Calculation of X-ray adsorption spectra at finite temperature: spectral signature of H-bond breaking in water P. Giannozzi Universit` a di Udine and Democritos National Simulation Center, Italy Work done in collaboration with Balazs Het´ enyi, Filippo de Angelis, Roberto Car Universit´ e Paris VI, 3 Novembre 2009 – Typeset by Foil T EX –
H-bond network in Water and Ice Current structural model for Ice and Water: • Ice (at = 0 ): hexagonal crystal P structure with well-defined H-bond network: each molecule has two ”donor” and two ”acceptor” Hydrogen bonds, with tetrahedral local arrangement • Water (at P = 0 ): crystalline order lost, H-bond network still present. How much of the H-bond network really survives in water?
Results from X-ray spectroscopy X-ray adsorption, Oxygen K -edge (from 1 s to empty states), especially near-edge fine structure (NEXAFS): • sharp bands in gas phase that broaden and shift in condensed phases; • in particular, pre-edge features (at ∼ 535 eV) observed in condensed phases, stronger in liquid (d,e) than in ice (a); • results for surfaces (b) similar to gas phase, different from bulk Ph. Werner et al., Science 304 , 995 (2004)
Interpretation of X-ray spectroscopy Calculations based on density-functional theory support the following interpretation (Werner et al.) : • pre-edge feature coming from molecules with one donor H-bond broken • sharp features at surface coming from molecules with all donor H-bond broken • as many as 80% of H-bonds broken in water at ambient conditions! The latter point is very controversial: both other experiments and Molecular Dynamics (MD) simulations yield a much smaller (10 ÷ 20 %) fraction of broken H-bond
Theoretical X-ray spectroscopy More accurate X-ray spectra may help in clarifying this controversy. Previous DFT calculations were based on small model clusters obtained with classical simulations. Present results ( B. Het´ enyi et al., JCP 120 , 8632 (2004)) : • based on ab-initio MD simulations at finite temperature • take into account the effect of matrix element and not only of the Density of States (DOS) of unoccupied orbitals: Γ = 2 π h | T i → f | 2 δ ( E f − E i ) , T i → f = � Ψ i | e · r | Ψ f � ∼ � ψ 1 s | e · r | ψ f � ¯ ( Ψ i,f and ψ 1 s,f are respectively many-body and one-electron initial and final states)
Theoretical approach • Ab-initio finite-temperature Car-Parrinello MD, using plane waves (PW) and pseudopotentials (PP), with PBE exchange-correlation; • Final states from excited-state configuration, produced by excited- core PP for O (electron removed from the system); • PAW reconstruction of all-electron orbitals from pseudo-ones: � | ψ n � = | � ( | φ j � − | � φ j � ) � β j | � ψ n � + ψ n � j (the tilde labels pseudo-orbitals; φ j are atomic (pseudo-)orbitals, the | β j � are PAW projectors) • Excited-core PP’s generated with both a full core-hole and a half core-hole, since the latter sometimes yields better results in molecules
Technical Aspects • Ice: 96-molecule supercell, 300 virtual orbitals, 0.6eV broadening • water: 64-atom supercell, 40 virtual orbitals, 0.4eV broadening, spectra is averaged over all possible hole locations. T increased by 50K to compensate for too high viscosity (known DFT problem). Check : O-O radial distribution function compares well with experiments. Fraction of broken H-bonds estimated to be ∼ 19% (criteria for existence of H-bond: d O − O = 2 . 2 ÷ 3 . 2 ˚ A, d H − O = � 1 . 2 ÷ 2 . 2 ˚ A, OHO = 130 ÷ 180 ◦ )
Results: water molecule and dimer Calculated spectra for molecule exhibits a sharp pre-peak (around ∼ 534 eV). Still present in the molecule with ”acceptor” H-bond of a dimer, displaced in the molecule with ”donor” H-bond. Little difference between half- and full-core results. • dimer-D : donor molecule • dimer-A : acceptor molecule • monomer : dashed line, half-core; dot-dashed, full-core (shifted spectra: only relative energies are available from calculations) . Solid line: experiments (S. Mynemi et al., J.Phys.:CM 14 , L213 (2002))
Results: liquid water and ice • left panel : theory (full core-hole); right panel : experiments (Mynemi et al.; units are arbitrary) . • Ice: solid line, calculations with Γ point; dashed line, better BZ sampling (Baldereschi point) Well-defined pre-edge feature is clearly visible Qualitative agreement with experimental results in the pre-edge region
Interpretation: spectra for selected configurations • 2A-2D : calculated spectrum averaged over the 27 ± 3 molecules having 2 donor (D) and 2 acceptor (A) H-bonds • 1A-2D : see above, 12 ± 2 molecules • 2A-1D : see above, 9 ± 2 molecules • 1A-1D : see above, 10 ± 3 molecules Pre-edge feature coming from molecules with 1 donor H-bond broken
Conclusions... • The observed pre-edge feature in water and ice is really coming from molecules with the donor H-bond broken • Finite-Temperature MD simulations give a semi-quantitative agreement with experimental spectra, even in presence of a modest amount of broken H-bonds • Agreement with experiments is less satisfactory in the main edge and post-edge region: in particular, the calculated spectra are narrower than in experiments
...and suite of the story New data show that pre-edge feature is present in water, but also in hexagonal (Ih), cubic (Ic), Low- and High-Density Amorphous (LDA and HDA) Ice. (J. Tse et al., Phys. Rev. Lett. 100 , 095502 (2008)) But the interesting result is that • water and HDA Ice have post- edge feature stronger than the main edge • Ih, Ic, LDA Ice have post-edge feature weaker than the main edge Puzzling: fraction of broken H-bond is small in both LDA and HDA
Calculated spectra Beyond DFT W. Chen, X. Wu, and R. Car, arXiv:0909.3752v1 [cond-mat.soft] : much better description of the entire spectra and of its T-dependence from GW calculations in the COHSEX approximation. Picture for pre-edge confirmed: broken H-bonds, but also local environment distorsions, important Strong post-edge feature of Ice comes from a peak in the DOS (a) Ic (b) water; theory (solid) vs exp. (dashed) (c) Water T=330K (blue), 363K (red), and (d) difference spectra, theory (solid) vs exp. (points)
Recommend
More recommend
