Zero-Point-Energy Driven Isotopic Exchange of the [H3O]− anion Probed by Mid-Infrared Action Spectroscopy

We present the first observation of vibrational transitions in the [H3O]− anion, an intermediate in the anion–molecule reaction of water, H2O, and hydride, H–, using a laser-induced isotopic H/D exchange reaction action spectroscopy scheme applied to anions. The observed bands are assigned as the fundamental and first overtone of the H2O–H– vibrational stretching mode, based on anharmonic calculations within the vibrational perturbation theory and vibrational configuration interaction. Although the D2O·D– species has the lowest energy, our experiments confirm the D2O·H– isotope to be a sink of the H/D exchange reaction. Ab initio calculations corroborate that the formation of D2O·H– is favored, as the zero-point-energy difference is larger between D2 and H2 than between D2O·H– and D2O·D–.


S1.1 Structural parameters, zero point energies
For the [H 3 O] -anion, two energy minima exist along the reaction pathway where X H,D.From this reaction pathway, we consider the two energy minima XO -• X 2 and XOX • X -for further investigation.The structural parameters within the Born-Oppenheimer approximation are shown in Table S1.1.These are obtained from geometry optimization, where single point energies (SPE) are calculated at CCSD(T)-F12/AVTZ-F12 level of theory.For the various isotopic species, we compute the zero point energies (ZPE) within the harmonic approximation at CCSD(T)-F12/AVTZ-F12 level of theory using Molpro1 .For the XOX • X -species, we additionally compute ZPEs at MP2/AVTZ level of theory both in the harmonic approximation and by the VPT2 aprroach from Barone et al.2 using Gaussian3 .All energies are listed in Table S1.2.

S2.3 VPT2 anharmonic frequencies for different isotopomers
As a first anharmonic correction, we calculate the PES as quartic force field (QFF) for subsequent vibrational perturbation theory (VPT2) calculations.Note that these calculations are limited in their comparability to the experiment, as they base on a rather local PES, using a Taylor series expansion.As shown in Section S3, the shape of the PES is actually dominated by a double minimum.
The VPT2 calculations for all isotopomers of the XO -• XX system show one common problem: the frequency for the q 1 mode is "negative".In some cases, also the q 2 comes with a "negative" VPT2 frequency.It is well-known that large amplitude motions, usually with a harmonic frequency below 150 cm −1 , can lead to such negative anharmonic (over)corrections 4 .Especially studies on molecular clusters are prone to such problems, and the modes with "negative" VPT frequencies are then usually neglected in the analyis 5 .
In the present work, we do not assign any of the XO -• XX vibrations to our experimental spectrum.Nevertheless, we present our VPT2 calculations in Table S2.13 to Table S2.20 for the sake of completeness and to demonstrate the limitations of VPT2 for the XO -• XX system.Figure S3.1:The XSURF algorithm generates a double-well potential for normal mode q 5 choosing relatively "harsh" parameters in scaling and shifting degree of displacement of the normal mode (sfac=1.850,shift= 6).The left minimum describes the equilibrium structure used for the PES expansion HOH • H -. The right minimum is most likely the second equilibrium structure HO -• H 2 .
S3.2 Convergence tests for a multi-mode PES including mode q 5

S3.2.1 Removing parts in the polynomial multi-mode PES representation
In order to minimize the errors due to poor fits, we tested automatic deletion of troublesome potentials during the fit by using the delauto keyword.Table S3.1 shows three different polynomial fits and the results of subsequent VSCF calculations relying on these polynomial PES representation.
While the actual 1D polynomial representations (Table S3.1, POLY, blue) do not change significantly upon increasing the delauto threshold, the resulting ca-VSCF effective potentials (Table S3.1, VSCF, green) indicate significant changes in the PES upon increasing the delauto threshold.In the case of delauto=1.d-5,all effective cs-VSCF potentials show positive slopes at the edges.This is preferable for the subsequent VCI calculations, where configurations are generated by "excitations" from the VSCF reference.Still, normal mode q 5 is prone to introduce problematic configurations due to its double-well potential shape.Hence, further VCI convergence test are performed using these POLY settings in Section S3.2.2.
Table S3.1:3-mode PES of (HOH)H-using CCSD(T)-F12/AVTZ-F12.The 1-mode potentials are shown as grid and polynomial representation.The 3-mode PES is shown via effective potentials from ca-VSCF., 3, 4, 2, 2, 1), where the index i of the vector elements denote the normal mode q i .In this particular configuration, all modes are in their maximum level of excitations defined by the user via the levex keyword.That means, there are multiple configurations with lower excitations, which are all considered in the VCI calculation.
In the following, we discuss the influence of the levex directive, by limiting all possible modes separately.
The convergence test from various VCI calculations for vibrational transitions below 2000 cm −1 are depicted in Figure S3.3 for the fundamentals and in Figure S3.4 for the overtones.In this Figure S3.2:Exemplary depiction of maximum excitations allowed for a VCI calculation using the levex directive.Each mode is allowed to be excited to a certain amount: Mode q 1 to 1, mode q 2 to 4, mode q 3 to 4, etc.All together, the total maximum excitations are limited to 15.In this first evaluation, it becomes already clear that increasing the level of excitations in the "higher" normal modes leads to divergence.From the discussion on the multi-mode PES in Section S3.2.1, we can expect that especially the mode q 5 causes troubles due to its double-well potential.
Hence, it may be useful to simply prohibit excitations in this mode.
For the fundamental transition ν 1 (A ′ ), figure S3.5 depicts the previous convergence tests with Figure S3.5:Benchmark for the VCI calculated fundamental transitions frequencies to ν 1 (A ′ ) with respect to the maximum level of excitation in generating the VCI configurations.For each mode, we set levex=1 and let the other modes vary.Reliable assignments are green.
Figure S3.6:Benchmark for the VCI calculated fundamental transitions frequencies to ν 2 1 (A ′ ) with respect to the maximum level of excitation in generating the VCI configurations.For each mode, we set levex=1 and let the other modes vary.Reliable assignments are green.

S3.3 Harmonic & VSCF frequencies up to 5000 cm −1
The following VSCF frequencies are not converged.This is mainly due to the problematic PES they are based on.As discussed in Section S3, the current multi-mode PES is troublesome due to the double-minimum subpotential of mode q 5 .This is also reflected in the VSCF results presented here.All the calculations shown here are based on the 4-mode PES of HOH • H -in a polynomial representation, where troublesome subpotentials have been excluded (delauto=1.d-5).We used the PESTRANS utility to obtain mass weighted PESs for the various isotopomers.All calculations are cc-VSCF.These calculations are merely a test whether the isotopic transformation works, and as one may see from the following tables, it does for the harmonic frequencies, but the VSCF calculations again are not converged.
Figure S3.2 depicts how we limit the configuration space in VCI using the levex directive.The configuration shown in the Figure is can be described by a vector (1, 3, 4, 2, 2, 1), where the index i benchmark, we investigate the change of the VCI transition frequency with the maximum level of excitation.Each calculated frequencies is associated with a combination of VCI configurations, where one configuration has the highest leading coefficient.If the relative leading coefficient is above 0.95, the assignment can be taken as reliable.In FigureS3.3we use a color-scale to highlight "reliable" transition frequencies.Lower leading coefficients can indicate physically sound resonances or numerical inaccuracies in the calculation and, thus, such transition frequencies must be evaluated carefully.

Table S1
.4: HH to HD exchange reaction at CCSD(T)-F12/AVTZ-F12 level of theory using harmonic ZPEs and the Molpro software.
Tables S2.4 to S2.11 list calculated harmonic and VPT2 frequencies for the XOX • X -species with X = H, D in cm −1 .We computed vibrations with up to 2 excited quanta, i.e., fundamentals, first overtones, and combination bands.
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