Electron detachment dynamics of Cu⁻(H₂O)_n (n = 1–3): a direct ab initio MD study

Abstract

Direct ab initio molecular dynamics (MD) has been applied to the electron detachment dynamics of Cu⁻(H₂O)_n (n = 1–3). The initial structures of Cu(H₂O)_n were generated randomly around the equilibrium point of anionic complex Cu⁻(H₂O)_n and then trajectories were run from the vertical electron detachment points of Cu⁻(H₂O)_n. It was found that three reaction channels compete with each other when n = 1: dissociation channel (the product is Cu + H₂O) and complex formation channel (the product is neutral CuH₂O complex). The complex channel is further classified to two kind of complexes: a strongly bound (I) complex and a weakly bound (II) complex. The dissociation channel occurred from an inner Franck–Condon (FC) region where the distance Cu⁻–H₂O is shorter than the equilibrium point. On the other hand, the complex formation channel occurred from the wide FC region. In case of n = 2 and 3, dissociation channels were the main products. The mechanism of the electron detachment dynamics was discussed on the basis of the theoretical results.

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1. Introduction

Determining the influence of solvation on reaction dynamics is one of the scientifically challenging problems in the field of chemical physics. There is particular interest in contrasting differences in the behavior and reactivity of ions in the gaseous phase compared to the condensed phase. The studying of clusters offers the opportunity to explore the change caused by solvation.^1–8 In particular, microsolvation of a metal ion by water molecules is clearly a key issue to determine the initial solvation process of metal ions from the metal surface in an aqueous environment.

Lineberger and co-workers investigated that microsolvation dynamics of metal–water systems of Cu⁻(H₂O)_n (n = 1 and 2) using femtosecond photodetachment-photoionization experiments.^9–11 Electron photodetachment of Cu⁻(H₂O) produces neutral Cu(H₂O) initially with the anion geometry and with an internal energy that is near the Cu–H₂O dissociation energy. Immediately after the birth of neutral Cu(H₂O), the water molecule will begin to rotate and vibrate with respect to Cu, and a fraction of the complexes will dissociate.

From a theoretical point of view, they calculated the structures of Cu(H₂O) and Cu⁻(H₂O) systems using high-level ab initio and wave-packet dynamics calculations and showed that Cu⁻(H₂O) is planar with a hydrogen atom oriented toward the copper anion. The neutral complex Cu(H₂O) has an oxygen atom oriented toward the copper atom and a shorter Cu–OH₂ separation compared to the anion.⁹ The calculated probability amplitude was in good agreement with the experiment. Thus, the decay process of Cu–H₂O following the electron detachment of Cu⁻(H₂O) and static electronic properties of Cu–H₂O system are well understood by their experiment and theoretical calculations. However, the time profile of molecular geometry was not clearly understood.

In the present study, the direct ab initio molecular dynamics (MD) method is applied to the electron detachment dynamics of Cu⁻(H₂O)_n (n = 1–3) to elucidate the dynamics features of the Cu–H₂O system. In particular, the dominant factor of the reaction channels was determined in the dynamical features. Also, the structural change of Cu–H₂O is visualized using the direct ab initio MD results. In previous papers,^12–15 we investigated the electron detachment and attachment dynamics of Na⁻(H₂O), (H₂O)_n and CF₂Cl₂ using the direct ab initio MD method. The mechanism and time scale of the reaction were determined. In this work, a similar technique was applied to the Cu⁻(H₂O)_n system.

2. Computational methods

The structures of anionic and neutral complexes, Cu⁻(H₂O)_n and Cu(H₂O)_n, were fully optimized at the MP2/6-311++G(2d,2p) level of theory. The electron detachment dynamics of Cu⁻(H₂O)_n (n = 1 and 2) were calculated by means of direct ab initio MD method at the MP2/6-311++G(2d,2p) level. The initial geometries were randomly generated around the equilibrium point of Cu⁻(H₂O)_n, and then the geometries having the energy lower than 1.0 kcal mol⁻¹ relative to the equilibrium point were selected. The trajectories for neutral system Cu(H₂O)_n were run from these selected points on the assumption of vertical electron detachment. The electronic state of the system was monitored during the simulation. We confirmed carefully that the electronic state is kept during the reaction. For Cu(H₂O)_n (n = 3), direct ab initio MD calculation was carried out at the MP2/6-311++G(d,p) level.

The equations of motion were numerically solved by the velocity Verlet algorithm method. No symmetry restriction was applied to the calculation of the energy gradients. The time step size was chosen as 0.10 fs, and a total of 10 000 or 20 000 steps were calculated for each dynamics calculation. The drift of the total energy is confirmed to be less than 10⁻³% throughout at all steps in the trajectory. The momentum of the center of mass and the angular momentum were assumed to zero. Details of the direct MD calculations are also described elsewhere.^12–15

Static ab initio and DFT calculations were carried out using Gaussian 03.¹⁶ To confirm the stability of the complexes at all stationary points, harmonic vibrational frequencies were calculated at the MP2/6-311++G(2d,2p) level of theory. All vibrational frequencies obtained were positive, indicating that all stationary points were located at local minima on the potential energy surface. The relative energies were also calculated at the MP4SDQ, CCSD, and QCISD levels of theory for comparison. The excited states of the neutral states were 2.0–3.0 eV higher than the anionic state (TD-DFT calculation). Therefore, we considered only the ground state potential energy surface of the Cu(H₂O) systems. The excitation energies of Cu(H₂O) after the electron detachment of anion system were calculated by means of symmetry adapted cluster/configuration interaction (SAC-CI) method with a 6-311++G(d,p) basis set.

3. Results

A. Structures of Cu⁻(H₂O) and CuH₂O

The structures of anionic and neutral complexes, Cu⁻(H₂O) and CuH₂O, were optimized at the MP2/6-311++G(2d,2p), MP4SDQ/6-311++G(2d,2p), CCSD/6-311++G(2d,2p), QCISD/6-311++G(2d,2p) and QCISD/6-311++G(3df,3pd) levels of theory. The geometry optimizations were started from several initial configurations of H₂O around Cu⁻ (or Cu atom). All levels of theory gave the similar geometrical parameters (all geometrical parameters are given in Table S1, ESI†). The optimized structures obtained at the MP2/6-311++G(2d,2p) level are given in Fig. 1.

Fig. 1 Optimized structures of (A) anion complex Cu⁻(H₂O), (B) neutral complex CuH₂O (I) and (C) CuH₂O (II) calculated at the MP2/6-311++G(2d,2p) level. (D) Potential energy curves for Cu–H₂O systems plotted as a function of R(Cu–O) distance.

In the case of Cu⁻(H₂O), one of the hydrogen atoms of H₂O orients to the copper anion with a hydrogen bond of H₂O. The structure is planar with a C_s symmetry. The Cu–O distance and angles (θ₁ and θ₂) in Cu⁻(H₂O) are calculated to be R₁ = R(Cu–O) = 3.508 Å, θ₁ = 100.1°, and θ₂ = 74.4°, respectively, at the QCISD/6-311++G(3df,3pd) level. This geometry is slightly distorted from a C_2v dipole orientation structure. This feature is similar to those of halogen ion–water systems, (X⁻·H₂O; X = F, Cl, and Br).¹⁷

In the case of neutral system Cu(OH₂), two complexes were found: a strongly bound complex (I) and a weak bound complex (II). In complex (I), the oxygen atom of H₂O binds directly to the copper atom. The structure of complex (I) is non-planar with a bending angle of H₂O. The Cu–OH₂ distances in complexes (I) and (II) are calculated to be R₁ = R(Cu–O) = 2.158 and 3.908 Å, respectively. It should be noted that MP2 calculation gives reasonable geometrical parameters for the Cu–H₂O system. These results are also in reasonable agreement with previous theoretical studies.^9,10

Harmonic vibrational frequencies of Cu⁻(H₂O) and CuH₂O (I and II) are calculated at the MP2/6-311++G(2d,2p) level. All frequencies are given in Table S2, ESI†. All frequencies are positive, indicating that the complexes are located on the local minima of the ground state potential energy surface. The frequencies of Cu⁻(H₂O) are calculated to be 3874 cm⁻¹ (O–H asym.), 3601 cm⁻¹ (O–H sym.), 1670 cm⁻¹ (H–O–H scission), and 538 cm⁻¹ (out of plane H–O–H bending). The neutral complex (I) showed 3917 cm⁻¹ (O–H asym.), 3794 cm⁻¹ (O–H sym.), 1649 cm⁻¹ (H–O–H scission), and 392 cm⁻¹ (out of plane H–O–H bending). The symmetric and asymmetric O–H stretching modes of H₂O are red-shifted by the interaction with both Cu⁻ and Cu. The intermolecular stretching modes for Cu⁻(H₂O) and CuH₂O (I) and (II) are calculated to be 169, 337, and 61 cm⁻¹, respectively, indicating that the curvature of intermolecular potential energy curve of complex (I) is larger than those of anion complex and complex (II). These features are in good accord with those in previous works.^9–11

The binding energies of H₂O to Cu and Cu⁻ are given in Table 1, and potential energy curves for Cu–H₂O systems are plotted in Fig. 1. For example, the binding energy (E_b) for Cu⁻ + H₂O is defined by

−E_b = E(Cu⁻(H₂O)) − [E(Cu⁻) + E(H₂O)] (1)

The binding energies of H₂O in Cu⁻(H₂O) and complexes (I and II) are calculated to be 10.3, 3.0 and 0.6 kcal mol⁻¹, respectively, at the MP2/6-311++G(2d,2p) level.

Table 1 Binding energies of Cu⁻(H₂O) and CuH₂O (I and II) (in kcal mol⁻¹) calculated at the MP2/6-311++G(2d,2p) and QCISD/6-311++G(3df,3pd) levels of theory

	Cu^−(H2O)	Cu(H2O) (I)	Cu(H2O) (II)
MP2/6-311++G(2d,2p)	10.3	3.0	0.6
MP2+ΔZPE(MP2)	9.7	2.0	0.4
QCISD/6-311++G(3df,3pd)	8.8	5.0	0.6
QCISD+ΔZPE(MP2)	8.2	4.0	0.4
Taylor et al. (ref. 10)	10.6	5.1	1.2

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After inclusion of zero point energies (ZPEs), the binding energies of H₂O are slightly changed to be 9.7 kcal mol⁻¹ in Cu⁻(H₂O), 2.0 kcal mol⁻¹ in complex (I), and 0.4 kcal mol⁻¹ in complex (II). These energies are in reasonable agreement with the values of QCISD/6-311++G(3df,3pd): namely, 8.2 kcal mol⁻¹ in Cu⁻(H₂O), 4.0 kcal mol⁻¹ in Cu(H₂O) (I), and 0.4 kcal mol⁻¹ in Cu(H₂O) (II).

B. Electron detachment dynamics of Cu⁻(H₂O)

The structure of the anion complex Cu⁻(H₂O) fluctuates around the equilibrium point due to thermal activation. The MP2 calculation of Cu⁻(H₂O) indicates that the bending angle of H₂O in Cu⁻(H₂O) vibrates in the range of ϕ = 0 ± 20° at the vibrational ground state (v = 0). Also, the intermolecular distance R(Cu–O) is distributed in the range 3.2–3.6 Å. Therefore, several initial points should be examined in the trajectory calculations. To elucidate the effects of the initial geometrical configuration on the reaction dynamics, 30 geometries were randomly selected and then the trajectories were run from the selected points, R(Cu–O) = 3.2–3.6 Å and ϕ = 0 ± 20°. The calculations showed that three reaction channels, one dissociation and two complex formation channels, were obtained as product channels.

In a direct dissociation channel, the water molecule is dissociated from Cu(H₂O) after the electron detachment of Cu⁻(H₂O). The complex channels can be further classified as strong and weak complex formations. In the strong complex formation, complex (I), expressed as Cu(OH₂) (I), is formed as a product. The other complex formation channel is a weakly bound complex formation (complex II). The reaction scheme is expressed by:

In the next section, the reaction dynamics for the dissociation channel is discussed.

C. Dissociation channel

The result for the dissociation channel is given in Fig. 2. Potential energy of Cu(H₂O) formed from the vertical electron detachment of Cu⁻(H₂O) decreases suddenly due to the structural change (points a → b). The potential energy reaches a minimum at time = 152 fs (−1.2 kcal mol⁻¹ at point b). This minimum corresponding to complex II. The Cu–O distance of Cu(H₂O) is gradually elongated from 3.200 Å (0.0 fs) to 3.978 Å (152 fs). After the minimum, the energy increases again and saturated to a limiting value (−0.75 kcal at point d). The vibrational structure appearing in the potential energy curve is caused by the H–O–H bending mode and O–H stretching modes. Time profile of R₁ = R(Cu–O) indicates strongly that Cu and H₂O separate smoothly from each other. The amplitude of the H–O–H bending mode (points c and d) is estimated to be 10°, which corresponds to a slight vibrational excited state of H₂O.

Fig. 2 Time propagations of (A) potential energy of the system and (B) Cu–O distance (R₁) after the electron detachment of Cu⁻(H₂O) in the equilibrium point. Snapshots are illustrated as insert figures. Dissociation channel was obtained as product channel. No symmetry restriction was applied to the calculation. The distances are in Å.

Snapshots of Cu(H₂O) are illustrated in Fig. 2 as insert figures (detailed snapshots at all points are given in the ESI†). At time zero (point a), the Cu–O bond distance is R(Cu–O) = 3.200 Å (point a). This distance approximately corresponds to an inner edge of the Franck–Condon (FC) region of Cu⁻(H₂O). After 152 fs, the Cu–OH₂ bond is elongated to 3.978 Å. The potential energy reaches a minimum at this point (point b). The H₂O molecule further leaves from Cu and the distance is 6.902 Å at 994 fs (point c). Finally, both H₂O and Cu are fully separated from each other. The distance is 9.189 Å at 1790 fs (point d). In the case of this trajectory, the rotational excitation of H₂O was not found. The relative translational energy between H₂O and Cu is calculated to be 0.1 kcal mol⁻¹, which is about 30% of the available energy for the reaction. Thus, the electron detachment of Cu⁻(H₂O) in the inner edge of FC gives a dissociation channel.

D. Complex formation channel (I)

A sample trajectory for the complex formation channel (I) is given in Fig. 3. After the electron detachment of Cu⁻(H₂O), the potential energy decreases slightly and is first minimized at point b (−0.6 kcal mol⁻¹ at time = 125 fs). The energy increases slightly and decreases again around point c (606 fs). At 756 fs, the energy reaches the lowest energy point (point d). The energy at the lowest point is −2.7 kcal mol⁻¹ relative to that of the starting point. After that, the energy increases suddenly at 780 fs due to the collision between Cu and H₂O. At 1063 fs, the potential energy shows −0.8 kcal mol⁻¹ (point e), and complex (I) is formed again at 1400 fs.

Fig. 3 Result of complex formation channel (I). (A) Time propagations of potential energy of the system, (B) Cu–O distance (R₁) after the electron detachment of Cu⁻(H₂O), and (C) snapshots.

Time evolution of the distance between Cu and H₂O (R₁) is plotted in Fig. 3B. The distance is 3.404 Å at the starting point (time zero). Once the distance shows a maximum at 380 fs with R₁ = 3.75 Å, and it is shortened gradually and reaches a shortest distance at 756 fs with R₁ = 2.075 Å. This result indicates that the water molecule leaves Cu after the electron detachment, but the water molecule returns and collides with the Cu atom. The collision occurs at 790 fs with R₁ = 1.98 Å. After that, the water molecule leaves from Cu, but the dissociation does not occur. Instead, the large amplitude stretching vibration between H₂O and Cu occurs continuously within complex (I).

Snapshots of Cu(H₂O) following the electron detachment Cu⁻(H₂O) are illustrated in Fig. 3 (right). At time zero, the Cu–O bond is R(Cu–O) = 3.404 Å (point a) and the dipole moment is oriented toward the Cu atom. This structure is close to that of the equilibrium point. In case of this sample trajectory, the initial bending angle is ϕ = 175°, meaning that the structure is a non-planar at time zero. After the electron detachment, the water molecule rotates a large amount. This structural change causes a decrease of potential energy. When the oxygen of H₂O orients toward the Cu atom, the potential energy reaches a minimum point. On the other hand, the energy increases if the dipole moment of H₂O orients to the Cu atom. At points c and d, the water closely approaches the Cu atom. After that, both rotation and stretching modes of H₂O occur around the Cu atom. Thus, it is clearly shown that the complex Cu(H₂O) has large amplitude motions after the electron detachment of Cu⁻(H₂O). This dynamical feature is common in all trajectories in the complex formation channel (I).

E. Complex formation channel (II)

The result for the complex formation channel (II) is given in Fig. 4. After the electron detachment of Cu⁻(H₂O), the potential energy decreases slightly and is minimized at point b (−0.65 kcal mol⁻¹ at time = 209 fs). The energy increases and decreases again around point d (1139 fs). One of the hydrogen atoms of H₂O is oriented to the Cu atom. The large amplitude complex was formed as shown in snapshots. The complex (II) is an intermediate to the dissociation product. If the excess energy is enough for dissociation and is concentrated into the Cu–O intermolecular mode, this complex can be easily dissociated to Cu + H₂O.

Fig. 4 Result of complex formation channel (II). (A) Time propagations of potential energy of the system, (B) Cu–O distance (R₁) after the electron detachment of Cu⁻(H₂O), and (C) snapshots.

F. The origin of the reaction channels

As shown in previous sections, the three reaction channels are competitive as product states. In this section, the dominant factor on the reaction channels is considered on the basis of the calculated results. The relation between initial bending angle (ϕ) and product channel is analyzed in all trajectories. The angle ϕ is defined as shown in Fig. 5, i.e. a measure of the deviation from planarity of Cu⁻(H₂O). From this analysis, it was found that the initial bending angle affects the product channel. If the complex Cu⁻(H₂O) has a near planar structure (namely, ϕ ≃ 180.0°), the trajectory calculations give the dissociation channel or complex (II). On the other hand, the trajectories with smaller bending angles (ϕ < ca. 177°) give complex channel (I). This feature is clearly shown in all trajectories.

Fig. 5 Potential energies for the complex formation channel (I). Three typical cases (ϕ = 160, 165, and 170°) are plotted as a function of time. T(ϕ) means elapsed time required for the complex formation from time zero.

Next, the elapsed time for the complex formation is analyzed in the trajectory leading to the complex channel (I). The results of trajectory calculations for three typical cases are given in Fig. 5. The initial angles are chosen as ϕ = 160, 165 and 170° for example. The elapsed time, expressed by T(ϕ), is defined as a time from the starting point (time zero) to minimum energy point. As clearly seen in Fig. 5, T(ϕ) is strongly dependent on the initial angle α: namely, T(170) = 1125 fs, T(165) = 936 fs and T(160) = 756 fs. This result strongly suggests that the increase of bending angle enhances the complex formation. Thus, it is found that the initial configuration of Cu⁻(H₂O) strongly affects the reaction channels.

G. Time evolution of excitation energies

The present calculations showed that the three reaction channels compete after the electron detachment of the anion system. Transient absorption spectra of Cu(H₂O) for complex (I) formation channel are given in Fig. 6. The first band with strong intensity corresponds to the ²S → ²P electronic transition of the Cu atom in CuH₂O complex. The directions of spectrum shift are slightly different from each other. In the case of isolated Cu atom, the electronic transition for the ²S → ²P band is observed at 3.81 eV. The present calculation gives 4.02 eV, which is in reasonable agreement with the experiment. Fig. 6 shows that the peak appears at E_ex = 4.03 eV at time zero. This band is gradually red-shifted as a function of time. At final stage, the peak is appeared at E_ex = 3.10 eV (756 fs), which corresponds to the absorption spectrum of Cu(OH₂) (I) complex. Thus, the ²S → ²P band is largely red-shifted in complex formation channel (I). On the other hand, the spectrum shifts were negligibly small in both the dissociation channel and complex formation channel (II).

Fig. 6 Transient absorption spectra of Cu(H₂O) (complex formation channel (I)). Excitation energies and intensities were calculated at the TDDFT-B3LYP/6-311++G(d,p) level.

Fig. 7 shows absorption spectra of Cu atom, Cu(H₂O) complex (I), and complex (II). Also, the absorption spectrum of Cu(H₂O) at the vertical electron detachment point is given. The peak of complex (II) is close to that of free Cu atom. Also, the vertical point has the peak at a similar position. The peak of complex (I) is significantly red-shifted from that of the Cu atom. This result indicates that the complex formation channel (I) is only observed as a large spectrum shift.

Fig. 7 Absorption spectra of Cu atom, Cu(H₂O) (complex (I)), Cu(H₂O) (complex (II)), and Cu(H₂O) at teh vertical excitation point. Excitation energies and intensities were calculated at the TDDFT-B3LYP/6-311++G(d,p) level.

Thus, the present study implies that measurement of spectrum shift gives an assignment of reaction channels. Muntean et al. observed the spectrum shift by the hydration: Cu(²S → ²P transition) is remarkably shifted by only one water molecule. This result is in accord with previous experiments.^9–11

H. Potential energy surfaces of Cu–H₂O system and reaction model

As shown in section 3F, it is found that the bending angle of H₂O (α and ϕ) relative to Cu strongly dominates the reaction channels. Two dimensional potential energy surfaces (PESs) plotted as functions of R₁ and α are given in Fig. 8. Fig. 8A and B show PESs for Cu⁻(H₂O) and CuH₂O systems, respectively. On the PES of Cu⁻(H₂O), the energy minimum dotted corresponds to the equilibrium point of Cu⁻(H₂O). The shaded region around the minimum point indicates the FC region projected onto the 2D PES at the vibrational ground state of Cu⁻(H₂O). These two modes are flexible and have a wide FC region. Therefore, several geometrical configurations are involved in the electron detachment dynamics.

Fig. 8 Potential energy surfaces for (A) anionic complex Cu⁻(H₂O) and (B) neutral complex Cu(H₂O) plotted as functions of Cu–O distance (R₁) and bending angle α. The values are calculated at the MP2/6-311++G(d,p) level. Shaded region schematically indicates Franck–Condon region of Cu⁻(H₂O). Paths a and b schematically indicate reaction paths for dissociation and complex formation channels, respectively. The values are drawn in kcal mol⁻¹.

The energy minimum corresponding to the equilibrium point of Cu(OH₂) is located at R₁ = 2.25 Å and α = 130° in Fig. 8B. However, the minimum is very shallow. The shaded region indicates the FC region from the electron detachment of Cu⁻(H₂O). The reaction paths a and b show schematic illustrations of typical trajectories leading to dissociation and complex formation channels, respectively. The trajectory for path a starts from the inner FC region (R < R₁) and near planar structure (ϕ ≈ 0°), and path b starts from a point with a large bending angle (α). The path a leads to a dissociation channel, whereas the path b reaches the Cu(OH₂) complex (I) after the electron detachment of Cu⁻(H₂O). Thus, the structural configuration before electron detachment correlates strongly with product reaction channels.

I. Electron detachment dynamics of Cu⁻(H₂O)₂

In this section, the direct ab initio MD method is extended to Cu⁻(H₂O)_n (n = 2). In the optimized structure of Cu⁻(H₂O)₂, two protons of water dimer orient to the Cu⁻ ion with bond distances of 3.29 and 3.68 Å. The bond distance of the hydrogen bond in the water dimer is 2.05 Å as an O–OH distance.

Rathbone et al. suggested from the photoelectron image and spectrum of Cu⁻(H₂O)₂ that two water molecules make a hydrogen bond around Cu⁻, and water molecules are not separated each other. The present calculation strongly supports their experiment.¹¹

In the direct ab initio MD calculation, a total of 20 trajectories were run around the equilibrium structure of Cu(H₂O)₂. Four channels were found as product channels (i.e., dissociation, partial dissociation, and complex channels I and II). The reaction channels are summarized in Table 2. The main product is a direct dissociation channel: [Cu(H₂O)₂]_ver → Cu + (H₂O)₂. The next channel is a partial dissociation channel where one of the water molecules (W₁) is preferentially dissociated: [Cu(H₂O)₂]_ver → Cu(H₂O) + H₂O. The other channels are minor. The time evolution of potential energy and snapshots of Cu(H₂O)₂ for the direct dissociation channel are given in Fig. 9. After the detachment, the potential energy largely decreases and is minimized at 50 fs (−4.5 kcal mol⁻¹). The magnitude of energy change with n = 2 is larger than that of n = 1 due to the large solvation energy when n = 2. The water molecule (W₁) is rapidly rotated and a proton of W₁ orients to the opposite direction from the Cu atom. At 280 fs, the water dimer is located in 4.30 Å (W₁) and 3.86 Å (W₂), indicating that the water dimer leaves gradually from the Cu atom. At 500 fs, the water dimer is significantly far from the Cu atom (5.04 and 4.47 Å). This result indicates that the water dimer leaves directly from the Cu atom after the electron detachment in n = 2.

Fig. 9 Time evolution of potential energy of the Cu(H₂O)_n (n = 2) system (direct dissociation channel) and snapshots for electron detachment of Cu⁻(H₂O)₂ obtained by direct ab initio MD calculation at the MP2/6-311++G(2d,2p) level. Values indicate bond distances between molecules in Å. Dissociation channel is obtained as product channel.

Table 2 Reaction channels obtained by the direct ab initio MD calculation of Cu(H₂O)_n (n = 2)

Channel	Product	Number of trajectory
Dissociation	Cu + (H2O)2	12
Partial dissociation	Cu(H2O) + H2O	4
Complex (I)	Cu(H2O)2	2
Complex (II)	Cu(HOH)(H2O)	2

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The time evolution of potential energy and snapshots of Cu(H₂O)₂ for the partial dissociation channel are given in Fig. S3, ESI.† In this channel, one of the water molecules (W₂) is preferentially dissociated. Atomic forces on the oxygen atoms of W₂ and W₁ at the vertical electron detachment point [Cu(H₂O)₂]_ver are calculated to be 19.7 and 12.2 mhartree bohr⁻¹, respectively. The atomic force on W₂ is significantly larger than that on W₁. Therefore, the water molecule (W₂) is preferentially dissociated from the [Cu(H₂O)₂]_ver.

At time zero, the water dimer orients to the Cu atom. After the electron detachment, the water molecule leaves rapidly from the Cu atom and the water molecule (W₁) is rotated. At 700 fs, the oxygen atom of W₁ orients toward the Cu atom and Cu–O strong bond is formed. The potential energy reaches a minimum point corresponding to the Cu–OH₂ (W₁) complex. The water dimer is still remained at this time. The excess energy is dissipated into the translational mode to W₂, so that the water molecule (W₂) can leave from the Cu–OH₂ system. The final product is [Cu(H₂O)₂]_ver → Cu–OH₂ + H₂O in the partial dissociation channel.

J. Electron detachment dynamics of Cu⁻(H₂O)₃

In the optimized structure of n = 3, the water trimer interacts with the Cu⁻ ion (Fig. 10). Three protons of the water trimer orient to the Cu⁻ ion. The distances of proton–Cu⁻ are ca. 2.60 Å, and three water molecules interact with the Cu⁻ ion.

Fig. 10 Time evolution of potential energy of the Cu(H₂O)_n (n = 3) system (direct dissociation channel) and snapshots for electron detachment of Cu⁻(H₂O)₂ obtained by direct ab initio MD calculation at the MP2/6-311++G(d,p) level. Values indicate bond distances between molecules in Å. The dissociation channel is obtained as product channel.

At time zero, the protons of water trimer (W₁–W₃) orient to the Cu atom. After the electron detachment, the protons rotate in the opposite direction to the Cu atom due to a repulsive interaction. The distance of water trimer to the Cu atom is slightly elongated from 3.42 Å (time = 0.0 fs) to 3.80 Å (104 fs). After the rotation of protons, the excess energy is mainly transferred into the translational mode between Cu atom and the water trimer, so that the water trimer leaves rapidly from the Cu atom. The Cu–O distances at 104 and 277 fs are 3.80 and 5.17 Å, respectively. At 806 fs, the water trimer is fully separated from the Cu atom (10.23 Å). Thus, the electron detachment of Cu⁻(H₂O)₃ gives a dissociation channel.

4. Discussion

A. Comparison with previous studies

In the present study, the electron detachment dynamics of Cu⁻(H₂O)_n has been investigated by means of direct ab initio MD method. The dynamics calculation for n = 1 showed that three reaction channels (dissociation and two complex formation channels) are competitive with each other after the electron detachment of Cu⁻(H₂O). It was also found that the initial geometrical configuration of Cu⁻(H₂O) affects strongly to the reaction channels. In particular, the bending angle of H₂O relative to the Cu⁻ ion in Cu⁻H₂O complex strongly couples with the formation of complex channel (complex I). If the electron detachment occurs from near the equilibrium point (C_s and near C_s, and α = 0°), the dissociation channel via region of channel (II) is dominant. The time scale of complex (II) formation is about 100–300 fs. The dissociation channel occurs via the region of complex (II). On the other hand, a deformed structure (α > ca. 3°) causes complex formation channel (I). Time scales for the complex formation are roughly estimated to be 500–1000 fs, and it decreases with increasing bending angle (α). Thus, the present calculation clearly visualizes the electron detachment dynamics of Cu⁻(H₂O) and selectivity of reaction channels.

The electron detachment dynamics of Cu⁻(H₂O) was experimentally investigated by Lineberger and co-workers using femtosecond photodetachment-photoionization spectroscopy.^9–11 They observed both complex and dissociation channels after the electron detachment of Cu⁻(H₂O). The present calculation strongly supports the experiments.^9–11

For n = 2, Taylor et al. investigated electron photodetachment dynamics of Cu⁻(H₂O)₂.¹⁸ It was found that the parent molecule from the initial ion Cu⁻(H₂O)₂ is not detected above a back-ground signal. On the other hand, Cu and Cu(H₂O) were found as products. The Cu atom is formed from direct dissociation of Cu(H₂O)₂ and via partial dissociation of Cu(H₂O). The partial dissociation occurs as [Cu(H₂O)₂]_ver → Cu–OH₂ (complex I) + H₂O, and then the complex I dissociates into Cu + H₂O. The present calculations found that the partial dissociation takes place after the detachment. This result is in good agreement with the experiments.

For n = 3, unfortunately, there is no experiment. The present calculation predicts that the main reaction channel is direct dissociation to form Cu + water trimer. As a result of the present calculations, it is predicted for n > 3 that the branching ratio of the complex formation channels becomes smaller because the repulsive interaction between Cu and (H₂O)_n at the vertical point becomes stronger in a larger system. This is due to the fact that the number of protons increases in the larger system.

For n = 6, we calculated the optimized structure of Cu⁻(H₂O)_n (n = 6), and the structure is given in the ESI.† In Cu⁻(H₂O)₆, two “cyclic water trimer”s interact with Cu⁻ from up and down positions. On the basis of present results, this form will give the product Cu + (water trimer) + (water trimer) after the electron photodetachment from Cu⁻(H₂O)₆.

In our previous paper,¹² we investigated the reaction dynamics of Na(H₂O) following electron detachment from Na⁻(H₂O) in a zero-point vibrational state. The photodetachment-photoionization spectra using 4.3–5.3 eV photons were theoretically predicted by the calculation. In the previous work, we considered only one solvent and calculated photodetachment photoionization spectra of Na(H₂O). On the other hand, in the present study, the reaction mechanism of Cu(H₂O)_n (n = 1–3) following the electron detachment was discussed in detail. The purpose of this study is much different from that of previous work.

The electronic non-adiabatic effect including spin–orbit coupling is frequently important in heavy atom system.^19,20 In the present study, we did not consider electronic non-adiabatic effects in the dynamics calculation. The Cu atom has a low-lying electronic excited state (²D) near ground state (²S). Therefore, more accurate dynamics including non-adiabatic effects and spin–orbit coupling may be needed to obtain a more detailed dynamic feature.

B. Temperature effect on the reaction channels

Muntean et al. reported temperature effects on the reaction channels in the electron detachment dynamics of Cu⁻(H₂O).⁹ A large temperature effect on the product channel was found. They showed that increase of temperature enhances the complex formation. The present calculation strongly supports their observation. Here, we propose a model of the temperature effect on the product channels. At low temperature, the initial complex Cu⁻(H₂O) vibrates slightly around the equilibrium point. The deformation from the planar structure is significantly small. The electron detachment from the structure leads to the dissociation channel. On the other hand, the structure of Cu⁻(H₂O) is deformed largely from the planar structure at high temperature. The bending mode (deformation from the planar structure) is excited due to the low frequency mode. This excitation enhances the complex (I) formation in the electron detachment of Cu⁻(H₂O). This is an origin of enhancement of complex (I) and temperature dependence. Thus, the present calculations qualitatively support their observation.

Acknowledgements

The author acknowledges a partial support from a Grant-in-Aid from JSPS (Project No. 2455000102).

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Footnote

† Electronic Supplementary Information (ESI) available. See DOI: 10.1039/c2ra20907a

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