XANES spectra of Bulk Water (Ph. Wernet, A. Nilsson, et al. Science 304, 995 (2004)) Pre-edge peak Post-edge

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1 XANES spectra of Bulk Water (Ph. Wernet, A. Nilsson, et al. Science 304, 995 (2004)) Pre-edge peak Post-edge

2 Transition State Potential Method Consider an electronic transition: Initial state Final state Transition state (A. R. Williams, R. A. degroot, C. B. Sommers, Journ. Chem. Phys. 63(2) 628 (1975) )

3 The energy difference is dependent on the occupation number, Which can be re-written as an integral and approximated as the value of the partial derivative at the center of the interval. The partial derivative of an orbital with respect to occupation number is the energy of that orbital.

4 The Hamiltonian is dependent on the charge density Where 1) A new charge density is calculated with the core occupation number of 1/2. 2) This charge density is used to calculate the Hamiltonian. It's eigenstates are calculated. 3) These are used to calculate the transition matrix elements and energies.

5 Oxygen environments in water (Nilsson, et. al. J. Phys. Condens. Matter 14, L213 (2002)) Tetrahedral, like ice. No pre-edge peak. Broken h-bond acceptor, no change in spectra. A broken donating h- bond, increase in preedge peak intensity.

6 Pre-edge peak and Hydrogen bond configuration Density functional transition state potential theory is used to calculate the spectra for small clusters around an absorbing atom. Three molecules from an 11 molecule cluster, chosen to show the changing peak intensity as a hydrogen bond is weakened. Used to show the relationship between the strength of the Hydrogen bond and the intensity of the pre-edge peak.

7 Pre-edge peak intensity related to number of broken Hydrogen bonds in water. Bulk liquid water XAS Ammonia terminated ice surface Ice surface Bulk ice

8 Assignment of Pre-edge peak in liquid water (Nilsson and Pettersson) Neighboring water molecules are not strongly coupled to the perturbed LUMO and LUMO+1 states on the absorbing molecule. Broken H-bond donor geometry pulls LUMO, LUMO+1 down in energy. Equivalent to bound exciton in Z+1 molecule. On ice, the LUMO and LUMO+1 states form a broad conduction band.

9 Liquid Water has many broken H-bonds Ph. Wernet, A. Nilsson, et. al. Science 304, 995 (2004) DFT-TP is used to assign the pre-edge peak in the XANES spectra of bulk water to the number of broken H-bonds. Surface sensitive photoemission spectra of ice and bulk liquid support this assignment. The relative intensities of pre and post-edge features are used to assign an average H-bond coordination number of ~2.2 to water. These results contradict those reached with most MD simulations ( H- Bonds per molecule). Argument: MD force fields were tuned to reproduce pair correlation functions between elements obtained from x-ray and neutron diffraction. They may not reproduce instantaneous states of the H-bond network.

10 A different argument J. D. Smith, R. J. Saykally, et. al. Science 306, 851 (2004) The Hydrogen bond coordination number can be calculated using an energy cutoff. Two configurations are assumed, with a broken Hydrogen bond and without. They are presumed to follow a Boltzmann distribution By varying the temperature and measuring the intensity ratio you can find the energy difference between the two states. A force field defines a region in configuration space with energies less than this energy. These are considered hydrogen bonded.

11 Liquid water has a tetrahedral H-bond structure J. D. Smith, R. J. Saykally, et. al. Science 306, 851 (2004) Water has a mostly tetrahedral H-bond structure. Even a slightly broken hydrogen bond causes a measurable change to the pre-edge peak. broken hydrogen bonds do not imply a drastic geometry difference. The temperature dependence of the pre and post-edge intensity ratios was used to derive an energy for breaking a hydrogen bond. MD simulations which use this energy to define a broken hydrogen bond reproduce the hydrogen bond coordination number (~2.2) even though the geometry is tetrahedral.

12 Electric Field Distribution in Liquid Water MD Simulation (T. Hayashi, T. Jansen, W. Zhuang, S. Mukamel, J. Phys. Chem. A, (2005))

13 Electrostatic Modelling of H-Bond Fluctuations of XANES in Water Run an MD simulation to determine the time-dependent electric field acting on a given water molecule. Calculate the XANES spectra for a water molecule with an electric field chosen from that distribution, using the DFT transition potential method. Average the spectra over the inhomogeneous distribution of fields. The approach has been applied to H-bonding fluctuations in the nonlinear IR spectroscopy of water. (T. Hayashi, T. Jansen, W. Zhuang, S. Mukamel, J. Phys. Chem. A, (2005))

14 b2 peak Exp a1 peak TP Liquid TP Molecule Oxygen K-edge XAS spectra of water. Solvation blueshifts and broadens peaks a1 and b2. The two theoretical spectra were redshifted (experimental results from Smith, Nilsson, et. al. Science 304, 995 (2005)).