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Response of Observables for Cold Anionic Water Clusters to Cluster Thermal History ´ da´m Madara´sz,† Peter J. Rossky,‡ and La´szlo´ Turi*,† A Eo¨tVo¨s Lora´nd UniVersity, Department of Physical Chemistry, Budapest 112, P.O. Box 32, H-1518 Hungary, and Department of Chemistry and Biochemistry and Institute for Computational Engineering and Sciences, 1 UniVersity Station A5300, UniVersity of Texas at Austin, Austin, Texas 78712-1167 ReceiVed: September 14, 2009; ReVised Manuscript ReceiVed: December 22, 2009
We have used mixed quantum classical molecular dynamics simulations to explore the role of structural relaxation when binding an excess electron to neutral water clusters. The structural and spectral properties of the water cluster anions were investigated as a function of the size (n ) 45 and 104), nominal temperature (Tnom ) 50, 100, and 150 K), and preparation method of the parent neutral clusters. In particular, we consider two different protocols for preparing the initial neutral clusters, which differ markedly in their thermal history. In the first, warm equilibrium neutral clusters are gradually quenched to increasingly lower temperature. In the second, neutral clusters are formed spontaneously at ∼0 K and then warmed to the same target temperatures, yielding inherently metastable, nonequilibrium structures. Electron attachment to these alternative sets of clusters shows that below a critical temperature (∼200 K), the metastable water clusters bind a surface state excess electron significantly more strongly than the quenched, equilibrium clusters. The structural analysis indicates that these cluster anions with larger vertical detachment energies (VDEs) more frequently stabilize the electron by double-acceptor-type water molecules and exhibit a weak temperature dependence of the VDE compared with the quenched clusters. These results suggest that the alternative classes of cluster anions seen experimentally may reflect differences in the thermal history of such clusters. I. Introduction 1
The physical properties of the hydrated electron and its finite size analogs, water cluster anions,2,3 have been investigated continuously in the last 40 years. A more recent wave of scientific interest is mainly due to the importance of the hydrated electron systems in various physical phenomena, including those in electrochemistry, photochemistry, biochemistry, and nuclear chemistry, to name a few.4 Path integral simulation studies5,6 predicted first that water cluster anions may have two distinct types of structures. In the so-called interior-bound (IB) clusters, the excess electron is localized in a solvent void surrounded by properly oriented water molecules. This structure is similar in structure to the hydrated electron.7,8 In surface-bound (SB) clusters, the electron density is localized, but at the surface, it is outside the cluster. The long-standing issue is establishing which structure is observed in a given experiment. A readily observed characteristic property of the water cluster anions is the so-called vertical detachment energy (VDE), which can be measured by photoelectron spectroscopy9-21 and computed by ab initio calculations22-30 or computer simulations.5,6,31-34 The VDE is the energy needed to remove the electron from the cluster anion without changing its nuclear geometry. A linear relationship between the VDE and n-1/3 (n is the number of water molecules of the cluster) is anticipated using the dielectric continuum theory for the IB states6 and SB states as well.35 This trend was already apparent in the earliest experiments.9 This correlation also provides information about the properties at the bulk limit by a linear extrapolation.36-38 * To whom correspondence should be addressed. E-mail: turi@ chem.elte.hu. Fax: (36)-1-372-2592. † Eo¨tvo¨s Lora´nd University. ‡ University of Texas at Austin.
Recently, it has become clear that more than one distinct linear VDE sequence can be observed for water cluster anions in molecular beam experiments.10,11 The water cluster anions are generated by nozzle-expanding water vapor into vacuum with Ar or He carrier gas and then crossing the resulting beam with an electron beam. Varying the backing pressure of the carrier gas revealed two main peaks in cluster anion VDE spectrum. The lower backing pressure (30 psi Ar) created water cluster anions with a larger VDE (denoted isomer I), whereas a higher backing pressure (70 psi Ar), which is generally associated with clusters at a lower temperature, resulted in anions with a smaller VDE (isomer II). On the basis of the size of the VDE, it was inferred that isomer I stabilizes the electron in an interior state, whereas isomer II is a surface state.10,39 The structure of isomer I is the focus of continued controversy. A mixed quantum classical molecular dynamics (QCMD) study, which investigated various size-equilibrated water cluster anions at different temperatures, found that the experimental VDE and absorption spectra are consistent with the trends of these physical properties for SB states but not IB states of water cluster anions.32,40 A very recent ab initio Born-Oppenheimer molecular dynamics (BOMD) study41 also supports this assignment. However, these molecular dynamics studies consider only equilibrium scenarios. The fate of the water cluster anions in real experiments, from the formation to the detection, may be very far from equilibrium, and some theoretical results suggest that this is the case.26 Up to now, there have been no attempts to simulate nonequilibrium behavior. It is a fundamental challenge because, in general, the full dynamical history plays a role. In a previous simulation study,33 we analyzed the very first step of the relaxation process, the electron attachment to neutral water clusters in a simplified model. The analysis of the interaction of neutral equilibrium water clusters with zero kinetic energy
10.1021/jp908876f 2010 American Chemical Society Published on Web 01/25/2010
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excess electrons confirmed that in the first moment of the relaxation process, the excess electron is always bound in a very diffuse surface state by the dipole moment of the neutral water clusters. In the present study, we go beyond the equilibrium assumption and attempt to model the process of the generation of the large water cluster anions from the creation of the neutral water clusters through the electron attachment and relaxation. Because there is only very limited information about the mechanistic details of the generation of the neutral water clusters, we consider two accessible limiting cases. In the first, the relaxation begins from equilibrium cold water clusters, whereas in a second scenario, we create metastable water clusters by spontaneous assembly from very low-temperature molecules. These models may bracket the behavior in experiments42,43 and in the evaporative cooling ensembles.44 We investigate the properties of the water cluster anions after relaxation following electron attachment as a function of the size of the clusters and the final temperature. Obviously, this is an oversimplified picture of the mechanism of cluster formation. Two components of the process, namely, water evaporation after electron attachment and water capture by anions in molecular collisions, are not included in the simulation. The structure of the article is as follows. First, we briefly review the simulation method, the electron-water pseudopotential, and the preparation of the neutral clusters, which serve as starting points for the relaxation process. In Section III, we present the simulation results. In Section IV, we discuss the results and draw our conclusions. The discussion focuses on the differences between the properties of the two types of relaxed water cluster anions, particularly those that may distinguish them experimentally. II. Methods We performed QCMD simulations to investigate the relaxation of an excess electron in its ground state after adding it to equilibrated and nonequilibrated neutral water clusters at different nominal initial temperatures (Tnom ) 50, 100, 150 K) and sizes (n ) 45, 104) in a microcanonical (constant NVE) ensemble. Because the applied QCMD simulation technique45 and its reliability33,46 have been described in the literature, we review only the most important features of the method here. In the simulations, the water molecules are treated classically, interacting via a three-site simple point charge (SPC) potential with internal flexibility,47 whereas the excess electron is described by a quantum mechanical wave function. The interaction of the electron and the water molecules is modeled by an approximate pseudopotential.48,49 The excess electron is treated in a plane-wave basis and represented on 32 × 32 × 32 evenly distributed grid points. The grid points span a cubic box (lbox ) 36.34 Å). The Schro¨dinger equation for the excess electron in the field of the classical water molecules is solved using an iterative and block Lanczos procedure.45 The water molecules evolve under the combined influence of the other classical molecules and the electron (using the Hellman-Feynman force). The nuclear evolution is adiabatic, with the electron confined to remain in its ground state. The equations of motion for the nuclear evolution are integrated employing the Verlet algorithm with a 1 fs time step.50 The applied QCMD simulation technique has provided a detailed picture of the molecular characteristics of electron solvation that has been largely validated via more sophisticated methods for more strongly bound electrons by moderately sized clusters.26,41 However, it is necessary to comment on the possible
Madara´sz et al. quantitative shortcomings of the method. The main sources of limitation are the use of the one-electron treatment of the excess electron, the flexible, nonpolarizable SPC water model, and the electron-water molecule pseudopotential. First, because most of the popular water models have been designed to model liquid water, the SPC potential is unlikely to describe correctly the details of water cluster energies precisely, particularly for smaller clusters. It has also been pointed out that the SPC model has limitations in anion simulations that tend to overemphasize the tendency for the excess electron to align dangling OH bonds.51,52 The present pseudopotential has been optimized to reproduce the Hartree-Fock electron density of an electron-single-watermolecule system in the static exchange limit and thus mainly neglects electron-molecule dispersion interactions.53,54 The “a posteriori”-introduced polarization potential part of the pseudopotential was chosen to reproduce bulk hydrated electron properties.48 The model is thus expected to become more reliable with increasing cluster sizes and at relatively large electron binding energies, the focus of the present work. The good agreement of the vertical detachment energies of water cluster anions computed with the present QCMD technique and those calculated from dielectric continuum theory for large cluster sizes further emphasizes this point.55 Recently, all-valenceelectron ab initio molecular dynamics (AIMD) simulations were cluster anion within the BOMD performed on a (H2O)32 framework41 and on the bulk hydrated electron (with 32 water molecules) using Car-Parrinello molecular dynamics (CPMD) technique.56 The results of the one-electron QCMD simulations and those of the AIMD studies are in good general agreement. We must also mention that one may expect uncertainties when transferring model potentials from liquid phase to low-temperature solids. The simulation of 13 crystalline phases of ice illustrates that although the use of the most common classical potentials in low-temperature simulations is unable to capture the subtleties of the properties of frozen water, the models are still able to predict qualitatively important aspects of the experimental behavior.57 Whether low-temperature clusters are solid remains somewhat open to question,58,59 and establishing the correct result from model calculations will require quantum treatment of nuclei. A quantum treatment would also correctly describe the energy distribution among internal versus intermolecular modes, which conceivably would alter the relaxation path and final state of metastable structures obtained via a given cooling protocol. Overall, these considerations suggest that the present pseudo-potential-based simulation technique can be used as a qualitative tool for analysis of the physics of water cluster anions over a considerable range of stabilization energies, although there is clearly room for improvement in future studies along the present lines. To create cold equilibrium neutral water clusters (“quenched water clusters”, QC), we decreased the temperature of the equilibrium clusters gradually (in 25 K steps) from 300 K to the nominal value by periodically reassigning from a MaxwellBoltzmann velocity distribution in every 100 fs. The quenching trajectory was 10 ps long between each successively lower temperature. For the preparation of the metastable neutral water clusters (MC), the water molecules were first placed randomly with random orientation in a cubic box (lbox ) 36.34 Å) with the restriction that two water molecules were not allowed to be closer to each other than 3 Å. Then, we performed classical molecular dynamics at T ) 0 K until the relative decrease in the potential energy became smaller than 10-7/100 000 steps. Then, the system was thermostatted for 1 ps at the desired (higher) target temperature using Maxwell-Boltzmann reas-
Observables for Cold Anionic Water Clusters
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Figure 1. Time evolution of the ground-state energy of an excess electron from time of attachment to quenched (QC) and metastable (MC) water clusters for representative trajectories at initially T ) 100 K. The nuclear dynamics are adiabatic. Note the different energy scales on the top and bottom panels.
signment sampling every 10 fs, starting in each case from the previous lower temperature. After the preparation of the neutral clusters, we carried out relaxation dynamics of the systems, adding an excess electron to the neutral water clusters. For each group of initial conditions (temperature, size, and preparation method), we ran 100-120 ps long relaxation trajectories starting from 20-50 different initial configurations of the neutral clusters. For the analyses of the relaxed properties of the clusters, we used 2000-5000 configurations for each group from the last 10 ps part of these trajectories. III. Results Starting from the neutral cluster geometry, initial rapid localization of the excess electron on the ground electronic state is followed by a substantial relaxation, in which the electron and the water molecules mutually interact, and both relax. We follow the details of the electron hydration relaxation by monitoring energetic and structural properties of the excess electron. Figure 1 shows some representative time evolutions of the electronic energy on QCs and MCs at 100 K for n ) 45 and 104 cluster sizes. The relaxation is found to always start from very weakly bound, diffuse surface electron states. An ultrafast component of the hydration takes place within the first ∼20 fs (not visible in the Figure). This time scale corresponds to the reorientation of dangling OH bonds with electron localization. The greatest part of the relaxation of the metastable water cluster anions after this ultrafast part typically takes about 1-10 ps. For the QC anions, the system characteristically persists in the initially relaxed, weakly bound state for a significant time without any further relaxation (for example, for 20-25 ps in Figure 1), usually followed by a sudden additional relaxation step. In a few cases, for the smaller quenched clusters (n ) 45), the electron simply remained in the initial weakly bound state without further noticeable relaxation during the
simulation time scale, which is typically terminated at 100-120 ps. It is also evident that although the neutral MC clusters are inherently less stable than QC clusters the VDE of the excess electron is significantly higher in MC anions than in QC anions. We note that in all examined cases (i.e., regardless of cluster size, temperature, and cluster preparation method), the relaxation ends in an SB excess electron state, and no transition was observed to IB states. Now we consider the statistical characterization of the electronic energy for relaxed water cluster anions. Figure 2 shows the ground-state energy distribution of the electron for each of the twelve cases. For the smaller clusters (n ) 45), at the lowest initial temperature (Tnom ) 50 K), a narrow peak appears at around 0.1 to 0.2 eV in each case, indicating the presence of very weakly bound states. These clusters did not relax significantly beyond the initial ultrafast part. At increasing temperatures, the excess electron is, in general, increasingly more stable, as indicated by the distribution shifting to more negative energies. More significantly, the distributions for MCs and QCs are qualitatively different. The quenched equilibrated clusters show a broad distribution of relaxed, well-bound electrons extending to more sizable negative energies, and this band is located at substantially more negative energies for the warmer clusters. For the metastable cases, the distributions for the colder clusters include contributions that are considerably more strongly bound than for the quenched cases. In fact, the metastables exhibit substantially less temperature dependence and overall more stable electron binding than the quenched case. This can be traced to the less stable metastable neutral cluster structures, as discussed in more detail below. It is additionally informative to consider the correlation of the individual binding energies with the actual temperature of each cluster. Because electron bonding releases energy, the kinetic energy will be higher than that of the initial neutral
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Figure 2. Ground-state energy distributions for an excess electron relaxed on quenched (QC) and metastable (MC) water clusters at T ) 50 (solid), 100 (dashed), and 150 K (dotted).
Figure 3. Correlation between the effective temperature (from mean kinetic energy) and the vertical detachment energy (VDE) for the quenched (red symbols) and the metastable (blue symbols) water cluster anions. Different temperatures are indicated by different symbols; T ) 50 (9), 100 (2), and 150 K (b). Diamonds show the average values for each of the 12 different groups, according to the size, temperature, and preparation method.
cluster, and because the MCs bind statistically more strongly, the difference will be larger in this case. We denote as the “effective temperature” the value of the nuclear kinetic energy expressed in kelvins. Figure 3 shows the effective temperature of each cluster as well as the average values for each of the 12 cases. We note that the shifts from the neutral cluster in temperature are not large, as one expects for the number of degrees of freedom. In the Figure, the binding energy (horizontal) axis is labeled as the VDE because in the present nonpolarizable water model, the electronic ground-state energy approximates the VDE. Clearly, although with some overlap, each of the 12 groups of clusters separates well, and they collect
in a relatively narrow temperature range. The averaged temperature-VDE data points ([ in Figure 3) evidence a linear relationship between temperature and VDE, with higher temperatures resulting in gradually greater excess electron stabilization, resulting from greater ability to accommodate the electron. The much more nearly vertical correlation for the metastable clusters corresponds to the weaker temperature dependence seen in Figure 2. Because the slopes of the lines for the metastable and quenched anions are different, the lines approach each other as the temperature increases. This convergent behavior reflects the expectation that the difference in physical quantities of differently prepared clusters should gradually disappear with
Observables for Cold Anionic Water Clusters increasing temperature when the temperature is sufficient to overcome barriers to equilibration. Next, structural properties of the relaxed cluster anions are considered and related to the electron VDEs. The radius of gyration of the electron (variance of the center of mass of the electron distribution) correlates well with increasing VDE. Larger clusters tend to bind the electron more strongly, and the effect is reflected in decreasing radius (for example, 4.15 vs 3.45 Å in n ) 45 and 104 MC clusters at T ) 100 K). The radius also becomes smaller within each group as temperature increases. An example is the tendency of the radii, 5.49, 4.18, and 3.44 Å for n ) 104 QC clusters at T ) 50, 100, and 150 K, respectively. Furthermore, it is clear that the excess electron is more compact on the MC clusters relative to the corresponding QC clusters. We have also performed a hydrogen bonding analysis similar to the one we used previously for an excess electron system at the water/air interfaces.46 In particular, we examine the structural role of unsatisfied water proton donors (not involved in water-water interactions). We also consider what role the unique, double-hydrogen-bonding acceptor (AA) molecules, observed originally by Johnson and coworkers in vibrational predissociation spectroscopy measurements on small water cluster anions,15,20 play in the relaxed structures. We use geometrical criteria for defining hydrogen bonds: two water molecules are hydrogen bonded if the intermolecular oxygen-hydrogen distance is shorter than 2.4 Å, the oxygenoxygen distance is shorter than 3.5 Å, and the corresponding O · · · O-H angle is
