Energy Transfer and Restructuring in Amorphous Solid Water upon Consecutive Irradiation

Interstellar and cometary ices play an important role in the formation of planetary systems around young stars. Their main constituent is amorphous solid water (ASW). Although ASW is widely studied, vibrational energy dissipation and structural changes due to vibrational excitation are less well understood. The hydrogen-bonding network is likely a crucial component in this. Here, we present experimental results on hydrogen-bonding changes in ASW induced by the intense, nearly monochromatic mid-IR free-electron laser (FEL) radiation of the FELIX-2 beamline at the HFML-FELIX facility at the Radboud University in Nijmegen, The Netherlands. Structural changes in ASW are monitored by reflection–absorption infrared spectroscopy and depend on the irradiation history of the ice. The experiments show that FEL irradiation can induce changes in the local neighborhood of the excited molecules due to energy transfer. Molecular dynamics simulations confirm this picture: vibrationally excited molecules can reorient for a more optimal tetrahedral surrounding without breaking existing hydrogen bonds. The vibrational energy can transfer through the hydrogen-bonding network to water molecules that have the same vibrational frequency. We hence expect a reduced energy dissipation in amorphous material with respect to crystalline material due to the inhomogeneity in vibrational frequencies as well as the presence of specific hydrogen-bonding defect sites, which can also hamper the energy transfer.


Introduction
Interstellar and cometary ices play an important role in the formation of planetary systems around young stars, and hence these ices have received quite a lot of attention in the astrochemical community. The main constituent of interstellar ices is amorphous solid water (ASW), 1 which is formed on dust grains in dark molecular clouds from atomic and molecular oxygen reacting with hydrogen atoms. [2][3][4] ASW is porous when deposited at low temperatures and pressures, but chemically formed ice is compact using the excess energy for restructuring of the ice. 5 Also, the excess energy of other surface reactions, the formation of H 2 for instance, can impact the structure of the underlying water surface. 6 This means that the excess energy can be transferred to an ice layer. Recent Molecular Dynamics simulations 7 showed that there is little energy transfer between different types of excitation (translational, vibrational, and rotational), but that vibrational excitation of a molecule on the surface can efficiently dissipate to an ASW surface through the admolecule-surface interaction. However, the efficiency of this process varies largely from case to case. The hydrogen-bonding network of ASW is likely a crucial component in this. The exact nature of the hydrogen bonding network in amorphous ices is not fully understood. So far, most vibrational excitation studies have focused on liquid water. [8][9][10][11][12] In solid materials, vibrational energy dissipation is generally investigated for crystalline materials, often metals, and the energy transfer is treated by interaction with a phonon bath. 13 It is, however, not clear to what extent this holds for amorphous, molecular materials.
ASW is a metastable state of ice, and vibrational energy could, in principle, lead to structural modification toward the stable crystalline structure. In the present work, structural changes are identified by infrared (IR) spectroscopy. As far as we are aware, only a handful of studies have focused on low-energy IR irradiation of ASW, [14][15][16][17][18] revealing wavelengthdependent irreversible structural changes of these ices. The exact oscillator frequencies of the O-H stretch of water molecules depend sensitively on the specific surroundings and hydrogen bonding structure of the particular water molecule. While this does not allow us to study long-range crystallization effects, local restructuring towards a perfect surrounding of two hydrogen-bond acceptors and two donors (DDAA) can be detected. We have used a similar method in the past. 17 The absorption feature associated with a perfect DDAA surrounding increased upon IR irradiation. Concurrently, a decrease in defect sites with missing hydrogen bonds was observed. The exact changes in absorption depend on the irradiation wavelength, but the effect was found for irradiation at stretch, bending, and libration frequencies. Irradiation at off-resonance frequencies did not result in observable changes. Classical Molecular Dynamics simulations using an oscillating electric field to sim-ulate the IR irradiation could reproduce the effect. They showed that the changes occur through local heating where classes of oscillators are excited.
The present paper aims to study the dissipation of vibrational energy and its consequences for restructuring of ices in more detail. Vibrational excitation can occur upon resonant irradiation in the IR and terahertz (THz) spectral ranges, and upon reaction, in particular bond-formation reactions. Here we use consecutive IR irradiation at different frequencies in the 3 µm O-H stretch region to study history-dependent and wavelength-dependent effects. Molecular Dynamics simulations supplement the experimental results. Two types of simulations are performed: sequential irradiation of ASW and vibrational excitation of individual molecules. Energy transfer is analyzed in terms of molecular vibrations, due to the amorphous and molecular nature of ASW.

Experimental and computational methods Experiments
Experiments were performed in the ultrahigh vacuum (UHV) Laboratory Ice Surface Astrophysics (LISA) end station at the HFML-FELIX facility, Radboud University in the Netherlands. The version of the LISA setup used in this work was described in Noble et al. 17 , i.e. a prior version of the setup compared to the most recent setup as presented in Ioppolo et al. 19 .
Briefly, the LISA setup has been designed and optimized to perform selective IR/THz irradiation of space-relevant molecules in the solid phase when coupled to the free-electron lasers (FELs) FELIX-1 (∼30-150 µm) and FELIX-2 (∼3-45 µm). At the center of the main chamber, a custom-made 30×30×50 mm (l×w×h) oxygen-free high thermal conductivity (OFHC) copper block substrate with four optically flat gold plated faces is in thermal contact with a closed-cycle helium cryostat system. The substrate temperature is controlled in the range of 15-300 K using a Kapton tape heater connected to the OFHC copper block and regulated with a temperature controller capable of reading temperatures through an uncalibrated silicon diode fixed at the bottom of the substrate. The OFHC copper block can be manipulated in the z and θ directions through a z-translator with a stroke of 50.8 mm and a rotary platform, respectively, allowing the exposure of its all four faces to the FEL beam at numerous different spots (i.e. a minimum of 6 unprocessed spots per block face).
For all experiments described here, deionized water was purified via multiple freeze-pumpthaw cycles and dosed onto the gold-coated copper substrate by background deposition through an all-metal leak valve connected to a 6 mm tube that faces one of the walls of the main chamber. Two ice morphologies were studied, namely, porous ASW (pASW) and compact ASW (cASW). Porous ASW samples were prepared in the main chamber with a base pressure better than 8×10 −9 mbar and a base temperature of 16.5 K. Porous ASW was deposited via background deposition for 370 seconds at 1.1×10 −6 mbar. A thickness of ∼0.25 µm for pASW was chosen to ensure that photons fully penetrated the ices, while the ice had a high enough IR signal-to-noise in absorbance to monitor subtle structural modifications via FTIR spectroscopy. Compact ASW samples were prepared with the substrate at 105 K and water deposited by background deposition at a pressure of 1.0×10 −6 mbar for 480 seconds. Compact ASW was then cooled to 20 K before exposure to FEL radiation. During deposition, FEL irradiation, and temperature-programmed desorption (TPD) experiments, ices were monitored by means of Fourier transform infrared (FTIR) spectroscopy (4000-600 cm −1 , 2.5-16.6 µm) at a grazing angle of 18 • with respect to the surface with a spot size of ∼3 mm in height (diameter) and at a spectral resolution of 0.5 cm −1 . The reference spectrum was measured with 512 scans, while the experimental spectra were measured with 128 or 256 accumulated scans.
Ices were then irradiated using the FELIX-2 IRFEL source (i.e. macropulses with a duration of about 8 ms at 5 Hz repetition rate and a micropulse spacing of 1 ns with a laser energy between 5-20 mJ) at frequencies in the mid-IR (2.7-3.25 µm). All IRFEL irradiations were carried out for 5 minutes to ensure complete saturation of any structural change in the ice layers. At all wavelengths, the laser fluence at the sample was approximately ∼ 0.2 J/cm 2 .
The spectral FWHM of the FELIX beam is on the order of 0.8 % δλ/λ for all wavelengths.
The FEL beam impinges the gold-plated flat substrate at an angle of 54 • with respect to the surface with a spot size of ∼2 mm in height (diameter) that fully overlaps with the FTIR beam. Since the FTIR beam was larger than the FEL beam, part of the ice probed by the FTIR was not exposed to FEL irradiation. Hence, FTIR difference spectra acquired before and after FEL irradiation were investigated to highlight changes in the ice. In this paper, we discuss FEL irradiations in terms of wavelength and FTIR spectra in wavenumbers to reflect the higher spectral resolution in the FTIR data as opposed to the transform-limited bandwidth of the FEL radiation. "Fresh", unirradiated ice spots were exposed to single FEL irradiations between 2.7 and 3.25 µm. The possibility of adjusting the sample height allowed us to start new irradiation series on other unirradiated ice spots obtained during the same single ice deposition. Results from FEL irradiations on "fresh" spots were compared to a series of irradiations at the same ice spot carried out from "high" to "low" and from "low" to "high" wavenumbers (hereafter referred to as "blue to red" frequencies (from 2.7 to 3.3 µm) and "red to blue" frequencies (from 3.3 to 2.7 µm), respectively) across the water OH stretching mode. Detailed experimental settings for all irradiation experiments can be found in the Supplementary Information.

Simulations
Classical Molecular Dynamics (MD) simulations were performed using the LAMMPS package (version 7/08/18). 20 Water molecules were treated flexibly using the TIP4P/2005f potential. 21 To confidently prove structural changes in the ice, either large samples are needed or many trajectories of small samples. TIP4P/2005f gives a good trade-off between computational cost and reproducibility of the experimental spectra. Polarizable flexible potentials would be more accurate in describing vibrations, since they also take the many-body effects on the vibration into account as well as the changing dipole with the vibration. Lambros et al showed in a comparison study that fq-MB-pol and MB-pol 22 are particularly good in this respect. 23 Two ASW samples of 2880 molecules were used: one mimicking porous ASW and one compact ASW. Both were obtained by quenching a water sample to 10 K after a simulation in the canonical ensemble (N V T ) at 400 K for 50 ps. The non-porous sample has a cubic simulation box with a length of 45.07Å, resulting in an average density of 0.94 g cm −3 , in agreement with the experimental density of ASW. The porous sample has a box of 48Å and an average density of 0.78 g cm −3 . In the latter case, the quenching simulation resulted in a sample with a large pore, effectively creating both surface and bulk in one simulation box.
The local density is rather similar in both cases. This is the unannealed cASW sample. The compact ice sample was further annealed by heating it to 70 K during 50 ps to create an annealed cASW sample. We think that the latter is more representative of the experimental cASW ice which is formed through deposition at higher temperatures.
Irradiation was simulated by employing an oscillating electric field of the desired frequency along the z-direction, with a maximum amplitude of 15 mV/Å. All simulations were done in the N V T ensemble where only 16 molecules out of 2880 were thermostated. The oscillating electric field was switched on for 2 ps and switched off again for 18 ps. This procedure was repeated 10 times. Properties were then calculated during another 20 ps while the full structure was thermostated. The whole procedure hence lasted 220 ps and was then repeated at a different wavelength. The 10 × 20 ps sequence aims to mimic the micropulses of the FEL irradiation. One should realize that the micropulse interval of FELIX is much longer (1 ns) than the 18 ps intervals with an electric field in the simulation.
However, the cooling rate of the thermostat, even when applied to only 16 molecules, is much higher than the experimental cryostat and the overall energy that is taken from the system during the light-off interval is higher in the simulation than in the experiments (see Ref. 17 for more details). The 16 molecules are randomly distributed across the ice.
A setup where the thermostated molecules are located together might be a more realistic represention of the experimental setup where only the bottom of the ice layer is connected to a thermostat. Simulations with such a setup resulted in inhomogeneous results with local hot spots far away from the thermostated region. However, this is in part due to the short time interval between pulse in the simulations (18 ps) whereas the experimental interval is 1 ns. The random distribution is hence a compromise and together with the high cooling rate this likely leads to a lower limit of the effect in the simulations. VMD 24  Analysis in terms of hydrogen-bonding structure Spectra were fitted by a combination of eight Gaussian functions (G1 -G8) to aid in the interpretation of the spectral changes observed in the experiments. The procedure, based on an in-house python script, has been previously described in Ref. 17 The different Gaussians account for the contribution of different oscillator families to the O-H stretch ice feature.
A combination of five known oscillator modes in the bulk of the ice spectrum (between ∼ 3050-3450 cm −1 ) plus three surface-specific modes (two dangling-H modes at 3720 and 3698 cm −1 , one dangling oxygen mode at 3549 cm −1 and the tetra-coordinated surface s4 mode at 3503 cm −1 ) were identified from literature data. 14,[25][26][27][28][29] For all experimental difference spectra, the same combination of these eight Gaussian functions (G1 -G8) was fitted to each spectrum, with identical constraints placed on peak position and full width half Similar hydrogen bonding information was obtained from the simulation trajectories by using an in-house python script. This script determined the hydrogen bonding structure for each water molecule in terms of donor and acceptor, taking into account the periodic boundary conditions. A radical cutoff of 3.5Å and a radial cutoff of 30 • was applied. 24 Averages and standard deviations of the total number of hydrogen bonding structures were obtained by averaging during 20 ps while the system is fully thermostated.

Irradiation of pristine ice
Before studying the effect of successive irradiation, the effect of irradiation on pristine ice is shown. Individual pASW samples were irradiated at 2.7, 3.1, and 3.25 µm. Panel a of Fig. 1 shows the spectrum before irradiation in blue and the difference spectrum after irradiation at 3.1 µm in red. The blue spectrum is scaled by a factor of 0.2 to ensure that both spectra can be plotted on the same scale. The difference spectrum shows both an increase and a decrease in absorption intensity. The spectra were analyzed in terms of hydrogen bonding structures. Figure 1b shows the relative change in hydrogen bonding structures with respect to the non-irradiated spectrum as a function of irradiation wavelength. The error due to constant low-level residual water deposition in the chamber was found to be 2% on the DA oscillator, <2% on DAA, and <1% on the other bands. This is hence within the size of the symbols of The overall changes are smaller at these wavelengths, and changes in the DA oscillators, which are mostly located at the surface, become more important.

Sequential irradiation in the 3 µm band
A porous ASW sample was prepared at 16.5 K and subsequently irradiated for 5 minutes at a wavelength of 2.7 µm after which a new spectrum was recorded. The resulting difference spectrum can be observed in Fig. 2

in cyan. A very small increase in absorption intensity
can be observed at 3200 cm −1 and a tentative decrease around 3500 cm −1 . The procedure was repeated at the same spot for irradiation at 2.8 µm. The difference spectrum with respect to previous irradiation can be seen in light green in Fig. 2. A larger difference can be observed and the decrease in the spectrum appears to occur at slightly lower wavenumbers.
Again the spectra are fitted with eight Gaussians representing the different oscillator classes.
The relative change in absorption after each irradiation is plotted in Figure 3a. It can be observed that the decrease in spectral intensity for 2.7 µm is mainly due to a decrease of the  This is understandable since both hydrogen bonding patterns are associated with surface structures and the total surface area is substantially smaller than for porous ASW because of the absence of pores.
Again, blue-to-red and red-to-blue irradiation lead to the same overall changes at the end of the irradiation sequences. The relative changes here are, however, much smaller than for porous amorphous solid water. Part of this might be due to the reduced surface area, but the main reason is likely that the ice is grown at elevated temperature, which means that the ice has already been annealed to some extent and that the restructuring events with a low barrier have already occurred.

Simulations of sequential irradiation
Molecular Dynamics simulations were performed to study the changing ice on a molecular level and study the role of energy dissipation. Six simulations were performed following the procedure described above. In each case, seven irradiation events at different wavelengths of the electric field have been simulated, each consisting of ten irradiation and subsequent cooling cycles. In three of the six simulations, the wavelength of the electric field increased throughout the seven irradiation events and the other two had a decreasing wavelength.   Figure 5: The simulated oxygen-oxygen pair distribution function after sequential irradiation compared to the initial g OO (r). A porous ASW sample is sequentially exposed to the electric field from blue-to-red. Once such a small structural change has occurred, these molecules are no longer available for further restructuring. Since these rearrangements can be triggered by different excitations, at different wavelengths, the irradiation order determines which defect sites can still restructure at a given wavelength. Figure 6c shows that many different molecules have changed hydrogen bonding structure at 3.0 µm. These are no longer available for changes when the ice is irradiated at 3.1 µm (Fig. 6e) where fewer molecules are affected. For red-to-blue irradiation, it is the other way around and more molecules are affected at 3.1 µm (Fig. 6f) than at 3.0 µm (Fig. 6d)

Dissipation of energy
IR irradiation excites molecules vibrationally, which ultimately leads to heating of the ice.
The experiments suggest that the energy will remain local. In this section, we will follow the energy transfer in the ice by MD simulation to study how fast and how far the energy is dissipated. In this case, the full ice is not exposed to the electric field but rather only a single molecule. The dissipation is then followed by monitoring the internal kinetic energy of this molecule and its surrounding molecules as a function of time. The internal kinetic energy is used as a measure of the vibrational excitation of the individual molecules. This is done at three different locations in the ice: at a bulk location, close to the surface of the pore, and at a location with a high defect density. Hereafter, we present one example from each of the three excitation locations. Figure 7 shows the excitation of a bulk molecule.
The excited molecule is molecule 1 in panel a and is indicated in dark blue in both panels.
Molecules 2 to 12 are the eleven molecules closed to molecule 1 and are ordered in centerof-mass distance to molecule 1. Only molecule 1 is exposed to a chirped electric field pulse 2.7-2.9 (a) shows that vibration wavelengths of the two bonds in molecule 1 are 2.93 and 3.07 µm (see Table 1). The latter becomes predominantly excited upon exposure to the electric field.  Table 1   shows, again, the internal kinetic energy, which looks very different from Fig. 7a. In Fig. 8a, many more molecules are involved in the dissipation of the energy, but at much lower energies as compared to the previous example. Table 2 shows that, in this case, the molecules are  Restructuring occurs through local heating of individual molecules that can then reorient themselves. It does not occur through excitation of the hydrogen bonding network. The internal kinetic energy of three specific hydrogen bonds was followed in time as a measure of excitation. We chose the hydrogen bonds between 1 and 4, and 1 and 5, as well as one that did not play any role in the energy dissipation. Very little time variation was observed for all three internal kinetic energy plots. This suggests that although hydrogen bonds play a role in the transfer of excitation, they do not become excited themselves. Figure 9 shows a third and final example. In this case, a molecule is selected in a region with a high defect density to further investigate the role of DDAAA sites in the dissipation of energy. Table 3 shows that this molecule is hydrogen bonded to three defect sites, two DDAAA and one DDA site. It is resonant with the oscillation of all three defect molecules. Panel a of Fig. 9 shows that both molecules 4 and 5 are excited by molecule 1,    This leads to local heating of the environment and structural changes. These structural changes are not limited to the molecules that are excited at the specific irradiation wavelength but can also include neighboring molecules. This causes the exact changes at a given irradiation wavelength to depend on the irradiation history of the sample, since restructuring pathways that are kinetically accessible might have already occurred during previous irradiation events. Most restructuring events concern translation or rotation of a water molecule without breaking existing hydrogen bonds. For more elaborate restructuring that can lead to crystallization, hydrogen bonds will need to be broken. The simulations show that vibrational excitation of the O-H bond does not lead to hydrogen bond breaking or to excitation of hydrogen bonds. For the latter, we likely need to irradiate at frequencies between 5 and 7 THz. Whether excitation of hydrogen bonds also results in large hydrogen bond rearrangement is beyond the scope of the current study. The authors of that study attribute the difference in heating lifetimes to the difference in dipolar coupling between crystalline ice and liquid water. We expect amorphous solid water to behave similarly to liquid water in this respect and indeed the 0. Defects with missing hydrogen bonding, like DAA and DDA, do not appear to impact the energy transfer, whereas DDAAA defects can block the transfer in some cases. Based on our results, we expect the vibrational energy transfer in ASW to be less efficient than in crystalline water ice for two reasons. First, the inhomogeneity in oscillation wavelengths is much smaller in crystalline material, as evidenced by the narrower O-H stretch band, and hence more molecules will be in resonance with each other leading to more dissipation channels. Secondly, DDAAA defect sites that can block energy transfer will not, or rarely, be present in crystalline water ice. Johari and Andersson showed that the thermal conductivity in amorphous solids is indeed generally much lower than in crystalline solids. 32 They attributed this to the lack of long-range phonons in amorphous solids. The present work studied energy transfer in a wavelength regime that is more suited to a molecular description of the energy transfer, since lattice vibrations are not excited at these wavelengths. Although we cannot exclude the role of phonons in the work by Johari and Andersson, our work shows that the difference in thermal conductivity between ASW and crystalline ice can also be explained in a molecular framework. Noble and S. Ioppolo. All authors contributed to data interpretation and commented on the paper.

Supporting Information Available
Experimental settings for the different irradiation experiments