This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 11015–11020 11015

Redox behavior of small metal clusters with respect to hydrogen.

The effect of the cluster charge from density functional resultsw

Galina P. Petrova,a Georgi N. Vayssilov*a and Notker Rosch*b

Received 16th March 2010, Accepted 10th May 2010

DOI: 10.1039/c004377j

Tetrahedral model iridium species [Ir4Hn]q+ of different charge and hydrogen loading

were described at the density functional level. The energy of dissociative adsorption of hydrogen

was calculated to vary in the small interval from �63 kJ mol�1 to �77 kJ mol�1 (per H atom).

Adsorption of hydrogen on Ir4 and Ir4+ induces an oxidation of the metal moiety, whereas the

highly charged cluster Ir43+ is reduced upon hydrogen adsorption. The ligand shell acts as charge

buffer as the metal moieties of the complexes [Ir4H12]q+ with maximum hydrogen loading carry

very similar effective charges, irrespective of the total charge q. Similar effects were confirmed

to occur on small clusters of other 4d and 5d transition metals.

1. Introduction

Small transition metal clusters in the gas phase or supported

on a metal-oxide surface have been thoroughly studied by

both experimental1–6 and computational techniques.1,7–9 Such

systems have been found useful in various catalytic or sorption

processes as supported species1–3 or directly in the gas phase as

neutral and charged clusters.1,4,10 The interaction of such

clusters with molecular hydrogen is particularly important,

for characterizing the properties of the clusters and their

application as catalysts.5,6 Therefore, we previously explored

computationally the dissociative adsorption of H2 from the

gas phase on isolated and zeolite-supported tetrairidium

clusters.11–13 These model studies showed both supported metal

clusters and metal clusters in the gas phase to adsorb up to

12 hydride ligands, i.e. 3 H ligands per Ir atom. Hydrogenated

Ir4 clusters adsorbed on a dehydroxylated zeolite support were

calculated to be the most stable. The formal charge of such

Ir4Hn moieties is 3 e as a result of reverse proton spillover from

bridging hydroxyl groups of the zeolite fragment. Yet, calcu-

lated charges of the Ir4Hn moiety were estimated to be notably

smaller, 1.07–1.64 e.13 From a comparison of the results for

supported clusters with those for neutral model clusters in the

gas phase, one expects the (effective) charge of the cluster to

have a notable influence on the properties of the hydrogenated

metal clusters.

To explore this effect of the cluster charge on the hydrogen

loading, we extended our studies on tetrairidium species to a

series of cationic species [Ir4Hn]q+ with total charges q= 1–3 e.

The highest value of q corresponds to the formal charge of the

zeolite-supported Ir4Hn moiety, while the value at the low end,

1 e, is close to the estimated charges of the supported species, as

just mentioned.13 In the present work, we show that this

variation by only of a few electrons on the whole cluster

changes the direction of the oxidation: the metal moiety is

oxidized for neutral systems or clusters with q = 1 e, but the

hydrogen ligands are oxidized when the cluster carries a charge

q = 3 e. Thus, the charge of the system strongly affects the

direction of the oxidation or reduction during hydrogen loading

of the metal cluster. These effects, first observed for iridium

clusters, also have been confirmed for hydrogenated clusters of

other 4d (Ru, Rh, Pd) and 5d (Os, Pt) transition metals.

2. Method and models

The electronic structure calculations were carried out with the

linear combination of Gaussian-type orbitals fitting-functions

density functional method (LCGTO-FF-DF)14,15 as imple-

mented in the program PARAGAUSS.16,17 We employed the

gradient-corrected exchange-correlation functional suggested

by Becke (exchange) and Perdew (correlation) (BP).18 We

applied a scalar relativistic variant of the LCGTO-FF-DF

method that affords an explicit description of relativistic

effects by treating all electrons with the Douglas–Kroll–Hess

approach of second order.15,19,20 The Kohn–Sham (KS)

orbitals were represented by flexible Gaussian-type basis

sets, contracted in generalized form: (6s1p) - [4s1p] for

H,21 (18s13p9d) - [7s6p4d] for Ru, Rh and Pd,22,23 and

(21s17p12d7f) - [9s8p6d4f] for Ir, Os, and Pt.22,23 The

auxiliary basis set, used in the LCGTO-FF-DF method to

represent the Hartree part of the electron–electron interaction,

was derived from the orbital basis set in a standard fashion.14

On each center (except H), this set was augmented by five

p- and five d-type polarization exponents, constructed as geometric

series with a factor 2.5, starting from 0.1 au (p) or 0.2 au (d). Only

the p-type series was added at hydrogen centers.

The current study comprises four series of hydrogenated

clusters in the gas phase with net charges q = 0–3 e (e denotes

a Faculty of Chemistry, University of Sofia, 1126 Sofia,Bulgaria. E-mail: gnv@chem.uni-sofia.bg

bDepartment Chemie and Catalysis Research Center,Technische Universitat Munchen, 85747 Garching, Germany.E-mail: roesch@mytum.de

w Electronic supplementary information (ESI) available: Table withcalculated energy characteristics and interatomic distances of theoptimized structures [Ir4Hn]

q+ (q = 0–3; n = 0, 3, 6, 9, 12); tablewith various characteristics of the electronic structure of the clustersmodeled; figure showing density of state plots of the Ir 2p core levels asa function of the cluster charge and the hydrogen loading; figure withthe optimized structures of [M4Hn]

q+ species (M = Ru, Rh, Pd, Os,Pt); figure with variations of the average shifts of the M 2p levels in theclusters [M4H12]

q+ for various charges q. See DOI: 10.1039/c004377j

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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11016 Phys. Chem. Chem. Phys., 2010, 12, 11015–11020 This journal is c the Owner Societies 2010

the elementary charge) of the complexes: Ir4Hn, [Ir4Hn]+,

[Ir4Hn]2+, and [Ir4Hn]

3+. Unlike in our previous study,13 we

did not apply any symmetry constraints during the structure

optimization. We considered the consecutive dissociative

adsorption of (formally) 3/2 H2 to the species Ir4Hn and in

this way generated structures that contain n = 0, 3, 6, 9, or

12 hydrogen ligands.13,24 The initial positions of the ligands

were chosen similar to those reported earlier for the zeolite-

supported hydrogenated moieties.13 Each stationary point was

checked with a normal mode analysis that incorporated all

degrees of freedom to ensure that the reported structures

correspond to local minima. In the spirit of this model study,

we did not search for isomeric structures.

We quantified the stability of a cluster [Ir4Hn]q+ via the

energy change DE of the formal reaction [Ir4]q+ + n/2H2 -

[Ir4Hn]q+, i.e. via its relative energies with respect to the

corresponding bare cluster [Ir4]q+:

DE([Ir4Hn]q+)=Etot([Ir4Hn]

q+)� Etot([Ir4]q+)� n/2Etot(H2)

(1)

Etot is the total energy of a system. A negative value of

DE reflects the favorable formation of [Ir4Hn]q+ from the bare

cluster after dissociative adsorption of the proper amount of

hydrogen. The basis set superposition error was estimated via

the counterpoise method to 3–6% of DE. The adiabatic ioni-

zation potentials of the bare, [Ir4]q+, and the hydrogenated

clusters, [Ir4Hn]q+ (q = 0–2), were calculated as differences of

appropriate total energies Etot. The spin contamination of the

KS determinant of open-shell systems never exceeded 2%.

Experimental core level energies cannot directly be com-

pared with energies of KS orbitals, but changes of KS energies

with respect to a reference provide adequately approximate

core level shifts.25 We estimated average energy shifts of the

Ir 4f shell of [Ir4Hn]q+ clusters, using the Ir 4f KS energies of

the bare tetrahedral clusters [Ir4]q+ as reference. A positive

value of the shift corresponds to a stabilization of the core

levels relative to the reference. We determined effective charges

q of metal moiety Ir4 by fitting the electrostatic potential.26

The quoted charges should be taken with due caution as

Kohn–Sham methods with common exchange-correlation

functionals tend to overestimate electron delocalization.27

To probe the general validity of our analysis, we also

modeled [M4Hn]q+ clusters, q = 0–3, of other 4d and 5d late

transition metals in the same way, but only for the loadings

n = 0, 6, and 12.

3. Results and discussion

3.1 Structures and stability

The optimized structures of the clusters [Ir4Hn]q+ are provided

in Fig. 1 The average values hIr–Iri and the spread DR of the

nearest-neighbor distances in the metal moiety are given in

Table 1. As in the case of zeolite-supported species,13 the

average Ir–Ir distance increases with the number of H ligands

coordinated at the cluster, from 247� 1 pm in the bare clusters

to 268 � 2 pm in the clusters with 12 H ligands. These averages

include clusters of all charges studied. The nearest-neighbor

Ir–Ir distances are not uniform within a cluster, as illustrated

by rather large values DR, up to B40 pm (Table 1). The

clusters [Ir4H9]3+ and [Ir4H12]

3+ exhibit a ‘‘butterfly’’ struc-

ture with one of the Ir–Ir distances elongated up to 308 pm.

The terminal H–Ir bonds, 158–163 pm, vary by a few

picometres only as the charge of the cluster changes. In

clusters with a large hydrogen loading, n = 9, 12, and a high

charge, q = 2 e or 3 e, activated H2 molecules, with inter-

atomic distances less than 94 pm,28 form at one of the Ir centers.

Such paired hydrogen ligands feature longer H–Ir bonds,

169–171 pm, than common terminal H ligands.

The relative energies DE of the hydrogenated species are

provided in Table 1 and compared in Fig. 2 as a function of

the number n of hydrogen ligands of the clusters. Similarly to

the data for the neutral tetrairidium clusters in the gas phase,13

the relative energies of the charged clusters [Ir4Hn]q+ increase

(by absolute value) almost linearly with the hydrogen loading

n along each series of clusters with a fixed charge q (Fig. 2).

The dissociative adsorption of H2 releases, on average,

D2E = 70 � 20 kJ mol�1 per H atom, but the variations

within each series at fixed q clusters are notably smaller, at

most �8 kJ mol�1. Hydrogen adsorption is calculated to be

most favorable on complexes with q = 3 e and on neutral

clusters, where D2E = �77 kJ mol�1 and �73 kJ mol�1,

respectively. The value for the neutral clusters is close to the

adsorption energy, �70 kJ mol�1, calculated for models with

C3 symmetry restrictions,13 but smaller than the corresponding

energies calculated for the neutral clusters Ir4H and Ir4H2 of

similar structure,�75 kJ mol�1 and�90 kJ mol�1, respectively.11

The corresponding adsorption energies for the clusters

[Ir4Hn]+ and [Ir4Hn]

2+ areB10 kJ mol�1 smaller,�63 kJ mol�1

and �66 kJ mol�1, respectively. This may be related to the

stronger redox interactions in complexes with charges q=0, 3 e,

compared to those with q = 1, 2 e (section 3.2). In summary, H

adsorption is quite favorable in all systems studied.11,13

3.2 Electron density distribution

Now, we turn to the central part of this work, the analysis of

the electron density distribution and of the (first) ionization

potentials of hydrogenated metal clusters of different charge.

Metal moieties of zeolite-supported tetrairidium clusters and

of neutral clusters in the gas phase are oxidized after adsorp-

tion of hydrogen ligands and the ligands carry a partial

negative charge.11,13 In the following we will discuss the

changes in the electron density distribution as the hydrogen

loading and the cluster charge increase. We will diagnose

these changes via potential-derived charges as well as average

shifts of selected Ir core levels relative to the energies of

the corresponding bare cluster (Table 1, Fig. 3, and Fig. S1

of ESIw).In the hydrogenated clusters Ir4Hn and [Ir4Hn]

+ (n 4 0) the

charge of the metal moiety is above the total charge q of the

system (Fig. 3b). Thus the metal moieties are oxidized through

the adsorption of hydrogen, similar to our earlier results for

zeolite-supported Ir4 clusters.13 The effect increases with the

hydrogen loading. At maximum hydrogen loading, n = 12,

the charge of the Ir4 moiety is 2.20 e in the neutral complex

and 2.37 e in the corresponding monocation. In the corres-

ponding dicationic hydrogenated complexes the charge

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alterations of the Ir4 moiety are quite small, from only �0.14 eto 0.38 e. On the other hand, the dissociative adsorption of

hydrogen on iridium tetramers of charge q = 3 e results in a

reduction of the metal moiety, as the positive charge of the

iridium moiety in the hydrogenated clusters is always below

the total charge q of the system. In [Ir4H12]3+ the charge of the

metal moiety is by 0.86 e lower than the charge of the bare

cluster, 3 e.

Interestingly, with increasing hydrogen loading, the

charges of the metal moiety approach one and the same value,

2.23 � 0.15 e (n = 12), independently of the net charge

q = 0–3 e of the complex (Fig. 3a). A Mulliken analysis

(see ESIw) reveals the same trend: here, the charge of the metal

moiety gradually decreases to a common value, 0.67 � 0.23 e,

in the clusters with the highest hydrogen loading. Thus, a shell

of adsorbed hydrogen ligands acts as a ‘‘charge buffer’’ with

respect to the metal cluster.

These charge effects are reflected by the shifts of the metal

core levels as a comparison of Fig. 3b and c reveals for the

example of the Ir 4f levels.29 Although core level shifts in

general are the compound result of several factors,30 the

charge of the metal moiety clearly dominates for the systems

Fig. 1 Optimized structures of [Ir4Hn]q+ species for q = 0, 1, 2, and 3 and energy changes for the subsequent adsorption of 3/2 H2 (in kJ mol�1).

Table 1 Various characteristics of the bare clusters [Ir4]q+ and the hydrogenated clusters [Ir4Hn]

q+ (n = 0, 3, 6, 9, 12; q = 0–3) from densityfunctional calculations

Nsa DE,b kJ mol�1 hIr–Iri,c pm DR,d pm q(Ir4),e e DE(Ir 4f),f eV

Ir4 0 — 248 1 0 —[Ir4]

+ 1 — 246 9 1 —[Ir4]

2+ 2 — 247 14 2 —[Ir4]

3+ 3 — 247 17 3 —Ir4H3 3 �196 252 17 1.36 1.07[Ir4H3]

+ 2 �179 252 14 1.89 0.17[Ir4H3]

2+ 1 �201 251 12 2.38 �0.14[Ir4H3]

3+ 0 �270 251 3 2.47 �0.56Ir4H6 0 �487 256 24 1.47 0.97[Ir4H6]

+ 1 �408 256 28 1.30 0.68[Ir4H6]

2+ 0 �427 255 26 1.86 �0.32[Ir4H6]

3+ 1 �475 258 38 2.17 �0.97Ir4H9 1 �637 262 32 1.83 1.52[Ir4H9]

+ 0 �555 262 38 1.62 0.89[Ir4H9]

2+ 1 �544 261 50 1.93 �0.23[Ir4H9]

3+ 0 �727 257g 60 2.05 �1.61Ir4H12 0 �888 267 7 2.20 1.67[Ir4H12]

+ 1 �761 270 14 2.37 0.88[Ir4H12]

2+ 0 �809 268 28 2.08 �0.50[Ir4H12]

3+ 1 �874 266g 42 2.14 �1.72a Number of unpaired electrons in the complex. b Relative stability of the hydrogenated cluster, see eqn (1). c Average nearest-neighbor distance of

the metal moiety. d Difference between the largest and the smallest nearest-neighbor distances of the optimized structure. e Potential-derived

charge of the metal moiety q(Ir4).f Average shift of the Ir 4f core levels with respect to the value of the corresponding bare cluster; positive values

can be considered to indicate oxidation of the metal moiety. g Distances exceeding 290 pm are not included when calculating the average.

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under study. This effect comprises two major contributions, the

stabilization or destabilization due to the effective charge of an

atomic center and the electric field of the other charged centers

(Ir or H) in the immediate vicinity. At each hydrogen loading n,

the Ir 4f core level shifts decrease with increasing charge of the

Ir4 moiety. In all systems studied, shifts are positive for the

neutral and the monocationic clusters, reflecting the oxidation

of the metal centers. In contrast, the metal moiety of the

complexes [Ir4Hn]3+ is reduced and, concomitantly, the Ir 4f

core levels are clearly destabilized, up to 1.73 eV in [Ir4H12]3+,

as result of the dissociative adsorption of hydrogen.

To rationalize the different redox behavior with respect to

hydrogen, depending on the clusters charge, we compare

calculated adiabatic ionization potentials (IPs) of the clusters

[Ir4]q+, 6.8 eV, 12.2 eV, 18.2 eV, and 24.7 eV, for q = 0–3,

respectively, to the (calculated) IP of a H atom, 13.6 eV.

The propensity for the Ir4 moiety undergoing oxidation or

reduction obviously correlates with the IP value of the cluster

[Ir4]q+, whether it is smaller or larger, respectively, than the IP

of hydrogen.

We also estimated the electronegativities w of pertinent

systems according to w = (IP+EA)/2, using the calculated

values of the adiabatic IP and the electron affinity (EA): 7.0 eV

for H, and 4.2 eV, 9.5 eV, 15.2 eV, and 21.4 eV for the bare

[Ir4]q+ clusters with q = 0–3 e, respectively. An alternative

evaluation of the electronegativities from the HOMO and

LUMO energies yields very similar values, 3.9 eV, 9.4 eV,

15.2 eV, and 21.3 eV, for the series of bare clusters, while w(H)

is reduced to 4.7 eV. As expected from the observed specific

redox behavior, the electronegativity of H is intermediate

between those of clusters with different charges. Yet, w(H)

appears between the w values of the clusters with q = 0 e and

1 e, while the change in the redox behavior is observed ongoing

from clusters with q= 1 e to 2 e. The reason for this difference

likely is the reference system, an isolated H atom, used for

comparison with the electronegativities of the metal clusters.

3.3 Comparison with clusters of other transition metals

To check whether the effects of the cluster charge, observed for

the series of neutral and positively charged clusters [Ir4]q+,

also holds for clusters of other similar transition metals, we

modeled in the same way tetragonal model clusters of various

4d (Ru, Rh, Pd) and 5d (Os, Pt) transition metals; the

optimized structures of these clusters are provided in Fig. S2

of ESI.w In these calculations we included only clusters

[M4Hn]q+ of selected hydrogen loading, n= 0, 6, 12. Similarly

to the series of iridium clusters, the average adsorption energy

per H on different clusters was evaluated by a least-squares

fit of the relative energies DE of the hydrogenated tetra-

mers [M4Hn]q+ on the hydrogen loading n (Table 2). The

values DE for the neutral clusters differ by B50 kJ mol�1,

Fig. 2 Relative energy, DE, of hydrogenated [Ir4Hn]q+ clusters as a

function of the total number of hydrogen atoms adsorbed on the metal

cluster, n: neutral Ir4Hn clusters (circles); [Ir4Hn]+ clusters (triangles);

[Ir4Hn]2+ clusters (rhombs); [Ir4Hn]

3+ clusters (squares).

Fig. 3 Potential-derived charges q of Ir4 moiety in [Ir4Hn]q+ clusters

(a), and variations of these charges (b), as well as average shifts of the

Ir 4f levels (c) with respect to the corresponding bare clusters as a

function of the total number n of hydrogen atoms adsorbed on the

metal moiety: Ir4Hn (circles), [Ir4Hn]+ (triangles), [Ir4Hn]

2+ (rhombs),

[Ir4Hn]3+ (squares).

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from �73.6 kJ mol�1 (Ir) to �24.3 kJ mol�1 (Pd). The values

for the clusters with q = 3 e spread over a smaller interval of

B20 kJ mol�1, �76.7 kJ mol�1 (Ir) to �53.7 kJ mol�1 (Ru).

The adsorption energies are lowest (by absolute value) for

q = 1 e or 2 e, and highest for q = 3 e, except for Os4 which

features a slightly larger adsorption energy than [Os4]3+. The

adsorption interaction can increase strongly with cluster

charge; for q = 3 e the energies released were calculated

25 kJ mol�1 (Rh) and 34 (Pd) kJ mol�1 more exothermic than

in the corresponding neutral clusters.

As for Ir, the oxidation or reduction of the M4 moiety upon

the hydrogen loading depends on the total charge q of the

complexes [M4Hn]q+. This can be seen from the calculated

difference between the adiabatic IPs of the hydrogenated

clusters [M4H12]q+ and the bare clusters [M4]

q+ (Table 2).

For all neutral systems, the IP of the hydrogenated clusters is

larger than the IP of the corresponding bare clusters: this can

be considered as indication of an oxidation of the metal moiety

upon hydrogen adsorption. In contrast, the IP values of the

hydrogenated clusters with q = 2 e are lower than those of the

corresponding bare cluster, i.e. the metal moieties are reduced.

These trends are corroborated by the core level shifts of the

metal atoms (Fig. S3 of ESIw).For all transition metals studied, the charge buffer effect of the

shell of hydrogen ligands on the metal clusters exists in the case

of the highest hydrogen coverage, 12 H; for platinum, this effect

can be identified even with only six hydrogen ligands. The spread

D between maximum and minimum calculated charges q(M4) of

the metal moieties for systems of total charges q = 0 e and q =

3 e varies, from very small for Rh (D o 0.1 e) to D E 1.0 e for

Pd. Surprisingly, the charge of the M4 moiety in [M4H12]q+,

averaged over q = 0–3 e, is quite similar, 2.08–2.23 e, for the 5d

metals, while these averaged charges vary notably for the 4d

metals, from 1.92 e for Rh4 to 2.62 e for Ru4. The similarity of

the transition metal clusters modeled may be due to the similar

values of the electronegativity of the clusters, reported in Table 2

for the complexes with q = 1 e or 2 e.

4. Conclusions

The results obtained for neutral and charged iridium clusters

show that a small change of the net charge of the complexes

studied, by only 2 e or less than one electron per metal center,

reverses the character of the redox interaction between the

metal moiety and the hydrogen ligands. While the dissociative

adsorption of hydrogen on the species Ir4 and [Ir4]+ leads to

an oxidation of the metal moiety, the highly charged metal

cluster [Ir4]3+ is reduced upon hydrogen adsorption. This

contrasting behavior with a variation of the charge on the

tetrairidium clusters can be rationalized by the increasing

propensity of the metal moiety to accept electron density with

increasing the charge, as reflected in the increasing ionization

potentials of the clusters [Ir4]q+ with the charge q = 0–3 e.

Such an increase of the ionization potential with increasing

positive charge is expected to occur also for other metal

clusters and indeed has been corroborated for various late

4d and 5d transition metals. At a ‘‘critical charge’’ value, the

IP of the metal moiety will be close to the IP of the ligand

system and thus the IP will be a convenient parameter for

evaluating the redox behavior of the metal clusters with

respect not only to hydrogen, but also to other ligands.

Therefore, all metal clusters should exhibit a characteristic

(positive) charge value at which the adsorption of hydrogen

changes from being an oxidative process of the metal moiety

to a reduction.

A comparison of the charge distributions in the complexes

[Ir4H12]q+, q = 0–3 e, with maximum hydrogen loading

showed that the charges of the metal moieties are very similar,

irrespective of the charge q of the complex. This observation

suggests that in these complexes an equilibration of the

electron density takes place such that the metal fragment

carries essentially the same charge, while the charge differences

are accommodated by the hydrogen ligands. In other words,

the dissociatively adsorbed hydrogen ligands act as a charge

buffer with respect to the metal cluster.

Acknowledgements

This work was supported by the Bulgarian National Science

Fund (Contract VUH-303/07), the Bulgarian National Center

of Advanced Materials UNION (Contract DO02-82/2008),

Deutsche Forschungsgemeinschaft, and Fonds der Chemischen

Industrie (Germany).

Table 2 Various characteristics of the bare clusters [M4]q+ and the hydrogenated metal clusters [M4Hn]

q+ for late 4d and 5d transition metalsM (n = 0, 6, 12; q = 0–3) from density functional calculations

q(M4),a e

DIP,b eV w,c eV D2E,d kJ mol�1

q = 0 q = 2 q = 1 q = 2 q = 0 q = 1 q = 2 q = 3

Ru 2.62 � 0.22 0.81 �0.96 8.93 14.82 �49.6 �43.0 �48.3 �53.7Rh 1.92 � 0.05 0.21 �2.77 9.93 16.08 �42.3 �38.8 �45.7 �67.5Pd 2.05 � 0.49 1.02 �2.31 10.08 16.39 �24.3 �18.4 �38.7 �58.3Os 2.20 � 0.23 1.21 �0.82 9.24 14.39 �64.9 �58.6 �54.4 �62.1Ir 2.23 � 0.15 1.30 �0.67 9.54 15.25 �73.6 �52.8 �65.8 �76.7Pt 2.08 � 0.17 1.83 �1.05 9.82 15.81 �62.2 �48.2 �60.2 �68.6a Charge q(M4) of the metal moieties of the clusters [M4H12]

q+ averaged for q = 0 e and q = 3 e; the variation of these values is characterized by

half of their difference D. b Difference between adiabatic ionization potentials of the clusters [M4H12]q+ and [M4]

q+; positive values can be

considered to indicate oxidation of the metal moiety. c Electronegativity of the [M4]q+ clusters estimated from the adiabatic ionization potentials

IP and electron affinities EA: w= (IP+EA)/2. d Average adsorption energy per H, evaluated by least-squares fits of the dependence of the relative

energies DE of the hydrogenated clusters [M4Hn]q+ (n=0, 6, 12; q= 0–3) on the hydrogen coverage n: DE([M4Hn]

q+)= D2E� n; see eqn (1). For

the iridium clusters, the whole set of data for n = 0, 3, 6, 9, 12 was used.

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792–794.28 G. J. Kubas, Chem. Rev., 2007, 107, 4152–4205.29 Other core levels shift by similar amounts. For instance, the

average shifts of the Ir 2p and Ir 5s levels change synchronouslywith the energies of the Ir 4f levels, with deviations of at most 0.03eV; see Table S2 of ESI.

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