We show that there is a family of adsorbate-substrate systems that do not follow the trends in adsorption energies predicted by the d-band model. A physically transparent model is used to analyze this phenomenon. We found that these adsorbate-substrate pairs are characterized by the repulsive interaction of the substrate d-band with the renormalized adsorbate states. The exceptions to the d-band model are mainly associated with the adsorbates having almost completely filled valence shell, and the substrates with nearly fully occupied d-band, e.g., OH, F, or Cl adsorption on metals and alloys characterized by d9 or d10 substrate surface atoms.

Developing predictive models of chemisorption on metal surfaces is critical for the understanding of surface chemical reactions.1–4 It has been shown that the d-band model4,5 of chemisorption, developed by Hammer and Nørskov, can predict the trends in chemisorption energies of various adsorbates on metal surfaces. The model correlates the central moment of the d-band projected on surface atoms (d-band center referenced to the Fermi level) with the surface reactivity. It has been used successfully to design novel metal surfaces for various catalytic reactions.6–8 In general, for a given adsorption geometry adsorbates bind to the surface of transition or noble metals more strongly if the d-band center of the surface atom is higher in energies.4,5 The model is very robust and most adsorbates follow the trends predicted by the model.4,5,9

In this letter, we show that there is a family of adsorbate-substrate systems that does not follow the trends in adsorption energies predicted by the d-band model. We discuss this exception to the d-band model by analyzing hydroxyl (OH) adsorption on a series of Pt and Pd skin alloys. This exception is important since OH adsorption on metals is crucial for the understanding of various catalytic, electrocatalytic, and photocatalytic reactions including oxygen reduction10 and water splitting reactions.11 It has been shown previously that Pt and Pd skin alloys are promising alternatives to conventional Pt catalysts in these chemical transformations.12 

Figures 1(a) and 1(b) show adsorption energies, calculated using density functional theory (DFT),13 of O (fcc site) and OH (we found that the top site binds OH the strongest) at 1/4 monolayer coverage on a number of Pt and Pd skin alloys as a function of the d-band center projected on the surface atoms. In the model system, the subsurface layer of the host metal slab (Pt or Pd) is substituted by a guest metal (3d, 4d, or 5d with more than half filled d-band). Similar models have been used previously to model skin alloys.14 The calculated d-band center, showing that for the subsurface elements to the left of a given row of the periodic table, the center of d-band projected on surface Pt or Pd atoms moves down in energies, are tabulated at the bottom of Fig. 1(a). Figure 1(a) shows that the adsorption of O follows the d-band model. On the other hand, the OH adsorption energies are reversely correlated with the d-band center as shown in Fig. 1(b), i.e., those substrates with the higher d-band center adsorb OH less strongly than the substrates with the lower d-band center. Figures 1(c) and 1(d) also show that the stronger chemisorption of OH on an alloy surface is accompanied with longer adsorbate-substrate bonds, which is counterintuitive. In addition, the stronger bonding of OH occurs on the Pt and Pd sites interacting with more chemically active subsurface atoms in the alloy (i.e., Cr is more chemically active than Ni), which is in contradiction to the principle of bond order conservation.15 

To understand this exception to the d-band model, we first discuss a physically transparent framework allowing us to analyze chemisorption of adsorbates on transition or noble metal substrates.3 Almost identical framework has been used previously to analyze the adsorption of CO and O on metal surfaces.1,5 The model assumes that there are two main substrate-specific components contributing to the difference in the adsorption energies: electronic (ΔEel) and electrostatic (ΔEes) interactions.3 It is generally assumed that the electrostatic contribution is similar for a given adsorbate on different transitions or noble metal surfaces.16 Our DFT calculations supported this point and showed that the electrostatic component of the adsorbate-substrate interaction calculated by multiplying the self-consistent subsurface atoms induced electric field (reference to induced electric field on pure metal surface) with the dipole moment of adsorbate on the surface is very similar for different skin alloys. The electronic contribution is due to the change of one-electron energies, and it is insightful to further divide this contribution into the sp-band and d-band contributions17 as shown in Eq. (1). We will treat the interaction of the adsorbate with the substrate sp-band as an adjustable parameter in the model,

ΔEel=ΔEsp+ΔEd
(1)

The interaction of the molecular orbitals of OH with the substrate d-band can be treated as an interaction between two localized molecular orbitals approaching each other and forming a chemical bond. It can be described by two terms: covalent attraction due to the orbital hybridization and repulsion due to the energy cost associated with the orbital orthogonalization (this term is sometimes referred to as Pauli repulsion).9 Since in the case of OH there are two molecular orbitals interacting with the d-band (d-orbitals of the substrate), populated 1π and empty 4σ orbitals, we need to account for the interaction of both orbitals with the substrate d-band as shown in Eq. (2),1 

ΔEd4[(1f)Vπ2|εdε1π|+(1+f)SπVπ]2[fVσ2|εdε4σ|+fSσVσ].
(2)

Here, f and εd are the respective filling and center of d-band projected on the surface metal atoms. ε1π and ε4σ are the energy levels of the renormalized adsorbate orbitals formed after the interaction with broad, free-electron-like substrate sp-band. S and V are the overlap integral and coupling matrix element describing the interaction between renormalized adsorbate orbitals and metal d-band, respectively. The first term in each bracket describes the covalent attraction, while the second term describes the Pauli repulsion. The coefficient in front of the bracket is the degeneracy of the adsorbate states.

To use the model in Eqs. (1) and (2) to analyze the adsorption of OH on the skin alloys, we need to evaluate the energy levels of the renormalized ε1π and ε4σ orbitals with respect to the substrate Fermi level. To accomplish this objective, we have investigated the evolution of these molecular states on the Al(111) surface. Since Al has no d-electrons, this system can mimic the interaction of OH with the sp-band of skin alloy surfaces.1 

In Fig. 2(b), we show the density of states projected on the molecular orbitals of the OH adsorbate on the Al(111) surface. The positions of molecular orbitals of OH (3σ, 1π, and 4σ) in vacuum are shown in Fig. 2(a). Comparison of Figs. 2(a) and 2(b) shows that the molecular orbitals of OH adsorbed on the Al(111) surface are broadened and shifted down in energies with respect to the molecular states of the gas phase OH.

FIG. 2.

(a) Density of states (DOS) of gas phase OH radical in vacuum. (b) DOS projected on the molecular orbitals of OH adsorbed on atop site of Al(111). (c) and (d) DOS projected on the molecular orbitals of OH adsorbed on atop site of Pd and Pt with 3d subsurface metal.

FIG. 2.

(a) Density of states (DOS) of gas phase OH radical in vacuum. (b) DOS projected on the molecular orbitals of OH adsorbed on atop site of Al(111). (c) and (d) DOS projected on the molecular orbitals of OH adsorbed on atop site of Pd and Pt with 3d subsurface metal.

Close modal

Due to the difference in the sp-electron density of the Al(111) surface compared to Pt and Pd skin alloy surfaces, the calculated positions of the renormalized adsorbate states on the Al(111) surface need to be recalibrated. This can be done straightforwardly since the low lying 3σ adsorbate state interacts mainly with sp-states on the Al(111) and skin alloy surfaces and therefore provides a reasonable reference. It is shown in Figs. 2(c) and 2(d) that 3σ orbital is shifted slightly upward on Pt and Pd skin alloys compared to the Al(111). We assume that renormalized states (1π and 4σ) have shifted upward by the same energy relative to the 3σ orbital of OH adsorption on Pd and Pt skin alloys, respectively. This assumption is reasonable since the level shift of renormalized adsorbate states will be mainly a function of the substrate sp density of states.18 This analysis shows that the renormalized 1π and 4σ states of OH on the Pd alloys are at −0.6 and 5.0 eV with respect to the Fermi level. The corresponding energy levels on the Pt alloy surfaces are at −1.0 and 4.6 eV.

We can now evaluate various parameters in Eq. (2). It has been shown previously based on muffin-tin orbital theory that the interatomic matrix element Vπ can be calculated from Eq. (3),19 

Vπ=ηpdπ2rd3/2md7/2.
(3)

ηpdπ=1.36 and 2/m=7.62eVÅ2 are constant. rd is the characteristic length of the d-orbitals of a surface atom. It is constant for a given surface atom. We use the values for rd tabulated in solid state table.19,d is the adsorbate-metal bond length. We use the bond lengths calculated in the DFT-GGA geometry optimization calculations.13 Equation (3) shows that the interatomic matrix element for a given adsorbate interacting with metal d-bands on a family of skin alloys (Pt or Pd) is only a function of d (metal-adsorbate bond length). To calculate the overlap integral S, we use a simple relationship SπαVπ, where α is an adjustable parameter.1,5 We also assume that the d-band filling of Pt and Pd surface atoms is 0.9, and it is equal for different alloys. This assumption is consistent with previous experimental measurements showing that the formation of alloys is not accompanied by charge transfer between d-states of constituent metal elements.20–22 Due to different geometric arrangements of π and σ orbitals, the overlap integral ratio of Sσ/Sπ is approximated to be 1.3, calculated previously for the adsorption of CO on transition metal surfaces.1 

Figure 3 shows a comparison between the OH adsorption energies obtained from DFT calculations and the prediction of the model with two adjustable parameters, α and ΔEsp. The adjustable parameters were obtained by minimizing the residual between DFT-calculated adsorption energies and the energies obtained from the model in Eq. (1). Figure 3 shows that for a series of Pd and Pt skin alloys with different subsurface atoms (3d, 4d, or 5d), the model captures the chemisorption of OH very well. Further inspection of the tabulated parameters in Fig. 3 shows that the interaction of the sp-band of the alloy substrates (ΔEsp) with the OH adsorbate is attractive. Furthermore, excellent agreement between DFT adsorption energies and the model-predicted energies can be obtained with a constant value of α and ΔEsp for skin alloys with subsurface elements in the same row of periodic table (3d, 4d, or 5d). Comparison between the contribution of sp-band and the total adsorption energies shows that the interaction with the substrate d-band is repulsive, and it differs significantly for different alloys as shown in Fig. 4(a). It is this repulsion term that drives the unusual behavior of OH on the Pt and Pd skin alloys.

FIG. 3.

Comparison of DFT- and model-calculated OH adsorption energy on Pd (a) and Pt (b) skin alloys. The parameters obtained from the model are tabulated in insert.

FIG. 3.

Comparison of DFT- and model-calculated OH adsorption energy on Pd (a) and Pt (b) skin alloys. The parameters obtained from the model are tabulated in insert.

Close modal
FIG. 4.

(a) The covalent attraction and Pauli repulsion contributions to the OH binding energy on Pt skin alloys with 3d subsurface atom calculated using the model discussed in the text. (b) Surf-OH bond distance and the coupling matrix element (V2) are plotted as a function of the number of sp-electrons on the surface substrate atoms. The number of sp-electrons was calculated as total Bader charge minus the d-band filling. (c) F and Cl adsorption energies on Pt and Pd skin alloys as a function of d-band center. (d) O and OH adsorption energies on Au and Ag skin alloys as a function of d-band center.

FIG. 4.

(a) The covalent attraction and Pauli repulsion contributions to the OH binding energy on Pt skin alloys with 3d subsurface atom calculated using the model discussed in the text. (b) Surf-OH bond distance and the coupling matrix element (V2) are plotted as a function of the number of sp-electrons on the surface substrate atoms. The number of sp-electrons was calculated as total Bader charge minus the d-band filling. (c) F and Cl adsorption energies on Pt and Pd skin alloys as a function of d-band center. (d) O and OH adsorption energies on Au and Ag skin alloys as a function of d-band center.

Close modal

As discussed above, the repulsion is the consequence of orbital orthogonalization between the renormalized adsorbate state and the metal d-states, which is proportional to SVαV2. This suggests that the adsorption energies of OH on Pt or Pd skin alloys are different due to different interatomic matrix elements (V). We showed above that the difference in the interatomic matrix element on Pt or Pd skin alloys arises from different metal-adsorbate bond lengths. The Pt or Pd alloys with larger metal-adsorbate bond lengths (skin alloys containing subsurface atoms to the left in periodic table) have smaller interatomic matrix element, and therefore the repulsion between the metal d-band and the renormalized adsorbate states is weaker. This explains the stronger chemisorption of OH on those alloy surfaces characterized with longer adsorbate-substrate bonds.

It is important to discuss why the Pt or Pd alloys with subsurface atoms to the left in a row of the periodic table have larger metal-adsorbate bond lengths compared to the alloys containing metals to the right in the periodic table. Adsorbate-substrate bond length is to a large degree governed by the substrate sp-electron density, i.e., the bond length is determined by the distance outside of the surface where the electron density around the adsorbate is optimal for adsorption.2,5 This is consistent with the model that shows that a large fraction of the absolute bond strength, and therefore the length of the bond, is due to the interaction of the OH adsorbate with the sp-band. Due to the difference in the electronegativity of the different metals in the skin alloys, there is an electron transfer between subsurface and surface metal atoms. It was shown previously, experimentally and theoretically, that mainly free-electron-like sp-states participate in this electron transfer.21,22 This transfer of sp-charge between subsurface and surface atoms of the substrate affects the adsorbate-substrate bond length. For example, for skin alloys with 3d subsurface metals to the left in the periodic table (i.e., Cr), there is larger driving force to have more electron transfer to the surface due to the increased difference in electronegativity between guest and host metal atoms compared to the subsurface atoms to the right in periodic table (i.e., Ni). In response to this increased electron transfer, the OH adsorbate will move away from the surface to maintain the optimal electron density, as shown in Fig. 4(b).

It is also important to understand why OH and O exhibit fundamentally different chemisorption behavior on the skin alloys as shown in Fig. 1. The main difference between OH and O is that the O atom in OH is more electron rich, i.e., there is a transfer of electron density from H to O in OH. This shift in electron density causes the OH adsorbate to require lower optimal electron density when adsorbed on a metal surface than the O adsorbate. Since the lower electron density is encountered further away from the surface atoms, the bond distance between the OH adsorbate and the substrate surface is larger than that for the O adsorbate. This larger bond distance results in smaller coupling matrix element for the adsorption of OH, ultimately yielding smaller spread between bonding and antibonding metal-OH states and causing the antibonding states (formed due to the hybridization of OH 1π molecular orbital with surface d-states) to be below the Fermi level. The populated antibonding state effectively means that the interaction between substrate d-states and the adsorbate states is repulsive.9 The position of the populated antibonding state with respect to the Fermi level for a given adsorbate is dependent on the position of the substrate d-band center; higher d-band center leads to higher energy of the populated antibonding state. The higher energy of the antibonding state means that the overall one-electron energy of the adsorbate/substrate system is higher. This explains the unusual observation that the substrates with higher d-band center bind the adsorbate less strongly than the substrates with lower energy of d-electrons. Unlike the OH adsorbate, atomic O binds closer to a metal surface, and the coupling matrix element is much larger. This large coupling matrix element pushes the antibonding metal-O states to be partially above the Fermi level, resulting in the dominance of the covalent attraction between the d-band and renormalized adsorbates states.

FIG. 1.

DFT-GGA adsorption energies of (a) O and (b) OH on Pd and Pt skin alloys are plotted as a function of the center of d-band projected on surface atoms. [(c) and (d)] Surf-O and Surf-OH distance are plotted as a function of DFT-GGA adsorption energies of O and OH on Pd and Pt skin alloys. The model system is shown at the left bottom of the figure. The d-band center (εd) projected on surface atoms of various skin alloys are shown in the table.

FIG. 1.

DFT-GGA adsorption energies of (a) O and (b) OH on Pd and Pt skin alloys are plotted as a function of the center of d-band projected on surface atoms. [(c) and (d)] Surf-O and Surf-OH distance are plotted as a function of DFT-GGA adsorption energies of O and OH on Pd and Pt skin alloys. The model system is shown at the left bottom of the figure. The d-band center (εd) projected on surface atoms of various skin alloys are shown in the table.

Close modal

OH adsorption on the Pt and Pd skin alloys is not the only exception to the d-band model of chemisorption. In fact any adsorbate characterized by the repulsive interaction between substrate d-states and renormalized adsorbate states will behave similarly, i.e., stronger bonding will be accompanied by larger bond length and lower energy of the center of d-band projected on surface atoms. These systems are always associated with substrates that have nearly fully occupied d-band (mainly d9 and d10 metals) and adsorbates with almost completely filled valence shell (OH, F, Cl, ). In Figs. 4(c) and 4(d) we show that F and Cl show similar dependence on the center of d-band projected on surface atoms of the Pt and Pd skin alloy compared with the OH adsorbate. The same trend follows the chemisorption of O and OH on Ag and Au skin alloys.

In summary, we show that there is a family of adsorbate-substrate systems that does not follow the trends in adsorption energies predicted by the d-band model. These adsorbate-substrate pairs are characterized by the repulsive interaction of substrate d-band with the renormalized adsorbate states. The exceptions to the d-band model are mainly associated with very electronegative adsorbates on substrates with almost completely filled d-band, e.g., OH, F, or Cl adsorption on metals and alloys characterized by d9 and d10 substrate surface atoms.

We gratefully acknowledge the support of the U.S. Department of Energy DOE-BES. S.L. also acknowledges DuPont Corporation for funds provided with DuPont Young Professor Award and the Camille & Henry Dreyfus Foundation for the Camille Dreyfus Teacher-Scholar Award.

1.
B.
Hammer
,
Y.
Morikawa
, and
J. K.
Nørskov
,
Phys. Rev. Lett.
76
,
2141
(
1996
).
2.
F.
Abild-Pedersen
,
J.
Greeley
,
F.
Studt
,
J.
Rossmeisl
,
T. R.
Munter
,
P. G.
Moses
,
E.
Skulason
,
T.
Bligaard
, and
J. K.
Nørskov
,
Phys. Rev. Lett.
99
,
016105
(
2007
).
3.
J. K.
Nørskov
,
Phys. Rev. B
26
,
2875
(
1982
).
4.
B.
Hammer
and
J. K.
Nørskov
,
Surf. Sci.
343
,
211
(
1995
).
5.
J.
Greeley
,
J. K.
Nørskov
, and
M.
Mavrikakis
,
Annu. Rev. Phys. Chem.
53
,
319
(
2002
).
6.
J.
Greeley
,
T. F.
Jaramillo
,
J.
Bonde
,
I.
Chorkendorff
, and
J. K.
Nørskov
,
Nature Mater.
5
,
909
(
2006
).
7.
V.
Stamenkovic
,
B. S.
Mun
,
K. J.
Mayrhofer
,
P. N.
Ross
,
N. M.
Markovic
,
J.
Rossmeisl
,
J.
Greeley
, and
J. K.
Nørskov
,
Angew. Chem., Int. Ed.
45
,
2897
(
2006
).
8.
J. K.
Nørskov
,
T.
Bligaard
,
J.
Rossmeisl
, and
C. H.
Christensen
,
Nat. Chem.
1
,
37
(
2009
).
9.
B.
Hammer
and
J. K.
Nørskov
,
Nature (London)
376
,
238
(
1995
).
10.
N.
Markovic
,
H.
Gasteiger
, and
P. N.
Ross
,
J. Electrochem. Soc.
144
,
1591
(
1997
).
11.
A.
Yamakata
,
T. aki
Ishibashi
, and
H.
Onishi
,
J. Mol. Catal. A: Chem.
199
,
85
(
2003
).
12.
J.
Greeley
,
T. F.
Jaramillo
,
J.
Bonde
,
I. B.
Chorkendorff
, and
J. K.
Nørskov
,
Nat. Chem.
1
,
552
(
2009
).
13.
The spin-unpolarized DFT calculations were performed using the ultrasoft pseudopotential plane-wave method with the generalized gradient approximation (GGA-PW91) coded in DACAPO. The wave-functions were expanded in plane-waves with an energy cutoff of 450 eV. The alloy surfaces were modeled by a 2×2×4 slab separated by 10 Å of vacuum space. The adsorbates and top two layers were allowed to relax until the total force on the atoms was less than 0.05 eV/Å. In the p(2×2) surface unit cell, 4×4×1 Monkhorst–Pack k-points were used for the Brillouin-zone integration. Convergence of the results with respect to various calculation parameters was verified in all cases.
14.
J. R.
Kitchin
,
J. K.
Nørskov
,
M. A.
Barteau
, and
J. G.
Chen
,
J. Chem. Phys.
120
,
10240
(
2004
).
15.
R. A.
van Santen
and
G. J.
Kramer
,
Chem. Rev. (Washington, D.C.)
95
,
637
(
1995
).
16.
J. J.
Mortensen
,
B.
Hammer
, and
J. K.
Nørskov
,
Surf. Sci.
414
,
315
(
1998
).
17.
B.
Hammer
,
Top. Catal.
37
,
3
(
2006
).
18.
J. R.
Schrieffer
,
J. Vac. Sci. Technol.
9
,
561
(
1972
).
19.
W. A.
Harrison
,
Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond
(
Dover
,
New York
,
1989
).
20.
E.
Nikolla
,
J.
Schwank
, and
S.
Linic
,
J. Am. Chem. Soc.
131
,
2747
(
2009
).
21.
N.
Schweitzer
,
H.
Xin
,
E.
Nikolla
,
J. T.
Miller
, and
S.
Linic
,
Top. Catal.
53
,
348
(
2010
).
22.
H.
Xin
,
N.
Schweitzer
,
E.
Nikolla
, and
S.
Linic
,
J. Chem. Phys.
132
,
111101
(
2010
).