Anharmonic Vibrational Frequencies of Water Borane and Associated Molecules

Water borane (BH3OH2) and borinic acid (BH2OH) have been proposed as intermediates along the pathway of hydrogen generation from simple reactants: water and borane. However, the vibrational spectra for neither water borane nor borinic acid has been investigaged experimentally due to the difficulty of isolating them in the gas phase, making accurate quantum chemical predictions for such properties the most viable means of their determination. This work presents theoretical predictions of the full rotational and fundamental vibrational spectra of these two potentially application-rich molecules using quartic force fields at the CCSD(T)-F12b/cc-pCVTZ-F12 level with additional corrections included for the effects of scalar relativity. This computational scheme is further benchmarked against the available gas-phase experimental data for the related borane and HBO molecules. The differences are found to be within 3 cm−1 for the fundamental vibrational frequencies and as close as 15 MHz in the B0 and C0 principal rotational constants. Both BH2OH and BH3OH2 have multiple vibrational modes with intensities greater than 100 km mol−1, namely ν2 and ν4 in BH2OH, and ν1, ν3, ν4, ν9, and ν13 in BH3OH2. Finally, BH3OH2 has a large dipole moment of 4.24 D, which should enable it to be observable by rotational spectroscopy, as well.


Introduction
Borane-containing molecules like ammonia borane are promising hydrogen storage media for use in fuel cells due to their high hydrogen density [1][2][3][4]. However, all of this storage capacity is of little use without a clean way to liberate the hydrogen into hydrogen gas. To this end, recent work has revived an interest in borane as a feedstock for generating hydrogen gas from water that dates back at least to the 1950s [5,6]. Combining borane [7] or diborane [5,7] with water can produce substantial amounts of hydrogen gas, which is becoming increasingly important as a source of alternative fuels [6,[8][9][10][11]. Current methods of producing hydrogen gas, however, still rely primarily upon fossil fuels, limiting the clean nature of the resulting hydrogen [7]. As shown previously [6,7], an important step along the hydrogen production pathway when using borane feedstocks is the formation of BH 3 OH 2 or water borane. This can then decompose with a submerged barrier into one equivalent of hydrogen gas and borinic acid, BH 2 OH. Such a pathway suggests that borane and its hydrated or ammonia-complexed variants may have a substantial role to play not only in the storage of large amounts of hydrogen but also in the generation of hydrogen from water.
Limiting the optimism surrounding such promise is the difficulty of isolating and then conclusively identifying individual borane complexes in the gas phase. Such identification is of the utmost necessity given the fact that borane tends to form dative bonds that are exquisitely sensitive to the surrounding environment [12,13]. In ammonia borane, in particular, this spectroscopic sensitivity has led theoretical work on the ammonia borane dimer to show shifts of up to 40 cm −1 in the B-N stretching frequency from the isolated require the cc-pCVTZ-F12 basis set [34]. The F12-TZ-cCR single-point energy computations additionally utilize canonical CCSD(T) with a cc-pVTZ-DK basis set to account for the effects of scalar relativity [35,36]. Double-harmonic and anharmonic infrared intensities are computed within the Gaussian16 suite of programs [37] using the MP2/aug-cc-pVTZ level of theory [38,39]. The harmonic values at this level of theory have been previously shown to yield semi-quantitative accuracy in the infrared intensities, and the differences from the anharmonic values are typically negligible [40][41][42].
For both the F12-TZ and F12-TZ-cCR QFFs, following the geometry optimization, displacements of 0.005 Å or radians are taken from the optimized geometry to map out the QFF. The symmetry internal coordinates (SICs) along which these displacements are taken are shown below for BH 3 OH 2 with atom labels corresponding to Figure 1. Similarly, the SICs for borinic acid with atom labels given by Figure 2 are Those for HBO with atom labels from Figure 3 are And those for borane with atom labels from Figure 4 are As shown by the symmetry labels in Equations (28)-(33), borane is treated in C 2v symmetry rather than its full D 3h symmetry to simplify the coordinate system. The SIC coordinate systems utilized herein for BH 3 OH 2 and BH 2 OH have been previously applied to the structurally similar AlH 3 OH 2 [43] and AlH 2 OH [44] molecules, respectively. The total numbers of single-point energy computations to generate the QFFs for BH 3 OH 2 , BH 2 OH, BH 3 , and HBO are 19585, 3161, 413, and 55.
After the single-point energy computations for either QFF energy, the QFF function is fit using a least-squares procedure with sums of squared residuals on the order of 10 −16 a.u. 2 in all cases. The first fit yields the equilibrium geometries and a subsequent refitting zeroes the gradients and produces a new equilibrium geometry along with the corresponding force constants. These force constants are transformed from SICs to Cartesian coordinates using the INTDER program [45]. The Cartesian force constants are then utilized by the second-order rotational and vibrational perturbation theory [46] implementations in the SPECTRO software package [47] to generate the rovibrational spectral data [48,49]. Type 1 and 2 Fermi resonances, Fermi polyads [50], Coriolis resonances, and Darling-Dennison resonances are taken into account to further increase the accuracy of the rovibrational data [50,51]. The Fermi resonances are listed in the Supplementary Information (SI) in Tables S4, S6, S8, S10, S12, S14, S24, S28, S34, S40, S47 and S54. Additionally, the rotational constants from the SPECTRO program are used in the PGOPHER software package [52] to simulate the rotational and rovibrational spectra for BH 2 OH and BH 3 OH 2 shown in Figures 5-8.

Benchmarks
As shown in Tables 1 and 2, the F12-TZ-cCR QFF fundamental frequencies demonstrate excellent agreement with the available gas-phase experimental data. In the case of borane, the largest difference occurs in ν 3 with a deviation of only 1.9 cm −1 , and the mean absolute error (MAE) or unsigned averaged deviation across the three modes is 1.1 cm −1 . This is in contrast to the F12-TZ results, which are a bit farther from the experimental values. Again for borane, the biggest deviation from experiment in the F12-TZ results is 7.5 cm −1 with an MAE of 3.8 cm −1 . The two are more comparable for HBO, where F12-TZ achieves a respectable MAE of 3.9 cm −1 relative to the two available experimental frequencies.
However, F12-TZ-cCR still has the slight edge with an MAE of 2.8 cm −1 . Such performance indicates that both F12-TZ and F12-TZ-cCR can adequately handle the vibrational spectra of these two molecules, but for a slight increase (3484 versus 5397 seconds of wall time for BH 3 ) in computational cost, F12-TZ-cCR provides a substantial increase in accuracy. Table 1. Harmonic and anharmonic vibrational frequencies (in cm −1 ), MP2/aug-cc-pVTZ harmonic and anharmonic infrared intensities (in km mol −1 , labeled f ), equilibrium, vibrationally averaged, and singly-vibrationally excited principal rotational constants (in MHz), and dipole (in D) for HBO. Descriptions of the vibrational frequencies are given as linear combinations of SICs and as qualitative descriptions along with the symmetries.

SICs
Description  The same is true upon examination of the principal rotational constants. While F12-TZ-cCR exhibits fairly large deviations from the experimental data for borane giving an overall MAE of 218.3 MHz, F12-TZ performs much worse with an MAE of 750.2 MHz. This is in line with previous work on both F12-TZ [22][23][24] and F12-TZ-cCR [28], which demonstrates that accounting for the effects of core correlation in F12-TZ-cCR is necessary for producing more accurate rotational constants. In the present case, neither of the methodologies utilized herein seems to be achieving real accuracy, but F12-TZ-cCR still has a clear advantage. For HBO, that advantage becomes even more pronounced. Whereas  Table 2. The two computational data sets agree very closely with each other in this case. Neither is more than 3 MHz away in the D constants (−32.746 compared to −29.834 MHz for D JK ) or 3 kHz in the H constants (17.898 compared to 15.047 kHz for H K J ) from the available borane experimental values, and most of the differences are even smaller.
Finally, but perhaps most promisingly, the same trend is clear in the borinic acid data shown in Table 3. Compared to the available experimental vibrationally-averaged rotational constants, F12-TZ has an MAE difference of 308.7 MHz. In stark contrast, F12-TZ-cCR manages an MAE of only 22.3 MHz, and most of this is concentrated in the difference from A 0 of 66.0 MHz. The F12-TZ-cCR values for both B 0 and C 0 agree to within just over 0.5 MHz. Such exceptional agreement even exceeds the expected performance of F12-TZ-cCR, which previously achieved an average agreement of roughly 7.5 MHz on similar B 0 and C 0 rotational constants [28]. This suggests that F12-TZ-cCR is very well suited to the determination of the vibrational spectrum of borinic acid and for the elucidation of both the rotational and vibrational spectra of water borane. The accuracy of the rotational constants in the case of water borane is particularly important given its massive dipole moment of 4.24 D, which should make its rotational spectrum easier to obtain if the molecule itself can be isolated experimentally. Table 3. Harmonic and anharmonic vibrational frequencies (in cm −1 ), MP2/aug-cc-pVTZ harmonic and anharmonic infrared intensities (in km mol −1 , labeled f ), equilibrium, vibrationally averaged, and singly-vibrationally excited principal rotational constants (in MHz), and dipole (in D) for BH 2 OH. Descriptions of the vibrational frequencies are given as linear combinations of SICs and as qualitative descriptions along with the symmetries.

Spectroscopic Data
In light of the performance of the F12-TZ-cCR QFFs on HBO, borane, and the rotational constants of borinic acid, as well as the lack of experimental data on the vibrational frequencies of borinic acid and water borane, the F12-TZ-cCR fundamental frequencies reported herein are the most accurate values available for these two molecules. In some cases, such as the high-frequency O-H stretches, the good agreement between F12-TZ and F12-TZ-cCR adds further support to the theoretical quantification of these frequencies. Across BH 3 OH 2 and BH 2 OH, the deviations in these frequencies are all less than 4 cm −1 with the largest difference occurring in ν 1 of BH 3 OH 2 at 3.9 cm −1 . However, the B-H stretches are less consistent between the levels of theory. The ν 3 antisymmetric B-H stretch of BH 3 OH 2 , for example, exhibits a difference of 12.1 cm −1 between F12-TZ and F12-TZ-cCR. The agreement is better across the board for BH 2 OH, but the ν 2 antisymmetric B-H stretch still exhibits a difference of 6.0 cm −1 between the two treatments. Properly handling this mode is particularly important in light of its high intensity for both molecules. In both cases, the antisymmetric B-H stretch is the most intense mode, with that of BH 2 OH having an intensity of 169 km mol −1 and that of BH 3 OH 2 even more intense at 206 km mol −1 . Table 4. Harmonic and anharmonic vibrational frequencies (in cm −1 ), MP2/aug-cc-pVTZ harmonic and anharmonic infrared intensities (in km mol −1 , labeled f ), equilibrium, vibrationally averaged, and singly-vibrationally excited principal rotational constants (in MHz), and dipole (in D) for BH 3   For BH 2 OH, the ν 4 B-O stretch at 1352.8 cm −1 is the next most intense mode with a value of 152 km mol −1 . The additional hydrogens in BH 3 OH 2 damp both the frequency and intensity of the B-O stretch, decreasing the frequency to 399.4 cm −1 and the intensity to 82 km mol −1 in ν 14 . This frequency is considerably lower than the previously computed value for the B-N stretch in ammonia borane at 644 cm −1 , but the intensity is much greater than the 12 km mol −1 reported therein [13]. Such a shift suggests that the B-O bond in BH 3 OH 2 is actually weaker than the B-N bond in ammonia borane, and this is corroborated by the slightly longer 1.74485 Å B-O bond length compared to the 1.67308 Å B-N bond. These expected trends in the bond strengths are supported by F12-TZ bond strength computations, which give a value of −9.7 kcal mol −1 for the B-O bond and −25.7 kcal mol −1 for the B-N bond. In contrast, the B-H bonds of BH 3 OH 2 are slightly shorter at 1.20516 Å compared to the 1.21685 Å observed for ammonia borane, and this is again consistent with the higher frequency B-H stretches observed in the present work.
Examining the rest of the anharmonic infrared intensities for BH 2 OH reveals that all but the ν 5 B-O-H bend have intensities greater than 50 km mol −1 , and even ν 5 itself still has an intensity of 22 km mol −1 . BH 3 OH 2 , on the other hand, has more low intensity fundamental vibrational frequencies, such as ν 7 , ν 8 , ν 10 , and ν 12 at 12, 23, 13, and 1 km mol −1 , respectively, but also more high intensity frequencies. Chief among these are the aforementioned antisymmetric B-H stretch of ν 3 , as well as the ν 1 antisymmetric O-H stretch with an intensity of 133 km mol −1 , the ν 4 symmetric B-H stretch at 135 km mol −1 , and the ν 13 symmetric B-O-H bend at 179 km mol −1 . For both molecules, the presence of these high intensity frequencies should help to facilitate their vibrational observation, if the molecules can be experimentally isolated in the gas phase. Further, the fact that there is little overlap between the frequencies of the most intense fundamentals means that the two can likely be disentangled if they are observed together in the same experiment.
The same is true for the rotational spectra of the two molecules also shown in Tables 3  and 4. Whereas the A 0 constant for BH 2 OH is close to 172 GHz, that for BH 3 OH 2 is much lower, near 87 GHz. Both molecules are near-prolate with κ values of −0.94 and −0.99 for BH 2 OH and BH 3 OH 2 , respectively. Clearly BH 3 OH 2 is much closer to prolate, as evidenced by the mere 452.6 MHz separation between its B 0 and C 0 constants, which are found at 17,269.0 and 16,816.4 MHz. Again, these are quite far away from those of BH 2 OH, which are found experimentally at 30,470.22 and 25,812.73 MHz, suggesting that the two should be readily distinguished if observed in the same experiment. The quartic and sextic distortion coefficients for these two molecules are shown in Table S15 of the SI. The microwave spectra for BH 2 OH and BH 3 OH 2 are shown in Figures 5 and 6, respectively, and the rovibrational spectra for ν 2 of BH 2 OH and ν 3 of BH 3 OH 2 are shown in Figures 7 and 8. Figure 5. Simulated rotational spectrum of BH 2 OH using A 0 , B 0 , and C 0 shown in Table 3, and ∆ J , ∆ JK , ∆ K , δ J , δ K , Φ K , Φ K J , Φ JK , and Φ J shown in Table S15 at a temperature of 94 K with Lorentzian line shapes with FWHMs of 0.015 cm −1 . Figure 6. Simulated rotational spectrum of BH 3 OH 2 using A 0 , B 0 , and C 0 shown in Table 4, and ∆ J , Table S15 at a temperature of 94 K with Lorentzian line shapes with FWHMs of 0.015 cm −1 .

Figure 7.
Simulated rovibrational spectrum of the first ν 2 transition of BH 2 OH using A 0 , B 0 , C 0 , A 2 , B 2 , and C 2 shown in Table 3, and ∆ J , ∆ JK , ∆ K , δ J , δ K , Φ K , Φ K J , Φ JK , and Φ J shown in Table S15 at a temperature of 94 K with Lorentzian line shapes with FWHMs of 0.015 cm −1 . Figure 8. Simulated rovibrational spectrum of the first ν 3 transition of BH 3 OH 2 using A 0 , B 0 , C 0 , A 2 , B 2 , and C 2 shown in Table 4, and ∆ J , ∆ JK , ∆ K , δ J , δ K , Φ K , Φ K J , Φ JK , and Φ J shown in Table S15 at a temperature of 94 K with Lorentzian line shapes with FWHMs of 0.015 cm −1 .

10 B Isotopologues
All of the data discussed above are for the 11 B isotope. Given the relatively high isotopic abundance of 10 B, the computations are repeated for these isotopologues, and the results are reported in Tables S16-S55 of the SI. Overall, the trends are much the same as those observed for the 11 B variants. Namely, the F12-TZ-cCR fundamental frequencies are all within 2 cm −1 of the reported gas-phase values for borane [29] and HBO [30]; and the MAE for the principal rotational constants of borane is comparable to that for the 11 B variant at 252.3 MHz. The difference in the B 0 rotational constant of HBO is 15.1 MHz. However, the MAE for the vibrationally-averaged principal rotational constants of borinic acid is quite a bit higher than that of the 11 B isotopologue at 312.4 MHz. Most of the deviation is again in the A 0 constant, but this time even B 0 and C 0 have deviations over 100 MHz. Regardless, the good general agreement with the available experimental results suggests that the F12-TZ-cCR spectral data reported herein for 10 BH 3 OH 2 and 10 BH 2 OH should be reliable as well.

Conclusions
This work presents the most accurate rovibrational spectroscopic data for water borane, BH 3 OH 2 , and borinic acid, BH 2 OH, currently available. The existence of gasphase vibrational and rotational experimental data for the related borane, BH 3 , and HBO molecules, as well as the vibrationally-averaged principal rotational constants of borinic acid, provide a wealth of benchmarking data for assessing the accuracy of the theoretical methods utilized for generating these novel data. In particular the recently developed F12-TZ-cCR QFF methodology performs substantially better than the more conventional F12-TZ methodology, which neglects explicit accounting for the effects of core correlation and scalar relativity. Both BH 3 OH 2 and BH 2 OH have several vibrational frequencies each with intensities over 100 km mol −1 , suggesting that these molecules will be readily observable in the infrared, if they can be experimentally isolated. Further, despite their structural similarity, these intense modes are sufficiently resolved that it should be possible to separate the two spectra if both molecules are produced in a single experiment. For BH 2 OH, the most intense modes occur at 2561.6 (ν 2 ), 1352.8 (ν 4 ), and 1171.1 (ν 6 ) cm −1 , while those for BH 3 OH 2 are found at 3704.8 (ν 1 ), 2488.4 (ν 3 ), 2452.3 (ν 4 ), 1176.8 (ν 9 ), and 528.4 (ν 13 ) cm −1 .

Supplementary Materials:
The following are available online, Table S1-S14: Geometrical Parameters and Fermi Resonances for the 11 B Isotopologues, Table S15: Quartic and Sextic Distortion Coefficients for BH 2 OH and BH 3 OH 2 , Tables S16-S55: Rovibrational Spectral Data for the 10