A theoretical study on the size-dependence of ground-state proton transfer in phenol–ammonia clusters

Toshihiko Shimizu ab, Kenro Hashimoto bc, Masahiko Hada b, Mitsuhiko Miyazaki a and Masaaki Fujii *a
aLaboratory for Chemistry and Life Science, Institute for Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan. E-mail: mfujii@res.titech.ac.jp
bDepartment of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, 192-0397, Japan
cDepartment of Liberal Arts, The Open University of Japan, 2-11 Wakaba, Mihama-ku, Chiba 261-8586, Japan

Received 2nd August 2017 , Accepted 25th October 2017

First published on 27th October 2017

Geometries and infrared (IR) spectra in the mid-IR region of phenol–(ammonia)n (PhOH–(NH3)n) (n = 0–10) clusters have been studied using density functional theory (DFT) to investigate the critical number of solvent molecules necessary to promote ground-state proton transfer (GSPT). For n ≤ 8 clusters, the most stable isomer is a non-proton-transferred (non-PT) structure, and all isomers found within 1.5 kcal mol−1 from it are also non-PT structures. For n = 9, the most stable isomer is also a non-PT structure; however, the second stable isomer is a PT structure, whose relative energy is within the experimental criterion of population (0.7 kcal mol−1). For n = 10, the PT structure is the most stable one. We can therefore estimate that the critical size of GSPT is n = 9. This is confirmed by the fact that these calculated IR spectra are in good accordance with our previous experimental results of mid-IR spectra. It is demonstrated that characteristic changes of the ν9a and ν12 bands in the skeletal vibrational region provide clear information that the GSPT reaction has occurred. It was also found that the shortest distance between the π-ring and the solvent moiety is a good indicator of the PT reaction.

1. Introduction

Proton transfer (PT) plays a crucial role in a variety of chemical and biological processes. This reaction has been studied for more than half a century owing to its substantial importance and complexity, and has been widely recognized as a central reaction in areas, such as acid–base chemistry,1–4 electrophilic addition,5,6 enzymatic catalysis,7–9 and primary photosynthetic steps.10,11

Molecular clusters generated in a supersonic jet expansion allow us to elucidate the PT reaction at the microscopic level by using advanced laser spectroscopies. The PT reaction has been studied so far mainly in regard to hydrated cluster radical cations, such as phenol+–(solvent)n (solvent = N(CH3)3, NH3, H2O),12,13 benzene+–(H2O)n,14 and aniline+–(H2O)n15 and protonated species, such as H+(HNO3)–(H2O)n,16 H+(CH3)2O–(H2O)n,17 and H+(CH3OH)–(H2O)n.18,19 In the past few decades, the critical size of solvent molecules necessary for PT reactions in these systems has been discussed on the basis of a competition for proton affinities (PA) between the solute and solvent cluster moieties. For neutral systems, the PT was investigated mainly by a theoretical approach on organic systems and biomolecules, like proteins,20 cytosine–water,21 1-naphthol–ammonia (1-NpOH–(NH3)n),22 phenol–ammonia (PhOH–(NH3)n),23 and phenol–water (PhOH–(H2O)n) complexes.24 An extremely limited number of experimental studies have also been reported on clusters, such as HCl–(H2O)n25,26 and PhOH–(NH3)n.27 Particularly, PT in the neutral ground state (GSPT) is the most popular in chemistry; however, to the best of our knowledge, almost no experimental approach has been reported on this topic. In this sense, the complexation of phenol with ammonia molecules is a rare and important example of GSPT that has been studied spectroscopically.

Since PhOH undergoes near-ultraviolet (UV) absorption and is feasible for laser spectroscopic studies, many research groups have been applying their specific spectroscopic methods to its solvated clusters. The critical amount of ammonia needed to promote PT in the excited state (ESPT) has been one of the central topics concerning studies on ESPT. Since the pKa value of PhOH is estimated to be greatly reduced by photoexcitation, an ESPT reaction between the photoacid and the base is expected to occur in clusters. ESPT reaction studies have emerged in recent decades producing models for an acid–base reaction from a microscopic point of view. While many researchers have tried to explain their experimental results with the ESPT model, there remain some contradictions. Eventually, in contrast to the initial expectation, the controversy has been settled by the introduction of a new concept concerning cluster reactivity: an excited state hydrogen transfer (ESHT) reaction takes place for n ≤ 5, and the ESPT reaction is not observed. The ESHT reaction can be observed only if PhOH is solvated with less than or equal to five ammonia molecules, suggesting the absence of proton/hydrogen transfer in S0 for these small sizes. Whereas the ESHT reaction has been established for clusters with n ≤ 5, no clear spectroscopic features in the electronic transition have been obtained for much larger sized clusters, and the reaction products of the ESHT reaction also suddenly disappear at n = 6. Accordingly, a ground-state proton transfer (GSPT) reaction was proposed as a possible scheme to explain this observation.

This was supported by a large low-energy shift of the ionization potential (IP) between n = 5 and 6, measured by vacuum ultraviolet (VUV) single-photon ionization efficiency curves.28 Ionization of the system results in deprotonation from the OH group and in the production of a phenoxy radical (PhO˙), [PhOH–(NH3)n]+ → PhO˙–H+(NH3)n. The low-energy shift of IP was explained by a better Franck–Condon geometry overlap between the cationic state and the ion paired neutral ground state produced by the GSPT reaction, PhOH–(NH3)n → PhO–H+(NH3)n. The size dependence of the reaction enthalpy in the GSPT reactions was also estimated based on the PA values of the phenolate anion (PhO) and (NH3)n; it was concluded that the enthalpy becomes negative, i.e., exothermic reaction, for n ≥ 6.27 Recently, ab initio geometry optimizations for up to n = 9 have been reported, and the proton transferred ion-paired structures might be more stable than the nontransferred structures for n ≥ 6, in agreement with former studies.27

Jouvet and coworkers reported that PhOH–(NH3)n with more than five ammonia molecules are proton-transferred species in the ground state. That is to say, in the case of PhOH–(NH3)n with six or more ammonia molecules, the most stable ground-state structure is the zwitterionic structure PhO–NH4+(NH3)n−1. They concluded that the GSPT reaction would occur in clusters with n ≥ 6. This conclusion, however, was based on rather indirect information concerning the electronic states, i.e., the change in IP between n = 5 and 6. Therefore, structural information for PhOH–(NH3)n (n ≥ 6) clusters is desirable. Infrared (IR) spectroscopy is a powerful tool to examine structural changes since it can directly monitor the nature of chemical bonds. The structures of hydrogen-bonded networks formed by NH3 molecules around the phenolic OH group are probed by the OH and NH stretching vibrations in the 3 μm region. These vibrations, in fact, have successfully been interrogated in nonreactive hydrated systems, such as PhOH–(H2O)n, to reveal the growth of a hydrogen-bonded network structure on the basis of characteristic band shifts of the OH stretching vibrations, and so forth. The OH stretching vibration, however, shows extensive broadening in the case of strong hydrogen bonding, as can be found in reactive systems, which results in a loss of structural information. In addition, the NH stretching vibrations are not as suitable as OH stretches because of an overlap due to the number of NH bonds, small shifts, weak band intensities, and anharmonic splitting caused by the bending mode. Thus, solvation structures of NH3 are not determined with ease if only the XH (X = O, N) stretching vibrations are analyzed. However, IR spectroscopy of the skeletal vibrations is widely used to investigate structures and reactions because the spectral features in this region can remain sharp, and can provide considerable structural information, even in the bulk. This advantage should also be true for gas-phase clusters in which a reaction is expected. In the present case of the GSPT reaction, the OH bond dissociation is expected to have large effects on the IR spectra in several vibrational bands. For example, the C–O–H bending mode should disappear, the C–O stretching mode should change to reflect a larger double-bond character, the C–C ring modes are expected to reflect any change in the aromaticity of the ring, and so forth.

In our previous work, well-structured spectra were observed in the two-photon excitation spectrum for PhOH–(NH3)n clusters.27 UV excitation and ionization via broad absorptions induce transitions to a high-energy portion of the potential surface. The large excess energy implemented by the excitation processes causes evaporation, which results in the loss of size selectivity. To suppress excess energy, two-color two-photon ionization was adopted, whose total energy was set to be as close as possible to the reported ionization potential of the clusters. This procedure should enhance the size selectivity of the measurement.

A theoretical study on the GSPT of PhOH–(NH3)n (n = 0–10) clusters by quantum chemical calculations using the DFT method is reported in the present work. The geometries and IR spectra in the mid-IR region have been presented to systematically investigate the critical size of the GSPT reaction. In addition, we have considered the minimal distance between the π-ring and the solvent moiety of the PhOH–(NH3)n clusters in S0.

2. Methods

The molecular structures of PhOH–(NH3)n (n = 0–10) in S0 were optimized by using the density functional theory (DFT) method. The M06-2X/cc-pVTZ level of approximation was used for geometry optimization. The initial geometries were generated based on smaller clusters by adding an ammonia molecule to the possible hydrogen-bonding sites. Convergence to an energy minimum was checked by calculating the vibrational frequencies. All of the structures have been confirmed to have all real vibrational frequencies. The relative solvation enthalpies at 0 K were computed using the zero-point vibrational energy (ZPE) correction by employing the scaling factor 0.941. This value was determined from the νOH ratio of the experimental and computational frequencies of the PhOH monomer. The program used was Gaussian 09.29

3. Results and discussion

A. Structures of PhOH–(NH3)n (n = 0–10) in S0

We calculated optimized structures in S0 for the n = 0–4 clusters, but all of the calculated structures are the non-PT ones. All of the calculated structures for n = 0–4 are summarized in Fig. S1 and S2 in the ESI; only the most stable structures are shown in Fig. 1. For the n = 5 clusters, we found 12 stable isomers, one of which is a PT structure (see Fig. S3, ESI). The ZPE corrected energies of the 12 isomers are plotted in Fig. 2. Here, the energies of the PT and non-PT structures are indicated by the red and blue horizontal bars, respectively. In previous work for ESPT in 1-NpOH–(NH3)n clusters, we assumed the population of the species to be within 0.7 kcal mol−1 in molecular beams, and succeeded in reproducing the experimental observations.30 The horizontal broken line in Fig. 2 indicates an energy of 0.7 kcal mol−1. If we take this value as the criterion of the population in the molecular beam experiments, no PT isomer will be observed for the n = 5 clusters. This is consistent with previous experimental reports, that no GSPT is found for clusters with five ammonia molecules or less.
image file: c7cp05247b-f1.tif
Fig. 1 The most stable optimized structures of phenol–(ammonia)n (PhOH–(NH3)n) clusters (n = 0–8) in S0 obtained at the M06-2X/cc-pVTZ level of theory. The OH distances are given in Angstrom. Molecular symmetry and relative energies (kcal mol−1) without and with the zero-point vibrational energy (ZPE) correction are given under each structure. The nitrogen atom of NH4+ in the PT type structures is marked yellow to distinguish it from NH3.

image file: c7cp05247b-f2.tif
Fig. 2 Relative energies (including ZPE correction) of PhOH–(NH3)n (n = 5–10) isomers in S0 obtained at the M06-2X/cc-pVTZ level of theory. PT and non-PT type structures are distinguished by red and blue bars, respectively. The broken line indicates the experimental threshold energy (0.7 kcal mol−1). Isomers that are more stable than that shown by the line are thought to coexist under standard experimental conditions, see text.

According to measurements of photoionization efficiency curves, the threshold of GSPT in PhOH–(NH3)n is reported to be n = 6.28 For n = 6 clusters, we obtained twenty four isomers including nine PT structures; the most stable non-PT and PT isomers are shown in Fig. 1 (see Fig. S4 in the ESI for all the structures). Here, the nitrogen atom of NH4+ is marked yellow to distinguish it from NH3. The energies of the calculated structures are also plotted in Fig. 2. As can be seen in Fig. 2, the energies of the PT isomers are significantly stabilized in comparison to the n = 5 clusters; however, they are still higher than the population criterion of 0.7 kcal mol−1. This strongly suggests that the critical size of GSPT in PhOH–(NH3)n clusters is greater than n = 6.

Since no theoretical evidence of GSPT with six ammonia molecules has been found, we extended the calculations toward larger species. Here, the most stable non-PT and PT structures for n = 7 and 8 are presented in Fig. 1, and all of the calculated ones are shown in the ESI (Fig. S5 and S6). The calculated energies of these non-PT and PT structures are also plotted in Fig. 2. Even with 7 and 8 ammonia molecules, we cannot find a PT structure that is more stable than the population criterion. However, one can see that the PT structures are stabilized according to the increase of the number of ammonia molecules.

The experimental study using IR spectroscopy suggests that GSPT takes place in all (or a significant amount of) clusters with nine ammonia molecules.27Fig. 3 shows the optimized structures of n = 9 clusters. We have found twenty one hydrogen-bonded clusters: IXa–IXr. All of these structures consist of a tricyclic to a heptacyclic hydrogen-bonded network with at most two exterior chains. Complexes IXa, IXc–IXe, IXi, IXl, IXm, IXo and IXr are the PT forms. The other nine remaining complexes IXb, IXf–IXh, IXj, IXk, IXn, IXp and IXq are the non-PT forms. The most stable complex IXb is the non-PT form, whereas the most stable PT form is IXa, which is only 0.7 kcal mol−1 less stable than IXb. We have found a PT structure that is more stable than the population criterion. Therefore, for n = 9 clusters, IXa and IXb coexist in a supersonic jet because of small differences in the relative energies. Here, it should be noted that the initial geometries are built up from the optimized structures of the smaller clusters (n = 8, in this case). We also generated geometries by MD simulation (NAMD31 with the CHARMM force field at 300 K with 100 ps duration) and used them as the initial geometries. However, the most stable geometry in this approach is still 3.7 kcal mol−1 higher in energy than that of IXa in Fig. 3. Although this cannot guarantee that the structures calculated in this work include the global minimum for each size, we tentatively concluded that the initial geometries in this approach give candidates of the global minimum.

image file: c7cp05247b-f3.tif
Fig. 3 Optimized structures of PhOH–(NH3)9 in S0 obtained at the M06-2X/cc-pVTZ level of theory. The OH distances are given in Angstrom. Molecular symmetry and relative energies (kcal mol−1) without and with the ZPE correction are given under each structure. The nitrogen atom of NH4+ in the PT type structures is marked yellow to distinguish it from NH3.

Fig. 4 depicts fifteen isomers of the hydrogen-bonded structures, Xa–Xo, for n = 10 clusters. As well as the structures of n = 9, all of these structures consist of a tetracyclic to a heptacyclic hydrogen-bonded structure with at most a single exterior chain. Complexes Xa, Xb, Xd and Xg–Xo are the PT forms, and the other three remaining complexes Xc, Xe and Xf are the non-PT forms. The most stable complex Xd has the PT form, while the second-most stable complexes, Xc and Xe, have the non-PT forms, which are only 0.1 kcal mol−1 less stable than Xd. The next most stable non-PT complex, Xf, is 0.4 kcal mol−1 less stable than Xd. Therefore, these four complexes are thought to coexist because of the population criterion.

image file: c7cp05247b-f4.tif
Fig. 4 Optimized structures of PhOH–(NH3)10 in S0 obtained at the M06-2X/cc-pVTZ level of theory. The OH distances are given in Angstrom. Molecular symmetry and relative energies (kcal mol−1) without and with the ZPE correction are given under each structure. The nitrogen atom of NH4+ in the PT type structures is marked yellow to distinguish it from NH3.

In almost of all of the PT structures, NH4+ locates in the first solvation layer. More exactly, NH4+ is attached to the negatively charged oxygen atom in PhO. This suggests that the energies of the PT structures are stabilized by the Coulombic interaction between NH4+ and O in the clusters. For the non-PT structures, the ammonia moiety locates on one side of PhOH, suggesting that the interaction with the benzene ring is important to stabilize the structures. On the other hand, the ammonia moiety in the PT structures grows around the ion pair of NH4+ and O; thus the positions of ammonia molecules are not restricted to a single side of the benzene ring. The formation of the negative charge on the oxygen also causes a higher coordination of the hydrogen-bonds. For example, Xa, the most stable PT structure in n = 10, has six hydrogen-bonds connected to O. The number of hydrogen-bonds at O decreases in the less-stable PT structures, but involves at least four coordinations. This is a clear contrast to the non-PT structures in which only three hydrogen-bond coordinations are possible to the OH group.

B. Assignments of IR transitions and relation to proton-transfer

One purpose of this study is to understand what types of vibrational motions are assigned as evidence of the GSPT reaction in PhOH–(NH3)n hydrogen-bonded complexes. In general, the OH and NH stretching vibrations can provide considerable insight into the hydrogen-bonded network in clusters. For PhOH–(NH3)n clusters (n ≤ 5), the IR spectra in the 3 μm region involve well-resolved vibrational structures, which prove that the OH bond keeps its original single-bond nature, and that no proton-transfer reaction occurs. However, in strong hydrogen-bonded clusters involving PT reactions, the hydrogen-bonded OH and NH stretching vibrations are strongly broadened. The free NH stretching is not sensitive to the overall hydrogen-bond structures. Thus, it is experimentally difficult to reach a firm conclusion about structural changes, such as PT from the IR spectra in the 3 μm region. Our previous report demonstrated the advantage of mid-IR spectroscopy for the analysis of GSPT reactions.27 The mid-IR spectra show the skeletal vibrations, some of which directly concern the presence and absence of PT reactions. These skeletal vibrations are mostly free from broadening due to hydrogen-bond formations; therefore, a clear signature of the PT reaction can be obtained. In the previous report, a theoretical analysis of the IR spectra was presented only for specific structures related to n = 9, and no vibrational analysis based on overall sizes and structures has yet been reported. Here, we calculated the IR spectra for all of the calculated structures from n = 0 to 10, and analyzed the relation between the vibrational signatures and the PT reaction.

As discussed in the previous section, the critical size of GSPT in PhOH–(NH3)n is suggested to be n = 9. Thus, the PT forms for n < 9 clusters do not contribute to the observed spectra. Therefore, we present the theoretical IR spectra of n = 5 to 8 in Fig. S7–S10 in the ESI, and summarize the spectral features concerning clusters of n = 5 to 8. Briefly, the spectra consist of umbrella vibrations, ν2, of NH3 (1100 cm−1 region), C–O stretching, νCO, of PhOH (∼1300 cm−1), ν19a of PhOH (∼1450 cm−1), and NH bending, ν4, of NH3 and NH4+ (∼1580 and ∼1400 cm−1, respectively). The spectral feature of isomers varies in the smaller clusters, but becomes similar to each other when going to larger clusters.

Fig. 5 shows the calculated IR spectra for the isomers IXa to IXr. The assignments of the vibrational transitions are also shown in the figure. The PT structures are aligned in the left column, while the non-PT ones are presented in the right column. The vibrational modes that were observed for n = 9 are the same as those in the spectra of the smaller clusters. First, we expected that the C–O stretching vibration would be blue shifted in the PT structures, due to the double-bond character after PT. However, the C–O stretching frequencies do not show any drastic difference between the PT and non-PT structures (see Fig. 5). It can be understood that the blue-shift due to the double-bond character can be compensated for by a red-shift induced by solvation. In the calculated spectra, the NH bending (ν2 and ν4) of NH4+ could be a marker band of PT in principle; however, it is difficult to use it as a signature of PT, because of spectral broadening in this region (see Fig. 3 in ref. 27). Another spectral difference between the PT and non-PT structures is the distribution of ν2 of NH3. In n = 9 clusters, there are eight or nine ν2 vibrations in the PT and non-PT structures, which are distributed around 1100 cm−1. As can be seen in Fig. 5, the ν2 vibrations distribute over a narrower region in the PT structures compared to the non-PT ones. However, this difference is not useful to distinguish the PT and non-PT structures, because the observed IR spectra in this region show only a broad band, and individual bands cannot be resolved. The skeletal vibration, ν19a, is totally insensitive to PT, and useless regarding this purpose. Therefore, the major and intense vibrations in this vibrational region are not suitable to distinguish any structural difference by the PT reaction.

image file: c7cp05247b-f5.tif
Fig. 5 Theoretical IR spectra for the PT and the non-PT type structures of PhOH–(NH3)9 in S0 obtained at the M06-2X/cc-pVTZ level of theory. The calculated frequencies have been scaled by 0.941.

In our previous spectroscopic study concerning the mid-IR region, it was found that characteristic sharp bands (990 and 1160 cm−1) at either side of the broad ν2 NH3 umbrella band appeared in the larger clusters.27 These bands are assigned to ν12 and ν9a of PhO, which are the signature of PT. Since the strong vibrational bands are not suitable to distinguish the structure related to PT, we focused on ν12 and ν9a, and examined the relation to PT. Fig. 6 shows the theoretical IR spectra of PhOH–(NH3)n (n = 9). The spectra are the same as those shown in Fig. 5, but are presented in a four times expanded scale of the horizontal axis for the region around the ν2 NH3 umbrella vibrations. The spectra of the PT and non-PT structures are presented in the left and right columns, respectively. The vibrational transitions that are assigned to ν12 and ν9a are indicated by red bars. The vibrational motions of these modes are added in Fig. S11 in the ESI to confirm the assignments. These vibrational motions are essentially the same as the ν12 and ν9a vibrational motions of monosubstituted benzenes.32 In the theoretical IR spectra of the PT isomers (left column in Fig. 6), ν12 and ν9a were calculated at ∼940 cm−1 and ∼1120 cm−1, respectively. In contrast, the ν12 of PhOH mostly disappeared in the IR spectra of the non-PT structures (right column of Fig. 6). The vibrational bands of ν9a are visible; however, their intensities are significantly weaker than those in the PT structures, and mostly covered by the ν2 umbrella vibrations of NH3. Such a clear contrast with and without PT confirms that ν12 and ν9a are good indicators of the PT reactions in the ground state. The IR spectra of the PT (IXa) and the non-PT (IXb) structures are directly compared to the observed IR spectrum of n = 9 in Fig. S12 in the ESI. The intense major vibrational structures are reproduced by both structures. Therefore, we should not exclude the possibility of the appearance of a non-PT structure (such as IXb). However, as described above, the reproduction of the sharp marker bands is better in the PT structure (IXa). Particularly, ν12 is clearer in IXa (PT) rather than IXb (non-PT). For ν9a, IXb (non-PT) gives a band at 1180 cm−1 which may be assignable to the observed sharp band (assigned to ν9a in the experiment). This band is an umbrella vibration of NH3 (ν2) and would have significant anharmonicity. Thus, the reproduction of this band may be accidental. This comparison does not provide any contradiction to the assignments by the PT structure, thus we would like to conclude that the threshold size of the GSPT is n = 9. Further theoretical research such as high-level calculations including anharmonicity will give the definite conclusion.

image file: c7cp05247b-f6.tif
Fig. 6 Magnified theoretical IR spectra in the ν2 umbrella vibration region for the PT and the non-PT type structures of PhOH–(NH3)9 in S0 at the M06-2X/cc-pVTZ level of theory. The vibrational transitions of ν12 and ν9a are shown by red bars. The calculated frequencies have been scaled by 0.941.

The same tendencies of ν12 and ν9a are also observed in the n = 10 clusters. The overall spectral features in the mid-IR region are shown in Fig. 7. Including the n = 9 clusters, the strong vibrational bands are not suitable as signatures of the PT reaction. The C–O stretching vibration at ∼1250 cm−1 is insensitive to whether the PT structure exists or not. As well as n = 9, other bands, such as the NH bending vibrations (ν2 and ν4) of NH4+, are not useful to distinguish the structural change because of broadening of the spectra in these regions. As shown in the IR spectra in the expanded scale (Fig. 8), ν12 and ν9a are slightly isolated from the clusters of the ν2 umbrella vibrations of NH3 in the PT structures, and almost disappear in the non-PT structures. Again, the appearance of ν12 and ν9a is confirmed to be the spectral signature of the PT reaction for n = 10.

image file: c7cp05247b-f7.tif
Fig. 7 Theoretical IR spectra for the PT and the non-PT type structures of PhOH–(NH3)10 in S0 obtained at the M06-2X/cc-pVTZ level of theory. The calculated frequencies have been scaled by 0.941.

image file: c7cp05247b-f8.tif
Fig. 8 Magnified theoretical IR spectra in the ν2 umbrella vibration region for the PT and the non-PT type structures of PhOH–(NH3)10 in S0 at the M06-2X/cc-pVTZ level of theory. The vibrational transitions of ν12 and ν9a are shown by red bars. The calculated frequencies have been scaled by 0.941.

C. Consistency with the experimental results

Our previous report presented that the non-PT structure coexists with the PT structure for n = 6–8, based on the results concerning the evaporation of two or three ammonia molecules from larger clusters of PhOH–(NH3)n clusters in S0.27 In other words, this conclusion is ambiguous because the number of evaporated ammonia molecules cannot be determined. Our calculations show that the PT structures in n = 8 or smaller clusters are not stable enough to be populated. Thus we concluded that the signature of PT for n = 6–8 would be caused by evaporation from the n = 9 or larger clusters.

The GSPT reaction of PhOH–(NH3)n was investigated by single-photon ionization spectroscopy using synchrotron VUV radiation and a photoelectron-photoion coincidence detection technique by Jouvet and coworkers.28 The ionization threshold significantly decreased from 7.15 eV to 6.7 eV between n = 5 and n = 6, and thus they concluded that the critical size of GSPT is n = 6. The ionization threshold decreases gradually with increasing n. However, one decade later they also reported that such a gradual decrease of the ionization threshold is not reproduced by theoretical calculations, and that the observed threshold is not the adiabatic, but the vertical ionization threshold.33 Here, it should just be mentioned that they did not take evaporation after ionization into consideration.

We also calculated the vertical ionization potential for the most stable non-PT and PT isomers for n = 5 to 10. The calculated results are listed in Table 1. For each size, the ionization potentials of the PT species are ∼1 eV lower than that of the non-PT species. Thus, the measurements of the ionization potential provide a good clue to detect PT in the cluster. However, the lack of any clear size dependence in both PT and non-PT clusters is far from the experimental observations by Jouvet and coworkers. Although they tried to explain it based on the vertical ionization potential, they did not consider the possibilities of evaporation. Here, we attempt a qualitative explanation based on the n = 9 threshold for GSPT. PT clusters have a lower ionization threshold regardless of their size. Thus, the species that has the lowest IP could be n = 9, or larger. Then, if VUV light is scanned to the higher frequency side, smaller clusters can be generated by evaporation from the n = 9 (or larger) cluster. Thus, size-selected measurements of the ionization threshold may give the dissociation threshold instead of the ionization threshold of smaller clusters. This interpretation is roughly consistent with the observed size dependence of the ionization threshold. The ionization potential of n = 9 is almost the same as or slightly lower than that of n = 8. The difference in the ionization threshold between n = 8 and 9 corresponds to the binding energy of an ammonia molecule in the cluster. In the large cluster, the dissociation of the ammonia in the outer region would be close to that of one solvent molecule loss in a neutral cluster, and thus the small change would be understandable. The ionization potentials of n = 5, 6 and 7 should be shifted to blue because they need more energy to evaporate neutral ammonia molecules. For n = 6, it could be generated by three ammonia molecules being evaporated from the n = 9 cluster. This means that the observed photoionization efficiency curves may not represent the size dependence of the ionization potential. Thus, this is consistent with our conclusion that the critical size for the PT reaction is n = 9.

Table 1 Vertical ionization potential (IPv) of the most stable PT and non-PT type isomers of PhOH–(NH3)n (n = 5–10) obtained at the M06-2X/cc-pVTZ level of theory
Non-PT isomer IPv/eV PT isomer IPv/eV
Va 8.05 Vl 6.30
VIa 7.94 VIo 6.98
VIIa 7.91 VIId 6.98
VIIIa 7.91 VIIId 6.97
IXb 7.96 IXa 7.06
Xc 7.86 Xd 7.10

D. Shortest distance between the phenol ring and hydrogen atoms of solvents

We found the shortest distance to be an indicator of PT in our previous studies concerning the ESPT of 1-NpOH–(NH3)n and 1-NpOH–(piperidine)n clusters in S1,30,34 and revealed that it is also true for the GSPT of 1-NpOH–(NH3)n in S0.35 More exactly, distances are calculated between all of the carbon atoms in the aromatic ring and the hydrogen atoms of the solvent molecules, and the shortest value is picked. The distance is shorter in the PT structures than that in the non-PT structures, and an individual cluster has a critical value that indicates PT. In the present work, we have calculated the shortest distance in PhOH–(NH3)n, and considered whether this indicator of GSPT also works for the clusters.

The results are given in Fig. 9 and Table S1 (ESI). The shortest distances are plotted for PhOH–(NH3)n (n = 5–10) in Fig. 9. The blue bars are the values of the non-PT forms, while the red bars represent the values of the PT forms. It has been revealed that all of the isomers that have a distance shorter than 2.58 Å (green horizontal line) are the PT forms. Those that have a distance longer than 2.58 Å are the non-PT forms, except for only three isomers of Vl (PT form) for n = 5, VIx (PT form) for n = 6, and VIIl (non-PT form) for n = 7. These three exceptional isomers are the most unstable optimized structure for n = 5 and 6, and the most unstable non-PT form for n = 7, respectively. In other words, these three exceptional isomers will not exist under the experimental conditions. Although three exceptions are found in this system, we conclude that the shortest distance is a good indicator of the PT reaction also in the GSPT of PhOH–(NH3)n. This suggests that the shortest distance between the aromatic system and the solvent molecules can be a general indicator of the PT reactions. At the moment, we do not have any direct quantum chemical explanation for why the shortest distance is the PT indicator, although it works well phenomenologically. One possibility is that the solute–solvent distance would be shortened by the extra-charge separation due to the PT reaction. Another possibility may be a perturbation of solvent to the aromatic system that strongly concerns the PT reaction. Further consideration is now under discussion involving a detailed orbital analysis.

image file: c7cp05247b-f9.tif
Fig. 9 The shortest distance from the benzene ring to hydrogen atoms of solvents in PhOH–(NH3)n (n = 5–10) isomers in S0. Values of the PT and non-PT structures are distinguished by red and blue horizontal bars, respectively. The green line indicates the threshold value (2.58 Å) that separates PT and non-PT type structures, see text.

4. Conclusions

The geometries and size dependence of the GSPT reaction in PhOH–(NH3)n (n = 0–10) clusters in the ground state have been studied using the M06-2X density functional level of theory. The structures are classified according to the hydrogen-bonded networks. The PT structures become stable according to the number of ammonia molecules in the clusters, and a mixture of non-PT and PT forms begins to appear from n = 9 under experimental conditions. The quantum chemical calculations indicate that the critical size of GSPT is n = 9. The theoretical IR spectra are also calculated, and support the previous spectroscopic analysis, particularly concerning the marker molecular vibrational transitions. These theoretical results on the critical size of GSPT are not contradictory to our previous experimental conclusion, and consistency with other experiments is also discussed. It is found that the shortest distance between the π-ring and the solvent moiety is a good indicator of the PT reaction.

Conflicts of interest

There are no conflicts to declare.


This work was supported in part by KAKENHI (JP205104008) on innovative area (2503), KAKENHI (JP15H02157, JP15K13620, JP16H06028), and the Cooperative Research Program of the “Network Joint Research Center for Materials and Devices” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The computations were performed at the Research Center for Computational Science, Okazaki, Japan. We acknowledge helpful discussions and suggestions on the MD simulations by Prof. Y. Sugita and Prof. K. Yagi in RIKEN.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp05247b

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