# Ab Initio Rovibrational Spectroscopy of the Acetylide Anion

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Electronic Structure Calculations

**CV:**- The CV effects are captured by conventional CCSD(T) calculation and a large (781 contracted Gaussian-type orbitals) aug-cc-pCV6Z basis set [70]. By subtracting the result of frozen-core CCSD(T) from that of an all-electron (ae) calculation the CV contribution is obtained.
**SR:**- Second-order Dogulas-Kroll-Hess calculations [71,72] are employed at the fc-CCSD(T) level to provide SR effects, where difference of calculations with the relativistic Hamiltonian employing a aug-cc-pVQZ-DK basis set [73] and non-relativistic calculations with an aug-cc-pVQZ basis [64,65] yields the contribution to the composite PES.
**HC:**- Three distinct HC contributions are employed. The first, which is termed (Q)–(T), corrects for the fully iterative treatment of triple excitations as well as for a quadruple excitation effect by a perturbative treatment. The second contribution Q–(Q) accounts for the full iterative treatment of quadruples. This partitioning has been shown to be rather efficient since larger basis sets can be used for (Q)–(T) compared to Q–(Q). Finally, the P–Q contribution incorporates pentuple excitation contributions.
**(Q)–(T):****Q–(Q):****P–Q:**

**DBOC:**- All-electron CCSD calculations are employed for the adiabatic DBOC correction [80,81,82] together with a cc-pCVQZ basis [70]. The DBOC calculations were perfomed with the Cfour program [83,84]. Due to the inverse mass dependence this contribution is important for hydrogen containing systems. It is evaluated for 6 possible H/D and ${}^{12}$C/${}^{13}$C combinations, i.e., H/D substitution and single ${}^{12}$C/${}^{13}$C switch, and in turn the inclusion of DBOC leads to 6 different adiabatic PESs for HCC${}^{-}$ isotopologues.

#### 2.2. Rovibrational Calculations

## 3. Results and Discussion

#### 3.1. Construction of the PES and EDMS

#### 3.2. Spectroscopic Parameters from VPT2

#### 3.3. Results of Variational Calculations

^{12}C

^{12}C${}^{-}$, H

^{13}C

^{12}C${}^{-}$ and, H

^{12}C

^{13}C${}^{-}$, deviate from experiment by not more than 0.1%.

^{12}C

^{12}C${}^{-}$, i.e., a deviation by 2.9% can be observed. As is well known, VPT2 based quartic centrifugal distortion constants ${D}_{\mathrm{e}}$ for linear molecules do not include contributions from bending vibrations and lack effects due to vibrational averaging [45,135,136,137]. In their determination of the rotational spectroscopic parameters both experimental works [16,26] fixed ${H}_{0}$ to a value recommended by Sebald and Botschwina based on the PES reported earlier [32]. Clearly this value is a reasonable choice as the present calculations yield almost the same value based on a much more accurate PES. Finally, the ZPVE of 3078.0 cm${}^{-1}$ calculated variationally for H

^{12}C

^{12}C${}^{-}$ is in perfect agreement with the VPT2 result as is expected for such a semi-rigid molecule.

^{12}C

^{12}C${}^{-}$ are provided in Table S6 of the Supplementary Materials. Based on previous experience with similar molecules [46,47,49,50,51,52] the vibrational term energies ${G}_{v}$ are expected to be accurate to within 1 cm${}^{-1}$ and rotational parameters should display the same level of accuracy as observed for the vibrational ground state. Comparing the variational results for ${G}_{v}$ in H

^{12}C

^{12}C${}^{-}$ with the corresponding composite VPT2 values for ${\nu}_{i}$ in Table 5 almost perfect agreement can be observed as expected for a semi-rigid molecule.

^{12}C

^{12}C${}^{-}$, D

^{13}C

^{12}C${}^{-}$, and D

^{12}C

^{13}C${}^{-}$, respectively, to be compared with the VPT2 results of 301.0, 282.2, and 286.2. Note that for H

^{12}C

^{12}C${}^{-}$ this analysis yields 299.0 MHz and 295.7 from variational calculations and VPT2, respectively, in good agreement. Upon inspection of the rovibrational wave functions the $(0,{2}^{0},1)$ state is identified as the perturbing state. The energetic situation is graphically depicted in Figure 4. Such a 1-3 Darling-Dennison resonance [107,146,147] can be analyzed in terms of the vibrational term energies by setting up an effective Hamiltonian of the form

^{12}C

^{12}C${}^{-}$, D

^{13}C

^{12}C${}^{-}$, D

^{12}C

^{13}C${}^{-}$, respectively. This yields ${G}_{0,{2}^{0},1}^{*}$ values of 2515.7, 2488.0, and 2481.5 cm${}^{-1}$, to be compared with the VPT2 results of 2515.5, 2487.6, and 2481.2, for D

^{12}C

^{12}C${}^{-}$, D

^{13}C

^{12}C${}^{-}$, D

^{12}C

^{13}C${}^{-}$, respectively, showing good agreement. The coupling constants differ only slightly between the isotopologues (cf. also Figure 4) with an average value of 6.6 cm${}^{-1}$. For a full analysis, i.e., for a deperturbation of rotational parameters, the effective Hamiltonian from Equation (10) would need to be extended to allow for the simultaneous ℓ-type resonance between $(0,{2}^{0},1)$ and the $(0,{2}^{2},1)$ state with e-parity [51]. However, no attempt in that direction has been undertaken here and therefore the parameters for DCC${}^{-}$ isotopologues have to be treated as effective parameters.

^{13}C

^{12}C${}^{-}$ and H

^{12}C

^{13}C${}^{-}$ are weaker by a factor of 100 in agreement with the reduced abundance of ${}^{13}$C. Both Q-branches of the ${\nu}_{2}$ bands in the ${}^{13}$C isotopologues are located inbetween the P- and Q-branch of H

^{12}C

^{12}C${}^{-}$ and thus might be possible to detect. Hot bands of H

^{12}C

^{12}C${}^{-}$ have slightly larger intensity compared to the other isotopologue bands and should therefor also be observable.

^{12}C

^{12}C${}^{-}$. These have been obtained by summing over individual rovibrational lines within a given vibrational transition.

## 4. Summary

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## Abbreviations

ae | all-electron |

fc | frozen core |

PES | potential energy surface |

QFF | quartic force field |

EDMS | electric dipole moment surface |

CBS | complete basis set |

CASSCF | complete active space self-consistent field |

CCSD(T) | coupled-cluster with single, double, and perturbative triple excitations |

CCSD(T*)-F12b | explicitly correlated coupled-cluster with single, double, and scaled perturbative triple excitations |

CCSDT(Q) | coupled-cluster with single, double, triple and perturbative quadruple excitations |

CCSDTQ | coupled-cluster with single, double, triple and quadruple excitations |

CCSDTQP | coupled-cluster with single, double, triple, quadruple and pentuple excitations |

ACPF | averaged coupled-pair functional |

MRCI+D | multi-reference configuration interaction with singles and doubles including the Davidson correction |

AQCC | averaged quadratic coupled-cluster |

CV | core-core and core-valence correlation |

SR | scalar-relativistic effects |

HC | higher-order correlation |

(Q)–(T) | difference between fc-CCSDT(Q) and fc-CCSD(T) |

Q–(Q) | difference between fc-CCSDTQ and fc-CCSDT(Q) |

P–Q | difference between fc-CCSDTQP and fc-CCSDTQ |

DBOC | diagonal Born-Oppenheimer correction |

VPT2 | second-order vibrational perturbation theory |

ZPVE | zero-point vibrational energy |

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**Figure 1.**Convergence of conventional CCSD(T) and explicitly correlated CCSD(T)-F12b harmonic vibrational frequencies for HCC${}^{-}$.

**Figure 2.**Dependence of smaller contributions to the HCC${}^{-}$ composite PES on the internal coordinates $\Delta r$ (CH-stretch, upper panel), $\Delta R$ (CC-stretch, lower panel), and $\theta $ (deviation from linearity, inset lower panel). The DBOC contribution is depicted for the main isotopologue.

**Figure 3.**Comparison of dependencies with respect to HCC${}^{-}$ internal coordinates for single reference and multi-reference based methods of calculating higher-order correlation contributions.

**Figure 4.**Energy level scheme of $(1,{0}^{0},0)$ and $(0,{2}^{\mathcal{l}},1)$ vibrational states involved in the 1-3 Darling-Dennison resonance in DCC${}^{-}$ isotopologues.

**Figure 5.**Comparison of stick spectra for the fundamental rovibrational transitions in HCC${}^{-}$ and DCC${}^{-}$at $T=300$ K. Line intensities are have been calculated using Equation (9) with $g=1$ to facilitate a direct comparison.

**Figure 6.**Calculated stick spectrum in the spectral region of the ${\nu}_{2}$ fundamental for HCC${}^{-}$ and its ${}^{13}$C isotopologues at $T=300$ K. Additional hot bands originating from the $(0,{1}^{1},0)$ state and the $(0,{2}^{\mathcal{l}},0)$ manifold are also included.

**Table 1.**Frozen-core CCSD(T) and CCSD(T)-F12b equilibrium bond lengths (in Å) and harmonic vibrational frequencies (in cm${}^{-1}$) for HCC${}^{-}$.

Method | Basis | ${\mathit{r}}_{\mathbf{e}}$ | ${\mathit{R}}_{\mathbf{e}}$ | ${\mathit{\omega}}_{1}$ | ${\mathit{\omega}}_{2}$ | ${\mathit{\omega}}_{3}$ |
---|---|---|---|---|---|---|

CCSD(T) | AVTZ | 1.07148 | 1.25467 | 3341.0 | 500.5 | 1813.6 |

AVQZ | 1.07120 | 1.25072 | 3346.8 | 514.1 | 1825.6 | |

AV5Z | 1.07087 | 1.24964 | 3347.4 | 517.5 | 1828.3 | |

AV6Z | 1.07080 | 1.24931 | 3347.9 | 518.4 | 1829.2 | |

AV7Z | 1.07076 | 1.24913 | 3348.5 | 519.3 | 1830.0 | |

AV8Z | 1.07071 | 1.24905 | 3349.1 | 520.3 | 1829.9 | |

CCSD(T)-F12b ^{a} | AVTZ | 1.07082 | 1.24988 | 3348.1 | 518.2 | 1828.9 |

AVQZ | 1.07065 | 1.24909 | 3350.2 | 519.8 | 1831.0 | |

AV5Z | 1.07067 | 1.24888 | 3349.2 | 520.4 | 1831.1 | |

CCSD(T*)-F12b ^{a} | AV5Z | 1.07072 | 1.24897 | 3348.6 | 520.2 | 1830.5 |

^{a}Employed geminal exponents are 1.2, 1.4, and 1.5 ${a}_{0}^{-1}$ for AVTZ, AVQZ, and AV5Z, respectively.

**Table 2.**Dependence of equilibrium bond lengths (in Å) and harmonic vibrational frequencies (in cm${}^{-1}$) on the contributions to the composite PES of HCC${}^{-}$.

Contribution | ${\mathit{r}}_{\mathbf{e}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{0.166667em}{0ex}}$ | ${\mathit{R}}_{\mathbf{e}}\phantom{\rule{1.em}{0ex}}$ | ${\mathit{\omega}}_{1}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}$ | ${\mathit{\omega}}_{2}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}$ | ${\mathit{\omega}}_{3}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}$ |
---|---|---|---|---|---|

F12bs | 1.07072 | 1.24897 | 3348.6 | 520.2 | 1830.5 |

+CV | −0.00162 | −0.00338 | +9.2 | +4.6 | +10.1 |

+SR | −0.00011 | −0.00019 | −0.2 | −0.2 | −0.2 |

+(Q)–(T) | +0.00011 | +0.00084 | −3.4 | −6.0 | −6.6 |

+Q–(Q) | −0.00008 | −0.00022 | +1.2 | +0.4 | +2.4 |

+P–Q | +0.00004 | +0.00018 | −0.6 | −0.4 | −1.8 |

+DBOC | +0.00011 | +0.00001 | −0.1 | +0.2 | +0.1 |

Composite | 1.06917 | 1.24621 | 3354.7 | 518.8 | 1834.5 |

Ref. [32] | 1.0689 | 1.2464 | 3355.4 | 518.7 | 1834.8 |

Ref. [33] | 1.06745 | 1.24702 | 3356.5 | 502.3 | 1828.5 |

Ref. [34] | 1.06945 | 1.24708 | 3355.5 | 524.4 | 1840.4 |

**Table 3.**Frozen-core CCSD(T) and CCSD(T)-F12b equilibrium dipole moments (in D) and fundamental band intensities (double harmonic approximation, in km/mol) for HCC${}^{-}$.

Method | Basis | ${\mathit{\mu}}_{\mathbf{e}}$ | ${\mathit{A}}_{01}$ | ${\mathit{A}}_{02}$ | ${\mathit{A}}_{03}$ |
---|---|---|---|---|---|

CCSD(T) | AVTZ | −3.2180 | 2.27 | 192.34 | 71.03 |

AVQZ | −3.2163 | 2.00 | 187.86 | 70.62 | |

AV5Z | −3.2186 | 1.84 | 187.28 | 70.59 | |

AV6Z | −3.2192 | 1.79 | 186.96 | 70.55 | |

CCSD(T)-F12b ^{a} | AVTZ | −3.2172 | 1.87 | 188.45 | 70.14 |

AVQZ | −3.2188 | 1.75 | 186.57 | 70.11 | |

AV5Z | −3.2197 | 1.73 | 186.89 | 70.30 | |

CCSD(T*)-F12b ^{a} | AV5Z | −3.2196 | 1.77 | 186.94 | 70.38 |

^{a}Employed geminal exponents are 1.2, 1.4, and 1.5 ${a}_{0}^{-1}$ for AVTZ, AVQZ, and AV5Z, respectively.

**Table 4.**Dependence of the equilibrium dipole moment (in D) and fundamental band intensities (double harmonic approximation, in km/mol) on the contributions to the composite EDMF of HCC${}^{-}$.

Contribution | ${\mathit{\mu}}_{\mathbf{e}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{0.277778em}{0ex}}$ | ${\mathit{A}}_{01}\phantom{\rule{0.222222em}{0ex}}$ | ${\mathit{A}}_{02}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.222222em}{0ex}}$ | ${\mathit{A}}_{03}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}$ |
---|---|---|---|---|

F12bs | −3.2196 | 1.77 | 186.94 | 70.38 |

+CV | −0.0059 | −0.25 | −1.73 | −0.97 |

+SR | +0.0043 | +0.07 | +0.63 | +0.24 |

+(Q)–(T) | +0.0017 | +0.79 | +0.50 | +0.06 |

+Q–(Q) | −0.0001 | −0.17 | +0.41 | +0.12 |

+P–Q | +0.0010 | +0.06 | −0.26 | −0.25 |

Composite | −3.2205 | 2.27 | 186.49 | 69.56 |

**Table 5.**Dependence of spectroscopic parameters obtained from VPT2 on the contributions to the composite PES of HCC${}^{-}$.

Parameter | Contributions | |||||||
---|---|---|---|---|---|---|---|---|

F12bs | +CV | +SR | +(Q)–(T) | +Q–(Q) | +P–Q | +DBOC | Comp. | |

${B}_{\mathrm{e}}$/MHz | 41,632.5 | +211.8 | +12.2 | −49.5 | 13.5 | −10.8 | −1.8 | 41,807.9 |

${\alpha}_{1}$/MHz | 294.1 | +0.7 | +0.4 | +1.2 | −0.7 | +0.2 | −0.2 | 295.7 |

${\alpha}_{2}$/MHz | −130.7 | −0.4 | −0.1 | −0.4 | −0.1 | +0.2 | 0.0 | −131.5 |

${\alpha}_{3}$/MHz | 304.3 | +0.5 | +0.3 | +2.9 | −1.6 | +1.1 | −0.1 | 307.4 |

${B}_{0}$/MHz | 41,464.0 | +211.5 | +11.9 | −51.1 | 14.9 | −11.7 | −1.7 | 41,637.8 |

${D}_{\mathrm{e}}$/kHz | 93.3 | +0.4 | +0.1 | +0.3 | −0.2 | +0.1 | 0.0 | 94.1 |

${H}_{\mathrm{e}}$/MHz | 76.5 | +1.5 | +0.1 | −2.3 | +1.4 | −0.9 | 0.0 | 76.3 |

${q}_{2}^{\mathrm{e}}$/MHz | 246.4 | +0.6 | +0.2 | +1.8 | 0.0 | 0.0 | −0.1 | 248.9 |

${q}_{2}^{J}$/kHz | −4.0 | 0.0 | 0.0 | −0.1 | 0.0 | 0.0 | 0.0 | −4.1 |

${q}_{2}^{K}$/kHz | 3.8 | 0.0 | 0.0 | +0.1 | 0.0 | 0.0 | 0.0 | 3.8 |

${x}_{11}$/cm${}^{-1}$ | −59.11 | +0.07 | −0.04 | −0.47 | +0.11 | −0.03 | +0.03 | −59.45 |

${x}_{12}$/cm${}^{-1}$ | −20.21 | +0.02 | −0.02 | −0.19 | +0.03 | −0.04 | +0.01 | −20.40 |

${x}_{13}$/cm${}^{-1}$ | −11.78 | +0.10 | −0.02 | −0.20 | +0.15 | −0.07 | +0.01 | −11.81 |

${x}_{22}$/cm${}^{-1}$ | 0.06 | −0.11 | 0.00 | +0.08 | 0.05 | +0.04 | 0.00 | 0.12 |

${x}_{23}$/cm${}^{-1}$ | −5.64 | +0.05 | 0.00 | −0.23 | +0.03 | −0.04 | +0.01 | −5.84 |

${x}_{33}$/cm${}^{-1}$ | −9.09 | −0.03 | −0.01 | −0.12 | +0.09 | −0.05 | 0.00 | −9.20 |

${x}_{\mathcal{l}\mathcal{l}}$/cm${}^{-1}$ | 4.17 | +0.05 | 0.00 | −0.04 | −0.02 | −0.02 | 0.00 | 4.15 |

${\nu}_{1}$/cm${}^{-1}$ | 3204.3 | +9.4 | −0.3 | −4.6 | +1.5 | −0.7 | 0.0 | 3209.5 |

${\nu}_{2}$/cm${}^{-1}$ | 511.7 | +4.3 | −0.2 | −6.0 | +0.6 | −0.3 | 0.2 | 510.2 |

${\nu}_{3}$/cm${}^{-1}$ | 1800.8 | +10.1 | −0.3 | −7.2 | +2.7 | −1.9 | 0.1 | 1804.4 |

${\Delta}_{1}$/cm${}^{-1}$ | −144.3 | +0.2 | −0.1 | −1.2 | +0.3 | −0.1 | 0.1 | −145.2 |

${\Delta}_{2}$/cm${}^{-1}$ | −8.6 | −0.2 | 0.0 | 0.0 | +0.1 | +0.1 | 0.0 | −8.6 |

${\Delta}_{3}$/cm${}^{-1}$ | −29.7 | 0.0 | 0.0 | −0.6 | +0.3 | −0.2 | 0.0 | −30.2 |

ZPVE /cm${}^{-1}$ | 3074.6 | +16.5 | −0.5 | −13.6 | +2.4 | −1.5 | 0.2 | 3078.0 |

${E}_{0}$/cm${}^{-1}$ | −2.3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | −2.3 |

**Table 6.**Zero-point vibrational energies (ZPVE, in cm${}^{-1}$) and rotational spectroscopic parameters (in MHz) for the ground vibrational state $(0,{0}^{0},0)$ in istopologues of HCC${}^{-}$ obtained from variational calculations. Where available experimental results are provided for comparison

^{a}.

Isotopologue | Method | ZPVE | ${\mathit{B}}_{\mathit{v}}$ | ${10}^{3}{\mathit{D}}_{\mathit{v}}$ | ${10}^{6}{\mathit{H}}_{\mathit{v}}$ |
---|---|---|---|---|---|

H${}^{12}$C${}^{12}$C${}^{-}$ | this work | 3078.0 | 41,641.6 | 96.871 | 0.119 |

exp. Ref. [26] | 41,639.23501(94) | 96.9039(62) | 0.13 ^{b} | ||

H${}^{13}$C${}^{12}$C${}^{-}$ | this work | 3052.0 | 40,639.6 | 92.581 | 0.106 |

exp. Ref. [25] | 40,637.441(5) | 92.6(2) | |||

H${}^{12}$C${}^{13}$C${}^{-}$ | this work | 3058.5 | 40,113.4 | 90.080 | 0.105 |

exp. Ref. [25] | 40,111.413(7) | 90.0(2) | |||

D${}^{12}$C${}^{12}$C${}^{-}$ | this work | 2537.0 | 34,437.6 | 63.98 | 0.11 |

D${}^{13}$C${}^{12}$C${}^{-}$ | this work | 2508.9 | 33,893.0 | 61.88 | 0.10 |

D${}^{12}$C${}^{13}$C${}^{-}$ | this work | 2517.1 | 33,193.1 | 59.42 | 0.100 |

^{a}One standard deviation of the last significant digit is given in parentheses.

^{b}Constrained to the theoretical value from Ref. [32].

**Table 7.**Vibrational term energies (in cm${}^{-1}$) and rotational spectroscopic parameters (in MHz) for singly excited vibrational states in istopologues of HCC${}^{-}$ obtained from variational calculations.

State | ${\mathit{G}}_{\mathit{v}}$ | ${\mathit{B}}_{\mathit{v}}$ | ${10}^{3}{\mathit{D}}_{\mathit{v}}$ | ${10}^{6}{\mathit{H}}_{\mathit{v}}$ | |
---|---|---|---|---|---|

H${}^{12}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 510.1 | 42,773.7 | 96.871 | 0.119 |

$(0,{0}^{0},1)$ | 1804.5 | 41,331.9 | 97.080 | 0.116 | |

$(1,{0}^{0},0)$ | 3209.6 | 41,342.6 | 96.183 | 0.125 | |

H${}^{13}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 506.0 | 40,756.9 | 95.167 | 0.136 |

$(0,{0}^{0},1)$ | 1776.3 | 40,340.1 | 92.777 | 0.103 | |

$(1,{0}^{0},0)$ | 3195.4 | 40,361.3 | 91.932 | 0.110 | |

H${}^{12}$C${}^{13}$C${}^{-}$ | $(0,{1}^{1},0)$ | 509.3 | 40,238.1 | 92.743 | 0.136 |

$(0,{0}^{0},1)$ | 1768.8 | 39,820.0 | 90.268 | 0.102 | |

$(1,{0}^{0},0)$ | 3208.7 | 39,828.8 | 89.445 | 0.108 | |

D${}^{12}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 405.5 | 34,607.1 | 67.402 | 0.173 |

$(0,{0}^{0},1)$ | 1709.5 | 34,225.5 | 64.006 | 0.110 | |

$(1,{0}^{0},0)$ | 2477.0 | 34,153.0 | 66.860 | 0.470 | |

D${}^{13}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 400.2 | 34,049.6 | 64.973 | 0.154 |

$(0,{0}^{0},1)$ | 1693.3 | 33,684.3 | 61.909 | 0.095 | |

$(1,{0}^{0},0)$ | 2448.9 | 33,624.1 | 64.164 | 0.390 | |

D${}^{12}$C${}^{13}$C${}^{-}$ | $(0,{1}^{1},0)$ | 405.5 | 34,607.1 | 67.402 | 0.173 |

$(0,{0}^{0},1)$ | 1677.4 | 32,991.2 | 59.454 | 0.097 | |

$(1,{0}^{0},0)$ | 2469.7 | 32,986.8 | 86.141 | 3.604 | |

State | ${\mathit{q}}_{\mathit{v}}$ | ${\mathbf{10}}^{\mathbf{3}}{\mathit{q}}_{\mathit{v}}^{\mathit{J}}$ | ${\mathbf{10}}^{\mathbf{6}}{\mathit{q}}_{\mathit{v}}^{\mathit{JJ}}$ | ||

H${}^{12}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 258.3 | −4.727 | 0.101 | |

H${}^{13}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 248.0 | −4.302 | 0.087 | |

H${}^{12}$C${}^{13}$C${}^{-}$ | $(0,{1}^{1},0)$ | 240.2 | −4.196 | 0.086 | |

D${}^{12}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 220.5 | −4.431 | 0.114 | |

D${}^{13}$C${}^{12}$C${}^{-}$ | $(0,{1}^{1},0)$ | 216.3 | −4.170 | 0.104 | |

D${}^{12}$C${}^{13}$C${}^{-}$ | $(0,{1}^{1},0)$ | 220.5 | −4.431 | 0.114 |

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Schröder, B.
Ab Initio Rovibrational Spectroscopy of the Acetylide Anion. *Molecules* **2023**, *28*, 5700.
https://doi.org/10.3390/molecules28155700

**AMA Style**

Schröder B.
Ab Initio Rovibrational Spectroscopy of the Acetylide Anion. *Molecules*. 2023; 28(15):5700.
https://doi.org/10.3390/molecules28155700

**Chicago/Turabian Style**

Schröder, Benjamin.
2023. "Ab Initio Rovibrational Spectroscopy of the Acetylide Anion" *Molecules* 28, no. 15: 5700.
https://doi.org/10.3390/molecules28155700