Vibrationally excited states of 1H- and 2H-1,2,3-triazole isotopologues analyzed by millimeter-wave and high-resolution infrared spectroscopy with approximate state-specific quartic distortion constants

High-resolution infrared, microwave, and millimeter-wave spectroscopies enable the accurate and precise determination of molecular spectroscopic constants. While centrifugal distortion constants can sometimes be neglected in microwave studies (low values of J and K), they become necessary for the accurate modeling of most spectra involving transitions at the higher values of J and K that are typical in high-resolution infrared (IR) or millimeter-wave spectroscopy. As a result, accurate centrifugal distortion constants are critical for molecular identification in the interstellar medium (ISM) and other harsh environments.^1–3 Centrifugal distortion constants are dependent on the masses comprising the molecule and their locations, as well as on the molecular potential energy surfaces.⁴ These constants are not simply empirical corrections to the rigid-rotor approximation used to accurately predict rotational transition frequencies; rather, they are physically meaningful terms that provide information about the mass distribution in a molecule and the vibrational motions of the atoms. Several decades ago, Watson provided reduced centrifugal distortion constants that are typically determined experimentally and predicted computationally.^5,6 Precise and accurate prediction of centrifugal distortion constants has become common within the spectroscopy community for ground-state species.

All of the spectroscopic constants (rotational and centrifugal distortion) change for vibrationally excited states, relative to the ground state, as the mass distribution changes upon vibration. The vibration–rotation interaction constants, or “α values,” which are the changes to the rotational constants from the ground-state values upon vibration, were described by Mills.⁷ Analogously, the vibration–rotation interaction centrifugal distortion constants, or “β values,” are the changes between the ground-state and vibrationally excited-state centrifugal distortion constants. Computational software has applied vibrational perturbation theory to predict rotational constants, centrifugal distortion constants up to sextic terms for the ground state, and vibration–rotation interaction (α) constants for vibrationally excited states. While numerous studies have determined centrifugal distortion constants for vibrationally excited states, their prediction is challenging and has not yet been implemented in any readily available computational chemistry software package. Computational predictions of the α and β terms are important, as vibrationally excited-state spectra are commonly obtained along with their ground-state spectra, particularly in millimeter-wave spectroscopy. Accurate predictions of these constants may assist in assigning the spectra of vibrationally excited states and the least-squares fitting where the centrifugal distortion constants are necessary to model the spectra but cannot be determined directly, e.g., Coriolis-coupled vibrationally excited states.^8–18 It is common practice in these cases to hold the vibrationally excited-state centrifugal distortion values at the corresponding ground-state values. There is a need for high-precision determination of the vibrationally excited-state centrifugal distortion constants and simultaneous determination of their computed values to provide important benchmarks.

Theoretical predictions for vibrationally excited-state quartic distortion constants have been sought for some time. Early efforts frequently targeted formulas specialized for certain atomic connectivities (D_3h triatomic, to name one example).¹⁹ The fact that there exist many specialized formulas, most of which are highly algebraically complicated, has impeded their adoption and implementation into popular software packages. Aliev published a general formula for linear polyatomic molecules in 1986. It seems, however, to have gone largely unappreciated.²⁰ Numerical implementations based on contact transformation theory have recently proven successful. In 2004, the A-reduced rovibrational constants of water were predicted fully to the sixth order by Seghir and co-workers.²¹ This comprises the equilibrium octic constants, the first vibrational correction to the sextics, up to second vibrational correction to the quartics, and up to the third vibrational correction to the rotational constants. At the time, their implementation was restricted to triatomic molecules. Watson discussed the vibrational dependence of the quartics in 2005.²² He presented an expression in terms of rotational operators and commutators and made applications to a handful of nonlinear triatomics. Demaison, Margulès, and Boggs predicted the vibrational dependence for NH₂ using the VIBROT code²³ and similar calculations have been performed for SO₂.²⁴ A recent review included examples of higher-order perturbation theory applied to molecules as large as pentatomics.²⁵ 

1H- and 2H-1,2,3-Triazoles (C₂H₃N₃, C_s, and C_2v, respectively), the subject of a recent semi-experimental equilibrium (r_e^SE) structure determination²⁶ and this work, are near-oblate asymmetric rotors as shown in Fig. 1. Although the equilibrium population of the 1H tautomer in the gas phase at room temperature is very small (ΔE = 4.2 kcal/mol; K_eq ∼ 10⁻³), the low population of the C_s tautomer (1H) is compensated by the fact that it is significantly more polar (μ = 4.24 D) than the C_2v tautomer (2H) (μ = 0.10 D). Consequently, the rotational spectra of both species are readily observable.^27–31 The rotational^26,32–35 and vibrational^36–39 spectra have been studied for the normal 1,2,3-triazole isotopologues, as well as several of their deuteriated counterparts.^{32–34,37,38}

We previously analyzed the rotational spectra of many isotopologues of 1H- and 2H-1,2,3-triazole in order to determine a highly precise semi-experimental equilibrium structure for each molecule.²⁶ As is typical of such millimeter-wave studies, we also observed the rotational spectra of vibrationally excited states for a number of the isotopologues. In the current study, we report the assignment and analysis of these vibrationally excited states. These studies are augmented, significantly, by incorporation of additional experimental data obtained by high-resolution infrared spectroscopy and by theoretical predictions derived from new computational algorithms for evaluating centrifugal distortion constants for vibrationally excited states. Analyses of vibrationally excited states of multiple isotopologues have previously been performed,^{15,17,18,40–48} often in the context of halogen isotopologues and usually involving fewer isotopologues than in the present work. The current study enables a more comprehensive comparison between the changes to spectroscopic constants upon vibrational excitation for several isotopologues. More importantly, it provides the opportunity to apply a practical and diagnostically useful computational prediction of vibrationally excited-state centrifugal distortion constants to a somewhat complex molecule. High-resolution infrared spectra for 2H-1,2,3-triazole and [2-²H]-2H-1,2,3-triazole provide the precise determination of vibrational state energies for their low-lying fundamental states.

As a neat liquid, 1,2,3-triazole exists predominantly as the 1H tautomer by virtue of the effects of polarity/solvation. 1H-1,2,3-Triazole was obtained from Sigma-Aldrich or Oakwood Chemical. The sample obtained from Sigma-Aldrich was pink and that from Oakwood was colorless. The material from the first commercial source contained pyridazine as a major impurity, identified by the previously determined rotational spectrum,⁴⁹ and pyrazole, identified using its rotational constants.^50–52 In order to observe low-abundance isotopologues, the sample was purified by Kugelrohr distillation. Triazole from the second commercial source was of higher purity and was used without further purification. Deuteriated samples for millimeter-wave spectra were prepared through three synthetic routes.²⁶ The high-resolution IR spectrum of [2-²H]-2H-1,2,3-triazole was obtained coincidentally while collecting the spectrum of the normal isotopologue, presumably due to hydrogen-deuterium exchange with deuteriated molecules that remained in the chamber from D₂O used in the preceding experiment.

Continuous broadband spectra in the 130–230 GHz and 235–375 GHz ranges were collected using 5–30 mTorr sample pressures at room temperature. The instrument has been described previously.^41,49,53 The spectrum from 130 to 375 GHz was obtained over approximately six days using the following experimental parameters: 0.045 kHz frequency increment, 0.6 MHz/s sweep rate, 10 ms time constant, and 50 kHz AM and 500 kHz FM modulation in a tone-burst design. Data for a given sample in these frequency ranges were combined into a single spectral file using Assignment and Analysis of Broadband Spectra (AABS) software.^54,55 In our least-squares fits, we assume a uniform 50 kHz frequency measurement uncertainty for all millimeter-wave transitions, including those from Stiefvater et al.³⁵ 

High-resolution infrared data presented in this work were recorded at the Canadian Light Source (CLS) Synchrotron Far-IR beamline (February 2022) using a Bruker IFS 125 HR Spectrometer, with synchrotron radiation and a 9.4 m optical pathlength difference providing a nominal resolution of 0.000 96 cm⁻¹. The aperture was 1.15 mm, using a KBr beamsplitter, KBr cell windows, and a Ge:Cu detector, housed in a QMC cryogen-free cryostat (cooled by a Cryomech pulsed-tube cooler). The gain was set to 6×. The cell is a 2 m, White-type multi-pass cell; the total pathlength is 72 m. These spectra were obtained from 400 to 1200 cm⁻¹ at a series of pressures for analysis of various vibrational states, which have substantially different infrared intensities. A uniform frequency measurement uncertainty of 0.000 18 cm⁻¹ (∼6 MHz) was assumed for all infrared measurements.

Software from the AABS suite was used for spectral combination and analysis.^54,55 Data were least-squares fit using ASFIT and ASROT,⁵⁶ as well as SPFIT and SPCAT.⁵⁷ AC and PIFORM programs were used for data formatting and presentation.^58,59 All least-squares fit files are provided in the supplementary material.

To facilitate the preliminary analysis of experimental spectroscopic data, geometry optimizations with subsequent anharmonic frequency calculations using an ultrafine grid (int = Grid = ultrafine) were completed using Gaussian 16⁶⁰ at the B3LYP/6-311+G(2d,p) level of theory for the isotopologues of interest, providing predicted energies for the fundamental states, as well as vibration–rotation interaction terms. Computed relative energies are inclusive of zero-point vibrational energy (ZPVE) contributions. Computational output files are provided in the supplementary material.

Detailed computational and theoretical studies of the tautomers of 1,2,3-triazole were performed using the CCSD(T) method: coupled-cluster theory with a full, iterative treatment of single and double excitations and a perturbative estimate for triple excitations.^61–64 Relative energies including ZPVE contributions were computed at the CCSD(T)/cc-pCVTZ level of theory, as were vibrationally averaged dipole moments with anharmonic corrections. Quartic force fields, excluding the ijkl type constants, were obtained for all isotopologues by numerical differentiation of analytical gradients as implemented in the CFOUR program (Coupled-Cluster techniques for Computational Chemistry).^65,66 The ANO1 basis set was used, and the frozen-core approximation was made.⁶⁷ Additionally, optimizations and harmonic frequency computations were carried out with the cc-pwCVQZ basis set with all electrons correlated.^68–70 The harmonic frequencies and rotational constants in the CCSD(T)/ANO1 quartic force fields were replaced with the corresponding CCSD(T)/cc-pwCVQZ values.^71,72

Rovibrational constants were predicted using a Vibrational Perturbation Theory (VPT) code written in Mathematica.⁷³ Anharmonic vibrational frequencies were evaluated with second-order vibrational perturbation theory (VPT2)—in some cases, treating Fermi resonances with the perturb-then-diagonalize schemes: VPT2+F or VPT2+K.^74,75 Fermi resonance interactions were treated explicitly if they displayed a variational-perturbational difference of greater than 1 cm⁻¹. The equilibrium sextic centrifugal distortion constants and vibrational corrections to the rotational constants were evaluated in the conventional way, from fourth-order vibrational perturbation theory (VPT4) and VPT2, respectively.^7,76–78 For the quartic centrifugal distortion constants, both the equilibrium values (from VPT2) and the first vibrational corrections (from VPT4) were evaluated. These fourth-order quartic distortion constants were obtained from an analytical implementation of a partially incomplete theory. Specifically, only the perturbation products proportional to J⁴ were considered, neglecting perturbation products with higher powers of J capable of being reduced to J⁴ through rotational angular momentum commutators.⁷⁷ In the notation used by Aliev and Watson, where the indices correspond to the number of vibrational and rotational operators, respectively, the following nine perturbation products were considered: H₃₂ × H₁₂, H₂₂ × H₂₂, H₂₂ × H₁₂ × H₃₀, H₁₂ × H₁₂ × H₄₀, H₂₂ × H₂₁ × H₂₁, H₁₂ × H₃₁ × H₂₁, H₁₂ × H₁₂ × H₃₀ × H₃₀, H₁₂ × H₂₁ × H₂₁ × H₃₀, and H₂₁ × H₂₁ × H₂₁ × H₂₁.^22,77 The full fourth-order expression and a thorough benchmark against experimental quartic constants will be presented in a later work. Although it is not obvious that the incomplete fourth-order treatment should be successful, preliminary comparisons have shown it to provide a reliable improvement over VPT2 for most molecules. Its performance is less satisfactory for small, light molecules like H₂O and H₂CO.

Both 1H- and 2H-1,2,3-triazole exhibit a typical oblate-top band structure in our frequency region. The most intense peaks are sets of degenerate R-branch transitions in the K_a = 0⁺ and 1⁻ series. The J values of the R-branch transitions decrease moving away from the bandhead and K_a values correspondingly increase. Eventually, these sets of transitions lose degeneracy, forming doublets of ^aR_0,1 transitions (in the case of C_2v isotopologues) or quartets (of ^aR_0,1, ^bR_1,−1, and ^bR_1,1 transitions in the case of C_s isotopologues). A small segment of the rotational spectrum, showing bandheads of each of the 1,2,3-triazole ground vibrational states of the normal isotopologues and the more widely spread bands of their much lower-intensity vibrational satellites, is presented in Fig. 2.

Transitions belonging to the four lowest-energy vibrationally excited states of 1H-1,2,3-triazole were observed: fundamentals ν₁₈, ν₁₇, ν₁₆, and ν₁₅. The vibrational manifolds up to 900 cm⁻¹ for 1H- and 2H-1,2,3-triazole isotopologues described in this work are plotted in Figs. 3 and 4, respectively. For 1H-1,2,3-triazole, the lowest-energy vibrationally excited state, ν₁₈ (561 cm⁻¹, A″), mainly comprises the out-of-plane N–H bend. The second fundamental, ν₁₇ (648 cm⁻¹, A″), involves a torsion of the C–C bond relative to the N-atoms, with an out-of-plane N–H bend. The third fundamental, ν₁₆ (715 cm⁻¹, A″), is the N2–N3 torsion relative to the rest of the ring. The motion associated with ν₁₅ (764 cm⁻¹, A″) is a symmetric, out-of-plane wag of the C–H bonds. Fortuitously, the observed vibrational states of the main isotopologue are sufficiently distant in energy that no perturbation due to Coriolis-coupling is apparent in the observed transitions. As expected, the frequency of the lowest-energy vibrationally excited state decreases when hydrogen is substituted with deuterium, easily observed in Fig. 3 for ν₁₈. Deuteriation of triazole results in several of the vibrationally excited states moving closer together in energy. Thus, it is expected that couplings will arise for some vibrational states of the [1-²H]-, [4-²H]-, [5-²H]-, and [4,5-²H]-1H-1,2,3-triazole isotopologues that were not observed for their normal-isotopologue counterparts.

For the normal isotopologue of 2H-1,2,3-triazole, we observed transitions for five vibrationally excited states: ν₁₂ (532 cm⁻¹, B₁), the out-of-plane N–H wag; ν₉ (667 cm⁻¹, A₂), the C–C bond torsion relative to the N-atoms; ν₁₁ (709 cm⁻¹, B₁), the symmetric, out-of-plane bend of the N–N–C bonds; ν₁₀ (828 cm⁻¹, B₁), the symmetric, out-of-plane wag of the C–H bonds; and ν₈ (880 cm⁻¹, A₂), an antisymmetric, out-of-plane C–H bond wag. Similar to the 1H-tautomer, deuterium substitution at the nitrogen atom results in a substantial decrease in the frequency of the lowest-energy vibrationally excited state.

Although the spectroscopic constants for the ground vibrational state of all isotopologues discussed herein have been reported previously,²⁶ the values are slightly modified here by the incorporation of computed approximate VPT4 centrifugal distortion constants for those centrifugal distortion terms that could not be determined. The least-squares fitted parameters for the five lowest-energy vibrational states of the normal isotopologue of 1H-1,2,3-triazole are provided in Table I, alongside the predicted constants for each observed state. Rotational and quartic centrifugal distortion constants for vibrationally excited states were predicted by calculating the change from computed ground-state value to computed excited-state value, i.e., $αx=B0x−Bvx$ and $βx=D0x−Dvx$ values, respectively, and applying this change to the experimentally determined ground-state value. All excited-state sextic centrifugal distortion constants that could not be determined were held constant at the corresponding ground-state value, as no computational values are available. While the dipole moment of 1H-1,2,3-triazole can compensate for its low population relative to 2H-1,2,3-triazole, allowing its rotational spectrum to be recorded in this work, the relative intensities of the infrared transitions are almost entirely dependent on the populations. Thus, 1H-1,2,3-triazole was not observed in the high-resolution infrared spectrum, and no vibrational energies were measured for its excited states. Rotational constants for the ground and excited vibrational states are predicted within 0.03% of their experimental values. For the ground state, where all quartic centrifugal distortion constants and several sextic constants could be determined, the purely computational values are in good agreement—all quartic terms are within 10% of their experimental values, and the three on-diagonal sextic terms other than H_J are within 12%. The experimental value of H_J is approximately one-half its predicted value. The experimentally determined value of H_J may be affected by the need to hold the off-diagonal terms constant at their predicted values and may not be reliable. The computational values of the quartic centrifugal distortion constants that could be determined for the vibrationally excited states are within 4% of their predicted values, which is quite good agreement. Importantly, there is nearly always better agreement between the computed values of the quartic centrifugal distortion constants with their experimental counterparts than the agreement between the ground- and excited-state centrifugal distortion constants.

Spectroscopic constants for [1-²H]-, [4-²H]-, [5-²H]-, [1,4,5-²H]-, and [4,5-²H]-1H-1,2,3-triazole and their observed vibrationally excited states are provided in Table II. The predicted rotational constants are all within 0.1% of their experimental values. On-diagonal quartic distortion constants are within 4%, as are most of the off-diagonal quartic distortion constants. The only large discrepancy occurs for [4,5-²H]-1H-1,2,3-triazole, whose ground-state experimental value of d₁ is nearly one-third its predicted value. The substantial error may be related to the quite small magnitudes of the computed and experimental constants, which are the smallest magnitude of any of the off-diagonal quartic distortion constants. The computed d₁ and d₂ values for ν₁₈ of [4,5-²H]-1H-1,2,3-triazole differ in both sign and order of magnitude from the computed and experimental ground-state values. Importantly, as with the normal isotopologue, there is consistently better agreement between the computed values of the quartic distortion constants with their experimental counterparts than with the ground-state values.

In addition to data from the millimeter-wave spectrum, the high-resolution infrared spectrum of 2H-1,2,3-triazole was measured, enabling the determination of several vibrational-state energies. Figure 5 displays a segment of the infrared spectrum, which includes the unintentional, but fortuitous and quite clear signals of the [2-²H]-2H-1,2,3-triazole isotopologue. Spectroscopic constants for the vibrational states of the normal isotopologue are provided in Table III. Rotational and centrifugal distortion constants for the ground state are fitted using a single-state model with only millimeter-wave data. Since several sextic and, in some cases, quartic centrifugal distortion constants could not be determined experimentally for the vibrationally excited states and had to be held constant, they are held constant at the corresponding ground-state (sextic) or computed (quartic) values. When infrared transitions are included in the least-squares fit, however, the spectroscopic constants for the ground- and exited-states become dependent on one another. As a result, holding excited-state terms fixed at the ground-state value while fitting that ground-state value results in a mild distortion of the ground-state constant. In order to avoid such perturbation of the constants, in the combined-state least-squares fit, the ground-state values were held constant at the values determined from millimeter-wave spectra and excited-state constants were allowed to be fit—these constants are provided in Table III.

As in the case of 1H-1,2,3-triazole, the rotational constants for all of the observed vibrational states for the normal isotopologue of 2H-1,2,3-triazole are predicted within 0.1% of their experimental values. Most of the quartic centrifugal distortion constants are predicted within 7% of their experimental values. The exceptions are d₁ of ν₁₀ (13%) and D_JK and D_K of ν₈ (13% and 35%, respectively). For the ground state, the predicted sextic distortion constants are within 40% (H_J), and the rest are within 11% of the values that could be determined. Overall, the spectroscopic constants are in good agreement between prediction and observation. While vibrationally excited-state sextic centrifugal distortion constants are yet beyond the capabilities of computational prediction, we have measured several such values for the first time for a few of the fundamental states of 2H-1,2,3-triazole. These values appear reasonably similar to those of the ground state, though ν₁₀ displays some changes in its sextic terms by an order of magnitude. This may be physically meaningful or may be a result of the limited number of rotational transitions that were able to be observed and used for least-squares fitting.

Several infrared bands that, while less intense than the most intense bands of 2H-1,2,3-triazole, were nevertheless quite clear turned out to belong to [2-²H]-2H-1,2,3-triazole. As previously mentioned, we attribute the abundance of this species to the fact that the experiment immediately preceding the triazole analysis involved deuterium oxide and an acid, which appear to have left a source of deuterium on the walls of the infrared cell. As a result, several vibrational energies of the [2-²H]-2H-1,2,3-triazole have also been measured and are provided in Table IV alongside the spectroscopic constants. As with the normal isotopologue, the ground vibrational state was initially least-squares fit independently and then combined into the multi-state fit with its constants held fixed to the determined values.

The predicted rotational constants for [2-²H]-2H-1,2,3-triazole, again, are within 0.1% of the experimentally determined values, and the quartic centrifugal distortion constants are within 13%, with one exception. The value of d₂ for ν₁₁ (the third lowest-energy fundamental state) is nearly an order of magnitude smaller than predicted. Although it appears to be well-determined by the value of its uncertainty, it is determined using only high-resolution infrared data, as it was too low in intensity to be observed in the millimeter-wave spectrum. Given the lower precision of infrared data relative to millimeter-wave, there is a possibility that this term is less accurately determined than it appears. As shown in Fig. 4, upon deuteriation at the nitrogen atom, the energies of ν₁₁ and ν₉ become quite close (ΔE_11–9 ∼ 3 cm⁻¹) for [2-²H]-2H-1,2,3-triazole. Since ν₉ has A₂ symmetry, its vibrational transitions have no infrared intensity. The rotational transitions of ν₁₁ and ν₉ were too weak in the deuteriated samples studied to be measured. As a result, the Coriolis-coupling interaction cannot be properly addressed between ν₁₁ and ν₉, providing additional uncertainty into the physical meaning of the ν₁₁ spectroscopic constants. The sextic centrifugal distortion constants of the ground state are very well predicted—within 14% of the experimental values.

Other deuteriated isotopologues of 2H-1,2,3-triazole were, unsurprisingly, not in sufficiently high abundance to be observed in the high-resolution infrared spectrum. The vibrationally excited states of several deuteriated isotopologues were, however, observed in our millimeter-wave data. The computed and resultant spectroscopic constants for [4-²H]-, [2,4-²H]-, [2,4,5-²H]-, and [4,5-²H]-2H-1,2,3-triazoles are provided in Table V. The agreement between predicted and experimentally determined rotational constants for the vibrational states of the additional deuteriated isotopologues is, as with the other 1,2,3-triazoles, spectacular—all are predicted within 0.1% of their experimental values. The on-diagonal quartic distortion constants are all predicted within 4% (many of which are predicted within 1%), and the off-diagonal quartic distortion constants are predicted within 41% of those values that could be determined experimentally. While this error may appear large, it is reasonable for the smaller magnitude of the constants and, in most cases, compares better than a comparison of the ground-state value to the excited-state value. This comparison illustrates the utility of the approximate VPT4 treatment of the quartic centrifugal distortion constants used here.

Considering the sometimes rather small changes in the spectroscopic constants between ground and vibrationally excited states, it is worthwhile to examine the α and β values, directly, because the apparent agreement between the computed and experimental spectroscopic constants could be due simply to the relatively larger size of the constant compared with the change. Such comparisons for the B3LYP (α-only) and CCSD(T) methods are provided in Table VI for 1H-1,2,3-triazole isotopologues and in Table VII for 2H-1,2,3-triazole isotopologues. Both computational methods estimate the α values for the A and B rotational constants reasonably well—often within 10%. The CCSD(T) method, however, is almost always better than B3LYP at predicting the α value for the C rotational constant, which is important, as the C_v value largely determines the spacing between bands and plays perhaps the largest role in the initial identification of the K_a = 0 series leading to the fitting of the vibrational-state spectrum. This, of course, becomes even more important when the species is in low abundance or otherwise has low transition intensities. The β values presented here are the result of the first documented attempt at a purely computational prediction of these values for larger molecules. Their agreement with the experiment is impressive. Nearly three quarters of the β values are predicted within 50% of their experimental values—a value that is reasonable for the quartic centrifugal distortion constants. (Quartic distortion constants, themselves, are typically reported on the scale of kHz, whereas these predictions are on the scale of Hz.) There are a few exceptions, with several β values being predicted with the wrong sign, but most of the same order of magnitude, e.g., D_J of ν₁₇ for [1-²H]-1H-1,2,3-triazole, d₁ and d₂ of ν₁₈ for [4-²H]-2H-1,2,3-triazole, or D_K of ν₁₂ for [4,5-²H]-2H-1,2,3-triazole. The β value of d₂ for ν₁₁ of [2-²H]-2H-1,2,3-triazole is predicted to be the opposite sign and an order of magnitude larger than that determined experimentally. This constant is determined from purely high-resolution infrared data without addressing the Coriolis-coupling to ν₉, which may not be an accurate experimental determination. Overall, the ability of the novel technique for predicting excited-state quartic centrifugal distortion constants may be deemed successful.