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Nov 27, 2013 - Department of Chemistry, Fu-Jen Catholic University, Xinzhuang, New Taipei City 24205, Taiwan, ROC. ABSTRACT: The Born−Oppenheimer ...
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Effects of Iodine on the Relaxation Dynamics of a Photoexcited I−(H2O)4 Cluster Wen-Shyan Sheu* and Mong-Feng Chiou Department of Chemistry, Fu-Jen Catholic University, Xinzhuang, New Taipei City 24205, Taiwan, ROC ABSTRACT: The Born−Oppenheimer molecular dynamics are used to examine the relaxation dynamics of the charge-transfer-to-solvent (CTTS) photoexcited electron in I−(H2O)4. The dynamics are initiated from the C1′ cluster configuration, which contains a dangling water molecule. The iodine atom is found to exert a repulsive force on the photoexcited electron at the beginning but an attractive force at later times of the simulation. This dual repulsion-and-attraction role of the iodine atom is found to be dependent on the ratio of the iodine−electron distance to the radius of gyration of the excited electron, d/r. In the region of d/r < ∼0.8, the iodine exerts an exclusion-repulsion force on the excited electron. Conversely, for values of d/r > ∼1.0, the iodine can exert an attractive force on the excited electron due to the induced dipole moment of iodine. However, at large iodine−electron distances, the iodine−electron interaction becomes very weak, and as a result, this attractive force is expected to fade away. Due to the heavy mass of the iodine atom, the evolution of the iodine−electron distance is driven by the motion of solvent molecules and not iodine itself. The dangling water molecules and the dipolar field of water molecules are also important in the solvent dynamics. The influence of temperature on the iodine effects and the experimental implications of the findings are also discussed.

1. INTRODUCTION The study on the charge-transfer-to-solvent (CTTS) excited states of simple anions in solvents is an important means for exploring ion−solvent, solvent−solvent, and electron−solvent interactions.1,2 This is because the CTTS excited states are supported by the polar fields of the solvent molecules and are not observed for the bare anions in the gas phase. An excited electron in the CTTS states was found to gradually transfer from its parent core to solvent molecules, with the resulting formation of a solvated electron. Because of the electron transfer, the ion−dipole interactions, which once held the ion and solvent molecules together in the ground state, disappear in the excited states. Consequently, significant solvent reorganization is needed to accommodate an excited electron in a solvent. This relaxation process provides a great opportunity to explore solvent dynamics.2−8 In addition to studies in bulk phases, interest has also developed in the cluster counterparts of the CTTS states to address their spectroscopic and dynamic properties. In the case of clusters, only limited numbers of solvent molecules are present, which makes it convenient to study molecular interactions at the molecular level. Among most studied cluster systems are iodide water clusters, I−(H2O)n. In 1996, Johnson and co-workers observed that the CTTS precursor peaks increased to ∼4.5 eV for n = 4 from ∼3.5 eV for n = 1, demonstrating the important collective role of water molecules in the absorption.9 The dynamics for the CTTS excited states of iodide water clusters, denoted as [I−(H2O)n]*, were also reported both experimentally and theoretically.10 Neumark et al. studied the dynamics of the CTTS states of I−(H2O)n and I−(D2O)n using time-resolved photoelectron imaging.10−13 Electron autode© 2013 American Chemical Society

tachment was reported to be the primary decay mechanism for small clusters.11,12 For n ≥ 5, the vertical detachment energy (VDE) of the excited electron was found to drop to the minimum value VDEmin before increasing several hundred meV to its maximum value VDEmax. At longer times, another VDE dropped by ∼50 meV to VDE(∞), which was attributed to the ejection of the neutral iodine from the cluster.12 However, the initial VDE drop was not observed for the case of n = 3, 4 clusters. In addition, they reported that the VDEmin values were similar to those of the water cluster anions with configurations called isomer II,12 in which the excess electrons are more loosely bound than those of the water cluster anions in the configuration of isomer I.13,14 Several theoretical simulations of the relaxation dynamics of [I−(H2O)n]* were also reported.15−20 Takayanagi et al.17,18 and Kołaski et al.16,19 reported that as the excited electron moved to water clusters, the iodide became neutralized within ∼100 fs after photoexcitation, and the newly formed neutral iodine played nearly no role in the subsequent solvent dynamics. A study by Mak et al. on dynamics simulations of [I−(H2O)5]* and the corresponding water cluster anion, e−(H2O)5, showed that the iodine core was important for initiating solvent reorganization in [I−(H2O)5]* relaxation dynamics at earlier times, but its influence on the cluster VDE was negligible after ∼200 fs.20 Moreover, by comparing the relaxation dynamics of [I−(H2O)6]* starting from two different initial configurations, namely, Bf and Bd, Takayanagi et al. found that the initial cluster configuration appeared to play a crucial role in the Received: June 20, 2013 Revised: October 29, 2013 Published: November 27, 2013 13946

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CTTS relaxation paths as well.17,18 In the Bf cluster configuration, there exists a “dangling water molecule”, which is defined as a water molecule with two dangling hydrogen atoms that do not participate in hydrogen bond formation with other water molecules. The cluster was found to possess a larger dipole moment and, hence, a larger VDE in the relaxation course for the dynamics initiated at the Bf-type cluster configuration compared to that initiated at the Bd-type cluster configuration, which contains no dangling water molecule.17,18 In addition, unique to the Bf initial configuration, the structure of the water molecules became chain-like at the later stage of the simulation, and its excited electron was mainly distributed over the two dangling hydrogens of the dangling water molecule,17 similar to the manner in which excess electrons are bound to the AA-type waters in water cluster anions, as reported by Johnson et al.21−26 Similar results were also reported for the relaxation of [I−(H2O)5]* starting from the Y41 initial configuration.19,20 These results were consistent with the recent conclusion drawn by Chiou and Sheu that a diffuse excess electron is more likely to be bound to both dangling hydrogens of a dangling water molecule.27 Other theoretical treatments have also been reported in the literature.28,29 In this paper, we report on the simulation of the relaxation of the CTTS excited states via molecular dynamics (MD) for n = 4 starting from the C1′ initial configuration. We report on a detailed analysis of the roles that the neutral iodine and other related properties play in the [I−(H2O)4]* relaxation process. The C1′ initial configuration was chosen mainly for two reasons. First, it contains a dangling water molecule (cf. Scheme 1) that is found in many low-energy configurations of n ≥ 5

configuration for the n = 4 cluster.30 A relaxation dynamics simulation starting from the C4 initial configuration was previously reported.18,19 Upon the photoexcitation of the C4 I−(H2O)4 cluster, its four-water ring structure rapidly became flat during the first ∼50 fs, resulting in a rapid drop in the cluster dipole moment to ∼0.0 D,18,19 which is too weak to bind the excited electron,31 and hence, electron autodetachment may occur within a short time. While this electron autodetachment may account for the predominating early photoelectrons generated for the n = 4 cluster in the experiments reported by Neumark et al.,11,12 it cannot satisfactorily explain the remaining VDE relaxation still found for this cluster.11,12 By considering the Boltzmann factor, C1′ is likely to coexist with C4 in an amount of about ∼9.4% at the presumably experimental conditions of ∼200 K,32 and the CTTS relaxation from this configuration may account for the experimental VDE relaxation found for the n = 4 cluster.

2. COMPUTATIONAL METHODS Several calculation methods and basis sets have been used to describe the CTTS relaxation dynamics of [I−(H2O)n]*.15−20 In the present study, Christiansen’s effective core potential was used to replace the core electrons of the iodide anion,33−36 while the outer valence electrons were described by triple-ζ basis functions,37 augmented by two sets of sp orbitals with exponents of 0.00736 and 0.001472. The MP2 result of the IP for I− is 3.02 eV,36 which is consistent with the experimental value of 3.06 eV for the 2P3/2 state of the iodine atom. In order to accurately describe the diffuse CTTS excited electron, sufficient basis sets are needed to avoid allowing the electron to appear in inappropriate locations.16,19 Here, 6-31++G(d,p) + diff(sp,2s) basis sets were applied to all water molecules. The extra basis sets diff(sp,2s) were formed by adding one additional sp orbital to O atoms and two additional s orbitals to H atoms, which were needed to describe the excited electron transferred to water molecules. The exponents for the extra sp orbitals were 1/5 of the outmost exponent value of the oxygen basis set, while those for the two extra s orbitals were 1/5 and 1/25 of the outmost exponent value of the hydrogen basis set. The basis sets adopted here were comparable or larger than those used in previous studies.15−20 Before starting the relaxation MD of the CTTS excited state, the geometric structures of the initial C1′ configuration of I−(H2O)4 were first optimized by the B3LYP/6-31++G(d,p) + diff(sp,2s) method. Scheme 1 shows the optimized cluster structure and symbols for atoms. In this configuration, there exists a dangling water molecule with the rest of the water molecules forming a ring via hydrogen bonding interactions. The oxygen atom, Od, of the dangling water molecule also forms a hydrogen bond with one of hydrogen atoms, Hw1, of a water molecule in the ring. Table 1 lists various optimal geometric parameters. Our optimized cluster geometries were very close to those reported by Kim et al.30 Once an electron in I−(H2O)n is excited by light, it would be expected to jump to singlet CTTS excited states because of selection rules. However, simulating the relaxation dynamics from singlet excited states is very time-consuming and computer-source-demanding. Fortunately, previous results have shown that the lowest singlet CTTS excited state has a similar potential energy surface28 and dynamical trend17,18 very close to those of the lowest triplet CTTS (LTCTTS) state. More recently, by including spin−orbit coupling in the calculation, Peslherbe et al. also showed that the LTCTTS

Scheme 1. Geometric Structure of the C1′ Configuration for I−(H2O)4a

“d” in the scheme denotes the dangling water molecule, and “r” denotes water molecules in the ring. Other symbols for atoms are also defined.

a

clusters.30 However, because there are fewer water molecules in the C1′ I−(H2O)4 cluster, the potential exists for discovering important features of the CTTS dynamics in a shorter simulation time. Therefore, the results obtained from a study of the CTTS dynamics of the C1′ [I−(H2O)4]* cluster may be useful in terms of addressing the dynamics for larger clusters that also contain dangling water molecules. For the other reason, the dynamics initiated for the C1′ configuration may account for the experimentally observed VDE relaxation for the n = 4 cluster.11,12 It should be noted that the C1′ configuration is higher in energy by ∼0.9 kcal/mol than the most stable C4 13947

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obtained by replacing the iodine atom in the cluster with a ghost atom (Bq) without changing the water geometry. This calculation was also done by the CASPT2(3,6) method with the same 6-31++G(d,p) + diff(sp,2s) basis sets for water molecules. Although the iodine atom was absent in these calculations, the basis sets used for describing the iodine atom were still retained to avoid the artificial basis set superposition error (BSSE). All calculations reported in this work were performed using the GAUSSIAN 03 package.39

Table 1. Optimized Geometric Parameters for the C1′ Configuration of the I−(H2O)4 Cluster Calculated at the B3LYP/6-31++G(d,p) + diff(sp,2s) Level of Theorya d(I−Or1) 4.62 d(Od−Hd1) 0.985

d(I−Or2)

d(I−Or3)

d(I−Od)

3.82 3.84 3.59 d(Od−Hd2) d(Or−Hi)av 0.966

0.975

d(I−Hd1)

d(I−Hi)av

2.63 d(Or−Hw)av

2.95 ∠HOHav

0.978

103.8

a

Hi: hydrogen atoms in the ring, which point to the iodine anion; Hw: hydrogen atoms in the ring, which form hydrogen bonds with other water molecules. The subscript “av” denotes an average quantity. Distances are in angstroms, and angles are in degrees.

3. RESULTS AND DISCUSSION The time evolution for the kinetic energy and the potential energy of [I−(H2O)4]* are shown in Figure 1.

was a good approximation to the lowest singlet CTTS state.38 Therefore, the LTCTTS state was used here as the initial CTTS excited state. In addition, the B3LYP DFT method was used to obtain the electronic configuration. The applicability of the B3LYP method was previously reported.18 Our VDE for the LTCTTS state in the C1′ configuration was 0.09 eV. Here, the VDE was obtained by calculating the total electronic energy difference between the anion cluster in the state of interest and the corresponding neutral cluster at the geometry of the anion cluster. This method was also tested with a larger basis set, 631++G(d,p) + diff(2sp,2s); the VDE obtained for the LTCTTS state was 0.10 eV, close to that obtained when the 6-31+ +G(d,p) + diff(sp,2s) basis set was used. Moreover, the VDE was also calculated using CASPT2(4,6) and CASPT2(6,6) methods. Here, the (4,6) active space consists of the four lowest unoccupied orbitals and two highest occupied 5p orbitals of iodine, while the (6,6) active space consists of the three lowest unoccupied orbitals and three occupied 5p orbitals of iodine. The VDEs obtained by the CASPT2 methods were all 0.08 eV (cf. Table 2). These results indicate the validity of the B3LYP method using the 6-31++G(d,p) + diff(sp,2s) basis set in the present calculation. Table 2. VDEs of the Lowest Triplet State of I−(H2O)4 Obtained by Various Levels of Theory and Basis Setsa

6-31++G(d,p) + diff(sp,2s) 6-31++G(d,p) + diff(2sp,2s)

B3LYP

MP2

CASPT2(4, 6)

CASPT2(6, 6)

0.09 0.10

0.09 0.09

0.08 0.08

0.08 0.08

Figure 1. The time evolution of kinetic and potential energies for the relaxation dynamics of [I−(H2O)4]* starting from the C1′ initial configuration. The potential energy is plotted relative to that at the initial time.

a The geometric structure is the C1′ configuration optimized at the B3LYP/6-31++G(d,p) + diff(sp,2s) level of theory. Energies are in eV.

These two energies are mirror images of each other, reflecting the energy conservation in the relaxation dynamics. As the cluster becomes more stable in potential energy with time, its molecules are more energetic and have more kinetic energy. This transformation of potential energy to kinetic energy provides the energy for the cluster configuration evolution after photoexcitation. The evolution for the VDE of the CTTS excited electron of [I−(H2O)4]* is shown in Figure 2a. In addition, snapshots of the [I−(H2O)4]* geometries and the surface plots of the singly occupied molecular orbital (SOMO) occupied by the excited electron at several selected times in the relaxation trajectory are also shown in Figure 3. The VDE shows an oscillatory behavior. It has a dip of ∼0.07 eV during the initial ∼170 fs, but a large increase in VDE (about ∼0.3 eV) occurs after ∼350 fs. This VDE time variation is similar to that for the relaxation of the photoexcited [I−(H2O)5]* initiated at the Y41 optimized ground-state geometry with finite initial velocities reported previously.19,20

The simulation of the relaxation dynamics was carried out using the Born−Oppenheimer molecular dynamics (BOMD) method as implemented in the GAUSSIAN 03 package, which was also employed by Takayanagi et al.17,18 The time step was within ∼0.1 and ∼0.8 fs, depending mainly on the diffuseness of the excited electron. All atoms were initially at rest. After completion of the dynamics simulation, the single-point calculation by the CASPT2(4,6) method was also done for the LTCTTS states of selected cluster configurations in the trajectory so that a more accurate time evolution of the VDE and other properties of the CTTS excited electron were obtained for analysis. To explore the effects of the iodine atom on the VDE and other properties of [I−(H2O)n]*, we also performed a singlepoint calculation for the lowest electronic state of the corresponding water cluster anion, e−(H2O)n, which was 13948

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diffuse set of diff(2sp,4s) is used, all of the VDE values become positive. To explore the effect of the iodine atom on the relaxation dynamics, the VDE of the excess electron for the corresponding water cluster anion e−(H2O)4 computed at the water cluster configurations of I−(H2O)4 is also shown in Figure 2a. The effect of iodine on the excited electron is clearly reflected by the difference between the VDE of the excess electron in e−(H2O)4 and that of the excited electron in [I−(H2O)4]*, defined as δVDE ≡ (the excess electron VDE of e−(H2O)4) − (the excited electron VDE of [I−(H2O)4]*). As shown in Figure 2a, δVDE is large (∼0.18 eV) at the beginning but rapidly decays in the first 50 fs. This result is similar to the case of [I−(H2O)5]* reported by Peslherbe et al.20 The higher initial δVDE was rationalized by the exclusion repulsion between the excited electron and the electrons of the neutral iodine,20 as originally proposed by Chen and Sheu.36 When the excited electron moves away from the neutral iodine (cf. Figure 3), the exclusion repulsion becomes smaller and so is δVDE. However, after ∼350 fs, the sign of δVDE changes and becomes negative, with a magnitude up to ∼0.1 eV. This indicates that the neutral iodine exerts an attractive force on the excited electron after ∼350 fs, so that the electron is stabilized by the iodine atom. To verify that the appearance of the attractive force is not due to the replacement of the singlet CTTS wave function by the LTCTTS wave function in the VDE calculation, we also calculated the VDE for the lowest singlet CTTS excited electron of [I−(H2O)4]* at several selected configurations in the relaxation trajectory. The results showed that the difference in VDE between the singlet excited state and the triplet state was within ∼0.02 eV, which confirms the existence of the attractive force of the iodine atom on the excited electron at the later period of the simulation. These results show that the iodine atom plays a dual role on the excited electron. It exerts a repulsive force on the excited electron at the beginning but an attractive force at later times of the simulation. In order to investigate how the excited electron is stabilized by the neutral iodine at later times, the evolution of the dipole moment of the corresponding neutral cluster, I(H2O)4, calculated at the geometry of [I−(H2O)4]*, is plotted in Figure 2b. In addition, the dipole moment of (H2O)4, obtained by extracting the neutral iodine from I(H2O)4, is also shown in the figure. As shown in Figure 2b, the dipole moments of the two clusters are almost the same during ∼30 < t < ∼350 fs, indicating that the presence of the iodine atom has a slight influence on the cluster dipole moment in this period. In addition, large dipole moment dips (>3.0 D) are seen during the initial ∼110 fs for both clusters, showing that the water molecules rapidly orient their dipole moments in different directions (cf. snapshots at 50 and 100 fs in Figure 3), so that the total dipole moment is reduced. However, at an earlier time (t < ∼30 fs) or a later time (t > ∼350 fs), it is noticeable that the dipole moment of I(H2O)4 is larger than that of (H2O)4 by ∼0.6 D, indicating that the presence of the neutral iodine helps to increase the dipole moment of the I(H2O)4 complex during these two periods. This increase in dipole moment, which is apparently due to the polarization of the iodine by water molecules,36 contributes to the further stabilization of the excited electron at t > ∼350 fs in the simulation. Nevertheless, no VDE enhancement is observed at t < ∼30 fs, even though the dipole moment also increases in the presence of the iodine. This is because the attractive force is canceled out by the strong

Figure 2. Evolution of the VDE for the excited electron as a function of time and the cluster dipole moment along the relaxation trajectory of the C1′ [I−(H2O)4]* cluster. The VDE and dipole moment of the corresponding water cluster anion e−(H2O)4, obtained by extracting the iodine atom, are also shown.

Figure 3. Snapshots of selected [I−(H2O)4]* geometries and surface plots of excited electron distributions along the relaxation trajectory initiated at the C1′ configuration. The values of the isosurfaces are 0.004 and 0.005 for configurations at 50 and 100 fs, respectively, and 0.008 for the remaining configurations.

However, the relaxation for the C1′ [I−(H2O)4]* cluster is faster in time than that for the Y41 [I−(H2O)5]* cluster reported by Peslherbe et al., even though there are no initial velocities in the present case. The faster relaxation time for the initial C1′ configuration can be attributed to a larger strain of the three-member ring in the C1′ configuration, compared with that of the four-member ring in the Y41 configuration. We noted that the VDEs at around t = 50 fs have small negative values. This artifact is attributed to the fact that the extra diffuse basis set of diff(sp,2s) is still insufficient to describe the very diffuse excited electron in this period because the cluster dipole moment is only slightly greater than 2.0 D. When a larger extra 13949

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From the above discussion, the iodine appears to play a dual repulsion-and-attraction role on the excited electron, and this effect is dependent on the iodine−electron distance. To further establish the criteria for the distance in this dual role, in Figure 5a, δVDE is plotted against the ratio of d(Bq−e−) to the radius of

exclusion repulsion between the excited electron and the electrons of the neutral iodine, as discussed above. The exclusion repulsion on the excited electron from the neutral iodine would be expected to be larger when the distance between them is closer. This effect can be more clearly seen in Figure 4, which shows the time evolution of the distance between the iodine and the center of mass (COM) of the excess electron of the corresponding e−(H2O)4, denoted as d(Bq−e−).

Figure 4. Time evolution of d(Bq−e−), the distance between the ghost atom Bq and the COM of the excess electron for water cluster anion e−(H2O)4. The water configurations are taken from the relaxation trajectory of [I−(H2O)4]*. d(Bq−e−) represents the distance between the iodine atom and the COM of the excited electron in [I−(H2O)4]* before the iodine−electron interaction is considered.

Here, the position of the ghost atom Bq in e−(H2O)4 is the location of the iodine atom before being extracted. The e−(H2O)4, instead of [I−(H2O)4]*, was employed to calculate the location of the excited electron because the COM of the excess electron of e−(H2O)4 is more representative of the true location of the electron before the exclusion repulsion from the neutral iodine is exerted on the excited electron. The d(Bq−e−) was found to increase swiftly and to have a larger oscillatory behavior at earlier times. As d(Bq−e−) rapidly increases by more than 2 Å in the first ∼50 fs, δVDE also promptly deceases (cf. Figure 2a) because of the smaller exclusion repulsion due to the decreasing overlap of the excited electron and the electrons of the neutral iodine. However, this rapid increase in d(Bq−e−) cannot be attributed to the relatively slow movement of the iodine and oxygen atoms because of their heavy masses. Instead, it is due to the motion of two dangling hydrogen atoms of the dangling water molecule. It was previously shown that an electron was bound to both OH bonds of a water molecule if the electron distribution was diffuse.27 Therefore, the diffuse excited electron is held by the two OH bonds of the dangling water molecule in the cluster, and the rapid increase in d(Bq− e−) in the first ∼50 fs is mainly due to the fact that the molecular axis of the dangling water molecule rotates away from the iodine (cf. Figure 3). After d(Bq−e−) reaches the first maximum, it decreases to a minimum at time t ≈ 150 fs, where a local maximum value of δVDE ≈ 0.05 eV is located, indicating that the exclusion repulsion reappears but is weaker this time. As the distance between the excited electron and the iodine increases, the fluctuation of d(Bq−e−) shows less influence on δVDE because the exclusion repulsion is weak. At t > ∼350 fs, where d(Bq−e−) is greater than 5.0 Å, the exclusion repulsion is insignificant. Instead, an attractive force due to the induced dipole moment of the iodine atom takes place, which stabilizes the excited electron.

Figure 5. The relation between δVDE and the d/r ratio for the configurations obtained from (a) the relaxation trajectory initiated at the optimized C1′ configuration and (b) five CTTS relaxation trajectories at ∼200 K. δVDE is the VDE difference between the excited electron of [I−(H2O)4]* and the excess electron in the corresponding water cluster anion e−(H2O)4. d/r is the ratio between d(Bq−e−) and the radius of gyration of the excess electron of e−(H2O)4. Detailed analyses are given in the text for the regions marked with an arrow.

gyration of the excess electron in the e−(H2O)4, which is denoted as the d/r ratio. (The radius of gyration is defined as ⟨(r − ⟨r⟩)2⟩1/2, where the average is taken over the SOMO of the excess electron.) The d/r ratio is employed because the exclusion repulsion depends not only on the distance between the iodine and the electron but also on the extent of distribution of the excited electron, which is determined by how strong the electron is bound. Figure 5a clearly shows that δVDE is positive for a small d/r ratio and decreases with increasing d/r ratio. On the basis of the d/r ratio, the effects of the neutral iodine on the excited electron can be roughly divided into three regions. In the region of d/r < ∼0.8, δVDE is greater than 0.044 eV, indicating that at a short iodine-to-electron distance, the iodine is inside of the cloud of the excited electron so that the exclusion repulsion is large. In the second region of ∼0.8 < d/r < ∼1.0, the iodine is close to the surface of the cloud of the excited electron, so that the exclusion repulsion is small or is canceled out with the attractive force resulting from the induced dipole moment of the iodine atom. In the region of d/r > ∼1.0, where the iodine is outside of the cloud of the excited electron, the exclusion repulsion is no longer important. Instead, the excited electron gains an additional stabilizing force from the attractive 13950

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less than 1.8 D within ∼200 fs in the CTTS dynamics initiated from a C4-like configuration. Therefore, these C4-like configurations cannot be responsible for the VDE relaxation observed in experiments11,12 because the dipole moment is too small to bind the excited electron. Hence, only the trajectories obtained by the CTTS relaxation dynamics initiated from C1′like configurations were used in the analysis of the iodine effects at ∼200 K. In Figure 5b, δVDE is plotted against the d/r ratio for the data obtained from five different CTTS relaxation trajectories of the C1′-like configurations. The result also serves as a demonstration of the dual role of the iodine effect on the excited electron, similar to the case shown in Figure 5a. Compared with those in the region of ∼0.8 < d/r < ∼1.0, larger (mean) δVDE values can be found for d/r < ∼0.8, indicating stronger repulsive forces of the iodine atom on the excited electron. However, for d/r > ∼1.0, negative δVDE values appear, demonstrating the emergence of an attractive force on the excited electron. Nevertheless, δVDE shows a larger fluctuation at each d/r value at ∼200 K, reflecting a larger variation of cluster structures and excited electron wave function distributions in the initial and later relaxation periods at a finite temperature. For the iodine inside of the electron cloud, because the exclusion repulsion is attributed to the wave function overlap of the excited electron and the electrons of the iodine atom, its magnitude is dependent on the compactness of the excited electron wave function and the location of the iodine atom in the excited electron cloud. Figure 6 shows that the dependence of δVDE on the dipole moment of the corresponding (H2O)4 cluster for configurations within a small range of 0.35 < d/r < 0.39.

interaction of the neutral iodine via the induced dipole moment. However, when d/r is very large, which is beyond the range of our simulation, the attractive force would be expected to fade out because the iodine−electron distance is too great for any interaction to occur between them. When this happens, the relaxed cluster becomes a water cluster anion. The results reported herein provide important information concerning the role of the iodine atom in the CTTS relaxation dynamics at initial and later times. Although the initial repulsion time between the iodine and the excited electron is short, relaxation is not possible without the presence of the iodine atom, as previously demonstrated by Mak et al.20 However, it should be noted that the relaxation is mainly due to the movement of water molecules, not the iodine atom, because of the heavy mass of the iodine atom. The initial rapid separation between the iodine atom and the excited electron, as evidenced by d(Bq−e−), is completed by the rotation of the molecular axis of the dangling water molecule away from the excited electron. At the same time, the ring structure in the C1′ configuration becomes flat, as in the case of the relaxation from the C4 initial configuration.18,19 As a result, the cluster dipole moment drops to a minimum of ∼2.0 D (cf. Figure 2b), and the VDE becomes small. However, this dipole moment is still sufficiently large to bind the excited electron,31 unlike the case in the relaxation of the C4 [I−(H2O)4]* cluster.18,19 The larger dipole moment in the case of the C1′ [I−(H2O)4]* cluster can be attributed to the presence of the dangling water molecule in the C1′ configuration, which forms a water dimer-like structure with one of the water molecules in the ring.40 After ∼350 fs, the VDE increases rapidly (cf. Figure 2a), which is due to the fact that the cluster has a broken water ring and assumes a chainlike structure (cf. Figure 3). At ∼550 fs, one of the water molecules leaves the chain (cf. Figure 3) and interacts as an additional dangling water with the excited electron. This additional interaction between the excited electron and the newly created dangling water molecule accounts for the large VDE after ∼550 fs (cf. Figure 2a), even though the cluster dipole moment is not substantial in this time frame (cf. Figure 2b). To verify that the dual role of the iodine atom on the excited electron is also present under experiment conditions,11,12 the CTTS relaxation dynamics were also carried out at a finite temperature. The ground-state (GS) BOMD dynamics for I−(H2O)4 was first carried out to generate the initial configurations for the CTTS dynamics. The basis set used for the GS dynamics was similar to that used for the CTTS dynamics except that the extra diffuse basis set of diff(sp,2s) was not added because the GS electron was not very diffuse. After allowing a period of time for the system to equilibrate at ∼200 K, we continued the GS dynamics for ∼5.0 ps to generate the initial configurations for the CTTS dynamics. Both of the C1′ and C4 configurations were used as the starting configurations in the GS dynamics. We found that the I−(H2O)4 cluster maintained structures that were similar to their starting structures and are hence referred to as C1′-like and C4-like configurations, respectively, and structure interconversion between the C1′-like and C4-like configurations did not occur during our GS simulation periods. Several configurations were evenly sampled out from the equilibrated GS dynamics as the initial cluster coordinates and velocities for the CTTS dynamics. Similar to the case for the CTTS relaxation dynamics starting from the optimized C4 configuration, the cluster dipole moment rapidly reached a value of

Figure 6. The relation between δVDE and the cluster dipole moment of (H2O)4 for configurations within a small range of 0.35 < d/r < 0.39.

The result shows that a larger dipole moment tends to have a larger δVDE value or stronger exclusion repulsion. This is because the excited electron is more tightly bound by a larger dipole moment, thus making its wave function more compact. However, for the iodine outside of the electron cloud, δVDE at each d/r value depends not only on the cluster dipole moment but also on the relative orientation between the iodine and water cluster. Figure 7 shows the dependence of δVDE on the dipole moment of the corresponding (H2O)4 cluster and the ∠(Bq−W4−e−) angle for configurations within a small region of 1.045 < d/r < 1.055, where ∠(Bq−W4−e−) is defined as the angle formed by the position of the ghost atom, the COM of (H2O)4, and the COM of the excess electron in the corresponding e−(H2O)4. The result clearly shows that at ∠(Bq−W4−e−) = ∼140°, δVDE has the largest negative value in this d/r range even though its dipole moment is not the largest, while at ∠(Bq−W4−e−) < 13951

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the iodine atom with the result that there is no attractive interaction between the excited electron and the iodine atom. This attractive interaction is determined by δVDE, whose average value is ∼0.04 eV in the present case, close to the experimental VDE drop of ∼0.05 eV reported by Neumark et al.12 In addition, because the excited electron is bound onto the corresponding water cluster anion, the separation of the iodine and the excited electron is controlled by the relative movement of the iodine and the COM of the water cluster anion, which takes tens of picoseconds to complete, as observed in experiment.12

4. CONCLUSIONS In the present study, we have employed the Born− Oppenheimer molecular dynamics to study the relaxation dynamics of the charge-transfer-to-solvent (CTTS) excited electron in I−(H2O)4 starting from the C1′ initial configuration. Because of a small singlet−triplet splitting and computational efficiency, the CTTS singlet excited state was modeled by the lowest triplet ground state and calculated by the B3LYP/6-31+ +G(d,p) + diff(sp,2s) method. However, after obtaining the relaxation trajectory, a further analysis of the electronic properties at each step was performed by the CASPT2(4,6) method. The findings indicated that the CTTS relaxation dynamics starting from the C1′ initial configuration were very similar to those of larger [I−(H2O)n]* clusters with dangling water molecules, showing that they had similar intrinsic CTTS dynamic behavior. However, the relaxation for C1′ [I−(H2O)4]* clusters was faster in time, presumably due to a higher strain of the three-member ring in the cluster. Our simulation revealed that the iodine atom exerted not only repulsive but also attractive forces on the photoexcited electron depending on the ratio of the iodine−electron distance to the radius of gyration of the excess electron of the corresponding water cluster anion, d/r. At d/r < ∼0.8, which occurred at an earlier time, the force acting on the excited electron from the iodine atom was repulsive. However, in the region of d/r > ∼1.0, which occurred in the later times of the simulations, the force could become attractive because of the induced dipole moment of the iodine atom. Nevertheless, when the iodine− electron separation becomes very large, this attraction force would be expected to fade out to form essentially a water cluster anion. The CTTS relaxation dynamics were also carried out at ∼200 K, and the dual role of the iodine atom on the excited electron was also found at a finite temperature. However, large fluctuations in VDE and iodine effects were observed, and the factors affecting these fluctuations were discussed. Due to the heavy mass of the iodine atom, the separation of the iodine−electron was mainly driven by solvent motion via the dangling water molecule. In addition, the evolution of the dipolar field from water molecules also played an important role in the relaxation dynamics. These results were used to interpret the long-time VDE drop and other properties observed in experiment.

Figure 7. The relation of δVDE with the cluster dipole moment of (H2O)4 and the ∠(Bq−W4−e−) angle for configurations within a small range of 1.045 < d/r < 1.055.

90°, δVDE can become slightly positive because the induced dipole moment of the iodine atom is in the opposite direction to that of (H2O)4 and hence exerts a weak repulsive effect on the excited electron. In the region of ∠(Bq−W4−e−) ≈ 100°, δVDE shows a complicated relationship with ∠(Bq−W4−e−) and the dipole moment of (H2O)4. Some implications of the present results to the experiments of time-resolved photoelectron imaging done by Neumark et al.11,12 are discussed as follows. It was previously stated that the relaxation from the C4 configuration failed to satisfactorily account for the VDE relaxation observed in the experiments carried out by Neumark et al. because its cluster dipole moment in the relaxation was once too small to bind the excited electron. However, the minima of the cluster dipole moments for the C1′ and C1′-like [I−(H2O)4]* clusters are higher than 2.0 D, which is still sufficiently large to bind an excited electron to form a dipole bound anion. Therefore, the relaxation from the C1′ and C1′-like initial configurations can be employed to account for the experimentally observed VDE. In addition, the relaxation dynamics are very similar to those reported for larger [I−(H2O)n]* clusters with dangling water molecules but faster in time.19,20 This allows us to discuss the CTTS relaxation dynamics more broadly. The initial drop in VDE observed for n ≥ 5 to the minimum value VDEmin is due to the randomization of water dipole moments, accompanied by the separation of the excited electron and the iodine atom. Therefore, the observed similarity of the VDEmin value with that of isomer II of the corresponding water cluster anion12 may be simply coincidental. This initial drop was not experimentally observed for n ≤ 4 because the time frame for its occurrence is faster than the time scale of the cross correlation of the pump and probe pulses, ∼180 fs. In addition, the large VDE increase from VDEmin to VDEmax may be due to the movement of water molecules after hydrogen bond cleavage (water ring breaking in the present case). This water motion after the breaking of hydrogen bonds suggests that the time scale for the VDEmin-to-VDEmax energy shift is 1.11 (=mD2O/mH2O) times faster in H2O clusters than that in D2O clusters as the result of an isotope effect, which is close to the experimental value of ∼1.2.12 Finally, the VDE drop from VDEmax to VDE(∞) at longer times can be attributed to the large separation of the excited electron from

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 13952

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ACKNOWLEDGMENTS The work was supported by the National Science Council, Taiwan under Contract No. NSC101-2113-M-030-007-MY2. We are also grateful to the NCHC for providing computing resources.

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