Chemisorption-Induced Spin Symmetry Breaking in Gold Clusters and

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Chemisorption-Induced Spin Symmetry Breaking in Gold Clusters and the Onset of Paramagnetism in Capped Gold Nanoparticles Carlos Gonzalez,*,‡ Yamil Simo´ n-Manso,†,‡ Manuel Marquez,†,‡ and Vladimiro Mujica*,†,‡,§ NIST Center for Theoretical and Computational Nanosciences, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, Interdisciplinary Network of Emerging Science and Technologies (INEST Group), PMUSA, Richmond, Virginia, and Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208-3113 ReceiVed: August 15, 2005; In Final Form: October 17, 2005

We present a simple model to describe the induction of magnetic behavior on gold clusters upon chemisorption of one organic molecule with different chemical linkers. In particular, we address the problem of stability of the lowest lying singlet and show that for some linkers there exists a spin symmetry-breaking that lowers the energy and leads to preferential spin density localization on the gold atoms neighboring the chemisorption site. The model is basically an adaptation of the Stoner model for itinerant electron ferromagnetism to finite clusters and it may have important implications for our understanding of surface magnetism in larger nanosystems and its relevance to electronic transport in electrode-molecule interfaces.

Introduction The appearance of ferromagnetism in thiol-capped gold nanoparticles (NPs) has been recently reported.1 This surprising finding reveals that under some conditions chemisorption seems to be able to induce permanent magnetism in small nanoparticles of a bulk-diamagnetic metal, such as gold, through an electronic mechanism, apparently involving the interaction of the sporbitals of adsorbates such as thiolates with the 5d-orbitals of gold, which leads to the emergence of 5d-localized holes as a result of significant charge transfer from the gold atoms to the sulfur atom in the adsorbate. The existence of these holes in gold NPs capped with thiolates has been demonstrated by Au L3-edge extended X-ray absorption near-edge structure (XANES) measurements performed by Zhang and Sham2 on alkanethiolate-capped gold NPs of 1.6, 2.4, and 4.0 nm. The magnetism observed in the thiol-capped NPs was found to be accompanied by a strong suppression of the plasmon absorption,1 an indication of the existence of strong interactions between the thiolate (adsorbate) and the gold atoms lying on the surface of the gold nanoparticle, which suppress the itinerancy of gold’s 5d electrons. Zhang and Sham2 report that in the case of gold NPs capped with thiolates, the suppression of plasmon absorption seems to be highly dependent on the size of the NP. Thus, for 4.0 nm NPs they observe a very distinctive plasmon absorption curve that disappears in the case of nanoparticles of 2.4 and 1.6 nm. Using nitrogen as a linker does not seem to have a noticeable effect either in inducing magnetism or for the disruption of the plasmon absorption.1 These results are in stark contrast to X-ray magnetic circular dichroism (XMCD) measurements performed by Yamamoto and collaborators,3 which indicate a significant ferromagnetic spin polarization of gold NPs with a diameter of 1.9 nm capped with a weakly interacting polymer such as polyallylamine hydrocloride. * Addresscorrespondencetotheseauthors.E-mail: [email protected] and [email protected]. † National Institute of Standards and Technology. ‡ PMUSA. § Northwestern University.

Reports of quenching or enhancement of local magnetic moments due to chemisorption in magnetic metals have long been known, and the reason for this behavior seems to be well understood.4 The opposite phenomenon is much more complicated because the onset of magnetism is a complex manifestation of electronic correlation and a delicate balance between the size effect of the nanoparticle and the strength of its interactions with the adsorbate. Historically, two schools of thought have attributed magnetism to either the appearance of localized magnetic moments in real space or the itinerant character of conduction electrons. The modern tendency is to unify these two seemingly contradictory points of view in a single correlated model of the electronic structure. In this work, we report on a quantum-chemical exploration of a symmetry-breaking electronic mechanism induced by single-molecule chemisorption that could provide a possible route for the onset of magnetism. The idea is simple and dates back to a perturbation method used to calculate NMR spinspin coupling constants of molecules.5 The system we consider here is a small cluster of 13 gold atoms and one chemisorbed molecule. Even though this system is much simpler than the actual nanoparticles studied in the experiments, it provides a reasonable prototype for understanding the basic electronic mechanism that might be responsible for the magnetism observed in these systems. We have probed the stability of the singlet state against a local breaking of the spin symmetry. Such a methodology is analogous to introducing an artificial external field, an approach that is used in problems where the effect of the perturbation is very small to be studied by conventional techniques. We find that, in agreement with the experimental results, for a sulfur linker, energetic stabilization is accompanied by the developing of spin localization preferentially in the gold atoms closest to the chemisorption site. For a nitrogen linker, no spin symmetry-breaking leading to lower energy states is found.

10.1021/jp054583g CCC: $33.50 © 2006 American Chemical Society Published on Web 12/22/2005

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Theoretical Basis Electronic structure calculations of molecules in singlet states indicate that in addition to the expectation value of the magnitude of the spin angular momentum operator being zero, there is a vanishing spin density around any atom of the system.6 This local condition implies the nonexistence of localized magnetic moments in “closed shell” molecules. A similar situation is observed in bulk metals such as gold characterized by a significant negative diamagnetic constant (χ ) -1.4 × 10-7 emu/gOe). To understand the appearance of magnetism in these nonmagnetic systems it is crucial to explore the feasibility of spin-symmetry breaking processes that could lead to nonzero local spin densities in a singlet state. The physical event responsible for such a broken symmetry in a nonmagnetic system would have to provide a mechanism for the redistribution of the charge and spin density of the system that, in general, requires a many-body and correlated description of the electronic structure. Spin-symmetry breaking implies the appearance, under the effect of a perturbation, of one or more states whose symmetry and energy are different from those of the parent eigenstate of the unperturbed Hamiltonian. One possible strategy for studying this situation entails the electronic structure calculation of the spin-polarized system to detect a very small energy difference corresponding to a change in spin-symmetry. As will be shown below, the magnitude of the change in spin densities associated with the spin-symmetry breaking is so small that these types of direct methods might not be appropriate. A different approach involves the solution of the electronic Schro¨dinger equation in the presence of an artificial external field that would magnify the energy difference and then use perturbation theory to determine the stability of the broken-symmetry solution. In this communication we adopt a simplified variant of this approach known as Finite Perturbation Theory (FPT), a scheme that has been widely used for the calculation of coupling constants in NMR.5 Our approach is also closely related to the Stoner model for the theory of itinerant electron magnetism,7 but adapted to a finite system. FPT can be easily formulated within the realm of Density Functional Theory (DFT). At each Self-Consistent Field (SCF) cycle, a finite perturbation of strength λ is added to the oneelectron Kohn-Sham operator hR,β µν , i.e., R,β N hR,β µν f hµν ( λAµν

(1)

where ANµν are matrix elements (in the atomic basis set {φµ}) of the Dirac delta function δ(R BN):

ANµν ) 〈φµ|δ(R BN)|φν〉 ) φµ(R BN)φν(R BN)

(2)

and R BN is the vector with the coordinates of atom N. The ( sign in the form of the perturbation (see eq 1) amounts to a local breaking of the zero spin condition (+ for R electrons and - for β electrons). Although FPT can be used in general for any spin symmetry, its practical value is limited to singlet states, because it is only for those states that a perturbation such as that described by eq 1 may have effects that can be differentiated from other spin rearrangements. The effect of the perturbation to hR,β µν can be interpreted as a probe to the energetic stability of the singlet state. It amounts to a separation of the R and β components of the spin density at the position of the nucleus N. It can also be viewed as the response of the system to an internal magnetic field (Weiss field) associated with a magnetic moment localized at R BN. In our

calculations, the perturbation (eq 1) is then used to compute the electron density and total energy of the system in a selfconsistent manner. The residual interaction between localized spins induced by the perturbation can be modeled by using an effective Heisenberg Hamiltonian:

H)-

Jijb s i‚ b sj ∑ i 0) or antiferromagnetic (Jij < 0). Using simple arguments, we will show that any linear perturbation of the local spin density during a particular iteration cycle in the self-consistent procedure used in the solution of the KS equations would translate into a quadratic dependence of the energy on this variable. Considering only the average value of the z-component of the spins, 〈sz,i〉, corresponding to the total spin density ni on a particular atomic site i, eq 3 can be simplified in such a way that the leading term corresponding to the perturbation can be readily obtained. Under this assumption, ni is given by the following expression:

ni ) 〈sz,i〉 ) ni,R - ni,β

(4)

where ni,R and ni,β are the R and β spin densities on atomic site i. Since for “closed shell” systems the total spin density is zero, the following condition must be satisfied:

∑i ni ) 0

(5)

where the sum runs over all atomic sites i. Assuming all coupling constants Jij to be similar and equal to J, and that the site spin densities are statistically independent of each other, one can write an approximate expression for the expectation value of the Heisenberg Hamiltonian ( eq 3) as:

ni) - J‚ ∑ ni‚nj ∑ i*A i,j*A

〈H〉 ) - J‚nA‚(

(6)

where A refers to the atomic site undergoing the perturbation leading to the corresponding spin-symmetry breaking. Introducing eq 5 into eq 6 leads to:

〈H〉 ) Ω + J‚χ‚nA + J‚nA2

(7)

where χ and Ω contain the contributions of all other interactions except those involving the site A. In cases where spin localization occurs preferentially on site A, (nA . ni*A), these terms can be assumed to be constant. In these cases, the energy difference relative to the ground state can be written as follows:

∆E(nA) ) Ω + J‚χ‚nA + J‚nA2

(8)

For a nonmagnetic state, the minimum energy is obtained for nA ) 0, whereas for a symmetry-broken magnetic state the minimum energy is obtained for nA > 0, with a coupling constant J > 0, Ω ≈ 0, and χ < 0. Choosing values of the perturbation parameter λ in eq 1 that lead to physically meaningful results is a subtle issue. In this work, we adopt the criterion that the electronic state of the system should remain a singlet, so that λ is varied in a range that does not lead to significant spin contamination as measured by the total spin eigenvalue S(S + 1). For each value of λ, we obtain a value of

Induction of Magnetic Behavior on Gold Clusters

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the spin density by means of the solution of the KS equations in a self-consistent manner. This spin density is the significant physical magnitude that describes the stabilization or destabilization of the system upon a symmetry breaking. As mentioned above, the approach adopted in this study is closely related to Stoner’s condition, which states that a nonmagnetic state for a metal will be unstable if the product of the spin-added density of states at the Fermi energy No(EF) and the coupling constant J (see eq 3) satisfy the relation No(EF)J > 1.7 If this condition is satisfied, a single band at the Fermi energy splits into two bands that correspond to the different spin symmetries. This splitting is accompanied by a reduction of the total energy with magnetization, a result analogous to eq 8 for negative χ and positive J. In this sense FPT provides an extension of Stoner’s condition for molecular or cluster-like systems. Theoretical Calculations Density Functional Theory (DFT) single-point energy calculations were performed by using the PBE gradient corrected exchange-correlation functional of Perdew, Burke, and Enzerhof9 with the double-ζ pseudopotential LANL2DZ basis set developed by the Los Alamos group.10 This level of theory is referred to as PBE/LanL2DZ throughout the rest of this work. All calculations were performed with the GAUSSIAN 03 suite of quantum chemistry codes.11,12 To apply the FPT methodology we perturbed the Au atom directly bonded to the linker. To assess the effects of the R-L-Au (L being a chemical linker and R an organic moiety) bonding on the spin symmetry, benzene-L adsorbates (e.g. C6H5-S- for sulfur and C6H5NH- for nitrogen), bonded to the Au13 cluster were studied. In these systems, only an “on top” bonding between the adsorbate and a gold atom in the Au13 cluster was considered. Given that the binding of thiolates to gold surfaces is highly dependent on the molecular approach of the substrate to the surface, additional configurations such as the one where the sulfur atom sits in a hollow site surrounded by 3 gold atoms or the one where the sulfur atom binds to 2 adjacent gold atoms in a “bridge” structure should be considered. The effect of these and additional configurations on the magnetism of the system is currently under study in our lab and the results will be reported in a future publication. The geometry of the Au13 cluster was extracted from the structure of the unreconstructed face-centered-cubic Au(111) surface with an averaged near-neighbor Au-Au bond distance of 2.88 Å.13 The geometry of the adsorbate C6H5-Land the S-Au bond distance (2.50 Å) were obtained from a constrained geometry optimization at the PBE/LanL2DZ level of theory where the coordinates of the gold cluster where fixed to the Au(111) geometry. In this study, two families of linkers (L ) O, S, Se and L ) N, P, As) were considered. Figures 1 and 2 depict the structure of the benzene thiolate-Au13 and the corresponding nitrogenated compound, respectively. From the outset it should be mentioned that this model structure provides just a simple prototype to study the ability of the system to localize spin as a result of the interaction between the chemisorbed species and gold. To gain a better understanding of the possible sources leading to induced magnetism recently observed in some thiol-capped gold nanoparticles,1 calculations of the electronic structure of systems of more realistic size including all contributions to the interactions between the nuclear magnetic moments and electrons as given by Ramseys’s treatment14,15 should be considered. Such studies are under way in our lab and the results will be reported in a future publication.

Figure 1. Geometry of the C6H5-S-Au13 system considered in this study.

Figure 2. Geometry of the C6H5-NH-Au13 system considered in this study.

Results and Discussion Figures 3 and 4 display the variation of energy as a function of the spin splitting parameter λ. There is a clear trend of the energy in one family (L ) O, S, Se) to decrease, whereas the other family (L ) N, P, As) exhibits the opposite trend. This result provides strong indication that the orbitals of the linker involved in the interaction with gold, essentially responsible for promoting magnetism, may have similar symmetries but differ widely in energy. The most favorable interaction was found to correspond to cases where the linkers possess orbitals whose energies are close to the Fermi energy of the gold cluster (not shown). A detailed discussion of these results will be reported in a forthcoming article.

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Figure 3. Relative energy of the C6H5-L-Au13 system (L ) O, S, and Se) as a function of the perturbation parameter λ computed at the PBE/LanL2DZ level of theory.

Gonzalez et al.

Figure 5. Relative energy (computed at the PBE/LanL2DZ level of theory) of the C6H5-S-Au13 system as a function of the spin density nau on the gold atom bonded to the sulfur linker.

for the case of N as a linker exhibits a minimum of energy at zero spin density, and a destabilizing antiferromagnetic coupling (J < 0), again in agreement with the theoretical model presented in this work and the experiment.1 Finally, using the value of the spin densities corresponding to the minimum of the plot displayed in Figure 5, we obtain a magnetic moment of 0.0025 µB per S-Au bond for C6H6-S-Au13, in very good agreement with the value of 0.0036 µB obtained by Crespo et al.1 in their measurements of magnetization on thiolate capped-Au nanoparticles. Finally, FPT calculations performed on the C6H6S-Au13 system, where perturbation is applied to a Au atom not bonded to the sulfur linker (e.g. Au[10] in Figure 1), predict a magnetic moment almost identical (0.0024 µB vs 0.0025 µB) with the one obtained when the perturbation is applied to the Au atom linked to the sulfur linker (Au[9] in Figure 1), confirming our conjecture that the source of magnetism in this system is the result of a local spin-symmetry breaking process resulting from the interaction between the S linker and the Au cluster, which should be independent of the choice of the atom where the perturbation is applied. Figure 4. Relative energy of the C6H5-L-Au13 system (L ) N, P, and As) as a function of the perturbation parameter λ computed at the PBE/LanL2DZ level of theory.

The most interesting case for further analysis is the thiolate compound. Figure 5 shows the energy as a function of the spin density at the gold atom directly linked to the sulfur atom. As expected, the plot shows a minimum in energy for a nonzero spin density, providing a clear confirmation of the instability of the unperturbed singlet and the existence of a more stable broken-symmetry magnetic state, in qualitative agreement with the experimental results of Crespo and collaborators.1 A leastsquares fit to the plot depicted in Figure 5 leads to the values of (in au) 0.0, -2.8133 × 10-6, and 1.2695 × 1013 for Ω, χ, and J correspondingly, indicating an effective ferromagnetic coupling (J > 0 in eq 3) for the dominant interaction between the larger spin moments. Although not shown, a similar plot

Conclusions In this work, a simple quantum chemical approach based on Finite Perturbation Theory to study magnetism in clusters and nanoparticles has been presented. This model is an extension of band structure calculations to finite systems. It has the distinct advantage that the response function is directly related to the symmetry-breaking perturbation, which can be too small to be detected by direct computation of the local magnetic moments in a spin-polarized electronic structure calculation. Our results seem to confirm the conjecture proposed by Crespo et al.1 that the interaction between S and Au orbitals is ultimately responsible for the onset of magnetism in thiol-capped gold nanoclusters. Our model also provides an explanation for the experimental observation that magnetism is only induced by certain chemical linkers, e.g., S but not N.

Induction of Magnetic Behavior on Gold Clusters The question of chemisorption-induced magnetism is an intriguing one that is particularly relevant to understand electron transmission experiments such as those reported by Naaman and collaborators.16 If the results obtained in this work for a small 13-atom cluster hold for nanoparticles and surfaces, it could provide a partial explanation for the puzzle related to the emergence of two-dimensional magnetic layers, as usually invoked to interpret Naaman’s experiments. Although the associated spin densities per site are rather small, they could further be stabilized via a spin-spin RKKY exchange interaction between pairs of localized spins. Finally, the qualitative agreement between the results of this study and the experiments of Crespo et al.1 is encouraging and suggests the possibility of using simple quantum chemistry models such as the one adopted in this work to shed some light on the fundamental understanding of the nature of symmetry-breaking magnetization in complex mesoscopic hybrid systems. Acknowledgment. We thank Prof. P. Crespo for discussing with us his fascinating results on magnetism in nanoclusters. We acknowledge Prof. F. Gonza´lez for stimulating discussions on the subject of surface magnetism. References and Notes (1) Crespo, P.; Litra´n, R.; Rojas, T. C.; Multigner, M.; de la Fuente, J. M.; Sa´nchez-Lo´pez, J. C.; Garcı´a, M. A.; Hernando A.; Penade´s, S.; Ferna´ndez, A. Phys. ReV. Lett. 2004, 93, 087204. (2) Zhang, P.; Sham, T. K. Phys. ReV. Lett. 2003, 90, 245501. (3) Yamamoto, Y. T.; Miura, T.; Suzuki, M.; Kawamura, N.; Miyagawa, H.; Nakamura, T.; Kobayashi, K.; Teranishi, T.; Hori, H. Phys. ReV. Lett. 2004, 93, 116801. (4) See for example: (a) Ro¨sch, N.; Ackermann, L.; Pacchioni. G.; Dunlap, B. I. J. Am. Chem. Soc. 1992, 114, 3550. (b) Ackermann, L.; Ro¨sch, N.; Dunlap, B. I.; Pacchioni, G. Int. J. Quantum Chem. 1992, 26, 605. (c) van Leeuwen, D. A.; van Ruitenbeek, J. M.; de Jongh, L. J.; Ceriotti, A.; Pacchioni, G.; Ha¨berlen, O. D.; Ro¨sch, N. Phys. ReV. Lett. 1994, 73, 1432. (5) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High-resolution Nuclear Magnetic Resonance, McGraw-Hill: New York, 1959.

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