Hiroto Tachikawa*a and
Tomoya Takadab
aDivision of Materials Chemistry, Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo 060-8628, Japan. E-mail: hiroto@eng.hokudai.ac.jp; Fax: +81 11706 7897
bDepartment of Material Chemistry, Asahikawa National College of Technology, Syunkodai, Asahikawa 071-8142, Japan
First published on 17th December 2014
A proton transfer process is usually dominant in several biological phenomena such as the energy relaxation of photo-excited DNA base pairs and a charge relay process in Ser-His-Glu. In the present study, the rates of proton transfer along a hydrogen bond in a water cluster cation have been investigated by means of a direct ab initio molecular dynamics (AIMD) method. Three basic clusters, water dimer, trimer and tetramer, (H2O)n (n = 2–4), were examined as the hydrogen bonded system. It was found that the rate of the first proton transfer is strongly dependent on the cluster sizes: average time scales of proton transfer for n = 2, 3, and 4 were 28, 15, and 10 fs, respectively, (MP2/6-311++G(d,p) level) suggesting that proton transfer reactions are very fast processes in the three clusters. The second proton transfer was found in n = 3 and 4 (the average time scales for n = 3 and 4 were 120 fs and 40 fs, respectively, after the ionization). The reaction mechanism was discussed on the basis of theoretical results.
From experimental points of view, photo-ionization of the water clusters has been investigated by means of several techniques.24–28 It was found that the reaction occurs as follows:24,27
(H2O)n + Ip → [(H2O)n+]ver + e− (ionization) |
[(H2O)n+]ver → (H3O+)(OH)(H2O)n−2 (complex formation) |
→ H+(H2O)n−1 + OH (OH dissociation) |
→ H+(H2O)n−k + (k − 1)H2O + OH (OH dissociation + H2O evaporation), |
Early experiments showed that the parent ion (H2O)n+ is observed only for the water dimer (n = 2), whereas the protonated water H+(H2O)m (m < n) is observed in the larger clusters. The OH formation was also observed in the larger clusters. The absence of the parent ion is consistently explained in terms of poor Franck–Condon overlaps between the neutral and the ionic states whose potential minima are largely displaced from each other (n = 2).28 Thus, the reaction channels are strongly dependent on the cluster size. In all clusters, the first proton transfer is an important trigger in the decay process of water cluster cation.
In the present study, direct ab initio molecular dynamics (AIMD) calculation29,30 was applied systematically to the ionization dynamics of water dimer, trimer and tetramer (H2O)n (n = 2–4) in order to estimate the reaction rates of the first and second proton transfer processes in the water cluster cation. In previous study,31 we preliminary investigated the ionization of water clusters (H2O)n (n = 2–6) using direct AIMD method at the Hartree–Fock (HF) level, and showed that a dissociation of hydroxyl radical (OH) becomes more dominant in the larger clusters. In the present work, we performed the direct AIMD calculation on more accurate potential energy surface (MP2/6-311++G(d,p) level) to estimate the proton transfer rate along the hydrogen bond in the water cluster cation. Especially, the ionization dynamics of water clusters were systematically investigated with the same procedure for n = 2–4, and the cluster size dependency of proton transfer rate was compared with each other.
Information on the structures and energetics for water cluster cation has been accumulated from both theoretical32–43 and experimental points of view.8–11,51–54 The neutral water dimer has a linear form in its equilibrium structure. The structure of the cationic state of the water dimer is largely distorted from the neutral one: the structure of (H2O)2+ is composed of the H3O+ ion and the OH radical, expressed by (H3O+OH), where the proton is transferred from H2O+ to H2O following the ionization of (H2O)2.12
Barrnet and Landman searched the stable structure of water cluster cations (H2O)n+ (n = 3–5) using ab initio calculations.32 Their calculations showed that the proton transferred complex (H3O+OH) exists as a core cation in the clusters for all cation clusters. Recently, the similar feature was reported by Lee and Kim using more accurate theoretical levels.33 IR spectroscopy observed by Fujii and co-workers indicated that water trimer cation is composed of proton transferred type.24
Formation processes of water cluster cation were investigated by several groups. Furuhama et al. applied partitioning method of the kinetic energy to the ionization of water tetramer cation (n = 4).34 Recently, Livshits et al. indicated that water pentamer cation causes a proton transfer and OH dissociation.35 These pictures were also obtained by us.36 Novakovskaya performed AIMD calculation of (H2O)n+ (n = 4–6).37 Snapshots of were obtained after the ionization of (H2O)n parent clusters. However, she handles only phenomenalism and did not perform the detailed argument about the proton transfer mechanism.
For the water dimer and trimer cations (n = 2–3), we investigated the ionization dynamics by means of direct AIMD method.38,39 The water dimer cation has two low-lying electronic states: the ground state (2A′′ state) and the first excited state (2A′ state). From our calculations, it was found that the ionization to the 2A′′ state gives a proton transferred product (H3O+–OH), whereas that to the 2A′ state gives hydrazine-like complex. Thus, the static structures and limited reaction dynamics calculations were carried out for (H2O)n+. There is no detailed analysis for the rate of proton transfer in water cluster cation.
In the direct AIMD calculation,41,42 first, the geometry of neutral clusters (H2O)n was fully optimized at the MP2/6-311++G(d,p) level. The trajectory on the ionic state potential energy surface of (H2O)n+ was started from the equilibrium point of parent neutral cluster. The velocities of all atoms and angular momenta were set to zero at time zero in the trajectory calculation. Also, temperature of the system and excess energy from the potential energy surface at time zero were fixed to 0 K and zero, respectively. The equation of motion was solved by the velocity Verlet algorithm43 with a time step of 0.05 fs. We checked carefully that the drift of total energy (=potential energy plus kinetic energy) is less than 0.05 kcal mol−1 in all trajectories. No symmetry restriction was applied to the calculation of the energy gradients.
The relation of total, potential and kinetic energies is expressed by
E(total) = E(kinetic) + E(potential) |
Since we used the microcanonical ensemble (NVE ensemble) in the AIMD calculation, the total energy of the reaction system is constant during the MD simulation. Instead, the potential and kinetic energies largely vibrate as a function of time. For example, the relation of these energies for a sample trajectory are plotted in Fig. S1, ESI.† Total energy was constant during the reaction.
In addition to the trajectory from the equilibrium point, the trajectories around the equilibrium points were run. A total of ten trajectories were run in each cluster. The selected geometries on Franck–Condon region were chosen as follows: first, the structure of (H2O)n (n = 2–4) was fully optimized at the MP2/6-311++G(d,p) level of theory. The total energy and optimized structure of (H2O)n (n = 2–4) are expressed by E0(n) and [(H2O)n]0, respectively. Second, the geometries of (H2O)n (n = 2–4) were randomly generated around the equilibrium points of [(H2O)n]0. The generated geometry is expressed by [(H2O)n]i, and total energy is expressed by Ei(n), where notation i is number of generated configurations of [(H2O)n]i. Third, the energy difference of Ei from E0 was calculated as ΔEi = Ei − E0. We selected the generated geometry with ΔEi less than 1.0 kcal mol−1 (ΔEi < 1.0 kcal mol−1). The direct AIMD calculations were started from the selected geometries. The trajectory calculations of (H2O)n+ were performed under constant total energy condition at the MP2/6-311++G(d,p) level.
In addition to the MP2 geometries of (H2O)n, the optimized structures obtained by QCISD/6-311++G(d,p) and CCSD/6-311++G(d,p) were examined as starting geometries of [(H2O)n+]ver in the direct AIMD calculations to check the effects of initial geometry on the proton transfer rate.
The molecular charges on the water molecules obtained by the natural population analysis (NPA) are given in Table 1. In water dimer, charges on W1 and W2 were +0.02 and −0.02, meaning that the charge is slightly separated in the dimer. On the other hand, the charges on all water molecules in (H2O)n (n = 3 and 4) were close to zero. At the vertical ionization states, charge distribution was largely changed: a positive charge and spin density were mainly localized on only one water molecule in each cluster cation. In vertical ionized state, [(H2O)2+]ver, the charge distribution on W1 and W2 were 0.95 and 0.05, respectively, where W1 and W2 are proton donor and acceptor water molecules, respectively. The spin density was localized on the proton donor in water dimer. This is due to the fact that highest occupied molecular orbital (HOMO) of water dimer is non-bonding orbital of the proton donor (see, Fig. S2 in ESI†).
W1 | W2 | W3 | W4 | ||
---|---|---|---|---|---|
Charge | n = 2(0) | 0.02 | −0.02 | ||
n = 3(0) | 0.00 | 0.00 | 0.00 | ||
n = 4(0) | 0.00 | 0.00 | 0.00 | 0.00 | |
n = 2(+)ver | 0.95 | 0.05 | |||
n = 3(+)ver | 0.91 | 0.07 | 0.02 | ||
n = 4(+)ver | 0.89 | 0.08 | 0.03 | 0.01 | |
Spin density | n = 2(+)ver | 1.00 | 0.00 | ||
n = 3(+)ver | 0.99 | 0.00 | 0.01 | ||
n = 4(+)ver | 1.00 | 0.00 | 0.00 | 0.01 |
The molecular charges in [(H2O)3+]ver, were 0.91 (W1), 0.07(W2), and 0.02 (W3). Each water molecule was located in different environment (see, Fig. S3 in ESI†). The charges on W1, W2, W3, and W4 of [(H2O)4+]ver are +0.89, +0.08, +0.03, and +0.01, respectively, at the MP2/6-311++G(d,p) level, indicating that the hole is mainly localized on W1. This is due to the fact that the structure of (H2O)4 was calculated without symmetry restriction. Hence, each water molecule was located in different environment. The spatial distribution of spin density is illustrated in Fig. 1, indicating that the unpaired electron is mainly localized on one water molecule (W1), although a part of spin densities is distributed on W4. The similar features were obtained for [(H2O)n+] (n = 2 and 3).
Snapshots for the dissociation channel where the OH radical leaves from the system are illustrated in Fig. 2. The position of proton of W1(H1) is located at r1 = 1.895 and r2 = 0.977 Å at time zero (point a). The oxygen–oxygen distance is R12 = 2.781 Å. After the ionization, the hole is mainly localized on one of the water molecules (W1) in the water trimer cation. The proton of W1+ was immediately transferred to W2: the distances of proton were r1 = 1.046 Å and r2 = 1.651 Å at time = 12 fs (point b), and the ion-radical pair (H3O+)OH is formed within very short time period (time = 12 fs at point b). The process of this proton transfer is the same as that of complex channel. In addition to the first proton transfer from W1+ to W2, the second proton transfer takes place in the OH dissociation channel. This process occurs from the protonated W2 (i.e., H3O+) to W3 around 100 fs. Fig. 2(c) shows that the proton transfer takes place from H3O+ to W3 at 100 fs. After the second proton transfer, the OH radical was fully separated from the H3O+ ion and was dissociated from W2. The OH radical leaved gradually from the system and reached to R12 = 4.501 Å at 250 fs (product d). Final product was H2O(H3O+) + OH in this trajectory.
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Fig. 2 Snapshots of water trimer cation (H2O)3+ after vertical ionization from optimized structure. The values are bond distance in Å. |
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Fig. 3 Snapshots of water tetramer cation (H2O)4+ after vertical ionization from optimized structure. The values are bond distance in Å. |
The second proton transfer occurred at 37 fs. The snapshot at 53 fs (point d) shows that the proton is located at the middle of W2 and W3 (r3 = 1.146 Å and r4 = 1.167 Å). This structure corresponds to the Zundel-like complex, indicating that the second proton transfer takes place via the Zundel-like complex. At 82 fs (point e), the H3O+(W3) ion was completely formed (r3 = 1.727 Å and r4 = 1.008 Å), and the attractive interaction between OH radical and H3O+ was disappeared by the separation by the H2O molecule (W2 at 82 fs). Hence, the OH radical was rapidly dissociated from W2. Finally, the solvated H3O+ ion was remained in the reaction system (128 fs).
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Fig. 5 Reaction time for the proton transfer in water tetramer cation plotted as a function of run number of trajectory. |
Time of first proton transfer (W1+ → W2) was distributed in the range 9.3–10.7 fs, and average value was 9.9 fs. This is a very fast process. The second proton transfer occurred at 40 fs after the ionization. This is a slow process. The third proton transfer occurred from W3+ to W2 (the reverse proton transfer). Time scales between first and second proton transfer processes are significantly different from each other (ca. 10 fs for the first proton transfer vs. ca. 40 fs for 2nd proton transfer). This is due to the fact that the first proton transfer proceeds as an extho-thermic reaction: H2O+(W1) + H2O(W2) → OH(W1) + H3O+(W2). On the other hand, the second proton transfer is iso-thermic reaction: H3O+(W2) + H2O(W3) → H2O(W2) + H3O+(W3). This is an origin of difference of time scales.
The similar analysis was carried out for n = 2–3, and the results are summarized in Table 2. In n = 2, only first proton transfer was found as W1+ → W2. Average time of the first proton transfer was 28.4 fs. In case of n = 3, the second proton transfer occurred around 120 fs after the ionization, which is much slower than that of n = 4.
Proton transfer | n = 2 | 3 | 4 |
---|---|---|---|
1st | 28.4 | 15.1 | 9.9 |
2nd | 119.6 | 39.6 | |
3rd | 143.1 | 49.5 | |
4th | 63.4 |
The first, second and third proton transfer rates obtained by MP4SDQ and CCSD geometries were 9.6 fs (9.6 fs), 40.7 fs (39.9 fs), and 51.9 fs (49.4 fs), respectively, where the CCSD values are given in the parenthesis. These values are in good agreement with MP2 values. Therefore, the present results are general in water tetramer cation.
The radical cation of water tetramer has several conformers. We found five structures of (H2O)4+. Among them, four stable structures are illustrated in Fig. 6. The most stable structure is complex 1 where the H3O+ ion interacts directly with the OH radical and is solvated by two water molecules. In complexes 2 and 3, the OH radical is separated from the H3O+ ion by water molecule. Both complexes 2 and 3 are 2.5 kcal mol−1 higher in energy than complex 1. In complex 4, the H3O+ ion interacts directly with the OH radical and is solvated by one water molecule. This complex is 5.1 kcal mol−1 unstable than complex 1.
Relative energies of stationary points for n = 4 are given in Table 3, and the energy diagram for the ionization process of water cluster is illustrated in Fig. 7. In case of n = 4, the radical cation of (H2O)4+ was 55.4 kcal mol−1 lower in energy than the vertical ionization point (ΔEstable). The energy level of OH dissociation channel is 7.9 kcal mol−1 higher than that of radical cation (H2O)4+, indicating that the OH dissociation takes place easily from the radical cation. The available energy of OH dissociation channel (ΔEavail) was 47.5 kcal mol−1. The OH dissociation reaction is exothermic in energy. The available energies for n = 2 and 3 were calculated to be −0.8 and 15.3 kcal mol−1, which are significantly smaller than that of n = 4. This result indicates that the OH dissociation occurs easily in n = 4.
(H2O)n | Method | ΔEstable | ΔEdiss | ΔEavail | Ip |
---|---|---|---|---|---|
n = 2 | MP2 | 21.5 | 22.3 | −0.8 | 11.7 |
CCSD | 21.5 | 21.5 | 0.0 | 11.4 | |
n = 3 | MP2 | 52.9 | 37.6 | 15.3 | 12.3 |
CCSD | 52.0 | 37.0 | 15.0 | 12.0 | |
n = 4 | MP2 | 55.4 | 7.9 | 47.5 | 12.2 |
CCSD | 60.3 | 12.9 | 47.4 | 11.9 |
It is noted that the MP2 values are in good agreement with the CCSD values, as shown in Table 3. This fact suggests that the MP2/6-311++G(d,p) calculation would be enough to represent the potential energy surface of water cluster cation.
Snapshots of the first proton transfer process from W1+ to W2 are superimposed in Fig. 8 (left). These snapshots were calculated from direct AIMD calculations of (H2O)4+ from the optimized structure of neutral state. The proton was rapidly transferred within 10 fs, and the change of position was significantly large. On the other hand, the positions of the other atoms were hardly changed. Fig. 8 (right) shows potential energy curve (static ab initio calculation) plotted along the proton transfer coordinate (R) together with potential energy of the system obtained by direct AIMD calculation. The shape of the curve indicates that the proton transfer takes place without activation barrier, and the reactant can reach smoothly to the proton transferred product. The potential energies of AIMD was always lower than PEC, indicating that the structural relaxation of the other geometrical parameter affect slightly to the stabilization of the system.
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Fig. 9 Time evolution of oxygen–oxygen (O–O) bond distances of neutral water tetramer at 10 K. Time is in atomic unit. Calculation was carried out at the B3LYP/6-311++G(d,p) level. |
On the basis of the present calculations, a reaction model of ionization of cyclic water tetramer is proposed. The reactions following the ionization of the water tetramer is summarized as follows:
(H2O)4 + Ip → [(H2O)4+]ver + e− | (1) |
[(H2O)4+]ver → (H2O)2–(H3O+)–(OH) complex | (2) |
→ (H2O)(H2O–H3O+) + OH dissociation | (3) |
Two reaction channels (complex and OH dissociation) were found from the direct AIMD calculations. By the ionization of water tetramer, a hole is localized on one of the water molecules in (H2O)4. In case of cyclic form, a proton is rapidly transferred from H2O+(W1+) to H2O (W2) along the hydrogen bond. Time scale of the proton transfer is about 10 fs (very fast process). Next, the second proton transfer occurred from W2(H+) to W3 with a time scale of 50–100 fs. The second proton transfer makes the separation of OH from H3O+ such as a configuration of H3O+–H2O–OH. When the separation is completed, the attractive interaction between H3O+ and OH is vanished by the H2O located in the middle of H3O+ and OH radical. Immediately, the OH radical is dissociated from the system.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra14763d |
This journal is © The Royal Society of Chemistry 2015 |