system with an accurate quantum approach is presently too complex due to the longer chain length.^{42}
Results and Discussion
C_{2}N^{−}: The single photon IRPD spectrum of C_{2}N^{−} tagged with H_{2} is shown in the top panel of Figure 1, which reveals two clearly visible vibrational bands. The second panel shows calculated vibrational band positions and intensities of bare C_{2}N^{−} for comparison. In Table 1 our values are listed together with the frequencies from Rocha and Linnartz,^{24} denoted VAR (an extended Table including harmonic calculations and combination bands is found in Table S1).
Mode 
State 
IRPD^{a} 
VCI ^{b} 
VAR^{c} 



freq./Int. 
freq./Int. 


ν_{1} (Σ^{+}) 
1698(1)/3.6 
1708/236.5 
1696.5 

ν_{3} (Σ^{+}) 
– 
1058/1.3 
1045.8 

(Π) 
454(1)/1.2 
452/28.4 
452.1 
2 
2ν_{1} (Σ^{+}) 

3393/73.4 

2 
2ν_{3} (Σ^{+}) 

2100/0.5 

2 
2 (Σ^{+}) 

893/3.5 

 ^{a} This work: Infrared predissociation on C_{2}N^{−}(H_{2}), ^{b} This work: Vibrational configuration interaction (VCI) calculations on a multimode PES with up to 3mode couplings at the CCSD(T)F12 level of theory, ^{c} Ref. [24]: Variational (VAR) solution of the threeatom Hamiltonian on a composite quartic force field at CCSD(T) level of theory.
The strongest feature is detected at 454(1) cm^{−1}. This value is in good agreement with the anharmonic frequency of 452 cm^{−1} obtained from our VCI calculations based on a multimode PES with up to 3mode coupling at the CCSD(T)F12/ccpVTZ−F12 level of theory. Assigning this vibrational band to the (ν_{2}) bending vibration is additionally supported by the accurate stateoftheart rovibrational quantum chemical calculations from Rocha and Linnartz,^{24} determining ν_{2} to be at 452.1 cm^{−1} using variational DVR3D calculations.
The bending vibration (ν_{2}) for C_{2}N^{−} was experimentally assigned by Garand et al. using highresolution photoelectron spectroscopy by slow electron velocity map imaging (SEVI). They assigned a value of 432 cm^{−1} to the bending fundamental.^{23} A different experimental estimate for the C_{2}N^{−} bending vibration, at 452.9±2.9 cm^{−1}, was derived by Rocha and Linnartz^{24} (shown as green vertical line in Figure 1). To derive this value, the photoelectron spectroscopic data of Garand et al.^{23} was combined with the revisited energy splitting in neutral CCN reported by Muzangwa et al..^{45} This revised SEVI value is in good agreement with our IRPD measurement, indicating that the H_{2} tag has only a minor impact on the band position.
A second strong feature was detected in the present work at 1698(1) cm^{−1}. The anharmonic frequencies from our VCI calculations predict the stretch vibration (ν_{1}) at 1708 cm^{−1}, slightly higher than the calculations by Rocha and Linnartz,^{24} supporting the assignment to the C−N stretch vibration. This vibration is predicted to be shifted by less than 2 cm^{−1} by the H_{2} tag based on harmonic calculations (see Table S4), supporting the argument of the innocent spectator in this system.
The deviations in the calculated frequencies between the present VCI calculations and the DVR3D results by Rocha et al. are about 10 cm^{−1} for the stretching vibrations. These deviations are most likely due to the different choice of electronic structure theory and in the different representation of the PES as a quartic force field or a multimode expansion. Our harmonic calculations of hydrogen tagged C_{2}N^{−}(H_{2}) calculated at the CCSD(T)F12/ccpVTZ−F12 level of theory show that the H_{2} tag does influence the bending vibrations only marginally, i. e., inducing shifts of about 3 cm^{−1} and about 1 cm^{−1} when the nitrogenside tagged or the carbonside are tagged, respectively (see Table S4). For this reason we compare with accurate anharmonic calculations of bare anions, instead of explicitly including the H_{2} tag at a lower computational accuracy.
The stretch vibration (ν_{3}) is predicted to be at at 1058 cm^{−1} by our VCI calculations and at 1045.8 cm^{−1} by Rocha and Linnartz.^{24} We did not detect a band in the range from 933 to 1203 cm^{−1}. Using the signaltonoise ratio from our experiment for the bending vibration ν_{2}, we can give an upper limit for the ν_{3} intesity. The noise level was approximately three times higher in the predicted region of the ν_{3} band. According to the VCI predictions, the intensity of ν_{3} should be about 20 times smaller than the bending one, resulting in an expected signaltonoise ratio of about 0.3. We did not observe such a weak feature (see also insert in Figure 1, suggesting that the ν_{3} vibration is indeed weak. Based on the agreement with the anharmonic calculations for ν_{2} and ν_{1}, the tag is unlikely to shift the band position significantly. The dipole moment for this transition may be weak, resulting in no detection.
C_{3}N^{−}: The third panel of Figure 1 shows the IRPD spectrum of C_{3}N^{−}(H_{2}). Several vibrational bands are observed in the covered range of 350 to 1850 cm^{−1}. The strongest feature is at 530(1) cm^{−1}. Yen et al.^{32} extracted the and bending modes from the SEVI spectra to be at 538±8 and 208±8 cm^{−1}, respectively. Our VCI calculation, shown in the fourth panel of Figure 1, supports this assignment with at 527 cm^{−1} and at 200 cm^{−1}. Thus, we assign the IRPD band at 530 cm^{−1} to the bending mode (see Table 2). Due to the strength of the fundamental band, also the 2 overtone is detected at 1068(1) cm^{−1}, supported by our VCI calculation of predicted at 1063 cm^{−1}. An extended Table with additional calculated values is found in Table S2.
Mode 
State 
IRPD 
VCI^{c} 
Anharm.^{d} 



freq./Int. 
freq./Int. 
freq./Int. 

ν_{1} (Σ^{+}) 
2180^{a} 
2178/804 
2182.3/476 

ν_{2} (Σ^{+}) 
1952^{a} 
1939/62 
1940.9/46 

ν_{3} (Σ^{+}) 
866(1)/3.1^{b} 
864/8 
866.7/10 

ν_{4}^{1} (Π) 
530(1)/5.8^{b} 
527/25 


ν_{5}^{1} (Π) 

200/6 

2 
2ν_{1} (Σ^{+}) 

4336/1 

2 
2ν_{2} (Σ^{+}) 

3865/2 

2 
2ν_{3} (Σ^{+}) 

1722/2 

2 
2ν_{4}^{0} (Σ^{+}) 
1068(1)/0.6^{b} 
1063/3 

2 
2ν_{5}^{0} (Σ^{+}) 
407(1)/0.3^{b} 
406/1 

 ^{a} Ref. [33]: (IRPD) of C_{3}N^{−}(D_{2}), ^{b} This work: IRPD of C_{3}N^{−}(H_{2}), ^{c} This work: Vibrational configuration interaction (VCI) based on a multimode PES with up to 3mode couplings at CCSD(T)F12 level of theory. ^{d} Ref. [28]: Vibrational perturbation theory (VPT2) based on a cubic force field at CCSD(T) level of theory.
The second strongest band is at 866(1) cm^{−1}, which matches the stretching mode (ν_{3}) predicted from VPT2 calculations by Kołos et al.^{28} Our VCI calculations substantiate this assignment. In general, for the bands ν_{1}, ν_{2}, and ν_{3}, we observe agreement between the VCI calculations and the VPT2 calculations by Kołos et al.^{28} of less than 4 cm^{−1}. Note, however, that the calculated VCI intensities are only qualitatively reproducing the experimentally detected intensities.
The lowestfrequency feature at 407(1) cm^{−1} is most likely the second overtone of the cis bending mode (2ν_{5}). The assignment is supported by our VCI calculations with position and intensity, predicting 2ν_{5} at 410(1) cm^{−1}. This assignment is based on the fact that the cis bending ν_{4} is the strongest one detected, allowing the assumption that also the trans bending (ν_{5}) will be strong. The ν_{5} fundamental lies at about 150 cm^{−1} below the FEL2 limit and was thus not covered in this study.
StancaKaposta et al.^{33} measured the C_{3}N^{−} IRPD spectrum from 1850 cm^{−1} upwards and detected the (ν_{1}) and (ν_{2}) stretching vibrations at 2180 and 1952 cm^{−1}, respectively. This spectrum is shown as an orange line in Figure 1(c). Please note that the intensities cannot be compared to those presented in our study. They were able to assign the experimental band position and intensities with harmonic frequency calculations at CCSD(T) level of theory. Our anharmonic VCI calculations support this assignment. All calculated C_{3}N^{−} values can be found in the extended Table S2.
After identifying all C_{3}N^{−} bare ion vibrational modes in the spectrum, three vibrational modes remain unassigned, at 713(1), 735(1) and 800(1) cm^{−1}. The feature at 713(1) cm^{−1} deviates from a Gaussian shape observed in the other features. When combined with the 735(1) cm^{−1} band, it fits the shape predicted by accurate quantum approach theory for the second overtone of the hindered rotation of H_{2} in the CN^{−}(H_{2}) system.^{42} The first two features might thus include an H_{2} contribution. The corresponding overtones were detected at 773 cm^{−1} for CN^{−}(H_{2})^{42} and at 755 cm^{−1} for CI^{−}(H_{2}).^{41} In this case, the last band detected at 800(1) cm^{−1} can tentatively be assigned to the hindered rotation of the H_{2} in combination with an H_{2} intermolecular stretching vibration, similar to CI^{−}(H_{2}). Alternatively, the peak at 735(1) cm^{−1} could consist or contain the combination of ν_{4}+ν_{5} predicted to be at 738 cm^{−1}, even though the calculation predicts a vanishing intensity (see Table S2).
The characteristic P, Q, and Rsubstructure, seen in the vibrational bands at high temperatures, collapse at low temperatures, as previously demonstrated by Jusko et al.^{37} In the ν_{1} and ν_{2} stretching band of the D_{2} tagged system, the P and R branches have been assigned to rotationally excited C_{3}N^{−}(D_{2}).^{33} StancaKaposta et al. concluded a mean rotational temperature of 75 K while maintaining a trap temperature of 15 K. It is known that the rotational temperature of trapped ions often does not fully thermalize.^{46} Simpson et al.^{47} used a similar trap to the one we employ here and found the best fit for the rotational temperature at 25 K. This, combined with the absence of a doublepeak structure in our presented spectra indicates that the ions in our experiment likely have a rotational temperature in the order of 25 K.
In the previously studied system of C_{3}N^{−}(D_{2}), the influence of the tag molecule has been discussed in detail.^{33} There, they find that the Cside tagged complex is preferred by 84 cm^{−1}. For C_{3}N^{−}(H_{2}), we can confirm the preference of H_{2} for the Cside tagging, where our calculations show an energy difference of 73 cm^{−1}. For all the newly detected fundamental stretching and bending vibrations our calculations predict band shifts induced by the H_{2} tag of less than 4 cm^{−1} independent of the tagging side using harmonic calculations (see Table S4), supporting the argument of the innocent spectator in this system. Due to our laser bandwidth being larger than the predicted shift, we can not distinguish between the different tagging sides experimentally. Considering that StancaKaposta et al.^{33} noted a shift of less than 1 cm^{−1} for the system of C_{3}N^{−}(D_{2}), we can conclude that the complexation of the tag, whether it is D_{2} or H_{2} has a negligible effect on the measured vibrational frequencies.
Although the singletagged anion is formed with highest abundance, multiple tags can be formed in small numbers in the cryogenic trap (single tagging efficiency for C_{3}N^{−}(H_{2}) is ∼6.0 %, double tagging ∼2.5 %). For the doubletagged system C_{3}N^{−}(H_{2})_{2}, we note a 3 cm^{−1} blueshift for the ν_{4} bending vibration (see Figure S1). To determine the actual shift caused by the single tag, it is necessary to compare the spectrum of the ionmolecule complex to that of the bare ion. Possible approaches to achieve this goal are spectroscopy by laserinhibition of cluster growth^{48} or the recently demonstrated leakout spectroscopy,^{49} both of which allow for tagfree spectroscopy.
StancaKaposta et al. predicted that the dissociation energy for the D_{2}loss channel is smaller than 350 cm^{−1}. Our calculations on the CCSD(T)F12/ccpVTZ−F12 level of theory predict a dissociation energy of 138 and 65 cm^{−1} for (H_{2})C_{3}N^{−} and C_{3}N^{−}(H_{2}), respectively (see SI and Table S3). This implies that also the ν_{5}, predicted at 200 cm^{−1} should be detectable with a suitable laser system.
Conclusion
Here, we present and discuss farinfrared and midinfrared predisscociation vibrational spectra of the weakly bound complexes C_{2}N^{−}(H_{2}) and C_{3}N^{−}(H_{2}) in the region of their lowlying stretching and bending modes of the bare anions and their intermonomer modes (300–1850 cm^{−1}). By using a cryogenic ion trap instrument coupled to the widely tunable freeelectron lasers at the FELIX laboratory, we observed for C_{2}N^{−}(H_{2}) the stretching vibration for the first time and can confirm the bending vibration of C_{2}N^{−} estimated by Ref. [24] with data from Garand et al.^{23} and Muzangwa et al..^{45} We could assign the bands with highlevel VCI calculations, supported by previous VAR calculations.^{24}
In the system of C_{3}H^{−}(H_{2}) we could access the lowwavenumber region between 300–1850 cm^{−1} where the lowlying bending and stretching bands are located. Combined with IRPD spectra on C_{3}N^{−}(D_{2}) by StancaKaposta et al.^{33} starting 1850 cm^{−1} upwards, we can assign all fundamentals and several overtones. VCI calculations aid the assignment. The spectrum is dominated by the bending vibration and the stretching vibration. As in the system of CN^{−}(H_{2}) we can tentatively assign one doublet feature to the second overtone of the bending vibration associated with the hindered rotation of H_{2}.
The observation by Stanca Kaposta et al.^{33} of a small shift in the vibrational frequency of less than 1 cm^{−1} is confirmed by our calculations and leads us to conclude that the complexation of the tag has a negligible impact on the vibrational frequencies also in the lowwavenumber regime. Thus the IRPD spectra obtained in the present work can be used as a substitute for the anions’ vibrational spectra in the tag's absence. In the future it will be interesting to study the influence of the H_{2} tag in more detail. This can serve as a benchmark for collisional excitation studies, see e. g.^{50, 51}
Methods
Experimental
Experiments were performed at the FELion cryogenic ion trap beamline at the Free Electron Lasers for Infrared eXperiments (FELIX) Laboratory. The FELion instrument and its use for vibrational spectroscopic studies employing infraredpredissociation action spectroscopy of raregas tagged molecular ions have been described in detail previously.^{37} Here we only report the specific details related to the current investigation of the C_{2}N^{−}(H_{2}) and C_{3}N^{−}(H_{2}) systems.
C_{2}N^{−} and C_{3}N^{−} anions were produced by dissociative electron attachment to acetonitrile CH_{3}CN and acrylonitrile C_{3}H_{3}N, respectively, in a Gerlichtype ion storage source^{52} using electrons with energies around 70 . We want to note that the C_{2}N^{−} yield was a factor of ∼100 smaller than the C_{3}N^{−} yield. Ions with a masstocharge ratio m/z of either 38 (C_{2}N) or 50 (C_{3}N) were massselected in a quadrupole mass filter and guided to the cryogenic 22 pole ion trap held at a fixed temperature of 15 K. At the beginning of the storage cycle, a mixture H_{2} : He of 1 : 2 was pulsed into the trap for 100 ms leading to cooling of the ions and the formation of C_{2}N^{−}(H_{2}) or C_{3}N^{−}(H_{2}) complexes. Normal H_{2} was used for the experiments described here. The complexes were stored between 1.5 and 2.6 s in the trap, where they were exposed to infrared radiation of the freeelectron laser FEL2 that delivered pulse energies varying from 20–35 mJ in the trap region at 10 Hz repetition rate with a macropulse duration of ∼10 μs. The laser was tuned in the region between 300–1850 cm^{−1}, and the depletion of the number of complex ions due to singlephoton IRPD was recorded as a function of the frequency. The FEL2 was optimized for narrow bandwidth, reaching typical rms widths of about 0.5–0.6 % of the center value,^{37} or a FWHM of about 12 cm^{−1} at 1000 cm^{−1} in the present experiment. To account for varying laser pulse energy E, pulse numbers n, baseline drifts due to varying source conditions, and saturation effects, the signal is normalized prior to averaging using , with S the number of complexes as a function of laser frequency and B the number of baseline complexes. As the photon wavelength increases 5fold from 300 cm^{−1} to 1800 cm^{−1}, the number of photons decreases 5fold assuming equivalent pulse energy. The reported experimental intensities are corrected to change in photon number as a function of wavelength.
Computational
The C_{n}N^{−} anion can be treated as a linear system^{21} in the point group, with the electronic ground state being a singlet (^{1}Σ) for the CN^{−} and C_{3}N^{−} species and a triplet (^{3}Σ) for the C_{2}N^{−} species. Note that also nonlinear geometries and different electronic states were studied for C_{2}N^{−},^{24} while for C_{3}N^{−} only linear constitutional isomers have been considered.^{53} The hydrogen molecule H_{2} is weakly bound to the C_{n}N^{−} anion and considered as a messenger molecule or tag. In this work, we distinguish between the (H_{2})C_{n}N^{−} (Cside tagged) and C_{n}N^{−}(H_{2}) (Nside tagged) conformers.
For the C_{n}N^{−}(H_{2}) and (H_{2})C_{n}N^{−} complexes with , we performed geometry optimizations within the explicitly correlated coupled cluster ansatz^{54, 55} using a triple zeta basis,^{56, 57} in brief CCSD(T)F12/ccpVTZ−F12. Compared to conventional coupled cluster theory, the F12 ansatz is known for faster basis set convergence so that our calculations may be best compared to CCSD(T) with a quintuple zeta basis, while maintaining reduced computational cost. On the same level of theory, we calculated the harmonic frequencies, dissociation energies as well as the thermochemistry within the rigidrotor harmonic oscillator approximation. The results are shown in the supplementary information. In accordance with Refs. [33,51,58], our calculations suggest that H_{2} tagging on the nitrogen side is favored for the CN^{−} species, while for the larger species, carbonside tagging is favored.
Anharmonic calculations were performed to improve upon the harmonic frequencies and to aid the interpretation of combination bands and/or overtones. In this respect, we calculated multimode PES expansions^{59, 60} with up to 3mode couplings using CCSD(T)F12/ccpVTZ−F12 level of electronic structure theory. The multimode PES expansion needs multiple single point calculations on a grid, hence, we rely on the CCSD(T)F12 ansatz with a triple zeta basis for both C_{2}N^{−} and C_{3}N^{−}, which has been shown to maintain a good reasonable compromise of computational time and accuracy in the calculation of the PES.^{61} Our choice of electronic structure theory is comparable to the CCSD(T) ansatz with a quadruple zeta basis chosen by Kołos et al.^{28} in their calculation of a cubic force field of C_{3}N^{−}. Note that the composite quartic force field for C_{2}N^{−} computed by Rocha and Linnartz^{24} is also based on CCSD(T) level of theory, however, they include corecorrelation, scalar relativistic contributions and estimation of higherorder electron correlation. Based on our multimode PES, we calculated the vibrational structure by configuration averaged vibrational selfconsistent field (CAVSCF)^{62} and subsequent vibrational configuration interaction (VCI)^{44, 63} with up to quadruple excitations (VCISDTQ). All calculations were performed using the Molpro 2022 software package.^{64}
In terms of notation, we use two types of labels: (1) The normal mode description, for instance, for the CCN bending notion and for CC−N stretching vibration. A visualization of the modes can be found in Figure S2 and S3. (2) The state identity description with the labels , where we use the subscript i as previously introduced in literature.^{23, 24} The prefix v denotes the vibrational quantum number and the superscript l denotes the absolute ltype doubling quantum number. Additionally, these labels comprise the irreducible representation in brackets.
Supporting Information
Additional references cited within the Supporting Information.^{65, 66}
Acknowledgments
We gratefully acknowledge the support of Radboud University and of NWO for providing the required beam time at the FELIX Laboratory, and the skillful assistance of the FELIX staff. This work was supported by the Max Planck Society. We thank the Cologne Laboratory Astrophysics group for providing the FELion ion trap instrument for the current experiments and the Cologne Center for Terahertz Spectroscopy funded by the Deutsche Forschungsgemeinschaft (DFG, grant SCHL 341/151) for supporting its operation. This work was supported by the Austrian Science Fund (FWF) through project No. I2920N27 and through the Doctoral program Atoms, Light and Molecules, project number W1259N27. The research leading to these results has received funding from LASERLABEUROPE (grant agreement no. 871124, European Union's Horizon 2020 research and innovation programme), and by the research programme ROSAA with project number 740.018.010, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).
Conflict of interest
The authors report there are no competing interests to declare.
Open Research
Data Availability Statement
The used geometries for calculation, scripts and raw data are available at https://doi.org/10.5281/zenodo.7965386.