Calculation of X-ray adsorption spectra atfinite temperature: spectral signature

of H-bond breaking in water

P. Giannozzi

Universita di Udine and Democritos National Simulation Center, Italy

Work done in collaboration with Balazs Hetenyi, Filippo de Angelis, Roberto Car

Universite Paris VI, 3 Novembre 2009

– Typeset by FoilTEX –

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)

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. Hetenyi 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 =2πh|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 ÷ 3.2A, dH−O =1.2÷ 2.2A, 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)