Ab initio molecular dynamics simulations reveal localization and time evolution dynamics of an excess electron in heterogeneous CO2–H2O systems Ping Liu, Jing Zhao, Jinxiang Liu, Meng Zhang, and Yuxiang Bu Citation: The Journal of Chemical Physics 140, 044318 (2014); doi: 10.1063/1.4863343 View online: http://dx.doi.org/10.1063/1.4863343 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Vibrational absorption and vibrational circular dichroism spectra of leucine in water under different pH conditions: Hydrogen-bonding interactions with water J. Chem. Phys. 137, 194308 (2012); 10.1063/1.4767401 A first principles molecular dynamics study of excess electron and lithium atom solvation in water–ammonia mixed clusters: Structural, spectral, and dynamical behaviors of [(H 2 O) 5 NH 3 ] − and Li(H 2 O) 5 NH 3 at finite temperature J. Chem. Phys. 134, 034302 (2011); 10.1063/1.3511701 Stepwise hydration of the cyanide anion: A temperature-controlled photoelectron spectroscopy and ab initio computational study of CN − ( H 2 O ) n , n = 2 – 5 J. Chem. Phys. 132, 124306 (2010); 10.1063/1.3360306 Structures of [ ( C O 2 ) n ( H 2 O ) m ] − ( n = 1 – 4 , m = 1 ,2) cluster anions. I. Infrared photodissociation spectroscopy J. Chem. Phys. 122, 094303 (2005); 10.1063/1.1850896 Ab initio studies of π-water tetramer complexes: Evolution of optimal structures, binding energies, and vibrational spectra of π-( H 2 O ) n (n=1–4) complexes J. Chem. Phys. 114, 4016 (2001); 10.1063/1.1343903

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THE JOURNAL OF CHEMICAL PHYSICS 140, 044318 (2014)

Ab initio molecular dynamics simulations reveal localization and time evolution dynamics of an excess electron in heterogeneous CO2 –H2 O systems Ping Liu, Jing Zhao, Jinxiang Liu, Meng Zhang, and Yuxiang Bua) School of Chemistry and Chemical Engineering, Shandong University, Jinan, 250100, People’s Republic of China

(Received 4 May 2013; accepted 13 January 2014; published online 29 January 2014) In view of the important implications of excess electrons (EEs) interacting with CO2 –H2 O clusters in many fields, using ab initio molecular dynamics simulation technique, we reveal the structures and dynamics of an EE associated with its localization and subsequent time evolution in heterogeneous CO2 –H2 O mixed media. Our results indicate that although hydration can increase the electronbinding ability of a CO2 molecule, it only plays an assisting role. Instead, it is the bending vibrations that play the major role in localizing the EE. Due to enhanced attraction of CO2 , an EE can stably reside in the empty, low-lying π ∗ orbital of a CO2 molecule via a localization process arising from its initial binding state. The localization is completed within a few tens of femtoseconds. After EE trapping, the  OCO angle of the core CO2 − oscillates in the range of 127◦ ∼142◦ , with an oscillation period of about 48 fs. The corresponding vertical detachment energy of the EE is about 4.0 eV, which indicates extreme stability of such a CO2 -bound solvated EE in [CO2 (H2 O)n ]− systems. Interestingly, hydration occurs not only on the O atoms of the core CO2 − through formation of O· · ·H–O H–bond(s), but also on the C atom, through formation of a C· · ·H–O H–bond. In the latter binding mode, the EE cloud exhibits considerable penetration to the solvent water molecules, and its IR characteristic peak is relatively red-shifted compared with the former. Hydration on the C site can increase the EE distribution at the C atom and thus reduce the C· · ·H distance in the C· · ·H–O H–bonds, and vice versa. The number of water molecules associated with the CO2 − anion in the first hydration shell is about 4∼7. No dimer-core (C2 O4 − ) and core-switching were observed in the double CO2 aqueous media. This work provides molecular dynamics insights into the localization and time evolution dynamics of an EE in heterogeneous CO2 –H2 O media. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863343] I. INTRODUCTION

Excess electrons (EEs) can be produced through cosmic and vacuum UV radiation and radioactive processes. Since most chemical reactions are closely associated with electron transfers, as the simplest chemical reactant, EEs have been studied quite extensively in the atmosphere, seawater, and other environmental and biological areas.1–9 EEs can exist as different structures and states depending on the properties and degree of aggregation of the media. Due to the universality and extensive application of aqueous solution, most experimental and theoretical studies5, 10–18 have been devoted to the explorations of the structures and states of EEs in water. A survey of EEs in water reveals three main kinds of states which have widely been accepted: interior-bound (IB) and surface-bound (SB) states, and hydrogen-bonding network permeating patterns.19 In a small water cluster, an EE can be stabilized by the dipole of the hydrogen-bonded water cluster surface as a SB state.20 But, in a large water cluster, or in bulk solution, an EE tends to form an IB state. In this state, a widely accepted structure for the EE is that it is trapped in a water cavity consisting of 6∼8 water molecules, with a a) Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0021-9606/2014/140(4)/044318/11/$30.00

cavity radius of about 2.1 Å.21, 22 However, the durations of such structures are only about 50∼90 fs in water,21 which implies that the cavity-like structure of a hydrated EE in water is not exclusive. In particular, an expanded cavity-like state for the hydrated EE was also suggested recently, in which the sphere-like EE cloud expands out of the first solvent shell,5 although this suggestion has been challenged.23, 24 In particular, it is suggested that an EE also prefers to distribute over many water molecules, forming expanded cavity-like states in water.5, 21 Clearly, it appears that the structures or states of hydrated EEs in various media are still poorly understood because of the high deformability and permeating characteristics of the EE cloud, and the complicated solvation properties of the surroundings. Moreover, EEs are ubiquitous in the atmosphere and they can participate in most atmospheric chemical reactions. As water and carbon dioxide (CO2 ) are important atmosphere components, studies of the reactivity of EEs in H2 O–CO2 clusters have practical application as well as academic significance. The behavior of an EE in such clusters is intriguing because neither a CO2 nor a H2 O molecule possesses a positive electron affinity independently. The large negative vertical electron affinity (−0.90 eV)25, 26 of an isolated CO2 implies that it cannot directly bind an EE. However,

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it has been shown that not only can solvation improve its EE-binding ability, but also its bending vibration can induce a transient dipole thus increasing its potential to bind an EE. CO2 cluster anions have been widely studied by experiments and theoretical calculations.27, 28 The states of an EE in pure CO2 clusters can be divided into two main categories: monomer anion (CO2 − ) and dimer anion (C2 O4 − ).25, 26, 29–34 An EE could reside on a single CO2 and turn it into a bent, polar one with the  OCO angle of about 135◦ in its ground state, and the lifetime of the formed CO2 − anion may be long up to 100 μs.35, 36 Calculations also suggest that an EE could be shared by two CO2 molecules, forming a C2 O4 − dimer anion with three stable isomers featuring D2d , D2h , and Cs symmetries.27, 34, 37 In particular, using ab initio molecular dynamics (AIMD) simulation, we recently found a novel result about the behavior of an EE in supercritical CO2 .38 Namely, besides the monomer and dimer anions, an EE could also exhibit a diffuse state in which the EE distributes over more than one CO2 molecule. These three kinds of the states convert from one to another via a combination of long lasting breathing oscillations and core-switching, and the diffuse state occurs for about half the trajectory time. Unlike in pure CO2 clusters and supercritical CO2 , in aqueous solution of CO2 , studies have demonstrated that an EE tends to reside on CO2 , forming a CO2 − anion, and solvation could enhance its EE-binding ability or stabilize the formed CO2 − anion.39–41 On the basis of density functional theory (DFT) calculations, Bondybey further investigated water-bound CO2 − by calculating electron affinities and solvation energies of small CO2 − (H2 O)n , n = 1–5, clusters and concluded that hydration can enhance the EE-binding ability of CO2 .39 CO2 even can react with small (H2 O)n − anion clusters, converting into CO2 − (H2 O)n , hydrated CO2 − anionic clusters, through electron transfer from the water-bound state to the CO2 , as found by cryogenic cluster ion spectroscopy and direct dynamics simulations.40 Klots demonstrated that, even for a water molecule, it could effectively prevent the autodetachment of an electron from a (CO2 )n − cluster.41 Although lots of structural and electronic information about an EE in the CO2 − (H2 O)n clusters has been acquired experimentally and theoretically, it remains unclear how upon attachment an EE transfers to CO2 and what are the roles of water and CO2 molecules during localization of the EE in CO2 –H2 O clusters or CO2 aqueous solution. Clearly, solvation or localization dynamics of an EE in such a case (an EE attaches to CO2 (H2 O)n , leading to CO2 − (H2 O)n ) should be different from that reported in Ref. 40 for a case (a CO2 attaches to (H2 O)n − , leading to CO2 − (H2 O)n ). In particular, for large CO2 -solvated clusters or even CO2 -solvated droplets, the bulk effect undoubtedly also governs the time evolution dynamics or localization mechanism of an injected EE, which makes these cases different from those observed in CO2 –H2 O clusters. However, relevant dynamics information about the solvation or localization of an EE in such heterogeneous CO2 –H2 O systems is still scarce. Such information is important in understanding the states, dynamics, and fate of radiation-produced EEs and in CO2 reduction in the atmosphere.

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The purpose of the present study on an EE in heterogeneous CO2 –H2 O systems is (a) to address some fundamental questions about localization of an added EE, (b) to clarify the important roles of water and CO2 molecules in localization, and (c) to explore the time evolution dynamics of the added EE. To this end, we perform AIMD simulations to study an EE in CO2 –H2 O clusters and also in CO2 aqueous solution, unveiling detailed dynamic mechanisms of the EE in its initial binding, localization, and subsequent time evolution in relevant states. Our main findings are that in such heterogeneous systems, an EE quickly flows to and resides on a CO2 , and the bending vibration of this CO2 plays the major role in the localization of the EE. Water molecules contribute to the stabilization of the formed CO2 − anion and hydration occurs not only on the O atoms but also on the C atom of the core CO2 − through formation of C· · ·H–O hydrogen bonds. II. SIMULATION DETAILS

Since pure CO2 clusters have widely been studied, in our present work, we choose the CO2 –H2 O clusters containing only one or two CO2 molecules to simulate the localization process of an EE in them, and the hydration effect of solvent water molecules. To similarly simulate the behavior of an EE in the CO2 –H2 O clusters, a series of hydrated clusters of a single CO2 , CO2 (H2 O)n , and a double CO2 hydrated cluster, (CO2 )2 (H2 O)50 , were considered by performing the same AIMD simulation procedure. To obtain equilibrated configurations of these CO2 –H2 O clusters, classical molecular dynamics (MD) simulations were first performed on two neutral CO2 (H2 O)120 and (CO2 )2 (H2 O)120 systems in periodically replicated cubic simulation cells (15.31 Å × 15.31 Å × 15.31 Å), which correspond to a density of 1.0 g/cm3 . The COMPASS force field and the method of Nos˙e and Anderson were employed in the simulation process to make sure that the system exists in the liquid environment. MD simulations were carried out within the canonical (NVT) ensemble, and the system temperature was kept around 300 K by using a Nosé-Hoover chain of thermostats.42, 43 The MD simulation time is about 5 ns, to make sure the system reaches equilibrium. All classical MD simulations were done using the Discover package implemented in the Cerius2 4.6 suite of program from Accelrys, Inc. A series of CO2 (H2 O)n clusters including CO2 (H2 O)11 , CO2 (H2 O)21 , CO2 (H2 O)32 , CO2 (H2 O)41 , CO2 (H2 O)50 , and CO2 (H2 O)100 were extracted from the above equilibrated CO2 (H2 O)120 system and were further optimized at a first principles level. The optimized cluster structures were taken as the starting configurations of the electron-binding motifs for subsequent AIMD simulations. Different sizes of the hydration clusters were considered, which were determined by varying the number of water molecules in a CO2 -centered hydration sphere. The selection of the cluster size is arbitrary and the size increment was set to 10 water molecules, because increasing or decreasing by a few water molecules for a large hydration cluster does not appreciably change the time evolution of an EE in these clusters. In optimization and subsequent AIMD simulation for each cluster, an EE was included in the spin-unrestricted calculations. The electronic structure

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was described by nonlocal DFT, using the Becke and LeeYang-Parr (BLYP) functionals, where the exchange and correlation functionals were from the works of Becke44 and Lee, Yang, and Parr,45 respectively. A double numerical plus pfunctions (DNP) atomic orbital basis set was employed to provide accurate results. AIMD simulations were carried out within the canonical (NVT) ensemble, and the system temperature was kept around 300 K by using the Nosé-Hoover chain of thermostats.42, 43 The integration time step was 0.5 fs, to ensure constant temperature throughout the whole process. The AIMD simulation time for each cluster is about 1 ps, which has proved to be sufficient for equilibrating the systems and acquiring reasonable information. Similarly, a (CO2 )2 (H2 O)50 cluster containing 50 H2 O and 2 CO2 molecules was extracted from the above equilibrated (CO2 )2 (H2 O)120 system and the same AIMD simulation procedure was performed. As a comparison for verifying the accuracy of our simulations, we also performed the same AIMD simulation on a pure water (H2 O)50 cluster, which was extracted from a (H2 O)120 periodic system equilibrated by an identical MD simulation procedure. Furthermore, to describe the behavior of an EE in an aqueous solution of CO2 accurately, we simulated a periodically replicated cubic simulation cell (12.47 Å ×12.47 Å ×12.47 Å) with [(CO2 )2 (H2 O)60 ]. The same simulation process as mentioned above was used, but the AIMD simulation time was 8 ps. All of the AIMD simulations were carried out with the DMol3 package46, 47 implemented in the Cerius2 4.6 suite from Accelrys, Inc. Complementary to AIMD simulations, traditional quantum mechanical calculations at the B3LYP/6-311++G** level of theory were performed to provide additional insight into the energetics and structures of the clusters. Mø´ llerPlesset second order (MP2) perturbation theory calculations were also performed to verify the accuracy of the B3LYP method. All of the ab initio calculations for the small CO2 − (H2 O)n (n = 2–6) clusters were performed using the GAUSSIAN 03 suite of programs.48

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isolated CO2 molecule has a large negative vertical electron affinity (−0.9 eV),25, 26 bending vibrations can induce a transient dipole, thus increasing the molecule’s potential to bind an EE. Furthermore, solvation by water molecules can also efficiently enhance its EE-binding ability. Thus, as found in our AIMD simulations on the [CO2 (H2 O)11 ]− , [CO2 (H2 O)21 ]− , [CO2 (H2 O)32 ]− , [CO2 (H2 O)41 ]− , [CO2 (H2 O)50 ]− , and [CO2 (H2 O)100 ]− clusters, an EE is finally trapped at the CO2 after a localization process for each case, leading to the formation of a bent CO2 − anion surrounded by water molecules (Fig. 1(a2)). In the above six clusters, the behavior of an EE is similar. That is, although an EE forms a diffuse state upon attachment in all the clusters, it quickly gathers toward the CO2 and then resides on it (Fig. 1(a) and Fig. S4 in Ref. 49). Fig. 1(b) displays the localization times of an EE in the six clusters. Interestingly, comparison among these clusters indicates that the size of the hydration cluster does not affect the localization rate of an EE. Although the geometries of all the above clusters are only at local minima on their respective potential energy surfaces, rather than their corresponding global minima, similar dynamic behavior and size-independent localization rates and efficiencies of an EE in these clusters fully reflect a general structural character of an EE in the heterogeneous [CO2 (H2 O)n ]− cluster series. To further clarify the mechanism of EE localization in the CO2 – H2 O clusters, and especially the important role of the CO2 , we performed an additional AIMD simulation on a different [CO2 (H2 O)50 ]− cluster. For this cluster, the  OCO angle of a CO2 is fixed at 176◦ . After attachment to the cluster, an EE initially forms a diffuse state and finally converts to a SB state (see Fig. S5 in Ref. 49), instead of a hydrated CO2 − anion. Together with the fact that a bending vibration induces a transient dipole in CO2, and thus increases its potential

III. RESULTS AND DISCUSSIONS A. Excess electron in heterogeneous CO2 –H2 O clusters

As reported previously, since a small neutral pure water cluster is not favorable to EE binding, an EE initially exists as a diffuse state in the [(H2 O)50 ]− cluster, upon attachment. But after about 200 fs, the attached EE localizes on the water cluster surface, forming a SB state. In the subsequent time evolution process, the EE mainly exists as such a SB state. The behavior of an EE in the pure water cluster and the vertical detachment energies (VDEs) (1.3–1.9 eV) of an EE in the SB state (Figs. S2 and S3 of the supplementary material49 ) are in good agreement with the previously reported results (VDE = 1.78 eV),11, 50 which indicates that the simulation method used here is reliable. For the CO2 –H2 O clusters, the key difference is that a CO2 molecule has low-lying unoccupied π ∗ orbitals, while a H2 O molecule does not. Although it is well known that an

FIG. 1. A schematic representation of the spin density distribution of an EE (green cloud) for the [CO2 (H2 O)21 ]− cluster. (a1) is a delocalized state after vertical attachment of an EE to the cluster (the initial state), and (a2) is a localized state of the EE in the time evolution process. The panel (b) represents the localization times of an EE to the core CO2 for different heterogeneous CO2 –H2 O anion clusters: (1) [CO2 (H2 O)11 ]− , (2) [CO2 (H2 O)21 ]− , (3) [CO2 (H2 O)32 ]− , (4) [CO2 (H2 O)41 ]− , (5) [CO2 (H2 O)50 ]− , and (6) [CO2 (H2 O)100 ]− . Panel (c) shows the spin density distribution of a localized state of the EE in the [(CO2 )2 (H2 O)50 ]− cluster.

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FIG. 2. Panel (a) shows the time evolutions of spin densities of the core-CO2 and its component atoms in the [(CO2 )2 (H2 O)50 ]− cluster (solid curves) and in solution modeled by a periodically replicated boundary cell (PBC) containing 2 CO2 and 60 H2 O molecules (short dotted curves). The black curves denote the spin density of the core-CO2 molecule and the red, blue and dark cyan curves denote the spin densities of the O, C, and O atoms, respectively. Panel (b) shows the time evolutions of the  OCO angles of CO2 (A) and CO2 (B) in the dynamic processes in the [(CO2 )2 (H2 O)50 ]− cluster (solid curves) and PBC (dashed curves) systems.

to bind an EE, this observation fully indicates that, in the [CO2 (H2 O)n ]− cluster, the bending vibration of CO2 plays a major role in driving and realizing the localization of an EE. To further examine the effect of CO2 on the time evolution dynamics of an EE, we also performed similar AIMD simulations on a medium-sized heterogeneous [(CO2 )2 (H2 O)50 ]− cluster containing two CO2 molecules. Unlike the single CO2 clusters, [CO2 (H2 O)n ]− , discussed above, for this double-CO2 cluster, we chose a special structure in which one CO2 is at the center of the cluster, denoted as CO2 (A), and another one is on the cluster surface (CO2 (B)). Although both CO2 (A) and CO2 (B) have the potential to bind an EE in the localization process, the EE is finally trapped at the interior CO2 (A) within 80 fs (Fig. 1(c)). This indicates that full hydration can increase the EE-binding ability of CO2 more effectively than partial hydration. Taking the [(CO2 )2 (H2 O)50 ]− cluster as a representative, we monitored the dynamics process in detail. Fig. 2(a) displays the spin density variation of CO2 (A) with respect to the evolution time. From the initial time to 40 fs, as the EE delocalizes over more water molecules, the spin density of CO2 (A) is close to zero. But, from about 40 to 70 fs, the spin density increases rapidly, implying that a part of the EE transfers

to the core CO2 . We also monitored the time evolution of the spin density of CO2 (B) (see Fig. S6 in Ref. 49). During the first 40 fs its spin density variation is similar to that of CO2 (A), but the corresponding value is slightly larger than that of CO2 (A). This should be attributed to the fact that the two CO2 molecules have approximately equivalent EE-binding ability, and thus have a competing relationship in this initial stage. However, after 40 fs, even if the spin density of CO2 (A) is slightly smaller than that of CO2 (B) before 40 fs, an EE gradually localizes on the CO2 (A) rather than the CO2 (B). A reasonable interpretation for this observation is that the solvent water molecules enhance the EE-binding ability of the CO2 (A). As reported previously31–33, 51, 52 and shown in Fig. S7 in Ref. 49, solvation in liquid or by water molecules could enhance the EE-binding ability of CO2 . It was also reported that the calculated electron affinity of the CO2 · · ·H2 O complex is 15.9 kJ/mol,39 and it increases with an increase in the number of water molecules. As each CO2 becomes surrounded by more H2 O molecules, we monitored the O· · ·H distance between an O of the core CO2 and a H of the first solvent shell H2 O molecules, as shown in Fig. 3. In this figure, different color lines represent different dangling H atoms of the hydrating water molecules around the core CO2 . Additionally, as

FIG. 3. Panel (a) is the time evolution of the O· · ·H distance between an O atom of CO2 (A) and a H atom of the water molecules in the first solvent shell of CO2 (A) in the [(CO2 )2 (H2 O)50 ]− cluster. Panel (b) is that associated with CO2 (B). Different colored curves denote different O· · ·H distances. Comparison between the panel (a) and (b) indicates that the hydration degree of CO2 (A) is higher than that of CO2 (B).

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there are two CO2 molecules in the [(CO2 )2 (H2 O)50 ]− cluster, the corresponding O· · ·H distance evolutions are shown for CO2 (A) (Panel (a)) and CO2 (B) (Panel (b)). Clearly, the O· · ·H distances associated with CO2 (A) are slightly shorter than those about CO2 (B), and the number of water molecules surrounding CO2 (A) is greater than that of CO2 (B). These observations fully indicate that hydration by water molecules is favorable to the trapping of an EE at CO2 , and vice versa, and CO2 (A), an interior CO2 , is a more attractive place for an EE to reside. After trapping of an EE at CO2 (A), the spin density on CO2 (B) drops to zero. In the following dynamic process, the spin density of CO2 (A) fluctuates around about 0.9 and the rest of about 0.1 is shared by the adjacent water molecules of CO2 (A). We also analyze the spin densities on each atom of CO2 (A), and find that an EE mainly resides on the C atom, with a spin density value of about 0.8 (Fig. 2(a)). This occurs because the empty, low-lying π ∗ orbital is contributed primarily by the carbon atom.35 In a previous study,53 spin densities of the C atom of small CO2 − (H2 O)n clusters were reported to be about 0.88. Our observed result is in good agreement with this literature value. After attachment of an EE, the neutral CO2 is converted into a bent, polar CO2 − anion (Fig. S1 in Ref. 49). Figure 2(b) shows the variations of the  OCO angle of two CO2 molecules in the [(CO2 )2 (H2 O)50 ]− cluster with respect to simulation time. In the initial 40 fs, because the EE-binding potential of the two CO2 is basically equivalent, the  OCO angles of these two CO2 molecules decrease simultaneously. However, after 40 fs, accompanying the gathering of negative charge mainly on CO2 (A), CO2 (A) gradually bends to hold the EE, whereas CO2 (B) recovers back towards linear geometry. Until 70 fs, the  OCO angle of CO2 (A) decreases smoothly and reaches a minimum of about 127◦ , indicating the formation of a CO2 − anion. After that, the  OCO angle of CO2 (A) oscillates in the range of 127◦ ∼142◦ with an average value of about 135◦ , while that of neutral CO2 (B) oscillates between 165◦ ∼180◦ . It was reported38 that in the supercritical CO2 system, (EE· · ·scCO2 ), the  OCO angle of the core-CO2 − anion oscillates in the range of 150◦ ∼180◦ , and along with the oscillation of  OCO angle, the EE cloud converts between localized and diffuse states. But, in our present simulations, such a conversion of EE states does not occur, and the  OCO angle oscillation cannot cause any variations of the distribution and state of the bound EE. This is because any of the solvent CO2 molecules in scCO2 has a competition with the core-CO2 , rather than just a stabilizing role played by water molecules in the [(CO2 )2 (H2 O)50 ]− cluster. Additionally, hydration also contributes to increasing the bending vibration period of the CO2 − anion to about 48 fs, which is approximately 1.5 times that (about 28 fs) of the neutral CO2 (Figs. 2(b) and S9 in Ref. 49). It has been widely accepted that VDE is the most fundamental energetic quantity of a hydrated electron. To characterize the stability of an EE in the mixed CO2 –H2 O clusters, VDEs were determined as shown in Fig. 4. The thick navy line in Fig. 4 presents the time evolution of the VDE of the mixed [(CO2 )2 (H2 O)50 ]− cluster. At the beginning, an EE is delocalized and weakly bounded in the cluster with a small

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FIG. 4. The colored solid curves present the time evolutions of VDEs of the solvated EEs for different clusters, CO2 (H2 O)n − . (1)–(6) denote six hydrated clusters: [CO2 (H2 O)11 ]− , [CO2 (H2 O)21 ]− , [CO2 (H2 O)32 ]− , [CO2 (H2 O)41 ]− , [CO2 (H2 O)50 ]− , and [CO2 (H2 O)100 ]− , respectively. The navy solid curve presents the VDE time evolution for the [(CO2 )2 (H2 O)50 ]− cluster, while the dashed curve denotes that in solution modeled by a PBC containing 2 CO2 and 60 H2 O molecules, [(CO2 )2 (H2 O)60 ]− .

VDE of about 0.75 eV. Due to EE transfer to CO2 , the VDE increases rapidly from 0.75 eV to 4.0 eV within 40 fs. Although the EE residence is not complete on CO2 (A) at 40 fs, the increasing potential of CO2 to bind the EE implies that the bound EE has been greatly stabilized in such a cluster. After trapping of an EE mainly at CO2 (A), the VDE is maintained at about 4.0 eV. With such a large VDE, it is difficult for an EE to detach or transfer to another CO2 . Clearly, this can explain why upon EE binding by a CO2 , the core-switching observed in the EE· · ·scCO2 system38 does not appear in that kind of hydrated CO2 cluster. Furthermore, as previously measured, the VDE for a cavity-shaped hydrated electron in bulk water is about 3.6 eV,54 which is lower than that of the solvated CO2 − anion. Using first principles molecular dynamics simulation, Boero et al.21 found that, in liquid water, an EE could transition from a diffuse state to being trapped in a cavity in about 1.6 ps. In our present simulation, the localization process of an EE on CO2 takes only about 40∼80 fs where, at such a short time scale, water molecules cannot be polarized or rotate to form a cavity to accommodate the EE. Although it was reported39 that CO2 could react with (H2 O)n − , the state of the EE is structurally ambiguous. Their experiment reveals that an EE may exist as either a diffuse or SB state. However, relative to these two states, the cavity-shaped state for an EE usually is the most stable one. From this point of view, it is natural to wonder if an EE could transfer from a solvated cavity to a CO2 . Thus, we ran another AIMD simulation to clarify the reactivity of a hydrated EE with CO2 . We prepared a new mixed CO2 (H2 O)n cluster containing a CO2 and a pre-built solvation cavity for an EE. The distance between the center of hydration cavity and the C atom of the CO2 is about 5.20 Å (Fig. 5). An EE is initially trapped in the solvent cage and presents as an s-type state, where the orbital is formed by a linear combination of the Rydberg orbitals of the O–H groups of water molecules in the first solvent shell. But, due to thermal fluctuations and molecular motion, and even the

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FIG. 5. The time evolution of spin density distributions of an excess electron in a mixed CO2 (H2 O)50 cluster with a CO2 molecule and a cavity-shaped hydrated excess electron, which shows the electronic structure change of the solvated EE from a cavity structure to a CO2 -cored structure.

attraction of CO2 , the EE· · ·H–O interaction is disturbed, and the EE gradually transfers to CO2 . Although thermal fluctuations and molecular motion can gradually break the solvent cavity, the solvent cavity still has the potential to bind the EE in the time evolution process, especially in the initial stage. Thus, to some extent, it can inhibit the EE transfer from the cavity site to the CO2 . Our present simulations have demonstrated that it needs more than 100 fs for an EE to finally reside on the CO2 . The solvent cavity is eventually destroyed, with a gradual reorientation of water molecules in the first solvation shell, converting to a normal H-bonding network structure as in water. This has further confirmed that in the mixed CO2 –H2 O cluster, CO2 can attract an EE with an absolute advantage when it is fully hydrated and then capture it, forming a hydrated CO2 − anion. B. Excess electron in aqueous CO2 solution

Although molecular clusters are widely studied as simplified models for the complicated molecular processes in solution due to their intermediacy between the gaseous and condensed phases, a periodically repeated cubic cell could be better suited to studies of the chemistry of solutions or droplets and even of large clusters. For the present CO2 –H2 O heterogeneous systems, an attached EE and an internally produced EE in a large CO2 –H2 O cluster certainly have different evolution dynamics. Thus, as a comparison to the gas phase clusters, and simultaneously with the aim of clarifying medium effects on the reactivity of CO2 with an EE, we performed a similar AIMD simulation on a [(CO2 )2 (H2 O)60 ]− system in a periodically replicated cubic simulation cell,

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which models a CO2 aqueous solution. This simulation indicates that, in this heterogeneous CO2 aqueous solution, the behavior of an EE is basically similar to that in the above discussed clusters. That is, an EE initially delocalizes on a number of water molecules, then flows to one CO2 and resides on it, converting the CO2 into a bent, polar CO2 − anion (Fig. 6(a)), surrounded by water molecules as a hydration shell. But, relative to the clusters, in the periodically repeated system, there are definite differences in the localization time, angle oscillations of the core CO2 , and VDE variation. In the periodically repeated cubic cell, all molecules exist in the liquid environment, with a typical H-bonding network among water molecules in addition to the H-bonding interaction with the core CO2 . Thus, the low-lying π ∗ orbital of CO2 is the only place for an EE to reside. In the cluster structures there is a surface environment, and the Rydberg orbitals of the dangling H atoms of the surface water molecules have a certain retarding effect on EE transfer to CO2 . Meanwhile, with the strong inhibiting interactions of an H-bonding network, water molecules need more time to reorient, and thus the formation of a stable CO2 − anion is kinetically preferred in solution. In the clusters, an EE takes about 40–80 fs to reside on a CO2 . EE transfer leads to polarization of the solvent surroundings, with reorientation of water molecules, thus stabilizing the newly formed anion. But in solution, EE localization takes place in only about 20 fs so that water molecules have no time to rearrange and find a new mode of interaction with the CO2 − anion. We also monitored the O· · ·H distance between the core CO2 and its surrounding water molecules in the first solvent shell, as shown in Fig. 6(b). The intrinsic structural reorganization of the solvent shell does not considerably affect the O· · ·H distance in this aqueous solution, just as in the clusters. Therefore, at the early stage of the formation of the CO2 − anion in solution, the EE-bound CO2 is more unstable, with small VDE than that in the clusters (Fig. 4), and the spin density fluctuates in a narrow range of 0.8–0.95 during the first 200 fs (Fig. 2(a)). Correspondingly, the spin density on the C site in solution is also smaller than that in the clusters. The instability of the bound EE makes the  OCO angle of the CO2 − anion fluctuate in a relatively large range of 120◦ ∼150◦ (Fig. 2(b)). After the CO2 − anion is stabilized by

FIG. 6. Panel (a) is a schematic representation of spin density distributions of an excess electron in aqueous solution (modeled by a periodically replicated boundary cell containing 60 H2 O and two CO2 molecules). Panel (b) shows the time evolution of the O· · ·H distance between the O atoms of the core-CO2 and the H atoms of solvent water molecules in the first solvent shell in aqueous solution.

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the solvating water molecules, spin densities in both aqueous solution and clusters are maintained at about 0.9 (Fig. S8 in Ref. 49). Meanwhile, both the VDE and bending vibration of the core CO2 in solution gradually become consistent with those in the clusters (Fig. 4 and S9 in Ref. 49). In addition, due to solvation by water molecules, spin densities of the CO2 − anion and its C site are slightly smaller than those of the CO2 − anion just formed. C. Structures of solvated excess electron and hydration character

Upon localization, an EE is basically distributed over the CO2 , forming a CO2 − anion core and all the water molecules solvate the core CO2 − anion. A survey of small CO2 − (H2 O)n clusters reveals that hydration occurs on the O atoms of the core CO2 − anion and water molecules interact with the core via O· · ·H–O linkages.53 Driven by electrostatic interaction, water molecules rotate with their H atoms directed toward more electronegative O atoms in the core. Although some of structural information about these small clusters has been acquired,35–37, 39, 55 dynamic information on hydration is still scarce. In the time evolution of the present system, after trapping of an EE at CO2 , the formed CO2 − anion is stabilized by H-bonding interactions, with the number of the coordinating water molecules of the CO2 − anion fluctuating around about 4∼7. To further depict the O· · ·H interaction, we evaluated the O· · ·H distance, using radial distribution functions (RDFs), where the O belongs to the CO2 − anion and the H denotes those of all water molecules. As shown in Fig. 7(a), the O· · ·H RDF curves for all the trajectories peak at about 2.0 Å. This peak represents an average distance between the O atoms of the CO2 − core and the H-bonding H atoms of water molecules in the first water shell, which is consistent with the distance in the CO2 − · H2 O dimer calculated at the B3LYP/6-311++G** level of theory.39 For the neutral CO2 (B) in the [(CO2 )2 (H2 O)50 ]− cluster, the O· · ·H RDF curve does not have a peak, indicating that the neutral CO2 cannot form strong H-bonds with water molecules. Another peak is also observed at 3.0 Å, which corresponds to the distance between the O atoms and other H atoms of water molecules in the first solvation shell. To verify the accuracy of the RDF,

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we randomly selected configurations from all the trajectories, and examined the O· · ·H distances between the O atoms of the CO2 − core and the H atoms of the first shell water molecules. The O· · ·H distances fall in a range of 2.85–3.64 Å with an average of about 3.2 Å, as shown in Table S1 in Ref. 49, which is in agreement with these two peaks in the RDF. Besides the O· · ·H–O H-bonding interaction, a C· · ·H–O interaction is also observed in our AIMD simulations as shown in Fig. 7(b). Information about the C· · ·H–O interaction has not been reported before. Saeki’s group37 studied the configurations of small CO2 − (H2 O)n clusters, and reported that water molecules interact with the CO2 − anion only through the O· · ·H–O linkages. In their work, geometrical optimization starting from the C· · ·H–O configuration leads to a structure with the O· · ·H–O linkage. However, in our AIMD simulations, hydration occurs not only on the O atoms but also on the C atom of the CO2 − core. As an EE mainly locates at the C atom, an increase of the negative charge of the C enhances its H-bonding ability, and thus enables the C site to be an H-bonding acceptor, to interact with the O–H groups of the surrounding water molecules. This case is similar to the cavity-shaped hydrated electron for which six electropositive dangling H atoms form a spherical cage to accommodate an EE, but the difference with the hydrated electron cavity lies in the feature that the EE is tethered by a CO2 . Such a C· · ·H–O H-bonding mode is more frequently observed in our AIMD simulations in the EE-bound CO2 aqueous solution than in clusters. To make a comparison, we also monitored the C· · ·H distance in solution, and statistically analyzed its RDFs using the periodically repeated system as representative. As shown in Fig. 7(b), g(r) has a peak at about 2.4 Å, which is slightly longer than the O· · ·H distance (2.0 Å) in the O· · ·H–O mode. This indicates that hydration at the O atom plays the major role in stabilizing the core CO2 − anion, while hydration at the C site by a C· · ·H–O interaction mode plays an assisting role. We also obtained several geometries (Fig. 8) for small CO2 − (H2 O)n (n = 2–6) clusters using the B3LYP/6-31+G* method, and the geometries with the C· · ·H–O and O· · ·H–O interactions for CO2 − (H2 O)n are shown in Fig. 8. These CO2 − (H2 O)n configurations can be divided into two types according to if they have a C· · ·H–O H-bond. In the configurations without the C· · ·H–O H-bond (the first row of

FIG. 7. Panel (a) is a schematic representation of the RDF of the O· · ·H distance between the O atoms of the CO2 − anion and the H atoms of solvent H2 O molecules in the clusters (solid curves) and solution modeled by a PBC (dotted curve). Panel (b) is that of the C· · ·H distance between the C atom of the CO2 − anion and the H atoms of solvent H2 O molecules in solution.

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FIG. 8. Schematic representations of spin densities of five small clusters, CO2 − (H2 O)n (n = 2–6), with different hydration modes. In the first row, water molecules interact with the CO2 − anion only through the O· · ·H–O hydrogen bonds, while in the second row, water molecules interact with the CO2 − anion through the O· · ·H–O and C· · ·H–O hydrogen bonds simultaneously.

Fig. 8), water molecules interact with the CO2 − anion only through the O· · ·H–O H-bonds, while in the second type of configurations (the second row of Fig. 8), water molecules interact with the CO2 − anion through both C· · ·H–O and O· · ·H–O H-bonding interactions. Comparing these structures reveals that configurations with the C· · ·H–O Hbonding mode exhibit considerable EE penetration to the Hbonding water molecule(s). The calculated C atomic charges and VDEs for some snapshot configurations are shown in Fig. 9. Clearly, these VDEs (2.0–3.45 eV) are slightly smaller by 0.2 eV than, and basically in agreement with, the literature values (2.28–3.50 eV) calculated using the MP2/6311++G** method for the similar [CO2 (H2 O)n ]− (n = 2–6) clusters.55 Further, the Mulliken charge of C has been greatly reduced after trapping of an EE at the CO2 compared with that of a neutral CO2 with a Mulliken charge on C of 0.749. However, it is still slightly positive, and even more positive than that of any O. Thus, the C· · ·H–O hydrogen bond is weaker than the O· · ·H–O hydrogen bond in these clusters. This can also explain why one H2 O does not form a C· · ·H–O hydrogen bond in the H2 O–CO2 − dimer. For the CO2 − (H2 O)n clusters with different hydration modes, the Mulliken charges on C increase as the number of water molecules increase, which is consistent with a previous report.39 This observation indicates that hydration could increase the amount of an EE on C. But, for the structures with same number of the coordinating water molecules, the Mulliken charge on C in the C· · ·H–O

FIG. 9. Changes of the VDEs and Mulliken charges for five small clusters, CO2 − (H2 O)n (n = 2–6), with different hydration modes. The black line and bar represent the changes of VDEs and Mulliken charges for the geometries which contain the O· · ·H–O hydrogen bonding interaction, respectively, while the red line and bar represent the changes of VDEs and Mulliken charges for the geometries that simultaneously contain the O· · ·H– O and C· · ·H–O hydrogen bonding interactions, respectively. O–H and C–H interactions denote the O· · ·H–O and C· · ·H–O hydrogen bonding modes, respectively.

H-bonded structure is smaller than that in the O· · ·H–O H-bonded one. This implies that the formation of the C· · ·H–O H-bond can promote localization of an EE on C. We also evaluated the O· · ·H distance of the O· · ·H–O H-bond, and the C· · ·H distance of the C· · ·H–O H-bond, as given in Table S2 of Ref. 49. These results are basically consistent with the RDF analyses. Further, the vibrational spectra of such small molecular clusters CO2 − (H2 O)n (n = 2∼6) are calculated at the B3LYP/6-31+G* level of theory, and shown in Fig. S12 of Ref. 49. There occurs a peak at about 3197 cm−1 for the cluster CO2 − (H2 O)2 only with the C· · ·H–O H-bond mode, which is considerably red-shifted compared with a peak at ∼3397 cm−1 for the CO2 − (H2 O)2 only with the O· · ·H–O H-bond mode (Fig. S12(A)).49 However, this C· · ·H–O peak is blue-shifted with the increase of the number of water molecules, becoming close to that of the O· · ·H–O H-bond (Fig. S12(B)).49 No corresponding experimental spectrum associated with the C· · ·H–O H-bond has been reported. But

FIG. 10. Panel (a) shows the time evolution of Mulliken charges of the C atom and the C· · ·H distance with respect to the simulation time for the solution case. These curves indicate an approximate cooperative relationship between the charge distribution and the C· · ·H distance in the EE-absorbed CO2 solution. Panel (b) shows the time evolution of Mulliken charges of two O atoms and the CO2 − core. The red and blue curves represent those of the two O atoms, respectively; the green one represents their summations; and the black one represents the time evolution of the total charges of the CO2 − core.

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FIG. 11. The time evolutions of Mulliken charge of the C atom and the C· · ·H–O distances (with two H2 O) for the solution case.

this C· · ·H–O H-bond mode is understandable because excess electron localization can result in the increase of the negative charge and electronegativity of the C site and thus increase its H-bonding ability (H-bond acceptor). Clearly, the redshift relative to the peak of the O· · ·H–O H-bond mode can be viewed as an IR spectroscopic character of the C· · ·H–O H-bond mode. Of course, a detailed study on the IR spectra and structure properties of such clusters containing the C· · ·H–O H-bonds are needed. Moreover, to depict the C· · ·H–O H-bonding interaction, the C· · ·H distances and the charges of the CO2 − anion were calculated for each snapshot configuration selected from the trajectory of the solution system, and its time course is displayed in Fig. 10. The C· · ·H distance is mainly affected by the Mulliken charge on the C atom. As the total Mulliken charge of the CO2 − anion essentially remains constant (about −0.75), oscillations of the charges on the two O atoms (the red and blue lines in Fig. 10(b)) along time evolution reveal intramolecular charge-flow, which is governed by an asymmetric stretching vibration of the core CO2 − . In addition, it should be noted that in time evolution, solution fluctuations and molecular thermal motion may change the C· · ·H distance, as shown in Fig. 10, and thus change the

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charge distribution over the C, and the interaction between the C site and the solvent H2 O molecules. Meanwhile, during the AIMD simulation of the periodically repeated system, the core CO2 − could form a C· · ·H–O interaction with only one water molecule, but such a water molecule is exchangeable with one of the other water molecules. As shown in Fig. 11, with the approach of the other water molecules, a metastable O–H· · ·C· · ·H–O H-bond mode can form, but it quickly vanishes, along with the departure of the original water molecule. The exchange of water molecules interacting with the C is affected mainly by solution fluctuations and molecular thermal motion. In the water molecule exchange process, the Mulliken charge of the C is slightly reduced due to the formation of the metastable O–H· · ·C· · ·H–O interaction. With solvation by water molecules, EE autodetachment becomes less favorable energetically. The bare CO2 − anion is unstable, with a VDE of about 1.4 eV, as measured experimentally.56 This value swiftly increases to about 4.0 eV in the mixed [CO2 (H2 O)n ]− clusters with more water molecules, which indicates that solvation by water molecules may prevent the EE from autodetachment. Irrespective of cluster or solution states (Fig. 4), their VDEs fluctuate around about 4.0 eV, after the CO2 − anion is stabilized by solvent water molecules. This also indicates that, relative to other water molecules, the water molecules in the first solvent shell play an important role in solvating or stabilizing the CO2 − anion. Moreover, the hydration effect and relatively weak EEbinding ability of solvent H2 O molecules make dual core and core-switching difficult to occur for the mixed CO2 – H2 O systems with two and even two adjacent CO2 molecules (Fig. S10 in Ref. 49). For an arbitrary cluster system, as an EE localizes very rapidly, its geometry can equilibrate within about 1 ps. Taking the (CO2 )2 (H2 O)50 − cluster as a representative system, we monitored its C· · ·O distance distribution of the CO2 − anion and O· · ·H distance of the H2 O molecules, after an EE resides on the core CO2 . As shown in Fig. 12(a), for the C· · ·O distance distribution, there is a peak at about 1.24 Å in its g(r), which is in agreement with the C–O bond length of the CO2 − anion. Similarly, the O· · ·H distance peaks

FIG. 12. Panel (a) is for the RDF of the C· · ·O distance of the CO2 − anion and the O· · ·H distance of the H2 O molecules after an EE resides on the core CO2 in the [(CO2 )2 (H2 O)50 ]− cluster. Panel (b) shows the time evolution of the  OCO angle of the core CO2 in an additional 1 ps simulation for the [(CO2 )2 (H2 O)50 ]− cluster. A–D denote schematic representations of the spin density of the EE for four snapshot geometries selected from 1600 fs–1800 fs. The red values represent the VDEs of these four snapshot geometries.

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at about 0.98 Å in its g(r), which agrees with the O–H bond length of neutral H2 O molecules. In addition, we also extended our AIMD simulation for another 1 ps, and monitored the C· · ·O and O· · ·H distance distributions. The acquired g(r) curves from this 2 ps AIMD simulation are consistent with the initial 1 ps-based ones. These observations indicate that such cluster systems can be equilibrated within 1 ps. As a supplement, we randomly selected a part of the trajectory, monitored the bond angle evolution of the core CO2 , and calculated the spin density and VDEs for four snapshot geometries. All of these are in agreement with the previous results, which further indicates that the present cluster systems have been equilibrated within 1 ps. Therefore, we recorded 1 ps trajectory for each cluster, but an 8 ps trajectory for the solution case. In all of these AIMD simulations, no dimer core or core-switching events were observed. As experimentally found for a CO2 − anion, its lifetime is about 60– 90 μs57, 58 which is far longer than our simulation time of a picosecond. In addition, hydration may further decrease the possibility of the occurrence of dimer core or core-switching. It has been reported that only in small [(CO2 )n (H2 O)2 ]− (n = 2, 3) and [(CO2 )n H2 O]− clusters in which a solvent effect is not present, core-switching and dimer core (C2 O4 − ) states could be observed.55 Fortunately, the CO2 − anion once formed lives long enough to explore detailed information about its states and time evolution dynamics in picosecond to even nanosecond time scales, before it dissociates or decays. Therefore, a longer time AIMD simulation may provide more information about the possible occurrence of dimer core and core-switching states. This work is underway in our lab.

IV. CONCLUSIONS

In summary, we explored the localization and time evolution dynamics of an EE in heterogeneous CO2 –H2 O systems by using AIMD simulations. In both H2 O–CO2 clusters and CO2 aqueous solution, the behavior of an EE is similar. As neither CO2 nor small water clusters favor EE-binding, an EE initially forms a delocalized state upon attachment to the CO2 –H2 O clusters or addition to solution. However, bending vibrations of CO2 lead to an instantaneous dipole that makes CO2 an EE attractor, causing EE localization. CO2 can even react with the hydrated electron, and cause an EE to transfer to it from a hydration cavity. The localization takes place in only a few tens of femtoseconds. The water cluster size hardly has an effect on the EE localization process, and the water molecules just play an assisting role. Upon trapping at a CO2 , an EE resides in its empty, low-lying π ∗ orbital, which converts a linear, neutral CO2 into a bent polar CO2 − anion through geometrical relaxation. After relaxation, the  OCO angle of the CO2 − anion oscillates in the range of 127◦ ∼ 142◦ with an average of about 135◦ . Hydration by the surrounding water molecules can lead to further stabilization of the CO2 − anion. For the hydrated structures of the solvated EE in the AIMD simulation trajectories, not only the O· · ·H–O H-bonding mode with an average O· · ·H distance of about 2.0 Å, but also the C· · ·H–O H-bonding mode between the core CO2 − anion

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and the first hydration shell water molecules was observed in both the anionic clusters and aqueous solution. Since an EE is mainly located at the C of CO2 , one dangling H of a solvent water molecule points to the C and binds the negative charge jointly with the C, similar to the trapping of an EE in a quasi-dimer solvated cavity through the O–H· · ·{e}CO2 interaction. This C· · ·H–O interaction has been frequently observed in aqueous solution with an average C· · ·H distance of about 2.4 Å. The C· · ·H H-bond is slightly longer than the O· · ·H H-bond; its corresponding IR peaks (3200–3340 cm−1 ) are red-shifted compared with that (∼3400 cm−1 ) of the latter, and thus the former is slightly weaker than the latter, which implies that this C· · ·H–O interaction plays an assisting role in the hydration of CO2 − . However, in the optimized geometries of some of small CO2 − (H2 O)n (n = 2–6) clusters, the observed H-bonding modes can be divided into two categories: pure O· · ·H–O interaction and a cooperative O· · ·H–O and C· · ·H-O interaction mode. Hydration at the C atom can also further increase the EE distribution at the C and, meanwhile, the EE distribution at the C regulates the strength of the C· · ·H–O interaction. In addition, the solvated EE also exhibits considerable penetration to the H-bonding water molecule in the C· · ·H–O mode. Additional evidence for an increase in stability due to hydration is that the VDEs of the trapped EE at CO2 for all the heterogeneous CO2 –H2 O systems are about 4.0 eV. This large VDE implies the impossibility of occurrence of dimer core or core-switching phenomena. Moreover, hydration elongates the bending vibration period of the core CO2 − anion to about 48 fs, about 1.5 times that (27 fs) of the neutral CO2 molecule. This work provides a microscopic picture of the behavior of an EE in the heterogeneous CO2 –H2 O systems. With the dynamical information about an EE trapping at CO2 , this work can provide not only a view of the quenching behavior of EEs, but also theoretical support for the interpretation of EE-related chemical reaction mechanisms in atmospheric and solvent-based chemistry. However, this is only the tip of the iceberg for the dynamical behavior of an EE in heterogeneous systems. Further research on this topic should be carried out.

ACKNOWLEDGMENTS

We gratefully acknowledge the support by the Natural Science Foundation of China (21373123, 20633060, and 20973101), Natural Science Foundation (ZR2013BM027) of Shandong province, and Independent Innovation Foundation of Shandong University (2009JC020), and thank Professor R. I. Cukier for reading the manuscript thoroughly and suggesting improvements. A part of the calculations were carried out at the Shanghai Supercomputer Center, National Supercomputer Center in Jinan, and High-Performance Computer Center at Shandong University-Chemistry. 1 E.

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