Dataset for "Infrared Predissociation Spectroscopy of cold trapped C2H-(H2) and C2H-(D2)"

C2H (H2) and C2H (D2) Computational Data S-1 Infrared predissociation spectroscopy of cold trapped C2H-(H2) and C2H-(D2) - Computational Data September 25, 2025 Sruthi Purushu Melath, Katrin Dulitz , Michael Hauck, Dasarath Swaraj, Franziska Dahlmann, Marius Gerlach, Dennis F. Dinu, Pavol Jusko, Klaus R. Liedl, Stephan Schlemmer, Sandra Brünken, and Roland Wester This document accompanies the computational data stored on Zenodo (C2H_calculation_data.zip), explaining the ab initio calculations that were performed for C2H–and the H2-tagged species, to support the assignment of infrared predissociation spectroscopy experiments on the cold trapped C2H–ions. We include tables for structural and spectroscopic parameters, harmonic wavenumbers, anharmonic wavenumbers from quartic force fields and vibrational perturbation theory (VPT2), details on the construction of a N-mode potential energy surface (PES) for vibrational self consistent field and configuration interaction (VSCF/VCI) calculations. Contents S1 General computational aspects S-2 S1.1 Structural parameters and spectroscopic constants ....................... S-2 S1.2 Energy of cluster formation .................................... S-3 S2 The C2H–bare ion S-4 S2.1 Normal modes ............................................ S-4 S2.2 Harmonic Approximation and Vibrational Perturbation Theory ................ S-6 S2.3 N-mode Potential Energy Surface ................................. S-8 S2.4 Vibrational Self-Consistent Field, Vibrational Configuration Interaction ........... S-10 S3 The H2-tagged C2H–molecule S-12 S3.1 Normal modes ............................................ S-12 S3.2 Harmonic Approximation and Vibrational Perturbation Theory ................ S-14 S3.3 N-mode Potential Energy Surface ................................. S-16 S3.4 Vibrational Self-Consistent Field and Configuration Interaction ................ S-18 S4 The D2-tagged C2H–molecule S-19 C2H (H2) and C2H (D2) Computational Data S-2 S1 General computational aspects S1.1 Structural parameters and spectroscopic constants The ground electronic state of C2H–is a linear singlet (X1Σ+) and the potential energy surface (PES) of C2H–tagged with an H2molecule, has a single minimum (H2at the C-end of the C2H–) with a well-depth of 924.96 cm−1. We have recomputed the structural parameters using (ae)CCSD(T)-F12 level of theory using basis sets up to CVQZ-F12 (cf. Table S1). With increasing basis set size, the bond lengths decrease. For the H2·C2H–system, we do not obtain the same bond lengths as Dumouchel et al., although we use the same level of theory. The discrepancy may be rooted in a different setup for the all-electron calculation, where we rely on three different exponents for Slater-type frozen geminal (keyword: gem_beta=[0.8,1.7,2.2]), rather than one. Table S1: Structural parameters (Born-Oppenheimer approximation) for the free C2H–and the H2-tagged species at (ae)CCSD(T)-F12 level of theory in the linear equilibrium geometry. The bond distances B1 - B4 are given in Å. All angles are 180.0 degree. The equilibrium rotational constant BBO , the vibrationally-averaged ground-state rotational constant Bva and the centrifugal distortion constants DJand HJfrom Vibrational Perturbation Theory are given in MHz. Ref: Doumuchel, 2023, DOI: 0.1063/5.0148119, (ae)CCSD(T)-F12b/CVQZ-F12, gem_beta=1.0. C2H–H2·C2H– CVDZ-F12 CVTZ-F12 CVQZ-F12 CVDZ-F12 CVTZ-F12 CVQZ-F12 Ref. B1 1.06943137 1.06913492 1.06899002 1.06927066 1.06895651 1.06881374 1.0596 B2 1.24628903 1.24564373 1.24540352 1.24578620 1.24513115 1.24488900 1.2516 B3 2.65802260 2.64499178 2.64669349 3.68 (c.o.m) B4 0.75343361 0.75347265 0.75324869 0.7666 BBO 41800.40 41840.80 41856.25 Bva 41633.88 41671.76 41686.96 DJ·10393.443 93.637 93.632 HJ·1060.077 0.078 0.078 Table S1 also lists the spectroscopic constants B, DJ, HJfor the linear C2H–molecule. We obtain the rotational constant BBO from the geometry optimization within the Born-Oppenheimer approximation. From 2nd order vibrational perturbation theory (VPT2), we get the vibrationally averaged rotational constant Bva as well as the centrifugal distortion constants DJand HJ, which can be used to model the pure rotational spectrum. For the simulation of ro-vibrational spectra, the rotational constants for vibrationally excited states and the l-type doubling constants are listed in the respective subsections for C2H and C2H- * H2. C2H (H2) and C2H (D2) Computational Data S-3 S1.2 Energy of cluster formation Table S3: Single point energies (SPE) and zero point energies (ZPE) in Hartree. Calculated within the rigid rotor harmonic oscillator (RRHO) approximation at (ae)CCSD(T)-F12/CVDZ-F12 level of theory. Single Point Energy (SPE) Zero Point Energy (ZPE) SPE + ZPE H2-1.17336049 0.01003763 -1.16332286 C2H–-76.70316822 0.01416652 -76.68900170 H2·C2H–-77.88033387 0.02693508 -77.85339879 ∆Eform (H2·C2H–) / Hartree -0.00107423 / meV -29.2 / cm−1-235.7 / kcal/mol -0.674 / kJ/mol -2.820 Table S3 shows the single point energies (SPE) and zero point energies (ZPE) for H2, C2H–and the cluster H2·C2H–and the energy of cluster formation ∆Eform. Thermodynamic corrections are available in the molpro output files. The listed results demonstrate that forming the H2-tagged species is energetically favorable, albeit with a relatively low energy gain. The calculated energy of cluster formation ∆Eform is very close to the thermal energy available at room temperature (kT = 25meV, RT = 2.479kJ/mol). However, as the experiments at FELIX are at very low temperatures and in a trapping environment, the cluster formation can be expected to be accessible for further spectroscopic studies. In the following, the vibrational structure of the free C2H–and the H2·C2H–is calculated using common approaches from quantum chemistry. This includes the harmonic approximation, 2nd order vibrational perturbation theory (VPT2), and more extensive N-mode potential energy surface (PES) expansions for the use in vibrational self-consistent field and configuration interaction (VSCF/VCI). C2H (H2) and C2H (D2) Computational Data S-4 S2 The C2H–bare ion S2.1 Normal modes The C2H–in its linear conformation in the C∞vpoint group has 3∗3−5=4normal modes, of which two are degenerate, as shown in Table S5. Hence, there are three fundamental harmonic vibrations to be expected, and according to the irreducible representations of the normal modes, all of these vibrations are IR active. The vibrations can be characterized based on visual inspection of the normal mode vectors in Table S5 and the normal mode decomposition into internal coordinates as shown in Figure S1. The contribution heat-map shows that all vibrations are significantly localized. Thus, the distinction between two stretching and two (degenerate) bending vibrations is straightforward. Table S5: Harmonic wavenumbers and normal modes of C2H–at (ae)CCSD(T)-F12/CVDZ-F12 level of theory. q1(E): C2H–"bending" 509.6 cm−1q2(E): C2H–"bending" 509.6 cm−1 q3(A1): CC "stretching" 1840.4cm−1 q4(A1): CH "stretching" 3358.8 cm−1 C2H (H2) and C2H (D2) Computational Data S-5 Figure S1: Normal mode decomposition for C2H–at (ae)CCSD(T)-F12/CVDZ-F12 level of theory. C2H (H2) and C2H (D2) Computational Data S-6 S2.2 Harmonic Approximation and Vibrational Perturbation Theory Table S6 lists the vibrational transitions of C2H–calculated at the (ae)CCSD(T)-F12 level of theory using various basis sets (and Table S8 the spectroscopic parameters). The degenerate bending modes of E1 symmetry show l-type doubling. As expected, compared to the harmonic calculations (HARM), the anharmonic correction based on 2nd order vibrational perturbation theory (VPT2) shifts the vibrations towards lower wavenumbers, most significantly for the CH stretching mode. The basis set size has only a minor effect on the stretching modes for the HARM and VPT2 calculations. However, a significant influence of the basis set on the bending mode is observed. This effect is passed on into the combination bands that include the bending mode (e.g. 31+ 11). Table S6: Harmonic and VPT2 results for C2H–at (ae)CCSD(T)-F12 level of theory using different basis sets. IR activity is determined based on the irreducible representation (Irrep). The results highlighted in bold font can be considered the most accurate in this table. CVDZ-F12 CVTZ-F12 CVQZ-F12 Mode Label Irrep IR active HARM VPT2 HARM VPT2 HARM VPT2 q4ν(CH) 31A1 yes 3358.59 3213.73 3357.57 3213.77 3359.20 3215.32 q3ν(CC) 21A1 yes 1840.32 1811.52 1841.18 1811.54 1842.19 1812.70 q2δ(CCH) 11(l1 = −1) E1 yes 510.97 499.53 521.10 504.99 525.98 509.42 q1δ(CCH) 11(l1 = +1) E1 yes 510.97 499.53 521.10 504.99 525.98 509.42 22A1 yes 3680.63 3604.81 3682.35 3604.93 3684.38 3607.24 12(l1 = −2) E2 no 1021.93 1005.83 1042.20 1014.62 1051.96 1023.29 12(l1 = +2) E2 no 1021.93 1005.83 1042.20 1014.62 1051.96 1023.29 12(l1 = 0) A1 yes 1021.93 1005.83 1042.20 994.21 1051.96 1002.59 31+ 11(l1 = −1) E1 yes 3869.55 3693.14 3878.67 3698.68 3885.18 3704.50 31+ 11(l1 = +1) E1 yes 3869.55 3693.14 3878.67 3698.68 3885.18 3704.50 21+ 11(l1 = −1) E1 yes 2351.28 2306.35 2362.28 2310.85 2368.17 2316.59 21+ 11(l1 = +1) E1 yes 2351.28 2306.35 2362.28 2310.85 2368.17 2316.59 C2H (H2) and C2H (D2) Computational Data S-7 Table S8: Spectroscopic parameters from Vibrational Perturbation Theory for C2H–at (ae)CCSD(T)-F12 level of theory given in MHz. Equilibrium rotational constant BBO is within the Born-Oppenheimer approximation. Vibrationally-averaged rotational constant Bva is given for each vibrational state denoted in ket-notation |sst >. Centrifugal distortion constants are listed for the quartic DJand sextic HJterms. The rotational l-type doubling constants QE, QJ, QKare given for the degenerate normal modes. CVDZ-F12 CVTZ-F12 CVQZ-F12 BBO 41800.40 41840.8 41856.25 Bav |000 >41633.47 41669.24 41684.41 |100 >41335.66 41371.47 41387.18 |200 >41037.85 41073.71 41089.95 |010 >41326.53 41362.9 41378.00 |110 >41028.72 41065.14 41080.77 |020 >41019.59 41056.57 41071.59 |001 >41768.93 41799.72 41814.40 |101 >41471.11 41501.96 41517.17 |011 >41461.99 41493.38 41507.99 |002 >41904.38 41930.2 41944.39 DJ·10393.44 93.633 93.629 HJ·1060.075 0.076 0.076 q1, q2 QE·103251955.29 248410.04 246770.02 QK·103-3.78 -3.61 -3.55 QJ·1033.54 3.36 3.31 C2H (H2) and C2H (D2) Computational Data S-8 S2.3 N-mode Potential Energy Surface Both the harmonic calculations (HARM) based on the approximation of a quadratic curvature at the minimum of the potential energy surface (PES), and the anharmonic VPT2 calculations from a conventional quartic force field (QFF), are inherently limited. These local descriptions of the PES tend to fail if the PES is very flat. We calculate an N-mode PES as an alternative, where the potential energy is calculated along normal mode displacements. Although this is still a relatively local description of the PES, it converges better than the Taylor series expansion used in conventional QFF. We also used the N-mode PES to obtain a QFF for the VPT2 calculations in Table S6. For the single C2H–molecule, the harmonic approximation does not yield any normal mode with very low harmonic wavenumbers ≤200 cm−1. Hence, we do not expect any large amplitude motions with flat PES curvatures. This is reflected in the N-mode PES expansions, as shown in Tables S10 -S12. The 1D cuts of the N-mode PES are represented by fitted polynomials towards an ab initio grid (black dots and blue lines). The 4D PES is represented with a projection of the 4D PES on a 1D effective potential by separate VSCF calculations for each mode (purple lines). We tested the automatic deletion of PES parts by neglecting those that do not fit the ab initio grid under a certain fitting threshold (keyword: delauto). As can be seen, the N-mode PES at (ae)CCSD(T)-F12/CVDZ-F12 level of theory should not be truncated too early, because this leads to unreasonable shapes in the VSCF effective potentials (cf. last column in Table S10). Although, once a triple or quadruple zeta basis set is chosen, the N-mode PES can already be considered more in terms of the polynomial fitting, it is unwise to set the threshold too high, because this would lead to artificial double minimum potentials (cf. last columns in Table S11 and S12). Consequently, we present merely the VSCF/VCI results with the largest possible basis set and no automatic deletion of fitted parts of the PES. Table S10: 4-mode PES of C2H–using CCSD(T)-F12/CVDZ-F12. The 1-mode potentials are shown as grid and polynomial representation. The 4-mode PES is shown via effective potentials from ca-VSCF. delauto=off delauto=1.d-5 delauto=1.d-10 POLY VSCF POLY VSCF POLY VSCF C2H (H2) and C2H (D2) Computational Data S-9 Table S11: 4-mode PES of C2H–using CCSD(T)-F12/CVTZ-F12. The 1-mode potentials are shown as grid and polynomial representation. The 4-mode PES is shown via effective potentials from ca-VSCF. delauto=off delauto=1.d-5 delauto=1.d-10 POLY VSCF POLY VSCF POLY VSCF Table S12: 4-mode PES of C2H–using CCSD(T)-F12/CVQZ-F12. The 1-mode potentials are shown as grid and polynomial representation. The 4-mode PES is shown via effective potentials from ca-VSCF. delauto=off delauto=1.d-5 delauto=1.d-10 POLY VSCF POLY VSCF POLY VSCF C2H (H2) and C2H (D2) Computational Data S-16 S3.3 N-mode Potential Energy Surface As stated before, the harmonic calculations and the anharmonic VPT2 calculations are inherently limited as they rely on local descriptions of the PES and tend to fail if the PES is very flat. In contrast to the single C2H–system, the H2·C2H–cluster can be expected to cause such problems due to the large amplitude motions discussed above. This is reflected in the difficulties in obtaining reasonable results for VPT2 calculations (cf. Table S18). Again, as an alternative, we calculate an N-mode PES in rectilinear normal coordinates, where the potential energy is calculated along normal mode displacements. However, it has to be expected that the large amplitude motions will also cause problems in expanding an N-mode PES representation, similar to the Taylor series expansion used in the QFF. Nevertheless, we here test the convergence for such an N-mode PES. For the H2·C2H–cluster, the harmonic approximation yields three normal modes q1−q3with very low harmonic wavenumbers <200 cm−1. Hence, we expect large amplitude motions with flat PES curvatures. This is reflected in the N-mode PES expansions, as shown in Table S22 for a PES expansion with a small basis set (CVDZ-F12). Mode q3stands out with a well-depth of 800 cm−1, compared to all other modes with well-depths of more than 2000 cm−1. It can be expected that mode-coupling with q3 yields troublesome potentials. While the 1D cuts of the N-mode PES, as represented by fitted polynomials towards an ab initio grid (black dots and blue lines), are themselves reasonable, the 4D PES, as represented with a projection of the 4D PES on 1D effective Potential by separate VSCF calculation for each mode (purple lines), show highly problematic shapes that cannot provide for a convergence in the VSCF calculations. Only automatic deletion (keyword: delauto) of such troublesome parts of the PES provides more reasonable and effective VSCF potentials. We found good VSCF results with a delauto-threshold of 1.d−10. Using a PES with a larger basis (CVTZ-F12) shows a different behavior regarding the automatic deletion of troublesome parts of the PES. Table S23 shows that the threshold for automatic deletion must be set tighter (delauto=1.d-13) to obtain reasonable VSCF effective potentials. However, these tests also show that automatic deletion has to be done carefully, as a too tight threshold can delete necessary information (cf. VSCF potential of mode q3for delauto=1.d-15 in Table S11). Table S22: 4-mode PES of H2·C2H–using CCSD(T)-F12/CVDZ-F12. The 1-mode potentials are shown as grid and polynomial representation. The 4-mode PES is shown via effective potentials from ca-VSCF. delauto=off delauto=1.d-5 delauto=1.d-10 POLY VSCF POLY VSCF POLY VSCF (Table continues on next page) C2H (H2) and C2H (D2) Computational Data S-17 Continuation of Table S22 POLY VSCF POLY VSCF POLY VSCF Table S23: 4-mode PES of H2·C2H–using CCSD(T)-F12/CVTZ-F12. The 1-mode potentials are shown as grid and polynomial representation. The 4-mode PES is shown via effective potentials from ca-VSCF. delauto=1.d-10 delauto=1.d-13 delauto=1.d-15 POLY VSCF POLY VSCF POLY VSCF (Table continues on next page) C2H (H2) and C2H (D2) Computational Data S-18 Continuation of Table S23 POLY VSCF POLY VSCF POLY VSCF S3.4 Vibrational Self-Consistent Field and Configuration Interaction VSCF and VCI calculations were successful for the N-mode PES by automatically deleting troublesome parts of the PES and show, in general, better convergence than the corresponding VPT2 calculations. As seen in Table S24, the VSCF and VCI results for the bending modes are too high compared to their harmonic values. Similar to what has been shown for the bare ion in Table S15, it can be expected that these issues partially originate in the truncation of the configurational space in VCI. A larger configurational space for the tagged ion leads to computationally demanding VCI calculations that are beyond the scope of the present work and, thus, remain subject to future theoretical studies. C2H (H2) and C2H (D2) Computational Data S-19 Table S24: Configuration-averaged vibrational self-consistent field (ca-VSCF) and vibrational configuration interaction (VCI) calculations of H2·C2H–relying on a 4-mode PES at CCSD(T)-F12/CVTZ-F12 with automatic deletion of troublesome parts (delauto=1.d-13). The harmonic (HARM) and 1D discrete variable representation (DVR) solutions are given for reference. L-type doubling is considered. The results in this table are very likely not well converged (see text). Mode Label Irrep HARM 1D DVR ca-VSCF IR Int VCI(5) IR Int. Coeff. q10 ν(H2) 71A1 4190.66 3919.50 3921.86 391.68 3919.45 388.91 0.9746 q9ν(CH) 61A1 3360.21 3255.76 3252.83 5.04 3203.87 5.03 0.9308 q8ν(CC) 51A1 1846.27 1827.36 1830.39 68.44 1818.95 67.15 0.9480 q6, q7τ(H2) 41|l4|= 1 E1 571.59 1082.68 1083.08 3.90 1083.01 4.13 0.9747 q4, q5δ(CCH) 31|l3|= 1 E1 525.88 693.65 694.20 127.38 695.38 128.78 0.9766 q3ν(H2·C2H–) 21A1 199.44 172.54 172.97 0.00 173.21 0.00 0.9752 q1, q2δ(H2·C2H–) 11E1 27.65 150.37 150.57 30.06 78.90 19.93 0.9430 ν(CC) 52A1 3692.53 3621.72 0.54 0.9261 42|l4|= 0 A1 1143.18 2381.53 4.55 0.6841 42|l4|= 2 E2 1143.04 2380.20 0.00 0.6848 δ(CCH) 32|l3|= 2 E2 1051.76 1490.20 0.00 0.6899 δ(CCH) 32|l3|= 0 A1 1051.55 1488.63 23.75 0.6910 22A1 398.88 321.57 0.00 0.9755 12|l1|= 0 A1 55.31 216.85 0.74 0.6470 11|l1|= 2 E2 53.89 204.26 0.00 0.6702 S4 The D2-tagged C2H–molecule Using the N-mode PES of H2·C2H–described in the previous section, we performed isotopic transformation (PESTRANS) to obtain the vibrational spectrum of the D2·C2H–species. The VSCF and VCI results using this PES are shown in Table S26. These results must be taken with care as they are prone to similar convergence problems as discussed for the H2·C2H–above. Table S26: Configuration-averaged vibrational self-consistent field (ca-VSCF) and vibrational configuration interaction (VCI) calculations of D2·C2H–relying on a (isotopically transformed) 4-mode PES at CCSD(T)-F12/CVTZ-F12 with automatic deletion of troublesome parts (delauto=1.d-13). The harmonic (HARM) and 1D discrete variable representation (DVR) solutions are given for reference. L-type doubling is considered. The results in this table are very likely not well converged (see text). Mode Label Irrep HARM 1D DVR ca-VSCF IR Int VCI(5) IR Int. Coeff. q10 ν(CH) 71A1 3360.21 3255.76 3251.80 5.07 3204.83 4.44 0.8868 q9ν(D2) 61A1 2964.40 2828.50 2831.06 185.23 2827.24 185.34 0.9737 q8ν(CC) 51A1 1846.26 1827.35 1829.83 68.69 1816.27 67.10 0.9468 q6, q7τ(D2) 41|l4|= 1 E1 526.00 693.04 693.72 129.11 688.72 94.23 0.8690 q4, q5δ(CCH) 31|l3|= 1 E1 405.14 715.60 716.43 1.07 723.29 37.85 0.8654 q3ν(D2·C2H–) 21A1 146.24 131.64 131.84 0.00 131.92 0.00 0.9745 q1, q2δ(D2·C2H–) 11E1 25.50 135.18 135.09 25.67 69.57 16.81 0.9431 ν(CC) 52A1 3692.52 3615.75 0.46 0.9003 42|l4|= 0 A1 1052.00 1491.08 20.06 0.8729 42|l4|= 2 E2 1491.43 9.91 0.0667 δ(CCH) 32|l3|= 2 E2 810.28 1583.63 0.12 0.4143 δ(CCH) 32|l3|= 0 A1 1584.22 1.27 0.5770 22A1 292.48 249.93 0.00 0.9746 12|l1|= 0 A1 51.00 194.30 0.62 0.6487 11|l1|= 2 E2 181.61 0.00 0.6714