Electron Capture Dynamics of a Water Molecule Connected to a Cyclic

Aug 19, 2010 - Electron capture dynamics of the water tetramer (H2O)n (n = 4) have been investigated by means of a full-dimensional direct ab initio m...
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J. Phys. Chem. A 2010, 114, 10309–10314

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Electron Capture Dynamics of a Water Molecule Connected to a Cyclic Water Trimer: A Direct Ab Initio MD Approach Hiroto Tachikawa* DiVision of Materials Chemistry, Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060-8628, Japan ReceiVed: June 21, 2010; ReVised Manuscript ReceiVed: August 1, 2010

Electron capture dynamics of the water tetramer (H2O)n (n ) 4) have been investigated by means of a fulldimensional direct ab initio molecular dynamics (MD) method at the MP2/6-311++G(d,p) level. Two structural conformers (branched and cyclic forms of the water tetramer) were examined as neutral water tetramers. The structure of the branched form is that a dangling water molecule binds to the ring composed of a cyclic water trimer. In the case of electron capture of the branched form, first, an excess electron was trapped by the dangling water molecule. Next, rotation of the water molecule located in the ring occurred rapidly, while a hydrogen bond of the ring was broken. The branched structure was gradually changed to a linear one. This change was caused by the increase of the dipole moment of the neutral water tetramer oriented toward the excess electron. The time scale of hydrogen bond breaking and solvation of the excess electron were estimated to be 100 and 400 fs, respectively. In the case of the cyclic water tetramer, a planar structure was only changed to a slight bent form. The mechanism of electron capture of the water tetramer (mainly the branched form) was discussed on the basis of theoretical results. 1. Introduction The hydrated electron has long been considered a distinct chemical species of relevance to many branches of chemistry1 and a subject of dramatic interest since its discovery in 1962.2 Experimental evidence has shown that not only bulk polar fluids can solvate easily the excess electron, but also the gas-phase water clusters can trap an excess electron.3-5 The mechanism of electron solvation taking place in the medium has been one of the important themes in radiation chemistry and in cluster chemistry.3-8 When an excess electron is injected into water, a hydrated electron is formed. The physical and chemical properties of the hydrated electron have been widely investigated from both experimental and theoretical points of view.2-8 However, it remains unclear how an excess electron is solvated by water molecule. In particular, the initial process after the electron attachment to water and also the time scales of solvation (solvent reorientation) are still unclear. Recent experiments reveal that the small-sized water cluster anions exist as relatively stable intermediates in the gas phase.9-13 As an early work, Haberland and his co-workers,9-11 using ion cyclotron resonance (ICR) and mass spectroscopy, showed that the smallest water cluster anion is a water dimer anion (H2O)2-. The strong intensities of mass spectra were measured for n ) 2, 6, 7, and 11, while weak intensities were obtained for n ) 3, 4, 5, and 8. Bragg et al. and Paik et al. used pump-probe photoelectron spectroscopy to elucidate the dynamics of photoexcited clusters containing 15-50 water molecules and 1 excess electron.14,15 The lifetime of the excited state was determined. Hammer et al. used vibrational predissociation spectroscopy to obtain the information for structures of smaller clusters with four to six water molecules and one excess electron.16 The vibrational spectra show that the excess electron binds in the vicinity of water molecules. * E-mail: [email protected]. Fax: +81 11706-7897.

The structures and energetics for small-sized water cluster anions (H2O)n- (n ) 2, 3, 4, 5, and 6) have been calculated by several groups using ab initio and density functional theory (DFT) methods.17-24 Simth et al. calculated the structures of water dimer, trimer, and tetramer anions. Kim et al. investigated the hexamer anion (n ) 6) and showed that the prism structure is most favorable in the gas phase.20-24 Structures of the water dimer anion were also investigated by several workers. Tsurusawa and Iwata suggested from that the water dimer anion possesses a positive vertical electron detachment energy.25 Although the energetics and structures of the water cluster anions have been thus extensively studied from a theoretical point of view, the dynamics of the electron attachment process is not clearly understood. In particular, the nature of the electron localization, that is, the time scale of electron localization and the hydrogen bond breaking time, is still unclear. In our previous papers,26,27 the electron capture dynamics of the water dimer and trimer have been investigated by means of direct ab initio molecular dynamics (MD) method. The time scale of hydrogen bond breaking and solvation of the excess electron (time scale of localization of the excess electron in the water trimer) were estimated. In the present study, the direct ab initio MD method is applied to the electron capture processes of the water tetramer (H2O)n (n ) 4). Especially, we show the results for an electronattachment process of branched and cyclic forms of the water tetramer. The benched tetramer is regard as a smallest model of dangling water adsorbed on a water cluster. The main purpose of this study is to elucidate the dynamics of electron localization and solvent reorientation as a function of time, that is, how the localization of an excess electron takes place in a water cluster after electron attachment to the clusters. The water tetramer has two stable conformers, as illustrated in Figure 1. One is a branching form where a water molecule binds to a cyclic water tetramer. Each water molecule in the branched form is located under a different environment. The other one is a cyclic form

10.1021/jp105731u  2010 American Chemical Society Published on Web 08/19/2010

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Hiroto 2. Method of Calculation Direct ab initio MD calculation28,29 was carried out at the MP2/6-311++G(d,p) level of theory. First, the structure of the neutral water tetramer was determined by static ab initio calculation. A total of 10 geometrical configurations were generated around the optimized geometry of the neutral state using the sampling method.30 Trajectories for the tetramer anion (H2O)4- were then propagated from the vertical electron capture point using the selected structures of the neutral water dimer. The calculated values of 〈S2〉 were less than 0.77 at all trajectory points. The equations of motion for N atoms in a water tetramer are given by

Figure 1. Optimized structures of neutral water tetramers (branched and cyclic forms) calculated at the MP2/6-311++G(d,p) level.

where four water molecules bind each other to the neighboring water molecules by hydrogen bonds. This is an interesting point in this system. Namely, the electron capture dynamics of these conformers are investigated and compared to each other in the present work.

dQj ∂H ) dt ∂Pj

(1)

dPj ∂U ∂H )) dt ∂Qj ∂Qj

(2)

where j ) 1 - 3N, H is the classical Hamiltonian, Qj is a Cartesian coordinate of the jth mode and Pj is the conjugate momentum. U is the potential energy of the reaction system. These equations were numerically solved by the velocity Verlet algorithm method. No symmetry restrictions were applied to the calculation of the energy gradients. The time step size was chosen to be 0.10 fs, a total of 5000-10000 steps were calculated for each dynamics calculation, and the trajectory calculations for (H2O)4- were performed under conditions of constant total energy ()potential energy + kinetic energy). The drift of the total energy was confirmed to be less than 1 × 10-3 % throughout all steps in the trajectory. Static ab initio calculations were performed with the Gaussian 03 program package31 using the 6-311++G(d,p) basis set in

Figure 2. Snapshots of the water tetramer anion after an electron attachment to the neutral water tetramer (branched form) obtained by direct ab initio MD calculation at the MP2/6-311++G(d,p) level. The trajectory was started from the optimized geometry of the neutral water tetramer. Spatial distribution means the spin density of an excess electron around a water tetramer.

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order to obtain sufficiently accurate energetics. In addition, a basis set in which a further diffuse function was added to the hydrogen atoms was used for comparative purposes in the static MP2 calculations (denoted by 6-311++G(d,p)+diffuse(5sp/ 2p)). The diffuse function on the hydrogen atom is composed of two p orbitals with exponents R1 ) 1.0 × 10-4 and R2 ) 2.0 × 10-5. For purposes of comparison, QCISD calculations were also carried out for the molecules at all stationary points. The derived structures and geometrical parameters of the stationary points are given in the Supporting Information. 3. Results A. Structures of the Water Tetramer. The water tetramer has two stable conformers, as illustrated in Figure 1. One is a branching form where a water molecule binds to a cyclic water tetramer. Four water molecules in the branched form are different in environment from each other. The other one is a cyclic form where four water molecules bind each other by hydrogen bonds. All water molecules are almost equivalent to each other. In the branched form, the oxygen-oxygen bond distances are r(O2-O3) ) 2.858 Å, r(O3-O4) ) 2.798 Å, and r(O2-O4) ) 2.754 Å. The distance of the dangling water molecule (W1) is slightly larger than the other distances, r(O1-O2) ) 2.906 Å. In the case of the cyclic water tetramer, the oxygen-oxygen bonds are almost similar in all bonds (2.75 Å). Harmonic vibrational frequencies were calculated to confirm the stability of these conformers. All vibrational frequencies were positive at the MP2/6-311G++G(d,p) level, indicating that both forms are located in the local minima (see Supporting Information). B. Electron Capture Dynamics of the Branched Water Tetramer. Snapshots and special distributions of the spin density of an excess electron are illustrated in Figure 2. At the vertical electron capture point (time ) 0.0 fs, panel a), an excess electron is first trapped by the dangling water molecule (W1). The spin density is largest in the direction of the dipole moment of the dangling water. Next, rotation of water molecule W3 takes place, and a hydrogen bond between W2 and W3 is rapidly broken at 87.0 fs (b). This is due to the electrostatic repulsive interaction (negative-negative interaction) between the excess electron and the negatively charged oxygen atom of W3. The water molecule W3 leaves gradually from W2. Also, rotation of W4 occurs, and the dipole moment of W4 orients toward the excess electron. However, the hydrogen bonds of W2-W4 and W3-W4 are still kept during the solvent reorientation. At 218.7 fs (c), the excess electron is distributed on two water molecules (W1 and W2). The dipole moments of the other water molecules (W3 and W4) move to orient to the excess electron. Namely, the excess electron is trapped by two water molecules (W1 and W2) in (c), and the other water molecules (W3 and W4) contribute as a dipole field. At the final stage of the solvation (360.1 fs, panel d), the excess electron is trapped by three water molecules (W1, W2, and W3), and the structure of W1-W2-W4-W3 is close to a linear form. The potential energy of the system is plotted as a function of time in Figure 3. The zero level corresponds to the energy at the vertical transition point in electron attachment to the neutral water tetramer with a branched form (a). The oxygen-oxygen bond distances of W1-W2 ()R1) and W2-W3 ()R2) and the bond angle of O2-O4-O3 ()θ) are also given in Figure 3B and C, respectively. After the electron attachment, the energy

Figure 3. Potential energy (A), intermolecular distances (B), and bond angle (θ ) O2-O4-O3) (C) of the water tetramer anion after an electron attachment to the neutral water tetramer (branched form). The corresponding snapshots are illustrated in Figure 2.

of the water tetramer anion decreases gradually due to the structural relaxation (mainly solvent reorientation of W3 and W4). The potential energy curve (PEC) shows a shoulder at 87 fs (b), where the excess electron is concentrated on one water molecule (W1). The energy becomes -1.9 kcal/mol at 87.0 fs (b). The hydrogen bond between W2 and W3 disappears due to rotation of W3. However, the triangle form composed of three water molecules (W2, W3, and W4) is still kept at this time. The angle (θ) is close to that of a triangle (60°). After that, W3 leaves gradually from W2 (increase of R2), and the triangle structure is varied to a linear form. The bond distances of R2 at times 0.0, 218.7, and 360.1 fs are 2.858, 3.810, and 5.309 Å, respectively. On the other hand, the bond distance of W1-W2 is almost constant during the reaction (R1 ) 2.8-3.0 Å). The energy reaches at lowest-energy point in panel d (-6.0 kcal/ mol). The distance of R2 and angle θ are 5.20 Å and 132° at this point, respectively, indicating that the structure is close to a linear form at the lowest-energy point. Time profiles of the dipole moment of neutral and anionic systems are plotted in Figure 4. The dipole moment of the neutral water tetramer increases gradually as a function of time. In this calculation, an excess electron is removed from e-(H2O)4, and then, the electronic state is calculated to obtain the dipole moment of pure (H2O)4. The increase of the dipole moment

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Figure 4. Time profiles of dipole moments of neutral and anionic systems. The corresponding snapshots are illustrated in Figure 2.

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Figure 6. Effects of initial conditions on the dynamics of the water tetramer anion. Potential energies of the water tetramer anion after an electron attachment to the neutral water tetramer obtained by direct ab initio MD calculation.

Figure 5. Spin densities summarized in the water molecules plotted as a function of time. The calculation is carried out at the MP2/6311++G(d,p) level.

corresponds to a change of stabilization energy of the potential energy of e-(H2O)4. This result suggests a structural change of (H2O)4 after the electron capture takes place as the dipole moment of the water tetramer becomes larger because this change causes the stabilization of the potential energy. On the other hand, the time dependence of the overall dipole moment of e-(H2O)4 decreases with increasing time because the increase of the dipole moment of the neutral water tetramer vanishes the overall dipole moment due to dipole-electron interaction. B. Spin Density on Water Molecules. The spin densities on the water molecules are plotted in Figure 5 as a function of time. At time 0, the densities on W1, W2, W3, and W4 are 1.18, -0.15, 0.0, and 0.05, respectively. The density on W1 decreases gradually as a function of time, whereas those of W2 and W4 increase. These results indicate that the excess electron can be trapped mainly by three water molecules. The other one water molecule (W3) contributes as an electrostatic field stabilizing the excess electron.

Figure 7. Potential energy of the water tetramer anion after an electron attachment to the neutral cyclic water tetramer. Snapshots of the water tetramer anion are also given. The trajectory was started from the optimized geometry of the neutral water trimer. Spatial distribution means the spin density around the water tetramer.

C. Effects of Initial Structures of the Water Tetramer on the Dynamics. In an actual system, the structure of the water tetramer fluctuates around the equilibrium point. To include the effects, geometrical configurations of the water tetramer were randomly selected, and then, the trajectories were run. The results of direct ab initio MD calculations from the five geometrical configurations are given in Figure 6. The calculations showed that all trajectories pass along the same route up to the lowest-energy points. Form this region, routes of the trajectories were slightly different from each other. These results

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Figure 8. A schematic illustration for a model of an electron attachment process to a dangling water molecule connected to a water trimer.

indicate that the trajectory started from the optimized structure is a typical one in the branched form. D. Electron Capture Dynamics of the Cyclic Water Tetramer. A similar calculation was carried out for the cyclic water tetramer for comparison. The results of the dynamics calculation are given in Figure 7. The structure of the cyclic form is near planar, where all water molecules are located on a molecular plane at time 0. After the electron capture of the cyclic form, the excess electron was equivalently distributed around four water molecules (a) due to the fact that the environments of the water molecules are almost similar to each other. After the electron capture of the water tetramer with the cyclic form, the potential energy of the system decreases suddenly and is minimized at 200 fs. This lowering is caused by the structural deformation of the water tetramer anion; the planar structure is changed to a bent form, where two water molecules are located above the molecular plane. Namely, the water molecules are separated to upper and lower water molecules. The spin densities on the water tetramer anion are illustrated in the upper panel of Figure 7. At time 0 (panel a), the spin density is equivalently distributed around four water molecules. After the structural relaxation (panel b; time ) 930 fs), the spin density distribution is split into two groups (upper and lower water molecules). In order to elucidate the energetics of the present system, first, the geometry optimizations of stationary points were carried out at the QCISD/6-311++(d,p) level, and then, the energies were calculated at the QCISD/6-311++G(d,p) +diffuse (5sp/ 2p) level. The static ab initio calculations showed that the cyclic form of the neutral water tetramer is 7.0 kcal/mol more stable in energy than that of the branched form. On the other hand, in anionic systems, the branched form of the water tetramer anion is 4.0 kcal/mol more stable than that of the cyclic form. This result suggests that the dipole orientation form (the linear form of the water tetramer anion) is most stable in the water tetramer anion. 4. Discussion A. Summary. In the present study, electron capture dynamics of water tetramers have been investigated by means of a direct ab initio MD method. Two conformers of the water tetramer (branch and cyclic forms) were examined in this study. After the electron capture of the branched form, the structure of (H2O)4- was drastically changed, and the potential energy of the system was gradually stabilized as a function of time. This stabilization was caused by the increase of the dipole moment

of the neutral tetramer of water, namely, the stabilization originated from the increase of the dipole moment of the neutral water tetramer oriented toward an excess electron. In the case of the water tetramer with a cyclic form, the hydrogen bonds were not broken. Instead, only deformation from the planar to bent form took place, whereas the hydrogen bond was still kept after the structural relaxation. The energy of e-(H2O)4 was strongly stabilized in the branched form, whereas that of the cyclic form was smaller than that of the branched form. By the large deformation in the branched form, the dipole moment of neutral water cluster became larger, so that the electron was stabilized by the dipole moment. In order to confirm these phenomena, the dynamics calculation was carried out for the other sized cluster (n ) 3) (see Supporting Information). The structure of the cyclic water trimer has a trianglar structure in the neutral state. The structure of the cyclic form of the water timer was gradually changed to a linear form after the electron capture of the neutral water trimer. The dipole moment of the water trimer (neutral) increased as a function of time from 1.1 to 7.2 D. Thus, the increase of dipole moment in n ) 3 is essentially similar to that of n ) 4, suggesting that the solvation structure is varied as the dipole moment of the neutral cluster is increased. B. Model of Electron Capture of the Dangling Water. On the basis of theoretical results, we would like to propose a model of the electron capture process of a dangling water molecule interacting with a water cluster. The dangling water molecule of the branched water tetramer (Wd) is also regarded as the smallest model of the dangling water molecule on an ice surface. Schematic illustration of the model of electron capture of the dangling water molecule is given in Figure 8. If a dangling water molecule (denoted by Wd) exists in the ice surface, first, an excess electron is easily trapped by the dangling water molecule because the dangling water molecule has a large dipole moment. After electron capture of the dangling water molecule, the solvation structure around the excess electron is gradually deformed; one of the hydrogen bonds of the second water molecule is broken. This deformation takes place as the dipole moment of water molecules around the excess electron becomes larger. Acknowledgment. The author is indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. I also acknowledge partial support from a Grant-in-Aid for Scientific Research (C) from the Japan Society for the Promotion of Science (JSPS).

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