Copyright © 2014 American Scientific Publishers Journal of All rights reserved Computational and Theoretical Nanoscience Printed in the United States of America Vol. 11, 511–520, 2014 EERHARTICLE RESEARCH
Adsorption Behavior of Noble Metal Clusters and Their Alloys
Stanley Herrmann1, Michail Stamatakis1 †, Antonis N. Andriotis2, and Giannis Mpourmpakis1 3 ∗
1Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA 2Institute of Electronic Structure and Laser, FORTH, Heraklion 71110, Crete, Greece 3Catalysis Center for Energy Innovation (CCEI), University of Delaware, Newark, Delaware 19716, USA
Metal-adsorbate bond formation is a fundamental step in catalysis that determines the activity and selectivity of a particular catalyst. The synthesis of novel materials with tailored bond strengths can lead to the design of catalysts with desired functionality. In this work, density functional theory
(DFT) was employed to determine the binding energy of several adsorbates (O, OH, H2O, H, C, CO) on 10-atom metal clusters of the d10 (Cu, Ag, Au) metals, namely the pure metals and their bimetallic combinations (CuAg, CuAu, AgCu, AgAu, AuCu, AuAg). A database of the adsorbate binding energies on these clusters was constructed, and descriptor-based models were developed, based on key electronic (d-band, electronegativity, charge) and structural (strain) properties of the clusters. In addition, the fundamental physicochemical properties of the catalysts that control metal- adsorbate bonding areIP: elucidated. 192.168.39.211 On: Sat, 02 Oct 2021 05:15:29 Keywords: Bimetallic, DFT,Copyright: Theory, American Descriptors, Scientific Binding. Publishers Delivered by Ingenta
1. INTRODUCTION metals they are made of.6 22 Once established, models of A fundamental understanding of catalyst-adsorbate inter- binding energy (BE) can be used with Brønsted–Evans– actions is vital for a wide range of fields including Polanyi type correlations to estimate reaction energy environmental chemistry and heterogeneous catalysis, as profiles16 23 and gain an understanding on a catalyst’s per- well as for biomedical, industrial, and electrochemical formance, such as activity and selectivity. applications.1–5 This area of research is of particular inter- Aside from periodic DFT, molecular orbital-based clus- est due to its potential in the rational design of catalysts ter DFT provides other means to simulate catalytic toward renewable energy production.6–8 behavior. One key advantage of molecular orbital based The immense computational power available nowadays cluster DFT is its ability to account for the size and shape facilitates the investigation of nanomaterials properties, of a nanoparticle in an efficient way, as well as its detailed among which are heterogeneous catalysts, through first- interaction mapping through molecular orbitals (LCAO principles calculations.9–15 Periodic density functional theory). Particularly in catalysis, it is often the case that theory (DFT) is commonly used to understand catalyst- reactions exhibit structure sensitivity and therefore, mod- adsorbate interactions. In particular, Nørskov and co- els accounting for different catalytic sites, such as cor- 8 workers16–18 have shown that trends in the binding of an ners, edges and planes of a nanoparticle are essential. adsorbate over a range of transition metal catalysts can be A major disadvantage of DFT is its computational cost, explained on the basis of the d-band center (dC )ofthe especially when simulating nanoparticles larger than 1 nm metal. Such trends have also been reported for near-surface in diameter. Since the computational cost of DFT increases alloys;19–21 the latter have become particularly important with the nanoparticle size, one must resort to efficient due to their unique properties compared to the parent schemes that can capture the desired features of the sys- tem being modeled. In previous work, we introduced a ∗Author to whom correspondence should be addressed. computational framework that makes use of small clus- †Present address: Department of Chemical Engineering, University ters to accurately represent the properties of the bulk College London, Torrington Place, London WC1E 7JE, UK. metal.24
J. Comput. Theor. Nanosci. 2014, Vol. 11, No. 2 1546-1955/2014/11/511/010 doi:10.1166/jctn.2014.3387 511 Adsorption Behavior of Noble Metal Clusters and Their Alloys Herrmann et al.
Herein, we expand the aforementioned work to study Spin unrestricted DFT calculations were performed 31 the binding of several adsorbates (O, OH, H2O, H, C, and using the software package Gaussian 03. The B3LYP CO) on the d10 pure metals (Cu, Ag, and Au: d10s1) and functional32 33 along with the LANL2DZ basis set were their bimetallic alloys (CuAg, CuAu, AgCu, AgAu, AuCu, applied. First, bare cluster optimization was performed and AuAg) and provide detailed analysis on developing during which the bond angles and dihedrals were frozen, empirical binding energy models. These adsorbates are of whereas the bond distances were allowed to relax. This particular interest in numerous catalytic reactions, such optimization scheme ensures that the cluster retains a as the water-gas shift reaction and the CO oxidation.25–30 3D bilayer structure. Each one of the 10-atom clusters Using molecular orbital-based cluster DFT calculations, was optimized at three multiplicities: singlet, triplet, and BE trends of these adsorbates were investigated and pos- quintet. sible descriptors characterizing the electronic and strain Subsequently, cluster-adsorbate interactions were stud- effects of the metal cluster were identified. Four descrip- ied. The adsorbates can interact with the catalyst at three RESEARCH ARTICLE tors were used in this study: different sites: hollow (O, OH, H, and C), bridge (O, OH, d (i) the -band center, H, C, and CO), and top (O, OH, H2O, and CO) (Fig. 1(a)). (ii) the strain of the surface layer due to the bimetallic To optimize the adsorbate on the catalyst, the optimized composition, bare cluster was frozen and the distance between the adsor- (iii) the difference in the electronegativities of the metals bate and the cluster was relaxed. For adsorbates consisting composing the cluster, and of more than one atom (i.e., OH), the atoms not directly (iv) the charge transfer between the surface and the sub- involved in binding (i.e., H of OH) were allowed to fully surface plane of the cluster. relax during the calculations. This study provides valuable insights into the physico- The BE of the adsorbates was calculated as follows: chemical properties of the metal clusters that markedly BE = E − E − E affect binding, and unravels the binding behavior of the A M–A M A (1) adsorbates through detailed electron density analysis. E E E where M–A, M , and A are the total electronic energies of the metal-adsorbate system, of the metal cluster, and of 2. COMPUTATIONAL METHODS the adsorbate, respectively. Small clusters, consisting of 10 atoms,IP: 192.168.39.211 were used to simu- On: Sat, 02The Oct methodology 2021 05:15:29 followed in this work results in highly late the metal catalyst structure. Each clusterCopyright: consisted American of a Scientific Publishers Delivered byefficient Ingenta (fast) calculations without sacrificing accuracy, 7-atom upper layer and a 3-atom lower layer (Fig. 1). This as shown by detailed test calculations that validated our configuration has one central surface atom with a coordi- computational scheme. In these calculations, an adsor- nation number of 9 which mimics the face-centered cubic bate was bound to the central top-site and the central (111) plane of the bulk metal. For the bimetallic clusters, metal atom was allowed to fully relax during the opti- the two layers are composed of different metals, represent- mization. The calculated BEs were less than 2 kcal/mol ing a near-surface alloy structure as seen in Figure 1(b). different than the ones involving a completely frozen M M M These clusters will be referred to as T B, where T cluster. denotes the metal composition of the top layer and MB denotes the metal composition of the bottom layer. 3. RESULTS AND DISCUSSION 3.1. Calculation of Binding Energies Bridge Table I presents the BEs for the most stable binding Top Hollow M configurations of each adsorbate on every cluster. A table MT T containing the BEs of all configurations investigated is MT MT provided in the supplementary information. The calculated MT BEs are in good agreement with periodic DFT calculations < MT MT reported in the literature (difference 6 kcal/mol), shown in Table II. With the exception of C, the BEs of adsorbates show a similar trend with respect to the clusters’ top layer com- MB MB position. These adsorbates exhibit the strongest binding on clusters with a Cu top layer and the weakest binding on MB clusters with a Au top layer. This will be referred to as the “primary trend” which can be summarized as: Fig. 1. 10-atom cluster model and adsorbate binding sites. MT and MB indicate the type of the metal constituting the top and bottom layer of the cluster respectively. In monometallic clusters, MT is the same as MB . BE[Cu top layer] > BE[Ag top layer] > BE[Au top layer]
512 J. Comput. Theor. Nanosci. 11, 511–520, 2014 Herrmann et al. Adsorption Behavior of Noble Metal Clusters and Their Alloys
Table I. Calculated binding energies of adsorbates in kcal/mol. The positive BEs values in parenthesis are provided because they were included in the input used to construct the models. EERHARTICLE RESEARCH Adsorbate Site CuAu CuAg CuCu AgAu AgAg AgCu AuAu AuAg AuCu
O Hollow −96 80 −90 98 −82 32 −59 60 −56 00 −51 41 −30 02 −25 08 −20 12 OH Hollow −85 31 −77 64 −70 72 −61 19 −55 94 −52 02 −30 64 −25 06 −21 05 − − − − − − − − H2OTop9 45 8 79 6 36 5 74 5 66 4 53 5 00 5 26 13 62 H Hollow −53 19 −47 81 −43 35 −39 80 −34 87 −31 84 −26 96 −28 68 −25 54 C Hollow −71 26 −69 30 −60 53 −39 55 −38 23 −34 67 −57 64 −56 06 −45 03 CO Top −8 63 −6 92 −2 66 −2 41 −2 28 −2 72 1 35 −2 92 2 45
Since the cluster consists of two layers, we also identify characteristics of the clusters. These characteristics can “secondary trends” pertaining to clusters with the same top be expressed by descriptors designed to capture the driv- layer composition (MT ): ing forces of adsorbate binding. Subsequently, quantitative models based on each adsorbate’s essential descriptors can M > M > M BE T Au BE T Ag BE T Cu be derived to accurately predict the BEs. or more specifically We considered four such descriptors, namely, (i) the dC , CuAu > CuAg > CuCu (all adsorbates) (ii) the top layer strain, (iii) the electronegativity difference between the metals AgAu > AgAg > AgCu (all adsorbates except CO) forming the bimetallic clusters, and AuAu > AuAg > AuCu (O, OH, C) (iv) the charge transfer between surface and sub-surface planes of the clusters. The energy differences of the secondary trends are much smaller than those of the primary trend. These energy dif- These descriptors account for the electronic interactions ferences become even smaller on weakly bound systems between the layers of the metal cluster, as well as the strain effect caused by the changes in the bond distances of the such as CO and H2O. As a result, the overall ordering of BEs on all clusters could be summarized as follows: top layer, since all of these factors have been reported to IP: 192.168.39.211 On: Sat,affect 02 Oct binding. 202116–18 05:15:29 21 24 In Figure 3 we present linear rela- CuAu > CuAg > CuCu > AgAu >Copyright:AgAg > AgCu American Scientifictionships Publishers between the BE of all the adsorbates and the Delivered byaforementioned Ingenta descriptors on clusters with Cu as the top > AuAu > AuAg > AuCu metal. Similar relationships hold for the clusters consist- This trend will be referred to as the “common trend” ing of Ag (AgAg, AgCu, AgAu) and Au (AuAu, AuAg, throughout the rest of this manuscript. Figure 2 shows the AuCu) as the top metal. 16–21 BEs presented in Table I versus the BE of atomic O on As suggested in literature, the dC was used as one the hollow site, which exhibits the common trend. This descriptor of these properties since it is the footprint of figure clearly shows the primary trend which is similar the electronic properties of the metal cluster. The dC can among all adsorbates except C and captures the common trend behavior (small BE deviations exist as we mentioned earlier).
3.2. Descriptor Development Based on the Physicochemical Properties of Clusters Having identified these BE trends, we are inter- ested in explaining them based on the physicochemical
Table II. Comparison of binding energies of this study to published periodic DFT calculations. Values are in kcal/mol.
Adsorbate/ Binding BE BE cluster site (our work) (literature) Refs.
O/AgAg Bridge −42 70 −48 43 34 OH/CuCu Hollow −70 72 −65 03 −65 72, 35 28 −73 33 −73 79 36 37 H O/CuCu Top −6 36 −4 84 36 2 Fig. 2. Binding energies of adsorbates versus the binding energy of H O/AuAu Top −5 00 −3 23 36 2 atomic O (the symbols in circle show the major binding energy differ- C/AgAg Hollow −38 23 −36 90 34 ences of C from the primary trend).
J. Comput. Theor. Nanosci. 11, 511–520, 2014 513 Adsorption Behavior of Noble Metal Clusters and Their Alloys Herrmann et al.
(a) the (bare) cluster, and is presented in Table III. A detailed description of the dC calculation on these clusters can be found in Ref. [24]. CuCu CuAg CuAu Further, we considered additional, secondary descrip- tors that explicitly quantify geometric and charge transfer processes on the clusters. The geometric properties were quantified by the strain effect. The charge transfer was accounted through (i) the electronegativities of the metals, and (ii) the charge density distribution between the two layers of the cluster. (b) These secondary descriptors are also provided in Table III. RESEARCH ARTICLE To assess the strain effect, the percent change in the average top layer bond length for a bimetallic cluster with CuCu CuAg
CuAu respect to the monometallic cluster of the same top layer composition was used. This was calculated using Eq. (2). a − a D = 0 · s a 100 (2) 0 Here, a represents the average bond length of the top layer a of the cluster, and 0 is the average bond length of the top layer of the monometallic cluster with the same top layer composition. This descriptor has a value of zero when cal- culated for the monometallic clusters. The values for a are (c) provided in Table IV, and Figure 3(b) shows the BE of the adsorbates versus this descriptor. The final two descriptors capture the electron distribu- IP: 192.168.39.211 On: Sat,tion 02 onOct the 2021 metal 05:15:29 cluster. The first one is the difference Copyright: American Scientificin the electronegativities Publishers of the elements that compose the Delivered bytwo Ingenta layers of the cluster, E , defined as: = − E top bottom (3) where the subscripts top and bottom refer to the metals of the corresponding layers. From this equation, it is appar- ent that this descriptor has a non-zero value only for the bimetallic clusters, as seen in Table III. Electronegativity, , is a measure of the tendency of an atom to attract electrons, and for the purposes of our study the Pauling scale was used. The electronegativities of the d10 metals (Cu, Ag, Au) are as follows: Fig. 3. Interaction trends on clusters consisting of Cu as a top layer: d (a) BE of adsorbates versus the C of the clusters, (b) BE of adsor- < < Cu 1 90 Ag 1 93 Au 2 54 bates versus the strain of the top layer of the cluster and (c) linear trends between the descriptors (strain: S, electronegativity difference: namely, Au is the most electronegative and Cu is the E q d d , charge transfer: , band center: C and the BE of O and C (O BE least electronegative of the three metals in consideration, follows the primary and common trend, whereas C adsorption deviates and therefore, Au is the most potent in attracting elec- from the adsorption trend of the rest adsorbates). dC is in eV. trons. Notably, the electronegativity trend is the reverse of be used as a BE descriptor for metals with filled d-bands, the primary BE trend discovered. This observation can be since explained in terms of the electron density redistribution (i) the dC determines to some extent the energy level of upon binding. More specifically, most of the adsorbates the metal’s s-orbitals which play important role in adsorp- that exhibit the primary trend bind through O, which is tion as we will show later, and much more electronegative than any of the three met- d = (ii) participates in back-donation electron processes ( metal als ( O 3 44). When two electronegative entities are to adsorbates’ molecular orbitals). brought in close proximity, a competition for electrons The dC was calculated as the median of the density of arises resulting in weaker adsorption with less electrostatic states (DOS) projected on the d-orbitals of all atoms in character. Therefore, the Au top layer would introduce a
514 J. Comput. Theor. Nanosci. 11, 511–520, 2014 Herrmann et al. Adsorption Behavior of Noble Metal Clusters and Their Alloys
Table III. Descriptor values used in the models. The descriptors are the d-band center of the metal, the strain on the top metal layer, the electroneg- ativity difference between the metals of the two layers and the charge transfer ratio between the two layers. EERHARTICLE RESEARCH CuAu CuAg CuCu AgAu AgAg AgCu AuAu AuAg AuCu dC (eV) −7 762 −7 650 −7 551 −9 283 −9 290 −8 965 −8 776 −9 063 −8 376 Strain (%) 6 40 5 70 0 00 0 20 0 00 −2 70 0 00 0 10 −2 40 Electronegativity difference −0 64 −0 03 0 00 −0 61 0 00 0 03 0 00 0 61 0 64 Charge transfer ratio −2 396 0 323 1 000 −1 957 1 021 1 655 0 877 3 106 3 843
Table IV. Geometric and electronic properties of the metal clusters.
CuAu CuAg CuCu AgAu AgAg AgCu AuAu AuAg AuCu
Average bond length (Å) 0 683 0 666 0 522 0 891 0 886 0 807 0 874 0 877 0 806 Top layer charge (e−)0 563 −0 076 −0 235 0 460 −0 240 −0 389 −0 206 −0 730 −0 903 Central atom charge (e−) −0 932 −1 141 −1 324 −1 022 −1 246 −1 456 −0 809 −1 020 −1 280 much stronger competition for electrons than that of the Although the two descriptors E and q are determined Cu and Ag top layers, which have lower electronegativi- by different methods, they represent the same physical ties. Thus, O-containing adsorbates bind weakly when the property, namely, the charge transfer between the layers top layer consists of Au, and increasingly more strongly of the metal cluster. This is reflected by the similar (abso- for Ag and Cu top layers. lute) slopes observed in Figure 3(c) of BE versus q and For the adsorbates that bind through C, the top layer BE versus E (negative sign on the values of q changes trend differs from the primary trend. This could be the slope direction). explained by the fact that the electronegativity of C Regarding the observed deviations from the primary and = ( C 2 55) is close to that of Au, and therefore the com- common trends, we found that these can be attributed to petition for electrons might not play such an important role the relative position of the HOMO and LUMO energy as for O binding. In the case of H binding, the primary levels of the adsorbates with respect to the dC -level. trend is observed, even though the electronegativity of H For example, as shown in Figure 4, C is the only adsor- = ( H 2 10) is lower than that of AuIP: and 192.168.39.211 higher than that On: of Sat,bate 02 whichOct 2021 places 05:15:29 its HOMO level at higher energies than Ag and Cu. All the observed BE deviationsCopyright: from the American major Scientificthe metals’ Publishers (and alloys’) dC -levels. This fact supports the trends can be attributed to additional factors whichDelivered seem byC-adsorption Ingenta deviation from the rest of the adsorbates. to play equally important roles in differentiating clusters Furthermore, clusters consisting of Cu as a surface metal exhibiting approximately equal descriptor values (i.e., val- (Cu, CuAg, CuAu) separate their dC from the dC val- d ues of C in Fig. 3(c)). One of such factors is the location ues of the rest clusters (Ag, AgAu, AgCu, Au, AuCu, of the adsorbate’s HOMO and LUMO energy levels with AuAg). On top of this, the energy separation of the dC d respect to the C -level of the adsorbing cluster as discussed levels of the Cu-based clusters (Cu, CuAg and CuAu) below. is almost constant. In addition, focusing on the strongly Furthermore, to quantify charge transfer effects, natu- bound adsorbates we notice that their HOMO levels are ral bond orbital (NBO) population analysis was applied. either higher (C) or lower (O, OH, H) than the dC of the This analysis reveals the electron density transfer between the two layers of the metal cluster, as well as toward the central atom on the top layer. The latter is of special sig- nificance because this atom is involved in all the binding configurations. The values of the charge transfer are shown in Table IV. It is worth noting that the charge transfer values exhib- ited by the clusters with the same top layer composition, are in perfect agreement with the secondary trends, for instance, the CuCu cluster has a more negatively charged top layer than the CuAg and CuAu clusters. We used a normalized value for the charge of the top layer of the cluster, which is: q = q q (4) Cu q Variable represents the top layer charge of the metal Fig. 4. HOMO, H(X), and LUMO, L(X), energy levels of the adsor- cluster, and q is the top layer charge of the monometallic X = d d10 Cu bates OH, H2O, H, CO, C, O versus the C of the mono- and Cu cluster (normalization constant). bi-metallic clusters used in this study.
J. Comput. Theor. Nanosci. 11, 511–520, 2014 515 Adsorption Behavior of Noble Metal Clusters and Their Alloys Herrmann et al.
Cu based clusters. This leads to the well-defined relation- of the adsorbates had multiple models with an R2 value 2 ships between the BEs of the adsorbates and the dC of Cu greater than 0.90. The models with the highest R values based clusters shown in Figures 3(a) and (c). are shown in Table VI, and the other models are presented Regarding the dC of the other clusters (Ag, AgAu, with their corresponding parameters in the supplementary AgCu, Au, AuCu, AuAg) it is observed that information. The parity plots for all the adsorbates and for (i) the dC of AgCu falls into the dC range of Au-based each of the models (2- and 3-variable linear, quadratic, and clusters, bilinear) are provided in Figure 5. Each parity plot pertains (ii) the dC of Ag and AgCu are approximately equal, to a specific model and the descriptors used are different (iii) the HOMO level of O, OH and H falls into the dC for each adsorbate. range of Au-based clusters, whereas, it is always higher The results presented in Table VI, reveal the most than the dC of Ag-based clusters. important physicochemical properties influencing the bind- ing of that particular adsorbate. One common descriptor, These factors contribute to altering the BE trends between RESEARCH ARTICLE important to all of the adsorbates was the d , in agreement different adsorbates and the creation of the BE deviations C with existing literature.16–21 Also, the parity plots show that from the observed primary and common trends. the 2-variable quadratic models predict the BE of most of Although the use of the adsorbates’ HOMO and LUMO the adsorbates better than that of the other models. levels as descriptors can account for some additional features of the adsorption behavior, they cannot be of 3.4. Electron Tracking practical use. This is because the HOMO/LUMO levels refer to properties related to the adsorbates and not the A more rigorous analysis of the electron transfer during catalysts. For this reason, we are going to consider only binding provides further insight in the common trend and those predictors which describe the catalysts’ properties. rationalizes the slight deviations observed for adsorbates that bind through C. This analysis is based on the expan- However, notice that for adsorbates exhibiting similar sion of molecular orbitals as linear combinations of atomic HOMO-LUMO values (O and OH, both binding the cat- orbitals (LCAO expansion). By comparing the coefficients alysts through O) the BE trends remain the same. This of the atomic orbitals directly involved in the binding, shows a possible fast-way of grouping the adsorbates into we can identify the ones participating in bond formation. different binding categories and defining possible homol- Further, by comparing the atomic orbital density of the ogous series of adsorption. IP: 192.168.39.211 On: Sat,monometallic 02 Oct 2021and 05:15:29 bimetallic clusters with identical top Copyright: American Scientificlayer composition, Publishers we can investigate the effect of the 3.3. Descriptor-Based Models Delivered bysecond Ingenta layer composition on the binding strength. For con- The ab initio BEs of each adsorbate in its most stable sistency, the adsorbate was analyzed on the top site con- adsorption site were fitted to various expressions of the figuration in all cases. This allowed for the atomic orbitals descriptors using the Matlab function lsqcurvefit. Lin- of the central metal atom to be compared and provided a ear, bilinear, and quadratic functional forms including two consistent binding site for all adsorbate bindings. or three of the descriptors were used, shown in Table V. Both O and OH adsorption on the clusters exhibit the All possible descriptor combinations were considered for same binding behavior. Clusters with an upper layer con- each of the fittings performed and a comprehensive list sisting of Cu or Ag, gain s-electron density, whereas of all of the fittings is provided in the supplementary clusters with Au upper layer lose d-electrons through their information. interaction with O and OH. This s-orbital contribution is The BEs of the adsorbates were best captured by more pronounced when the top layer consists of Cu. Inter- 2-variable quadratic functions of different descriptor pairs estingly, in the case of clusters with Au in the top layer, for each adsorbate except for H2O which was best fit- there is no s-orbital contribution. Charge transfer between ted by the 3-variable bilinear function. Table VI provides the adsorbates and the metal has been shown to be an the descriptors, the constants, and the R2 value of each important component in modeling BE trends of adsorbates fitting. Note that the descriptors are listed in the order with almost completely filled valence shells, like O, to 38 (xi xj )or(xi xj xk) depending on the fit used. Some metals with nearly fully occupied d-bands. This observa- tion provides an atomistic justification for the occurrence > > Table V. Fitting equations considered for descriptor-based models. of the primary trend (Cu Ag Au) that was previously attributed to the electronegativity of the metal. Model Functional form H2O also binds through O, and its BE has a strong b · x + b · x + b dependence on the electronegativity difference. However, 2-variable linear 1 i 2 j 3 b · x2 + b · x2 + b · x · x + b · x + b · x + b 2-variable quadratic 1 i 2 j 3 i j 4 i 5 j 6 the BEs of H2O are similar among all clusters, and this is b · x + b · x + b · x + b 3-variable linear 1 i 2 j 3 k 4 reflected by the fact that there is minimal electron redistri- b · x · x + b · x · x + b · x · x + b · x + b · x 3-variable bilinear 1 i j 2 j k 3 i k 4 i 5 j bution upon its binding. Yet, the fact that the BE of H O + b · x + b 2 6 k 7 depends on the electronegativity difference of the met- Notes:‘x’ denotes a descriptor and ‘b’ denotes a constant. als composing the cluster and the strain (see Table VI),
516 J. Comput. Theor. Nanosci. 11, 511–520, 2014 Herrmann et al. Adsorption Behavior of Noble Metal Clusters and Their Alloys
Table VI. Coefficients and descriptors used for the 2-variable quadratic descriptor-based model as indicated in Table V. H2O is modeled by the bilinear model, and all others are represented by the quadratic model. EERHARTICLE RESEARCH b b b b b b b R2 Adsorbate/site Descriptors 1 2 3 4 5 6 7
O/hollow DE dC 12 2 −38 816 6 172 −673 −2960 – 0 950
OH/hollow DE dC 10 3 −31 511 6 129 −543 −2380 – 0 934 D D d − − − − − H2O/top S E C 4 75 21 3 0 360 3 19 197 0 166 7 46 0 988
H/hollow DQ dC −0 233 −14 11 50 15 4 −245 −1100 – 0 967
C/hollow DS dC 0 953 21 9 −1 61 −19 5 358 1390 – 0 963
CO/top DS dC −0 0858 −5 81 −0 847 −7 18 −97 2 −405 0 909 shows that the point charges developed on the surface of a surface of a material dramatically affect the weak (van- the catalyst (and the point charge-water distance through der-Waals) type of interactions with adsorbates.40 strain) affect the BE of water. This behavior is explained The binding trend of H follows the common trend and by investigating the metal growth mechanisms in water the descriptor based model relied on the dC and the charge solvent,39 where it is shown that the orientation and the transfer. All metals interact with H by donating d-electrons binding of water molecules on small clusters is affected and accepting s-electrons. In general, the clusters with a by the cluster’s charge state. Point charges developed on Cu top layer have the greatest gain in electron density
(a) (b)
IP: 192.168.39.211 On: Sat, 02 Oct 2021 05:15:29 Copyright: American Scientific Publishers Delivered by Ingenta
(c) (d)
Fig. 5. Parity plots for each of the functional forms for the descriptor-based models: (a) 2-variable linear, (b) 2-variable quadratic, (c) 3-variable linear, and (d) 3-variable bilinear.
J. Comput. Theor. Nanosci. 11, 511–520, 2014 517 Adsorption Behavior of Noble Metal Clusters and Their Alloys Herrmann et al.
followed by those with a Ag top layer, and lastly those atom of each bare bimetallic cluster with that of the bare with a Au top layer. This helps to explain the BE trend of monometallic cluster with identical top layer composition. H to the top layer metals. It was thus determined that the Cu atom in the center of the Both C and the CO species exhibit BE trends different top layer of the bimetallic clusters (CuAu and CuAg) has than the common trend pertaining to O binding. One of a lower s-electron density compared to the CuCu cluster. the reasons for this difference could be the high HOMO Bimetallic clusters with Ag top layer composition exhibit level of C (see Fig. 4) and the lower electronegativity of a mixed behavior when compared with the AgAg cluster. C compared to O adsorbed species (O, OH). These could More specifically, the central Ag atom in the top layer of explain why the strain effect is a more important descrip- the AgCu cluster gains density on its s orbital, whereas tor than the DE in modeling the binding of C and CO the central Ag atom of the AgAu cluster remains the same (Table VI). A comparison of the BE trend of atomic C as that in the AgAg cluster. Lastly, the central Au atom of adsorbed to the hollow site and the common trend, reveals, the bimetallic clusters (AuCu and AuAg) gains s-electron RESEARCH ARTICLE that in contrast to the common trend, the clusters with a density when compared to that of the AuAu cluster. top composition of Ag provide weaker binding than those The orbital density redistribution just noted has a pro- with a top composition of Au in the C-adsorption: found effect on the BE trends of O, OH, and possibly other nucleophilic adsorbates. As mentioned before, the CuAu > CuAg > CuCu > AuAu > AuAg > AuCu binding strength of O and OH adsorbates decreases with respect to the top layer composition, according to the pri- > AgAu > AgAg > AgCu mary trend (Cu > Ag > Au). This effect was explained by s This difference indicates that in clusters with the the metal’s -orbital gain through bonds with the adsor- same top layer composition the effect of the subsurface bates. We can extend this rational to explain the secondary layer is overshadowed by the properties of the surface trends as well. For example, since the top central atoms s layer. of the (bare) CuAg and CuAu clusters show less -orbital In the case of atomic C binding, the Au atoms show density than the CuCu cluster, they exhibit a higher affin- the most significant donation of d-electron density fol- ity to receiving electron density from the adsorbates. This lowed by Cu. Interestingly, the central metal atom shows is the reason why the CuAg and CuAu clusters bind O and a loss in s-electron density for the clusters with a top OH stronger than the monometallic CuCu cluster. Similar layer composition of Cu and Ag,IP: but 192.168.39.211 the clusters with On: top Sat,trends 02 Oct can 2021 be extracted 05:15:29 between the O and OH BE behav- Copyright: American Scientific Publishers X = layers consisting of Au show a gain in s-electron den- ior on AuX and AgX clusters ( Cu, Ag, Au) and the Delivered bys Ingenta-orbital change on the central atom of the cluster. In addi- sity for the central metal atom. The increased donation of tion, the BE of CO is affected by the s-orbital density the d-electron density and the increased gain of s-electron change on the surface of the clusters. The presence of this densities explain why the clusters with a top layer com- s-orbital density on the surface of the clusters hinders the posed of Au bind C stronger than those with a top layer forward electron donation.41 (from 5 orbital of CO to composed of Ag. the d s orbitals of the metal). For this reason the CuCu Note that CO, which also binds through C, exhibits z2 cluster binds weaker the CO than the CuAg and CuAu. weak binding (see Fig. 2) which makes it difficult to Similar behavior is followed in H adsorption with respect establish a binding trend. This effect can be attributed to to the s-orbital density on the surface (central atom) of the the minimal redistribution of electron density between the clusters. It is important to note that the s-orbital change metal atoms and the C atom. However, by tracking this on the surface of the clusters with the same M , usually small electron density change we found that metal clus- T correlates with the secondary descriptors (electronegativ- ters with an upper layer consisting of Cu lose d-electron ity, strain, or charge ratio), highlighting their importance density and gain s when interacting with CO, whereas, in developing adsorption models. clusters with Ag upper layer lose s-electron density and clusters with Au upper layer appear unaffected. The lat- ter is due to the fact that CO practically does not bind to 4. CONCLUSIONS clusters consisting of Au as top layer. In this study, we considered descriptors that quantify fun- Synopsizing this section, the adsorption process involves damental properties of the d10 metals and their alloys, s d s p the metal’s outer , and the adsorbate’s , atomic in order to describe the binding of O, OH, H2O, CO, orbitals. Furthermore, upon O-bonding to Cu and Ag C and H to 10-atom clusters. In agreement with litera- surfaces, and upon H-bonding on every metal surface, the ture we find that the BEs of most adsorbates correlate metal gains s-electrons. In the case of C-bonding however, with the dC of the metal. However, we demonstrated that there is a loss in metal s-electrons for Cu and Ag surfaces additional properties (secondary descriptors) must also be and a gain for the Au surface. considered for an accurate model. These additional prop- To further our understanding of the trends found, we erties depend on the strain effects and electronic charac- compared the atomic orbital density of the central metal teristics of the atom through which the adsorbate binds
518 J. Comput. Theor. Nanosci. 11, 511–520, 2014 Herrmann et al. Adsorption Behavior of Noble Metal Clusters and Their Alloys
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Received: 6 December 2012. Accepted: 23 December 2012. RESEARCH ARTICLE
IP: 192.168.39.211 On: Sat, 02 Oct 2021 05:15:29 Copyright: American Scientific Publishers Delivered by Ingenta
520 J. Comput. Theor. Nanosci. 11, 511–520, 2014