Letter pubs.acs.org/JPCL
Excitation Energy Transfer and Low-Efficiency Photolytic Splitting of Water Ice by Vacuum UV Light Angela Acocella,† Garth A. Jones,*,‡ and Francesco Zerbetto† †
Dipartimento di Chimica “G. Ciamician”, Università di Bologna, V. F. Selmi 2, 40126 Bologna, Italy School of Chemistry, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
‡
S Supporting Information *
ABSTRACT: Experimental estimates of photolytic efficiency (yield per photon) for photodissociation and photodesorption from water ice range from about 10−3 to 10−1. However, in the case of photodissociation of water in the gas phase, it is close to unity. Exciton dynamics carried out by a quantum mechanical timedependent propagator shows that in the eight most stable water hexamers, the excitation diffuses away from the initially excited molecule within a few femtoseconds. On the basis of these quantum dynamics simulations, it is hypothesized that the ultrafast exciton energy transfer process, which in general gives rise to a delocalized exciton within these clusters, may contribute to the low efficiency of photolytic processes in water ice. It is proposed that exciton diffusion inherently competes with the nuclear dynamics that drives the photodissociation process in the repulsive S1 state on the sub-10 fs time scale. SECTION: Spectroscopy, Photochemistry, and Excited States
A
The number of theoretical and experimental studies of water clusters is rapidly growing.14−27 Of note is the water hexamer, a small multicyclic hydrogen-bonded structure, which is the building block of bulk water and is sometimes referred to as “the smallest drop of water” or “the smallest piece of ice”.15,17 The physical and chemical properties of these clusters are central to many phenomena that include phase transitions,28−30 chemical reactions in the Earth’s atmosphere and interstellar space,31−37 cloud formation,38,39 global radiative transfer in planetary atmospheres,31,33,40 and dust formation in the outer solar system and the interstellar medium.35,37 Electronic energy transfer (EET) is a process whereby electronic excited states in molecules and supramolecular systems are transferred between chromophores.41−43 The mechanism, sometimes referred to as resonance energy transfer, is often associated with the name of Förster.44 The mobile excited state is often called the exciton. EET is central to the solar energy harvesting process in biological photosynthetic systems, and it could, in principle, be exploited for solar energy harvesting in artificial systems.45−47 Direct experimental evidence of ultrafast electronic energy transfer across a water dimer bridge was recently discovered.48 This opens up the important question of whether EET may compete with photodissociation processes occurring within water ice. If so, this could explain the low efficiency of photolytic water splitting. In the current work, we address this question with the use of a quantum dynamical model that is applied to a series of
water molecule and its dimer exposed to vacuum UV light spontaneously and quantitatively dissociate.1−7 The first electronically excited state of water, Ã ,1B1, is unbound and proceeds directly to produce H(2S) + OH(2Π).8 This process affords one of the simplest photochemical reactions and is of interest in astrochemistry because it produces the photolysis of ice. The astrophysical conditions differ greatly from those where standard photophysics is usually investigated in the laboratory. However, a wealth of data is available. The H atoms produced upon irradiation at 193 nm have been attributed to the photodissociation of water molecules on the ice surface, while 157 nm light led to a mixture of surface and bulk photodissociations.9 Exothermic and endothermic reactions were proposed as formation mechanisms for singlet and triplet O2.10 Unimolecular dissociation of water to H2 + O(1D) was also identified as a major photoprocess. The surface recombination reaction of OH radicals was shown to produce H2O2 as one of the major photoproducts.11 Interestingly, on the basis of the experimental results of Westley et al.12 and Watanabe et al.,13 photolytic efficiency (yield per photon) for ice is estimated to be in the range of 10−3−10−1. Although the definition of “photolytic efficiency” is study-dependent, these experiments indicate that the photodissociation process, fundamental to many of the subsequent reactions, is significantly less than unity in the case of ice. The question of why the dissociation path is much less efficient in the bulk than that for the isolated molecule is intriguing, especially because the barrierless process of dissociation is expected to produce quantitative water splitting. The reason must lie in the emergent properties of bulk water, which result from the complex interactions between the individual water molecules. © 2012 American Chemical Society
Received: October 11, 2012 Accepted: November 21, 2012 Published: November 21, 2012 3610
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where, εn is the energy of the S0 → S1 transition of water molecule n of the hexamer in its environment and Vnm is the electronic coupling between the nth and mth water molecules. In order to describe the coupling, we employ a Coulomb point dipole approximation, as employed in the Förster theory of energy transfer42,43
water hexamer isomers. In a previous computational study,49 we used a coupled electron−nuclear dynamics approach to show that photodissociation of a water molecule in S1 in the presence of an external oscillating field occurs within 10 fs, which is in line with other studies.1,2 This study focuses on eight of the most common isomers of the water hexamer, namely, the two book isomers (book-1 and book-2), the three cyclic isomers (cyclic-boat-1, cyclic-boat-2, and cyclic-chair), and the cage, prism, and bag structures (see Figure 1). Quantum dynamics simulations are performed on
Vnm =
1 κnm|μn ||μm | 3 4πε0 R nm
where μn and μm are the transition dipole moments of the nth and mth water molecules to S1 and Rnm is the distance between them. The term κnm is the orientation factor given by κnm = μn̂ ·μm̂ − 3(R̂ nm·μn̂ )(R̂ nm·μm̂ )
each of these isomers to gain insight into the energy-transfer process occurring in water hexamers within the first few femtoseconds after photon absorption. The quantum dynamics simulations are performed in the site basis. Equation 1 describes the formal Frenkel−exciton Hamiltonian used in the simulations 6 n=1
−1 ⎛ iH δt ⎞ ⎛ iH δt ⎞ |Ψ(t + δt )⟩ = ⎜1̂ + S ⎟ ⎜1̂ − S ⎟|Ψ(t )⟩ ⎝ 2ℏ ⎠ ⎝ 2ℏ ⎠
n,m≠n
(4)
The time-dependent system wave function used in the dynamics, Ψ(t), represents the distribution of the exciton over the entire water cluster during the quantum trajectory and is described by |Ψ(t)⟩ = ∑i ci(t)φi, where ci are complex-valued amplitudes and {φi} are the set of orthonormal basis functions
6
∑ εn|n⟩⟨n| + ∑
(3)
where all of the vectors are unit vectors. All eight of the clusters were optimized at the CAM-B3LYP/ 6-31++G** level of theory.50,51 All stationary points were found to correspond to genuine minima according to harmonic frequency analyses. The B3LYP functional is known to produce accurate geometries of water hexamers,21 and the 6-31++G** basis set is appropriate for hydrogen-bonded systems because it includes both diffuse and polarization functions on the oxygen and hydrogen atoms. We find that CAM-B3LYP also produces geometries similar to the MP2 optimized ones (see the Supporting Information (SI) for details). For each of the water molecules, the S0 → S1 transition energies, εi, and the transition dipole moments, μi, are calculated at the TD-CAM-B3LYP/631++G** level. This functional was chosen because it provides a better description of charge-separated states than the popular B3LYP functional and should be well-suited to excited-state calculations of water clusters. To correctly describe the excitation energies and transition dipole moments in the site basis, all of the calculations for the individual water molecules were performed in the presence of a background point charge distribution, which mimics the presence of the other water molecules in the cluster. This was achieved by distributing the Mulliken charges obtained from the optimized ground-state structures at the CAM-B3LYP/6-31++G** level. To assess the quality of this approximation, the electric dipole moments of the individual water molecules were summed and the resultant vectors shown to be similar in both direction and magnitude to electric dipole moment of the associated cluster. Full details of the S0 → S1 transition energies, transition dipole moments, and the electric dipole moments are supplied in the SI. For comparative purposes and as a further validation of the theoretical methodology employed in this study, excited-state calculations on the water molecule and water dimer at both the EOM-CCSD/cc-aug-pVTZ and the TD-CAM-B3LYP/6-31+ +G** levels of theory were preformed. Details can also be found in SI. In the quantum dynamics simulations, the exciton wave function is propagated by employing the numerical quantum propagator52
Figure 1. CAM-B3LYP/6-31++G** optimized geometries of the eight water hexamer isomers: (a) book-1, (b) book-2, (c) cyclic-boat-1, (d) cyclic-boat-2, (e) cyclic-chair, (f) prism, (g) cage, and (h) bag. The same molecule ordering is used in Figures 2 and 3.
HS =
(2)
(Vnm|n⟩⟨m| + Vmn|m⟩⟨n|) (1) 3611
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corresponding to the water molecule sites. In effect, it is a linear combination of the S1 states associated with each water molecule. The matrix, 1̂, is the unit matrix, and δt is the time step used in the simulations (2 atomic units ≈ 0.05 fs). In the simulations, instantaneous excitation is assumed, and an explicit field term is not included in the Hamiltonian. At each point of a trajectory, the density matrix is constructed from the wave function, eq 5. The diagonal elements of the density matrix correspond to the exciton populations for each of the water molecules at time t. ρnm (t ) = cn(t )cm*(t )|n⟩⟨m|
(5)
Further details on our implementation of this propagator can be found in ref 49 and references within. The exciton dynamics was carried out on water hexamer isomers, a−h of Figure 1. Six trajectories for each isomer were run with the exciton initially localized on each of the six water molecules (i.e., one of the wave function amplitudes is initially set to unity, with all of the others set to zero). A seventh trajectory was added for each isomer, with the exciton initially delocalized over all of the water molecules in the cluster (i.e., each of the wave function amplitudes are initially set to 1/√6). The geometries of the clusters remain stationary during the quantum dynamics simulations. This particular set of water hexamers was chosen with the intent of providing an ample set of ground-state structures and hence provided a good sampling of the potential energy surface. In a sense, the eight structures of the water hexamer are used in the place of randomly generated Monte Carlo structures. By performing the set of trajectories with seven different starting conditions for all of the hexamers considered, we are able to investigate the two limiting scenarios, namely, the case of an initially localized exciton (starting on any water molecule in the cluster) and that of a fully delocalized exciton. The methodology employed here is in line with the fact that most experimental measurements were performed at 90 K and is relevant to the low temperatures of astrophysical conditions with a range of 10−100 K.53 Figure 2 displays examples of population dynamics for trajectories with initially localized states, for each of the isomers. In each case, the fastest exciton dynamics is displayed. Different colors are associated with a different water molecule site. The exciton dynamics displays a quasi-oscillatory character typical of electron dynamics in atomic and molecular systems. For all of the cases, the exciton rapidly moves from its initial site to other water molecules within the cluster. For some clusters, the oscillating behavior is similar to the Rabi cyclic behavior of a two-state quantum system. This is most clear in the case of the book-2 and bag isomers. This effect dominates when two of the water molecules are more strongly coupled to one another (eq 2) than to the others. For other trajectories, the exciton simultaneously moves to multiple sites, effectively delocalizing over the cluster (e.g., cyclic-boat-1). The plots shown in Figure 2 are marginally faster than most of the others that are not shown (see the SI for all other trajectories). However, in nearly all cases, EET to multiple sites occurs within a fraction of the period of an OH stretch (
