Large amplitude motion in cold monohydrated dihydrogen phosphate anions H 2 PO 4 ( H 2 O ) : infrared photodissociation spectroscopy combined with ab initio molecular dynamics simulations †

The vibrational spectroscopy of monohydrated dihydrogen phosphate anions, H2PO4 (H2O), is studied in the O–H stretching (2700–3900 cm ) and the fingerprint regions (600–1800 cm ). Assignment of the experimental infrared multiple photon photodissociation spectra based on the predicted harmonic spectra of energetically lowlying 0 K structures is not conclusive. Ab initio molecular dynamics simulations reveal that the water molecule undergoes large amplitude motion, even at low internal temperatures, and that the dipole time correlation function qualitatively captures the anharmonic effects of the low-barrier isomerization reaction on the infrared intensities.

Phosphate anions play a key role in biological and agricultural systems. [1][2][3] They are found in various esters, e.g. in adenosine phosphates, and in aqueous solution in the form of conjugate base anions H 3Àx PO 4 xÀ with x = 1-3 (inorganic phosphates  7,[11][12][13] An alternative arrangement with the water in an acceptor-donor (AD) motif is found to be higher in energy. 11 However, no experimental gas-phase data regarding the cluster structures are available. Infrared multiple photon dissociation (IRMPD) spectroscopy of size-selected ion-solvent complexes has emerged as a powerful tool for the structural characterization of microhydrated ions in the gas phase. [14][15][16][17][18][19][20][21][22][23][24] It is becoming increasingly evident that the interpretation of IRMPD spectra, in particular when hydrogen bonding is involved, requires theoretical tools beyond the harmonic approximation. [25][26][27][28][29][30][31] Here, IRMPD spectra of bare and monohydrated H 2 PO 4 À clusters are presented. We first try to understand the spectra based on a comparison to simulated harmonic IR spectra. However, the spectra of H 2 PO 4 À (H 2 O) exhibit pronounced anharmonic effects that can only be understood on the basis of the results derived from ab initio molecular dynamics (AIMD) simulations.
In order to check that dihydrogen phosphate anions are actually formed by electrospray, we recorded the IRMPD spectrum of H 2 PO 4 À in the fingerprint region by monitoring the H 2 O loss channel ( Fig. 1). Comparison of the experimental band positions to those in the simulated MP2/aug-cc-pVDZ harmonic vibrational spectra of H 2 PO 4 À and PO 3 À (H 2 O) yields satisfactory agreement only with the spectrum of dihydrogen phosphate, allowing assignment of the four IR-active features to the antisymmetric (H, 1299 cm À1 ) and symmetric (I, 1094 cm À1 ) PQO stretching, POH bending ( J, 1049 cm À1 ) and antisymmetric P-OH stretching (K, 770 cm À1 ) modes. Poorer agreement between 600-1400 cm À1 as well as the lack of any signal in the water bending region (B1700 cm À1 ) rules out any contribution from the monohydrated metaphosphate anion, which is predicted to lie +37.4 kJ mol À1 higher in energy. Discrepancies regarding the IRMPD vs. the linear harmonic intensities are attributed to the high predicted dissociation energy of H 2 PO 4 À of 49.7 kJ mol À1 for water loss and the even higher calculated barrier of 122.1 kJ mol À1 for this channel (MP2/aug-cc-pVDZ level including zero point energy and BSSE corrections). Hence, absorption of many IR photons is required for IRMPD. 32 The experimental IRMPD spectrum of H 2 PO 4 À (H 2 O), recorded from 550-1800 and 2600-3950 cm À1 and followed via H 2 O loss, is shown in Fig. 2. Six features, labeled A-F, are observed in the O-H stretching region (>2700 cm À1 ). Only band A lies above 3600 cm À1 , which is in the region of the free O-H stretching modes. 21 Consequently, bands B-F (o3600 cm À1 ) are attributed to progressively more strongly hydrogen-bonded O-H stretching modes, which is also reflected in the increasing width of these features with decreasing energy. In contrast, all bands below 1800 cm À1 (G-L) appear relatively narrow. The band around 1700 cm À1 (G) is assigned to the water bending mode. 33 The bands below 1500 cm À1 , similar to those observed for bare H 2 PO 4 À (Fig. 1), are due to P-O and PQO stretches, as well as bending and other lower-frequency modes 9 (see Table S1 for band positions and assignments in the ESI †). The two most stable predicted structures for H 2 PO 4 À (H 2 O) are the complexes containing either a DD-or an AD-water molecule, labeled 1-1 and 1-2, respectively, as shown in Fig. 3 The energetic ordering of these two isomers depends on the model used. B3LYP predicts 1-2 as the global minimum energy structure and 1-1 +0.8 kJ mol À1 higher in energy, including zero point energies (ZPE). In contrast, MP2 places 1-2 +0.1 kJ mol À1 above 1-1. These two minimum energy structures are separated by a small barrier (B3LYP: +3.5 kJ mol À1 ; MP2: +6.5 kJ mol À1 ) at  the first-order transition state (TS) 1-3 (Fig. 3), indicating a fairly flat potential energy surface. In structure 1-3, the H 2 O molecule forms only a single HB with a phosphoryl group. The MP2/aug-cc-pVDZ binding energies between H 2 PO 4 À and water in 1-1 and 1-2 are 52.8 and 50.0 kJ mol À1 including zero point energy and BSSE corrections, respectively, which are close to the experimental value of 58.6 kJ mol À1 determined mass spectrometrically. 8 Simulated MP2 harmonic spectra of 1-1 and 1-2 are shown above the experimental IRMPD spectrum in Fig. 2 (see Fig. S1 and S2, ESI † for detailed assignments). Upon first glance, a satisfactory agreement between experiment and harmonic theory is observed for isomer 1-1, especially below 2000 cm À1 . The harmonic spectra of 1-1 and 1-2 account for all the experimentally observed peaks (G-L), while the spectrum of 1-2 predicts additional intense bands at 1170 cm À1 (symmetric OQPQO stretch) and 966 cm À1 (water wag) that are not observed in the experiment. Above 2000 cm À1 , the spectrum of 1-1 also accounts for peak A (free PO-H stretch) and the doublet C (hydrogen-bonded water symmetric and antisymmetric stretches) at B3450 cm À1 . However, the harmonic spectrum of 1-1 leaves bands B and D-F unassigned. On the other hand, the harmonic spectrum of 1-2 yields reasonable assignments for bands A (free HO-H stretch), B (hydrogen bonded PO-H stretch) and F (hydrogen bonded H-OH stretch) in the O-H stretching region, leaving C-E unassigned. In particular, the strongest hydrogen bond in 1-2 (1.64 Å) nicely accounts for the characteristically red-shifted band F (2700-3100 cm À1 ), even though its width cannot be rationalized at the harmonic level. In summary, neither harmonic IR spectra of the two isomers nor a linear combination of the two can satisfactorily explain the experimental IRMPD spectrum shown in Fig. 2.
To disentangle the discrepancies between the harmonic and experimental IRMPD spectra, we performed ab initio molecular dynamics (AIMD) simulations (see Section 1B in the ESI † for details). Briefly, vibrational profiles at finite temperature are obtained by the Fourier transform of the dipole time correlation function (DTCF), which accounts for anharmonic as well as dynamic effects. Two sets of long AIMD simulations were performed at 140 K and 180 K for a more extensive sampling of the phase space. At each temperature, two trajectories were simulated, one starting with 1-1 and the other with 1-2, each lasting 200 ps. Each trajectory was then cut into 10 ps intervals that were Fourier-transformed, and all 40 frequency profiles were then added up to produce the DTCF spectrum at a specific temperature. The DTCF spectra from both trajectories differ only slightly from each other as shown in Fig. S3 (ESI †), indicating that 1-1 and 1-2 interconvert readily at these temperatures. DTCF spectra were also determined from AIMD simulations at 20 K (10 ps trajectory) starting from the two isomers. All simulations are shown in Fig. 2.
The AIMD simulations at 20 K are helpful to test the quality of the potential energy surface, but do not correspond to a physically achievable temperature since zero-point energies are not considered. The general appearance of the 20 K DTCF spectra is indeed similar to the previously discussed harmonic spectra, with the hydrogenbonded O-H stretching modes showing the largest shifts due to the use of different methods (PBE vs. MP2). Interestingly, the relative band intensities of experimental features A-C and G-L, with the exception of band H, are reproduced better by the 1-1 simulation already at 20 K compared to the harmonic spectrum (Fig. 2). The spectrum of 1-2 at 20 K, on the other hand, still mainly reflects the harmonic intensities, but does capture the pronounced red-shift of band F. To determine ZPE and finite temperature effects, the simulation temperature is raised to 140 K and 180 K.
There is considerably better agreement between the experimental spectra and the DTCF spectra at higher simulation temperatures (140 K or 180 K) throughout the spectral range for band positions and relative intensities. At these simulation temperatures, isomers 1-1 and 1-2 are interconverting. The complexity of the features in the O-H stretching region as well as the number and relative intensities of the bands in the fingerprint region are qualitatively reproduced. The increased broadening of the hydrogen-bonded O-H stretching bands B-F with the strength of the hydrogen bonds, i.e., with the red shift of the corresponding IR band, is also captured.
In more detail, peak A remains sharp at 140 K and 180 K, indicative of a O-H stretching mode of a free PO-H group. Comparison of DTCF spectra from both trajectories in Fig. S3 (ESI †) shows that both 1-1 and 1-2 contribute to peak A. Peak B is due to the O5-H7 stretch in 1-2 (Fig. 3). The O8-H9 and O8-H10 stretches in 1-1 are responsible for the double peaks C. These three peaks are similar in width (around 50 cm À1 ) and the lengths of the respective hydrogen bonds involved are all predicted close to B2.1 Å, indicating comparable hydrogen bond strengths. Band F is the broadest predicted and observed feature and involves the strongest hydrogen bond (O3Á Á ÁH9 in 1-2). Consequently, the integrated intensity of the sharp peak F in the harmonic spectrum (and also in the 20 K spectrum) of 1-2 is distributed over a much larger energy range. Similar broadening has been observed for other cluster ions. [35][36][37][38][39][40][41] The reduced relative intensity and broadening of the water bending mode (band G) relative to the harmonic spectra, is also reproduced by the DTCF spectra.
Between 1000 and 1300 cm À1 , eight IR active PQO stretching and the P-O-H bending modes, three for 1-1 and five for 1-2, are predicted by the harmonic analysis, while in the experimental spectrum only three bands, two intense bands (H and I in Fig. 2) and one weaker band (J), are observed. The DTCF spectra better reproduce this region too. The reason for this becomes apparent in the partial density of state (PDOS) plots shown in Fig. 4. The PDOS plots are based on the Fourier transform (see Section 1B in the ESI †) of the velocity correlation function for a specific atom. They also indicate that there is loss of the relative peak intensity due to broadening in the 900-1800 cm À1 region. However, the broadening is limited to the POH bending bands (H6 and H7 contributions in Fig. 4(a)), while the widths of the bands involving only the heavier atoms are not much affected by the elevated temperature in the simulations. Consequently, the two intense bands correspond predominantly to the antisymmetric (H) and symmetric (I) PQO stretching modes, while the weaker feature J is attributed to the water wagging band.
In the region below 900 cm À1 , there are several bands related to wagging and rocking modes (harmonic analysis). The mode involving H atoms is broadened and smeared out at a simulation temperature above 140 K. Only the antisymmetric (K) and symmetric (L) stretching modes of P-OH bonds, are left, which is in good agreement with the experimental observation of peaks K and L.
The above analysis leaves bands D and E unassigned, as these cannot be attributed to normal modes of either structure 1-1 or 1-2. Is there a third species responsible for these absorptions? The DTCF spectrum at 180 K indeed reproduces a broad feature centered at 3161 cm À1 , near the experimental peak E. This feature is also observed in the 140 K spectrum but with much less intensity. Interconversion between 1-1 and 1-2 involves considerable displacement of the water molecule (see the structures shown in the left column in Fig. 4) across a nearly flat potential energy surface with a barrier of less than 7 kJ mol À1 . At 140 K, the cluster is mainly confined in the potential well of 1-1 or 1-2 and does not visit the transition region (1-3) much. Increasing the simulation temperature to 180 K leads to a different situation. The cluster spends considerably more time around 1-3. The transition region is loosely bound and favored by entropy. The clusters thus undergo large amplitude motion, and as a consequence vibrational frequencies associated with structure 1-3 contribute to the spectrum. Comparison of the DTCF spectrum and PDOS plots in Fig. 4(b) shows that this peak is indeed due to the O-H stretching of water in 1-3. This assignment is further supported by MP2 harmonic analysis on 1-3, which predicts this mode at 3220 cm À1 (Fig. 2). To sum up, these results indicate that peak E is due to the hydrogenbonded O-H stretching mode of water in the transient structure 1-3. Similar signature of broken hydrogen-bond networks from finite ion temperature have been seen in Ar-tagged Br À (H 2 O) 2,3 complexes. 21 Note that the roaming water molecule observed in the present study is qualitatively different from the water migration reported for cold anion monohydrates in the excited OH stretching manifold. 42 Here, water migration occurs on the vibrational ground state potential and over larger distances, involving hydrogen bond cleavage and formation.

Conclusions
In summary, the IRMPD spectra of H 2 PO 4 À (H 2 O) show evidence for isomerization even at cryogenic temperatures, wherein the clusters undergo large amplitude motion over a small barrier. As a result, key aspects of the spectra cannot be interpreted within the framework of the harmonic approximation. AIMD simulations provide insight into these effects and qualitatively reproduce the experimental IRMPD spectra. The remaining differences can be attributed to approximations in the simulations, including the limited sampling time, the use of pseudopotentials and the neglect of nuclear quantum effects. Experimentally, the measured IRMPD intensities deviate from the linear absorption cross sections. The isomerization at low temperatures observed here may be indicative of a highly functional water network around dihydrogen phosphate and therefore it will prove important to also study the larger hydrated clusters, work that is currently in progress. Such studies can then also resolve the questions regarding the interconversion of H 2 PO 4 À (H 2 O) n to PO 3 À (H 2 O) n+1 that is predicted for n > 1.