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1 DOI: /NCHEM.1680 On the nature and origin of dicationic, charge-separated species formed in liquid water on X-ray irradiation Stephan Thürmer, 1 Milan Ončák, 2 Niklas Ottosson, 3 Robert Seidel, 4 Uwe Hergenhahn, 5 Stephen E. Bradforth, 4 Petr Slavíček, 2* and Bernd Winter 1* 1 Helmholtz-Zentrum Berlin für Materialien und Energie, and BESSY Berlin, Germany 2 Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, Prague, and J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, Prague 8, Czech Republic 3 FOM Institute AMOLF, Science Park 102, 1098 XG Amsterdam, The Netherlands 4 Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA 5 Max Planck Institute for Plasma Physics, EURATOM Association, Wendelsteinstr. 1, Greifswald, Germany Estimate of the onset of Auger spectra for 2h and 1h 1h states We can conveniently investigate energetics of charge localized and charge delocalized states with the use of constrained density functional technique; see below for computational details. 1 We have then modeled Auger spectra of (H 2 O) 3 and (D 2 O) 3 using reflection principle based on path-integral molecular dynamics simulations. 2 The results are presented in Figures S1 and S2. We consider three types of final states: (a) Two holes localized on the initially O1s ionized water molecule this is the 2h final state corresponding to normal Auger process yields an energy distribution with a peak maximum near 498 ev for singlet doubly charged state, and 499 ev for triplet final state. The value is in fairly good agreement with the experimental value of the main peak at 504 ev (for bulk water) if we took the solvent polarization contribution (estimated at the polarizable continuum model to be approximately 3 ev) into account. (b) Delocalization of the two holes, each on one water molecule, shifts the lowest-energy peak to about 505 ev and 509 ev for singlet and triplet final states, respectively. (c) Delocalization of the two holes on the entire water trimer yields a maximum at 507 ev and 510 ev for two multiplicities. Note that we should again add the polarization stabilization to the calculated energies, and therefore the electrons corresponding to NATURE CHEMISTRY 1

2 delocalized final states in the original water geometries should appear around ev. These numbers roughly fall into the observed side peak in the experiment. The important result here is that the peaks corresponding to the local Auger and ICD final states, are the same for (H 2 O) 3 and (D 2 O) 3 trimer. Hence, with H 2 O(aq) and D 2 O(aq) having the same ICD final-state energies, hydration geometries and molecular structure cannot be the reason for the experimentally observed difference in Auger signal intensities. Figure S1 Photoionization spectra of the water trimer with a) constrained 2+ charge on one molecule; b) constrained 1+ charge on two water molecules; c) charge 2+ on the whole water cluster. Singlet states are shown. Figure S2 Photoionization spectra of the water trimer with a) constrained 2+ charge on one molecule; b) constrained 1+ charge on two water molecules; c) charge 2+ on the whole water cluster. Triplet states are shown. NATURE CHEMISTRY 2

3 Computational details: The energetics of doubly ionized final states with localized and delocalized charge in the ground-state water geometry was estimated for the water trimer. The energies of doubly ionized states for the trimer ensemble was calculated with constrained density functional theory (CDFT) method 1 as implemented in NWCHEM programme 3. The CDFT method allows for a computation of ground state energies with a charge confined to a specific molecular unit. We have used the BHandH functional and aug-cc-pvdz basis set. The Auger spectra were modelled for an ensemble of structures, considering the two positive charges delocalized either over two or three water molecules or localized on a single molecule. The lowest-energy states with the singlet and triplet multiplicities were considered. Ground-state distributions of the clusters for light and heavy water have been obtained with path integral molecular dynamics (PIMD) technique 2. The energies and forces were calculated at the RI- DFT/PBE level using g** basis set. The simulation was performed at a temperature of 180 K, using 30 beads, with the overall simulation time of 150 ps. Equations of motion were propagated with reversible reference system propagator algorithm (r-respa) and canonical ensemble was guaranteed by coupling the system to a chain of Nose-Hoover thermostats. The overall duration of the PIMD simulations was 150 and 50 ps for trimer and pentamer, respectively, using a time step of 20 a.u. (~0.5 fs). The kinetic energies of Auger electrons were calculated here as E Auger = E DI (in ev) where the value of ev (538.1 ev in water) corresponds to binding energies of 1s electron in water clusters 4 and E DI is the double ionization energy of the respective clusters. The probability of Auger-type transition was considered to be independent of the molecular geometry for a give type of final state. The effect of the long-range polarization in the Auger electron kinetic energy was estimated within a polarizable continuum model (PCM), considering second ionization in water. Only the optical part of the solvent response was considered, as the electron ejection within Auger decay is essentially a vertical process. Different dynamical processes in the water pentamer upon core ionization Figure S3 shows potential energy curves for core-ionized states of water pentamer. The pentamer coordinates were taken from I h ice optimized with the TIP4P/2005 empirical potential. The pentamer was chosen as it represents the simplest model for liquid water with the water molecule tetrahedrally solvated. We consider various possible reaction coordinates for hydrogen atom: (A) dissociation of a free O H bond; (B) hydrogen transfer of the central unit water; (C) NATURE CHEMISTRY 3

4 bending motion of the central water unit; (D) rotation of two water molecules solvating the central units. It follows from panel (A) that a dissociation of a free OH bond is not possible in the ionized state. This contrasts with the situation for a core-excited system in which the OH bond readily dissociates. This observation explains why no significant dynamical effect on the Auger spectrum is observed in the gas phase for the core-ionized molecule while the Auger spectrum broadens for core excited isolated H 2 O. However, in a hydrogen bonded system the O H bond dissociation is energetically feasible. Core-ionized water molecule releases the positively charged hydrogen atom which is accepted by a neighboring water molecule. The driving force for this reaction is not very strong but the vibrational O H wave packet is full of energy, and its dispersion is thus very fast. Motion along the remaining two coordinates, (C) and (D), is also energetically allowed. However, the energy deposited in the zero-point motion in the bending motion and librational motion is smaller compared to the O H vibration. It is therefore expected that O H dissociation is the dominant dynamical process following the core ionization. Figure S3 Energies of the ionization states in the water pentamer for (A) dissociation of a free O-H bond; (B) hydrogen transfer from the central water molecule; (C) bending of the water molecule; (D) rotation of two water molecules. The potential energy curve corresponding to the core ionization in the central water units is marked by red color. NATURE CHEMISTRY 4

5 Comparison of singlet and triplet ionized states curves for the water dimer Figure S4 compares potential energy curves of singlet and triplet doubly ionized states for the water dimer system along the proton transfer coordinate. The dimer coordinates were taken from I h ice optimized with the TIP4P/2005 empirical potential, the O O distance was set to 2.7 Å typically found in condensed-phase water (compared to longer O O distances observed in gasphase molecular clusters). It is seen that both curves are qualitatively similar, predicting in both cases a steep decrease of the final energy of the local Auger process (lowest-energy states with a localized charge are marked by red color). Figure S4 (A, B) Energy of doubly ionized states of the water dimer with singlet and triplet multiplicity for hydrogen transfer coordinate with respect to the ground state of neutral water molecule. The lowest-energy states with two holes on a single (hydrogen donor) water molecule are marked by red dots. NATURE CHEMISTRY 5

6 References 1 Kaduk, B., Kowalczyk, T. & Van Voorhis, T. Constrained Density Functional Theory. Chem. Rev. 112, , (2012). 2 Svoboda, O., Oncak, M. & Slavicek, P. Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. II. Photoionization. J. Chem. Phys. 135, (2011). 3 Valiev, M. et al. NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations. Comput Phys Commun 181, , (2010). 4 Björneholm, O., Federmann, F., Kakar, S. & Möller, T. Between vapor and ice: Free water clusters studied by core level spectroscopy. J. Chem. Phys. 111, (1999). NATURE CHEMISTRY 6

7 Cartesian coordinates of the structures used (in Ångstrom) Water dimer O H H O H H Water pentamer O O O O O H H H H H H H H H H NATURE CHEMISTRY 7