Partial Ionic Character beyond the Pauling Paradigm - American

Subscriber access provided by BALL STATE UNIV

Article

Partial Ionic Character Beyond the Pauling Paradigm: Metal Nanoparticles Kaining Duanmu, and Donald G. Truhlar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511055k • Publication Date (Web): 12 Nov 2014 Downloaded from http://pubs.acs.org on November 20, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Nov. 8, 2014

1

Partial Ionic Character Beyond the Pauling Paradigm: Metal Nanoparticles Kaining Duanmu and Donald G. Truhlar* Department of Chemistry, Chemical Theory Center, Inorganometallic Catalyst Design Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota, 55455-0431, United States *e-mail: [email protected]; telephone: 1-612-624-7555 ABSTRACT A canonical perspective on the chemical bond is the Pauling paradigm: a bond in a molecule containing only identical atoms has no ionic character. However we show that homonuclear silver clusters have very uneven charge distributions, for example, the C2v structure of Ag4 has a larger dipole moment than formaldehyde or acetone; and we show how to predict the charge distribution from coordination numbers and Hirshfeld charges. The new charge model is validated against Kohn-Sham calculations of dipole moments with four approximations for the exchange-correlation functional. We report Kohn-Sham studies of the binding energies of CO on silver monomer and silver clusters containing 2 to 18 atoms. We also find an accurate charge model is essential for understanding the site dependence of binding. In particular we find that atoms with more positive charges tend to have higher binding energies, which can be used for guidance in catalyst modeling and design. Thus the nonuniform charge distribution of silver clusters predisposes the site preference of binding of carbon monoxide, and we conclude that nonuniform charge distributions are an important property for understanding binding of metal nanoparticles in general. KEYWORDS: atomic charge · catalyst design· CO binding energy · coordination number · metal cluster

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 17

Nov. 8, 2014

2

Introduction The partial ionic nature of chemical bonds has long been understood in terms proposed by Pauling.1 He supposed that a bond between two identical atoms could be considered as a normal covalent bond; whereas if one atom is more electronegative than another, there will be some ionic character within the bond. This paradigm has become a dogmatic way of thinking of chemical bonds, so it might be surprising to see our calculations (details below) showing that the equilibrium C2v structure of Ag ! has a dipole moment of 3.4 D, larger than those2 of some polar organic molecules, such as the similarly shaped formaldehyde with a dipole moment of 2.3 D or thioformaldehyde (1.7 D). This unusual large dipole moment indicates polar charge distributions in homonuclear metal clusters that take us beyond the Pauling paradigm. In order to find an accurate description of the charge distribution on metal clusters, we developed a simple charge model for silver clusters (as a prototype) in which charge distributions are predicted simply from geometry, and we note that an accurate charge model is very useful for understanding CO binding energy. There is a large experimental and theoretical literature3,4,5,6,7,8,9,10,11,12,13 on gold (especially) and silver nanoparticles being used as catalysts in the carbon monoxide oxidation reaction. The first step of the reaction is the adsorption of CO on the catalyst, and an important question about this process is which adsorption site on the catalyst is most preferred and why. Most theoretical studies of nanoparticle metal catalysts have focused on important factors such as the support14,15 and the size,14,16 although there has been some discussion of the charge effect as well. For example, Solov’yov et al.17 and Donoso et al.18 studied the charge distributions in cationic and neutral alkali metal clusters. Zhou et al.19 calculated the binding energies of CO with neutral and charged silver clusters and found that positively charged clusters tend to have higher binding energies. Neumaier et al.20 studied the binding energies of CO on gold and gold-silver cations and showed that adsorption sites with lower electron density tend to have higher binding energies. The Zhou et al. study shows that the overall charge state of a silver cluster significantly affects the CO binding energy, and the Neumaier et al. study shows that the local electron density, which is conceptually very close to partial atomic charge, largely affects the CO binding energy as a function of adsorption site. Our focus here is on partial atomic charges even in neutral metal clusters, and by applying our new charge model, we further show that partial atomic charge is one of the major determinants of preferential binding sites of CO on the metal particles. Charge models may be sorted into four classes.21 Class I charges are derived without reference to quantum mechanics, e.g., by assigning charges based on geometries and experimental multipole moments. Class II charges are based on atomic population analysis of wave functions or reference wave functions obtained from quantum mechanical calculations, yielding procedures such as Hirshfeld population analysis,22 Mulliken population analysis (MPA),23 and natural bond orbital population analysis (NPA).24,25 The Hirshfeld method, based on a so called shareholder analogy, has the advantage of being formally independent of the locations of the basis functions,


Page 3 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

3

provided that the charge density is well converged, but it systematically underestimates charges.26 Class III charges, such as CHELPG27,28 and Merz-Kollman-Singh (MKS)29,30 charges, are those fitted to reproduce a calculated physical observable, usually the electrostatic potential (ESP), from an approximate electronic structure calculation. Class IV charges are parametrized mappings of class II charges to new charges that reproduce experimental or high-level quantum mechanical observables, such as dipole moments. The most broadly applicable class IV charges are CM5 charges.31 The CM5 model makes up on average for the systematic underestimate of the polarity of heteronuclear bonds by the Hirshfeld method, but for homonuclear clusters, CM5 charges are the same as Hirshfeld charges. For silver clusters, there is not enough experimental data to assign class I charges, and one is limited to the quantum mechanical approaches of classes II, III, and IV, but all previous models of these types have deficiencies for silver clusters. For example, traditional class II charges, such as MPA charges, are unstable for extended basis sets. Hirshfeld charges, although reasonably independent of basis set, tend to underestimate multipole moments, and class III charges suffer from ill conditioning for buried atoms in molecules28,32 or extended structures, such as systems with periodic boundary conditions or large clusters. For silver clusters, we found that although CHELPG and MKS charges reproduce the dipole moments well, they often give very different partial atomic charges even though the only difference between the two methods is that they use different points in space for ESP fitting; furthermore, we found that the buried atoms in large clusters are usually assigned unphysically large charges by these two methods. Therefore, we need a new accurate charge model to describe the uneven charge distribution on metal clusters. In the present article dipole moments are calculated by Kohn-Sham density functional theory. Kohn-Sham density functional theory has been well validated against experimental results for dipole moments and is known to give reasonably accurate dipole moments for molecules both without and with metal atoms.33,34,35,36,37,38 We further validated Kohn-Sham density functional theory for small metal clusters by carrying out high-level wave function calculations, in particular CCSD(T)/aug-cc-pVQZ-PP39 calculations. The resulting dipole moments of the C2v structures of Ag3 and Ag4 are 0.86 D and 4.20 D, while the Kohn-Sham density functional dipole moments of these two clusters, averaged over four exchange-correlation functionals, are 0.83 D (3% lower) and 3.44 D (18% lower) respectively. With the unknown exact exchange-correlation functional, Kohn-Sham density functional would give the exact charge distribution and dipole moment since they are one-electron properties, and the evidence is that the results are reasonably accurate with available approximate exchange-correlation functionals.

Theoretical and Computational Methods The CCSD(T) method with aug-cc-pVQZ-PP basis set is used for validating dipole moments of C2v structure of Ag3 and C2v structure of Ag4. The optimizations of silver clusters for parametrization, and all



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 17

Nov. 8, 2014

4

binding energy calculations were performed using Kohn-Sham density functional theory with the N1240 exchange-correlation functional, which is a nonseparable gradient approximation. The basis set is 6311+G(2df,2p)41 for carbon and oxygen atoms, jun-cc-pVTZ-PP42,43 for silver in molecules containing up to seven silver atoms, and cc-pVDZ-PPError! Bookmark not defined. for silver in molecules containing more than seven silver atoms. All Kohn-Sham calculations are carried out with a locally modified version (MNGFM–v6.4) of Gaussian 09.44,45 The CCSD(T) calculations were carried out with MOLPRO software package.46,47

Results and Discussion Charge Model 5 (CM5) maps Class II charges from Hirshfeld population analysis onto class IV charges using equations (1)-(3): 𝑞!!"! = 𝑞!!"# +

𝑇!! ! 𝐵!! !

(1)

! ! !!

𝐵!! ! = exp[−𝛼(𝑟!! ! − 𝑅!! − 𝑅!!! )] 𝑇!! ! = 𝐷!! !!!

(2) (3)

where 𝑞!!"! , 𝑞!!"# , 𝑍! , and 𝑅!! are respectively the CM5 and Hirshfeld charge, the atomic number, and the covalent radius48 of atom k, 𝑟!! ! is the distance between atoms k and k´, and 𝛼, 𝑇!! ! , and 𝐷!! !!! are the model’s parameters. Note that 𝐵!! ! can be interpreted as the Pauling

bond order of the k, k´ atom pair.49,50 These equations show that CM5 attempts to correct systematic errors in Hirshfeld population analysis by transferring charges between atoms with finite bond orders and different atomic numbers, but this leads to no correction for homonuclear clusters. For Figure 1, we performed Kohn-Sham density functional calculations for an equilibrium C5v structure of Ag6 and a non-equilibrium structure of Ag8 created by adding one atom to an equilibrium D5h structure of Ag7. The Ag6 structure has one five-coordinated atom and five

µref = 0.47 D µHPA = -0.32 D

µref = 1.15 D µHPA = 1.72 D


Page 5 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

5

Figure 1. Comparison of dipole moments. The dipole moment calculated from the electron density with the N12 exchange-correlation functional is µref, and the dipole moment calculated by Hirshfeld population analysis is µHPA. The arrows show the direction of the accurate dipole moment; in the case on the left the central Ag atom is above the plane of the page, and the arrow (whose tipped side is the negative direction) points toward the viewer. three-coordinated atoms; because of the symmetry there is a unique partial atomic charge assignment that reproduces the dipole moment. The charge on the central atom must be -0.081, whereas the Hirshfeld charge is 0.055, which yields the wrong direction of the dipole. The Ag7 structure has zero dipole moment, but when an extra atom is added, the Kohn-Sham dipole moment increases to 1.15 D, whereas the Hirshfeld dipole moment is 1.72 D, with nearly a 50% error. The negative charge is on the side of the extra atom, and the positive charge is on the Ag7 side. These examples show that a negative correction on multi-coordinated atoms may give more accurate dipole moments. Here we propose a way to correct this systematic error by making a pairwise correction dependent on the coordination number (N); adding such a pairwise correction to CM5 yields a model we call CM5M (CM5 for metals). The required new equations are 𝑇!! ! =

𝐷!! !!! (𝑍! ≠ 𝑍! ! )

𝜆!! [tanh (𝜈!! 𝑁!! ) − tanh(𝜈!! 𝑁!!! )] (𝑍! = 𝑍! ! )

𝑁!! = ! ! !!

𝑒𝑥𝑝 −𝛼 𝑟!! ! − 𝑅!! − 𝑅!!!

(𝑍! = 𝑍! ! )

(4) (5)

where the quantities 𝜆!! and 𝜈!! are new parameters to be fit. Notice that 𝑇!! ! is nearly proportional to the difference of coordination numbers for a small difference of coordination numbers, but then it saturates and approaches a limit; this allows us to treat large coordination numbers (some of the clusters in this study have N as large as 12). We take α = 2.474 Å-1 as in CM5. We optimized the two parameters against the dipole moments of 39 silver clusters. Seventeen of these are the structures in references 51 and 52 that have nonzero dipole moments; we optimized the geometries of these structures with Kohn-Sham density functional calculations. The other 22 structures are nonequilibrium structures created by adding a chain of one or two silver atoms to the optimized ones because the added atoms have smaller coordination numbers than the atoms in the big clusters, and this increases the diversity of our training set. The largest optimized structures are Ag14-18 clusters, which have a width range of 1.0-1.1 nm; the largest nonequilibrium structures are Ag14-18 with a chain of two atoms sticking to them, which have a width range of 1.4-1.6 nm, where the width is defined as the largest Ag-to-Ag distance plus twice the van der Waals radius (with the latter from Ref. 48). The parameters λ and 𝜈 were optimized for these structures (labeled J = 1 to 39) to minimize the error function:



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 17

Nov. 8, 2014

!

!"

6 !"# !

!"!! 𝜇!" − 𝜇!"

𝜒=

(6)

!!! !!!

where 𝜇 !"# is the dipole moment calculated from the Kohn-Sham density, and 𝜇!"!! is the dipole moment calculated from the CM5M partial atomic charges. The first sum in equation (6) indicates that we averaged the results calculated by Kohn-Sham density functional calculations with four exchange-correlation functionals, namely, N12,40 M06-L,53 M06,54 and TPSS.55 The final parameters are 𝜆!" = –0.080, and 𝜈!" = 0.36. In Table 1 we can see that minimum-basis-set Mulliken population analysis (MBS)56,57 and natural bond orbital population analysis (NPA), which are both class II charge models, do not reproduce the accurate dipole moments. Although the class III models (CHELPG and MKS) have small errors in dipole moments, they are still not generally applicable models because of the deficiencies we discussed above (problems that become more serious as the size of the particle increases). The class IV model that was our starting point, namely CM5, has errors intermediate to the other two types of models. The new model CM5M has physical charges, the quality of dipole moments is as good as class III models, and the method is straightforwardly applicable even to buried atoms, extended systems, and calculations with periodic boundary conditions. Table 1. Mean unsigned errors (MUE) in magnitude of dipole moments (Debye). The percentage errors are also calculated using the averaged dipole moment over all 39 structures 𝝁=1.29 D. CM5M CM5 CHELPG MKS MBS NPA MUE 0.17 (13%) 0.35 (27%) 0.25 (20%) 0.12 (9%) 0.54 (42%) 1.30 (100%) Next we consider the interaction of CO with silver clusters. The binding energy (ΔH0) of CO on a silver cluster Agn is: ΔH0 = E(Agn)+ E(CO) – E(AgnCO)

(7)

where the energies (E) include electronic energy, nuclear repulsion, and zero point vibrational energy. The partial atomic charges and binding energies of all structures are tabulated in supporting information. We first studied neutral, cationic, and anionic silver monomers and dimers. Since bond lengths of silver dimers with different charge states are very close, the charge state can be considered as essentially the only factor determining different CO binding energies. Each of these clusters has one unique binding site, so the atomic charges can be determined by symmetry from the total charge, e.g. the atomic charge on each atom of Ag ! ! is 0.5. Table 2 shows that the positively charged silver monomer and dimer have the highest binding energies, while the negatively


Page 7 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

7

charged silver monomer and dimer have the lowest binding energies. The results in Table 2 suggest that positively charged sites tend to have higher binding energies. Table 2. Binding energies of CO on silver monomer and dimer with different charge states. Complex AgCO! AgCO AgCO! Ag ! CO! Ag ! CO Ag ! CO!

Binding energy (kcal/mol) 31.0 6.8 4.5 21.9 12.6 11.3

Next we studied nine neutral Agn clusters with n = 4–8 and 10, where each of the clusters has two or three different binding sites. The cluster size and symmetry, the CM5M partial atomic charge on the binding site, and the binding energy are listed in Table 3. We postulate that the more positively charged atoms tend to have higher binding energies, and we find that six out of nine cases strictly follow the postulate. While the C2v structure of Ag5 and the C3v structure of Ag7 do not strictly follow the postulate, each of the two clusters has three binding sites, and the most negative atoms do have the smallest binding energies, although the other two sites have the reversed order. Only the C5v structure of Ag6 has the opposite trend to our postulate for the relationship between charge and binding energy. Based on the results in Table 3, we can see that there is a trend, although not a strict rule, that in a silver cluster, atoms with more positive partial atomic charges are more likely to be sites of higher binding energy. Table 3. CM5M charges and corresponding binding energies for silver clusters with two or three different binding sites. Cluster

Symmetry

Ag4

D2h

Ag5

C2v

Ag6

C3v

Ag6

C5v

Ag6

C2v

CM5M Charge on the binding atom 0.070 -0.070 0.014 0.001 -0.030 0.025 -0.025 0.003 -0.015 0.028 0.027 -0.036

Binding energy (kcal/mol) 20.6 6.0 10.0 11.5 8.6 8.6 5.2 9.5 16.5 12.1 9.8 5.7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 17

Nov. 8, 2014

8

Ag7

D5h

Ag7

C3v

Ag8

D2d

Ag10

D2d

0.011 -0.028 0.020 -0.009 -0.031 0.030 -0.030 0.032 -0.006 -0.053

10.1 9.1 9.8 11.5 8.7 8.8 7.1 11.1 9.9 4.8

Finally, we studied large neutral silver clusters: Ag9, Ag11, Ag17, and Ag18, in which each cluster has more than three different binding sites. Figure 2 shows the atomic charges and binding energies on different binding sites of Ag17 and Ag18. For each cluster, the number of unique binding sites is less than the number of atoms because of symmetry. Structures of these clusters include the icosahedral Ag13 structure as a substructure which is slightly distorted by the additional atoms. The Ag13 structure has one center atom and twelve atoms surrounding the center one. In Ag17, atoms 2, 3, 4, and 17 can be viewed as extra atoms added to Ag13; in Ag18, atoms 2, 3, 4, 17, and 18 can be viewed as extra atoms added to Ag13. Topographically, if the surface atoms of Ag13 are apex atoms, these extra atoms flatten the nearby surfaces, thus making nearby atoms less “sharp” and more like edge atoms or face atoms. We noticed that positive charges are more likely to be on apex atoms, while negative charges are more likely to be on edge and face atoms. For example, in Ag17, the most two positive charges are on atom 9 and 13, which are apex atoms; the two most negative charges are on atom 6 and 7, which are on much flatter surfaces. For Ag18, the most two positive charges are on atom 9 and 14; the most two negative charges are on atom 1 and 12, which still follow the trend. Our finding parallels Neumaier’s et al.20 calculations of electron densities and CO binding energies on Au! !" . In their ! studies, the structure of Au!" is a tetrahedron of 20 atoms with one extra atom binding to it, so there are 5 apex atoms (four vertexes of the tetrahedron and the extra atom), 12 edge atoms and 4 face atoms. They found the 5 apex atoms have the lowest electron densities, while the 4 face atoms have the highest electron densities. Coordination number (N) is also related to the topography. Edge and face atoms are in general bonded to more atoms than apex atoms, and thus they have larger coordination numbers. For example, in Ag17, atom 6 has N = 6.0, whereas atom 9 has N = 4.8. In Ag18, atom 1 has N = 6.1, while atom 9 has N = 4.9 (N is calculated using eq 5). This correlation is consistent with our new charge model, which has a negative correction on multi-coordinated atoms.


Page 9 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

9

Figure 2. CM5M partial atomic charges and binding energies for C2 structure of Ag17 (left) and Cs structure of Ag18 (right). Atomic charges are in red color, binding energies (kcal/mol) are in blue color.

We diagrammed all binding energies and partial atomic charges on corresponding atoms in Figure 3, which shows a nearly linear dependence of binding energies on charges, and the trends we found in the smaller clusters are also followed in large silver clusters. Zhou et al.19 performed DFT studies of CO binding energies of neutral and charged Agn with n = 1–7. They found that clusters with positive charge states have the highest binding energies, while clusters with negative charge states have the lowest binding energies. Their work show that the overall charge state of a silver cluster significantly affects the CO binding energies, and our work further shows that the partial atomic charge is a major determining factor for binding site preference. We also studied the charges on the adsorbed CO molecules and found that for small silver clusters, there is a general trend that the more charge transferred from CO to silver clusters, the higher the binding energy is. However for large silver clusters with more than three binding sites (Ag9, Ag11, Ag17, and Ag18), there is no linear correlation between charges on adsorbed CO and binding energies.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 17

Nov. 8, 2014

10

ΔH0 (kcal/mol) 20.0 15.0

R² = 0.84 R² = 0.78

R² = 0.79

Ag9 Ag11 Ag17 Ag18

10.0 R² = 0.74

5.0

-0.06

-0.04

-0.02

0.0 0.00 Charge

0.02

0.04

0.06

Figure 3. CM5M partial atomic charges and binding energies for four large size silver clusters. R2 denotes the square of the correlation coefficient.

Figure 3 shows that a change in partial atomic charge equal to a small fraction of the unit charge (i.e., a small fraction of the charge on a proton) yields a significant change in binding energy. For example, in Ag17, the charges of the most positive atom and the most negative atom differ by only 0.079, while the two corresponding binding energies differ by 12.4 kcal/mol; in Ag18, a difference of 0.073 in charge causes a difference of 13.4 kcal/mol in binding energy. Therefore it is necessary that a charge model, to be maximally useful, should be accurate to within a few hundredths of a charge unit. In addition to providing an understanding of preferred binding sites, the new charge model is expected to be useful for catalyst design; for example, one could use a support to make coinage metals more positive and increase their capabilities to adsorb CO. All other things being equal, coarse surfaces of particles not only increase the ratio of surface to volume – a well known effect, but also they create more active binding sites for CO because bumpy surfaces have more peaky atoms with more positive atomic charges – which is a previously unappreciated aspect. Conclusions We found that homonuclear silver clusters have very uneven charge distributions. We proposed a Class IV charge model, CM5M that yields accurate charges by considering both Hirshfeld population analysis and the coordination numbers of the atoms in the cluster. CM5M is validated by showing that it yields accurate dipole moments for silver clusters. Applying CM5M to the study of interaction of CO and silver clusters, we find that silver atoms with more positive charges are more likely to have higher binding energies, and an accurate charge model is


Page 11 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

11

essential to correctly understand the connections between charges and CO binding energies. Charges are important for binding and hence for catalysis, and coordination number is one of the factors that helps determines charges. It would be interesting to in future work to study the effect on the charge distributions of placing the metal clusters on an oxide substrate as is employed in many catalytic setups. We believe that the role of the uneven charge distribution in homonuclear metal particles has not been widely enough appreciated, and we hope the present findings will change that situation. The results have widespread implications for understanding binding by subnano and nano metal particles, not just for silver but for all metal clusters.

Acknowledgments This research was sponsored in part by the Inorganometallic Catalyst Design Center and supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences under Award DE-SC0012702. Supporting Information Available: Density-based and charge reproduced dipole moments, coordinates and structures of the silver clusters, CO binding energies on silver monomer and dimer and larger silver clusters. This material is available free of charge via the Internet at http://pubs.acs.org.

References

1 Pauling, L. The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms. J. Am. Chem. Soc. 1932, 54, 3570–3582. 2 Lide, D. R. Dipole Moments. CRC Handbook of Chemistry and Physics 2011-2012, 92nd edition; Haynes, M. M., Eds; CRC Press: Boca Raton, FL, 2011; pp. 9-51–9-59. 3 Burghaus, U.; Conrad, H. Evidence for the Oxidation of CO by Molecular Oxygen Adsorbed on Ag (110). Surf. Sci. 1996, 364, 109–121. 4 Wu, X.; Senapati, L.; Nayak, S. K.; Selloni, A.; Hajaligol, M. A Density Functional Study of Carbon Monoxide Adsorption on Small Cationic, Neutral, and Anionic Gold Clusters. J. Chem. Phys. 2002, 117, 4010-4015. 5 Haruta, M.; Daté, M. Advances in the Catalysis of Au Nanoparticles. Appl. Catal. A-Gen. 2001, 222, 427–437.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 17

Nov. 8, 2014

12

6 Kimble, M. L.; Castleman, A.W. Jr.; Mitrić, R.; Bürgel, C.; Bonačić-Kouteckŷ, V. Reactivity of Atomic Gold Anions Toward Oxygen and the Oxidation of CO: Experiment and Theory. J. Am. Chem. Soc. 2004, 126, 2526–2535. 7 Haruta, M. Nanoparticulate Gold Catalysts for Low-Temperature CO Oxidation. J. New Mat. Electr. Sys. 2004, 7, 163–172. 8 Qu, Z.; Cheng, M.; Huang, W.; Bao, X. Formation of Subsurface Oxygen Species and Its High Activity Toward CO Oxidation Over Silver Catalysts. J. Catal. 2005, 229, 446–458. 9 Chen, L.; Ma, D.; Pietruszka, B.; Bao, X. Carbon-supported Silver Catalysts for CO Selective Oxidation in Excess Hydrogen. J. Nat. Gas Chem. 2006, 15, 181–190. 10 Xu, C.; Su, J.; Xu, X.; Liu, P.; Zhao, H.; Tian, F.; Ding, Y. Low Temperature CO Oxidation Over Unsupported Nanoporous Gold. J. Am. Chem. Soc. 2007, 129, 42–43. 11 Kung, M. C.; Davis, R. J.; Kung, H. H. Understanding Au-Catalyzed Low-Temperature CO Oxidation. J. Phys. Chem. C 2007, 111, 11767–11775. 12 Johnson, G. E.; Mitrić, R.; Bonačić-Kouteckŷ, V.; Castleman, A.W. Jr. Clusters as Model Systems for Investigating Nanoscale Oxidation Catalysis. Chem. Phys. Lett. 2009, 475, 1–9. 13 Christopher, P.; Xin, H.; Linic, S. Visible-Light-Enhanced Catalytic Oxidation Reactions on Plasmonic Silver Nanostructures. Nature Chem. 2011, 3, 467–472. 14 Haruta, M. Size- and Support-Dependency in the Catalysis by Gold. Catal. Today 1997, 36, 153–166. 15 Wang, Y.; Yoon, Y.; Glezakou, V.; Li, J.; Rousseau, R. The Role of Reducible Oxide−Metal Cluster Charge Transfer in Catalytic Processes: New Insights on the Catalytic Mechanism of CO Oxidation on Au/TiO2 from ab initio Molecular Dynamics. J. Am. Chem. Soc. 2013, 135, 10673−10683. 16 Lee, T. H.; Ervin, K. M. Reactions of Copper Group Cluster Anions with Oxygen and Carbon Monoxide. J. Phys. Chem. 1994, 98, 10023–10031. 17 Solov’yov, I. A.; Solov’yov, A. V.; Greiner, W. Structure and Properties of Small Sodium Clusters. Phys. Rev. A 2002, 65, 053203-1–053203-18. 18 Donoso, R.; Cárdenas, C.; Fuentealba, P. Ab Initio Molecular Dynamics Study of Small Alkali Metal Clusters. J. Phys. Chem. A 2014, 118, 1077–1083.


Page 13 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

13

19 Zhou, J.; Li, Z.; Wang, W.; Fan, K. Density Functional Study of The Interaction of Carbon Monoxide with Small Neutral and Charged Silver Clusters. J. Phys. Chem. A 2006, 110, 7167–7172. 20 Neumaier, M.; Weigend, F.; Hampe, O.; Kappes, M. M. Binding Energy and Preferred Adsorption Sites of CO on Gold and Silver–Gold Cluster Cations: Adsorption Kinetics and Quantum Chemical Calculations. Faraday Discuss. 2008, 138, 393–406. 21 Storer, J. W.; Giesen, D. J.; Cramer, C. J.; Truhlar, D. G. Class IV Charge Models: A New Semiempirical Approach in Quantum Chemistry. J. Comput. Aid. Mol. Des. 1995, 9, 87–110. 22 Hirshfeld, F. L. Bonded-Atom Fragments for Describing Molecular Charge Densities. Theor. Chim. Acta 1977, 44, 129–138. 23 Mulliken, R. S. Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I. J. Chem. Phys. 1955, 23, 1833–1840. 24 Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211–7218. 25 Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735–746. 26 Davidson, E. R.; Chakravorty, S. A Test of the Hirshfeld Definition of Atomic Charges and Moments. Theor. Chim. Acta 1992, 83, 319-330. 27 Chirlian, L. E.; Francl, M. M. Atomic Charges Derived from Electrostatic Potentials: A Detailed Study. J. Comput. Chem. 1987, 8, 894–905. 28 Breneman, C. M.; Wiberg, K. B. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis. J. Comput. Chem. 1990, 11, 361–373. 29 Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comput. Chem. 1984, 5, 129–145. 30 Besler, B. H.; Merz, K. M. Jr.; Kollman, P. A. Atomic Charges Derived from Semiempirical Methods. J. Comput. Chem. 1990, 11, 431–439. 31 Marenich, A. V.; Jerome, S. V.; Cramer, C. J.; Truhalr, D. G. Charge Model 5: An Extension of Hirshfeld Population Analysis for the Accurate Description of Molecular Interactions in Gaseous and Condensed Phases. J. Chem. Theory Comput. 2012, 8, 527–541.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 17

Nov. 8, 2014

14

32 Francl, M. M.; Carey, C.; Chirlian, L. E.; Gange, D. M. Charges Fit to Electrostatic Potentials. II. Can Atomic Charges Be Unambiguously Fit to Electrostatic Potentials? J. Comput. Chem. 1996, 17, 367–383. 33 Wang, J.; Johnson, B. G.; Boyd, R. J. Electron Densities of Several Small Molecules as Calculated from Density Functional Theory. J. Phys. Chem. 1996, 100, 6317-6324. 34 Scheiner, A. C.; Baker, J.; Andzelm, J. W. Molecular Energies and Properties from Density Functional Theory: Exploring Basis Set Dependence of Kohn-Sham Equation Using Several Density Functionals. J. Comp. Chem. 1997, 18, 775–795. 35 Prezhdo, O. V. Assessment of Theoretical Approaches to the Evaluation of Dipole Moments of Chromophores for Nonlinear Optics. Adv. Mater. 2002, 14, 597–600. 36 Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. Parameterization of Charge Model 3 for AM1, PM3, BLYP, and B3LYP. J. Comp. Chem. 2003, 24, 1291–1304. 37 Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. 38 Furche, F.; Perdew, J. P. The Performance of Semilocal and Hybrid Density Functionals in 3d Transition-Metal Chemistry. J. Chem. Phys. 2006, 124, 044103-1–044103-27. 39 Peterson, K. A.; Puzzarini, C. Systematically Convergent Basis Sets for Transition Metals. II. Pseudopotential-Based Correlation Consistent Basis Sets for the Group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) Elements. Theor. Chem. Acc. 2005, 114, 283–296. 40 Peverati, R.; Truhlar, D. G. Exchange-Correlation Functional with Good Accuracy for Both Structural and Energetic Properties While Depending Only on the Density and Its Gradient. J. Chem. Theory Comput. 2012, 8, 2310–2319.

41 Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-Consistent Molecular Orbital Methods. 25. Supplementary Functions for Gaussian Basis Sets. J. Chem. Phys. 1984, 80, 3265–3269. 42 Papajak, E.; Leverentz, H. R., Zheng, J.; Truhlar, D. G. Efficient Diffuse Basis Sets: ccpVxZ+ and maug-cc-pVxZ. J. Chem. Theory Comput. 2009, 5, 1197–1202. 43 Papajak, E.; Truhlar, D. G. Efficient Diffuse Basis Sets for Density Functional Theory. J. Chem. Theory Comput. 2010, 6, 597–601. 44 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision C.01, Gaussian, Inc., Wallingford CT, 2009.


Page 15 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

15

45 Zhao, Y.; Peverati, R.; Yang, K.; Truhlar, D. G. Minnesota Density Functionals Module 6.4, (MN-GFM 6.4); University of Minnesota: Minneapolis, MN, 2014. http://comp.chem.umn.edu/mn-gfm (accessed Nov. 3, 2014). 46 Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby F. R.; Schütz, M. Molpro: A GeneralPurpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242-253.

47 Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G. et al. MOLPRO, version 2012.1, A Package of ab initio Programs. 2012. http:// http://www.molpro.net (accessed Nov. 12, 2014) . 48 Mantina, M.; Valero, R.; Cramer, C. J.; Truhlar, D. G. Atomic Radii of the Elements. In CRC Handbook of Chemistry and Physics, 2014-2015; 95th edition; Haynes, W. M., Ed.; CRC Press: Boca Raton, FL, 2014; pp 9-49–9-50. 49 Pauling, L. Atomic Radii and Interatomic Distances in Metals. J. Am. Chem. Soc. 1947, 69, 542–553. 50 Johnston, H. S.; Parr, C. Activation Energies from Bond Energies. I. Hydrogen Transfer Reactions. J. Am. Chem. Soc. 1963, 85, 2544–2551. 51 Fournier, R. Theoretical Study of the Structure of Silver Clusters. J. Chem. Phys. 2001, 115, 2165–2177. 52 Yang, M.; Jackson, K. A.; Jellinek, J. First-Principles Study of Intermediate Size Silver Clusters: Shape Evolution and Its Impact on Cluster Properties. J. Chem. Phys. 2006, 125, 144308-1– 144308-8. 53 Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101-1–194101-18. 54 Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215–241. 55 Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401-1–146401-4. 56 Montgomery, J. A. Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822–2827.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 17

Nov. 8, 2014

16

57 Montgomery, J. A. Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532–6542.


Page 17 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nov. 8, 2014

17

Table of Contents Graphic:


Partial Ionic Character beyond the Pauling Paradigm - American

Recommend Documents