Calculation of X-ray adsorption spectra at finite temperature: - - PowerPoint PPT Presentation

Calculation of X-ray adsorption spectra at finite temperature: spectral signature

• f 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 FoilT EX –

H-bond network in Water and Ice

Current structural model for Ice and Water:

• Ice

(at P = 0): hexagonal crystal 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 1s 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 ∼ 535eV)
• bserved 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
• ne 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

• ther 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

• btained 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 = 2π ¯ h |Ti→f|2δ(Ef−Ei), Ti→f = Ψi|e·r|Ψf ∼ ψ1s|e·r|ψf (Ψi,f and ψ1s,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:

|ψn = | ψn +

• j

(|φj − | φj)βj| ψn (the tilde labels pseudo-orbitals; φj are atomic (pseudo-)orbitals, the |βj 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: dO−O = 2.2 ÷ 3.2˚ A, dH−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

• f 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)