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Free Energy Assessment of Water Structures and Their Dissociation
on Ru(0001)
Guillem Revilla-López,† Piotr Błoński,‡ and Núria López*,†
†

Institute of Chemical Research of Catalonia, ICIQ, Avenida Països Catalans 16, 43007 Tarragona, Spain
Institute of Nuclear Physics, Polish Academy of Sciences, ulica Radzikowskiego 152, PL-31-342 Krakow, Poland

‡

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S
* Supporting Information

ABSTRACT: The free energy landscape of the structures and dissociation degree of the
first water and heavy water adlayers on Ru(0001) surface is presented. Thermodynamically
favored interconversion routes connecting different experimentally reported structures are
suggested based on free energy calculations. On going from low to high water coverage,
one-dimensional (1D) periodic chain-like structures with small, or zero, water dissociation
degree like Chain-4a motifs are found to be very stable intermediates in the formation of
dissociated and molecular ice-like bilayers, respectively. The isotopic effects on the
dissociation degree of the ice-like bilayers are estimated: a preference for the halfdissociated form is found for H2O at temperatures below 275 K followed by energetic
degeneration between all bilayers dissociated over that threshold. Instead, for heavy water
this temperature is shifted to 225 K. Moreover, the configurational entropy due to the
different arrangements of dissociated and molecular flat molecules further contributes to set the energies of all these structures
within a small energy window that make experimental identification difficult.

■

INTRODUCTION
Water adsorption on metal surfaces remains an area of intense
research, as it is involved in corrosion, electrochemistry and
heterogeneous catalysis.1 Many of these studies have focused
on the structure of the first water layer adsorbed on Ru(0001)
for which a myriad of apparently unconnected motifs have been
reported depending on the experimental conditions.
Initially, the full coverage structure of the water layer on
Ru(0001), coverage 0.67 ML, was described as an hexagonal
ice-like, Ih-like Figure 1a. In this structure, the motifs are
formed by hexagonal water clusters linked in a honeycomb
network with flat and down (up) molecules in a 1:1 proportion.
The degree of dissociation was suggested to be variable,2−11
Figure 1b, where some of the down molecules split into
hydroxyls and protons that are attached to the surface. The
number of hydroxyls in the motifs is still a matter of discussion
and can range from half Ih-4/8 of the molecules to 0, the Ih-0/8
motif, the dissociation degree has been reported to strongly
influence the catalytic activity of Ru(0001) in an aqueous
environment.12 Both temperature-programmed desorption
(TPD) and scanning tunneling microscopy (STM) results
were found to be strongly dependent on the dosing
temperature and the hydrogen isotope (either protium or
deuterium).13−15 In addition, the bias voltage in STM could
induce further bond cleavages. All these hurdles have rendered
the question of the dissociation degree a difficult point to assess
experimentally.16 In parallel, other isoforms corresponding to
the same coverage such as chains,15 Figure 1c, were found to
coexist under certain conditions. In the chain structure, rows of
flat and down molecules are found as connected strips. The
main difference from Ih is the local coordination of each water
© 2015 American Chemical Society

Figure 1. Axial and longitudinal views on Ru(0001) of (a) Ih-0/8, (b)
Ih-4/8, (c) chains; (d) island; (e) rosette, and (f) C4a-2/12. Oxygen,
hydrogen, and ruthenium atoms are represented by red, black, and
white spheres, respectively.

molecule. For instance, in chains, flat molecules have in their
first coordination sphere at least two flat molecules, a pattern
never found in Ih structures.
Received: December 11, 2014
Revised: February 10, 2015
Published: February 13, 2015
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Γ-point only. D2 O frequencies were reevaluated after
considering the mass of deuterium.
The water/metal interface of Ih-0/8 bilayer was represented
by a periodically repeated supercell containing w = 32 total
water molecules, 16 H-down and 16 flat, forming a 4√3x4√3
− R30.0° pattern on 48 metal atoms, m (see Figure 1a). In this
structure, intermediate dissociation degrees were built by
reassociating water molecules from the half-dissociated that
presents a 0.5 dissociation degree, that is, four dissociated Hdown momers per each eight total water molecules (4/8, Figure
1b). Thus, 0 (0/8, Ih-0/8), 0.13 (1/8), 0.25 (2/8), and 0.38 (3/
8) dissociation degrees were evaluated.
As for the low coverage regime, the island model consisted of
w = 32 and m = 108, thus rendering a 0.33 ML, Figure 1d;
chains contain w = 8 and m = 12, 0.67 ML in Figure 1c, and the
rosette contains w = 24 and m = 48, 0.5 ML in Figure 1d. The
C4a motif reported by Salmeron et al.18 presents 1D periodicity
formed by incomplete chains separated by four rows of bare
metal atoms, Figure 1f. C4a contains w = 12 and m = 30 with
0.40 ML coverage and two dissociated water molecules, C4a-2/
12; the molecular form of this system, C4a-0/12, has also been
considered in this work.
The adsorption energy, Eads in eV/H2O, is defined with
respect to the gas-phase water monomer: Eads = Esys − (Eslab +
nw · Ew), where Esys is the energy of the metal slab with
adsorbates, Eslab is the energy of the bare metal slab, nw is the
number of adsorbed water molecules, and Ew is the energy of an
isolated water molecule in the gas-phase. The zero-point
vibrational energy of adsorption, ΔEZPV, is calculated as ∑i(h/
ads
2)vi, where vi stands for the vibrational frequencies and h is the
Planck constant. All structures were confirmed as real minima;
no imaginary vibrational modes were found. Of the 3N-6
vibrations, the very low energy modes would be better
represented as frustrated rotations as demonstrated by van
Santen et al.31 Following common practice in molecular studies
and to avoid the spurious contributions of thermal and entropic
contributions of these low energy modes when treated with
standard vibrational partition functions, we removed all the
frequencies below 100 cm−1. The free energy of adsorption,
Gads was then calculated according to Gads = Gsys − (Gslab +
nw·μH2O), where μH2O is the chemical potential of water per
molecule at 1 bar pressure and a given temperature, and Gsys is
the free energy of the system according to Gsys ≈ Hcorr − TSvib;
sys
sys
Hcorr = Esys + kBT. T and kB stand for temperature and
sys
tot
Boltzmann constant. The methodology follows that in ref 32.
For partially dissociated structures, the different distributions
between molecular and dissociated molecules can present
different configurations, leading to a configurational entropy in
terms of free energy, Gsys ≈ Hcorr − TSvib − TSconf. In our case,
sys
sys
this has only been assessed for the complete Ih structures as
w !
wdw
follows: Sconf = −kB ln Ω, where Ω = wdiss = (w − wdw ) ! w ! ,

The interconversion of different motifs and how the
complete covering of the surface by increasing quantities of
water occurs remains open. Besides, the question remains of
how the intermediate coverages turn into either an Ih or chain
motif. In particular, at low coverages (0.33 ML), isolated
clusters in the form of island motifs that combine 10 sixmembered cycles and a five-membered one (Figure 1d)17 have
been reported. Other islands like the rosette, Figure 1e, present
a central flat six-membered ring water core surrounded by six
more hexagons. This is the pattern at the core of Ih except for
the fact that the core presents the coordination motif of the
chains (flat molecules are first neighbors to other flat
molecules), and it is strongly corrugated, as only the core is
in contact with the metal. Recently, Salmeron et al.18 via a
combined STM−density functional theory (DFT) study have
pointed that water bilayer formation on Ru(0001) might be
mediated by a chain-like structure. This new chain motif
presents a central strip made of six-membered rings made of
four flat water and two dissociated H-down monomers. Two
more H-down monomers are adsorbed at two opposite
vertexes, thus forming five-remembered uncompleted hexagons
at each side of the central strip. In total, this structure contains
12 water molecules, of which 2 are dissociated, 2/12, and there
are four rows of bare metal atoms in the y direction between
motifs, hereafter referred to as C4a in Figure 1f. The rationale
for this central role lays on the one-dimensional (1D)
periodicity of the motif in combination with its intermediate
coverage, 0.40 ML.19 The latter coverage lies in-between that of
the ice-like bilayer and the rosette, which presents an exclusion
zone for water adsorption around it due to the arrangement of
the H-down water monomers in the vertexes.
DFT calculations have provided electronic adsorption
energies for most of these motifs at 0 K.20 Yet, experiments
are performed at finite temperatures for which thermal effects
contribute and might rule provided that small energy
differences are involved. This work presents the free energy
landscape of H2O adsorption on Ru(0001) and the heavy
water, D2O, to assess the energy differences between the
structures proposed at intermediate and bilayer coverages.

■

COMPUTATIONAL DETAILS
All DFT calculations in this work were carried out with the
Vienna Ab initio Simulation Package (VASP).21,22 The
electron−ion interactions were described using the projectoraugmented-wave (PAW) formalism.23,24 The plane-wave set
contained components with energies up to 400 eV, and both
energies and structures remain unchanged from this cutoff up
to 700 eV. The Perdew, Burke, and Ernzerhof (PBE) functional
was used for electronic exchange and correlation effects in the
generalized-gradient approximation (GGA).25 Dispersion energies were accounted for by the semiempirical DFT-D226−28
approach with the parameters optimized in the group for the
Ru metal surface.29 The electronic degrees of freedom were
relaxed until the change in total energy between successive
iteration steps was below 10−6 eV. The five layers of the Ru slab
were kept in their bulk-like positions interleaved by 16 Å
vacuum and the water molecules were left free to move until
the forces acting on them were lower than 25 meV/ Å 2. The
Brillouin zone was sampled using 3×3×1 Γ-centered k-point
mesh, and a Methfessel-Paxton30 smearing of 0.2 eV was
applied. Vibrational modes were obtained within the harmonic
approximation by diagonalization of the numeric Hessian
matrix obtained by ±0.01 Å displacements and calculated at the

( )

dw

diss

diss

where wdw stands for the number of H-down water monomers
in the ensembles and wdiss accounts for the dissociated ones
within this set. For the Ih structures, we are reporting the
system surface energies, γsys = Gsys/A.33

■

RESULTS AND DISCUSSION

Cohesive energy in three-dimensional (3D) hexagonal ice, Ih,
has traditionally been taken as the energy threshold for adlayer
stability on metals.34 The cohesive energy values, ΔEZPV,
ads
according to our calculations is −0.54 eV/H2O, and the
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Figure 2. Eads in eV·H2O−1 is presented (gray marks right scale). EZPV in eV·H2O−1 (black scale left) for the adsorption of H2O (blue) and D2O
ads
(red). For each ensemble, the coverage is described at the top in ML. Systems: Wd isolated dissociated water; Wnd molecular water; island; the chains
reported by Salmeron et al.:18 C4a-2/12 and C4a-0/12; rosette; chains and different Ih-d/total models with different amount of dissociated (d)
molecules. The black line is the 3D ice EZPV. All energies are in eV/H2O. The equivalent in terms of interaction energy per surface is presented in
ads
Supporting Information Figure S1.

experimental value is −0.61 eV/H2O.5 In key places of our
figures, comparisons to the cohesive energy of bulk ice are
presented to simplify the comparison to the literature.34
However, we have preferred to present water-normalized
adsorption energies: Eads and EZPV as in Figure 2.
ads
The larger stability of the dissociated single H2O adsorption,
EZPV Figure 2, over the molecular one agrees with previous
ads
estimates by Michaelides et al.7 Moreover, dissociative
adsorption is far more stable than any other water molecule
belonging to an ensemble. In addition, dissociated H2O
adsorption is stabilized over D2O, which is opposite to the
observed tendency for the rest of ensembles. This change is
related to the lower mass of protium, which makes the
vibrational frequencies of split H and OH higher than for D and
DO. As coverage increases, the island motif (0.33 ML, Figure
1d) shows up, forming a noncontinuous overlayer with
multimembered cycles. In terms of energy per molecule, the
island motif is metastable with respect to the C4a-2/12 by 166
meV/H2O, while it is virtually isoenergetic, EZPV = −0.740 eV/
ads
H2O; with the rosette, −0.755 eV/H2O,19,34 and with the C4a0/12, −0.717 eV/H2O. C4a-0/12 can develop exothermically,
by simple water addition and a few rearrangements, into chains.
The difference in the adsorption energies is rather small ΔEZPV
ads
= −67 meV/H2O obviously, the total energy is lower for the
system with more molecules. Moreover, chains can evolve into
Ih-0/8 bilayer by a few rearrangements, but the Ih is less stable
by 87 meV/H2O. Instead there might exist a direct path that
relates C4a-0/12 to Ih-0/8 as it implies fewer molecular
rearrangements, only 1 in 6 water monomers, and the energies
per molecule are closer (21 meV/H2O). In parallel, the
formation of partially dissociated Ih-like bilayers could be based
on C4a-2/12. This structure is virtually isoenergetic in
normalized energies with Ih-2/8, ΔEZPV = 15 meV/H2O.
ads
Moreover, partially dissociated Ih isoforms seem energetically
degenerate, all lay within 11 meV/H2O, and metastable with
the half-dissociated form by 50 meV/H2O, which opens the

thermodynamic possibility to rapid interconversion between
these structures.35
Heavy water (Figure 2) slightly alters the relative energy
scales discussed for water. The energy difference from C4a-0/12
to chains remains unchanged at −67 meV/D2O in sharp
contrast with the Chains to Ih-0/8 at 103 meV/D2O.
Conversely, the C4a-0/12 to Ih-0/8 unbalance increases to 27
meV/D2O, only 6 meV more than the values corresponding to
H2O. The energy difference between Ih-2/8 and C4a-2/12 is
similar to H2O, 18 meV/D2O. The most important point,
though, concerns the energy span for the partially dissociated
Ih-like forms that are reduced to 5 meV/D2O for heavy water.
D2O also tightens the gap between all the Ih-like bilayers: the
gap between Ih-0/8 and Ih-4/8 is reduced by 13 to 246 meV/
D2O, and a similar reduction, 11 meV, is observed between Ih4/8 and the other partially dissociated configurations.
Figure 3 shows the free energy of adsorption, Gads, in the
temperature range between 125 and 300 K for all continuous
H2O (panel a) and D2O (panel b) motifs. Surface-normalized
energies are reported in Figure S2 in the Supporting
Information. The energy ranking in terms of EZPV for H2O is
ads
mostly maintained when temperature effects are included. As
can be seen, C4a-0/12 (Figure 3a) is more stable than the Ih-0/8
bilayer by 44 meV/H2O. On the other hand, C4a-2/12 is
isoenergetic with the partially dissociated Ih-like bilayers and
metastable with Ih-4/8 up to 225 K. Over this temperature, the
ranking is turned upside down, and C4a-2/12 becomes the
lowest energy structure as Ih-4/8 and Ih-2/8 are slightly
disfavored, by 10 and 15 meV/H2O, respectively. Further on,
all the partially dissociated forms and C4a-2/12 are within an
energy span of 39 meV/H2O. Ih-4/8 bilayer is always more
stable than the partially dissociated forms and the Ih-0/8 below
275 K, whereas over this temperature all dissociated structures
become degenerate. The differential stabilization found for D2O
in terms of EZPV is also reproduced by Gads, Figure 3b.
ads
Throughout the temperature range, the adsorption energy of
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275 K, but including C4a-2/12, is reproduced since previous
gaps are reduced to 8 and 2 meV/D2O, respectively.
Figure 4 presents the surface normalized free energy
differences, Δγ, of the dissociated bilayers from the molecular
form in meV·Å−2. The overall energy for the complete
ensemble for 32 molecules is presented here. In Figure 4a,c,
the total energy is always favorable to the Ih-4/8 and after
(Figure 4b,d), considering the configurational entropy. The
number of configurations for the dissociated and nondissociated structures, Ω, peaks for the partially dissociated
Ih-2/8 structure being 1 for the two extremes: Ih-0/8 and Ih-4/8.
The entropic contribution leads to a stabilization of Ih-2/8 over
Ih-1/8 and Ih-3/8 throughout the range. Yet, Ih-4/8 remains the
lowest energy isoform within the considered finite temperatures. A virtual energy degeneration is detected for H2O over
250 K and for D2O over 220 K since all dissociated ensembles
are within a span of 3 and meV·Å−2. The thermodynamic
degeneration form can explain the different degree of
dissociation reported in the experiments. Moreover, as the
energy differences are small, dynamic behavior is expected.
Thus, the highly variable dissociation rate found in the
experiments is explained not only by the thermal contributions
but also by the configurational component.
The work function, ϕ, is a widely used experimental
technique employed to characterize water adlayers on metals.
Changes in the work function can be attributed to changes in
the dipole moment of adsorbates on the surface,36−38 which in
polyatomic molecules is related to the orientation of molecules
with regard to the surface, the coverage, and the structure of the
ensemble formed by them. The values for the systems studied
in this work have been calculated by subtracting the Fermi level
to the average electrostatic potential energy at the half height of
the z direction, right in the vacuum of the slab system. These

Figure 3. Gads in eV/H2O and eV/D2O, as a function of temperature
for the different ensembles in the present work.

C4a-0/12 is more exothermic than that of Ih-like bilayer by 47
eV/D2O, whereas all dissociated forms of Ih-like bilayers and
C4a-2/12 are within a range of 30 meV/D2O. Ih-4/8 presents
the lowest adsorption energy below 225 K, with C4a-2/12 and
Ih-2/8 being disfavored by 17 and 30 meV/D2O, respectively.
Over 225 K, the same energy degeneration found for H2O over

Figure 4. Surface adsorption energy relative to the Ih-4/8 system, Δγ, in meV·Å−2, of the dissociated bilayers as a function of temperature for H2O
(a,c) and D2O (b,d). Energies without (a,b) and with (c,d) configurational entropy contributions.
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́
computing Center). We thank Dr. Max Garcia-Melchor, Dr.
́
Luca Bellarosa and Msc. Rodrigo Garcia-Muelas for fruitful
discussion of vibrational modes and free energy calculations.

measurements reveal relevant differences between both the
lowest and highest coverage motifs and slight gaps between the
molecular and dissociated states of the ice-bilayer, 4.64 and 4.89
eV, respectively. These values represent −0.31 and −0.06 eV
variation of the work function, Δϕ, with respect tothat of the
bare Ru(0001) surface, 4.95 eV. That is in nice agreement with
previous theoretical calculations by Schnur and Groβ.36
However, when the values for the partially dissociated bilayers
are regarded, 4.84, 4.86, and 4.89 for the 1/8, 2/8 and 3/8
dissociated forms, respectively, the differences with Ih-4/8 fade
away, while those with the molecular form are maintained. In
addition, island and rosette motifs present values of 4.73 and
4.64 eV, whereas chains and the C4a-0/12 and C4a-2/12 present
4.67, 4.67, and 4.72 eV, respectively. These results are in line
with the value for the molecular Ih-0/8 bilayer, which suggests
that work function by itself is partially useful to discern the
dissociation state, as previously reported,3−5 and hardly useful
for discriminating between different coverage regimes.

■

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■

CONCLUSIONS
In conclusion, the free energy landscape of experimentally
reported H2O motifs on Ru(0001) has been described. EZPV
ads
points at the key role of C4a-0/12 and C4a-2/12 in the
formation of Ih-0/8 bilayer and its dissociated forms,
respectively. The latter is unaffected by the use of H2O or
D2O. Thus, the importance of bilayer forming pathways
through isolated two-dimensional (2D) clusters like the rosette
and island has been downgraded to enhance those through
chain-like 1D periodic structures. D2O induces a stabilization of
the partially dissociated Ih-like bilayers by making them
isoenergetic with Ih-4/8 over 225 K in sharp contrast with
H2O, for which Ih-4/8 is preferred until 275 K. Configurational
entropy differentially stabilizes the partially dissociated states of
the Ih-like bilayer over Ih-4/8 because of the higher number of
feasible configurations for intermediate dissociative states. The
latter, combined with the energy closeness of partially
dissociated systems, is the cause of the high interconversion
rates between structures and the variable observed dissociation
degree. Finally, the work function has been found to be a
descriptor of the dissociation state of the aqueous adlayer, but
not for discerning between intermediate coverages and the
structure of the motif formed by water.

■

ASSOCIATED CONTENT

S
* Supporting Information

XYZ coordinates and energies of systems employed in this
work and rescaled versions of Figures 2 and 3. This material is
available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: nlopez@iciq.es.
Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS
This work has been supported through the ERC Starting Grant:
Biomass to Chemicals: Catalysis design for sustainable chemical
industry-Theoretical Simulations (ERC-2010-StG-258406).
The simulations have been done in the supercomputer
MareNostrum at Barcelona Supercomputing Center - Centro
Nacional de Supercomputación (The Spanish National Super5482

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DOI: 10.1021/jp512328h
J. Phys. Chem. C 2015, 119, 5478−5483