sp magnetism in clusters of gold-thiolates

Using calculations from first principles, we herein consider the bond made between thiolat e with a range of different Au clusters, with a particular focus on the spin moments inv olved in each case. For odd number of gold atoms, the clusters show a spin moment of 1.~ $\mu_B$. The variation of spin moment with particle size is particularly dramatic, with t he spin moment being zero for even numbers of gold atoms. This variation may be linked w ith changes in the odd-even oscillations that occur with the number of gold atoms, and is associated with the formation of a S-Au bond. This bond leads to the presence of an extra electron that is mainly sp in character in the gold part. Our results sugg est that any thiolate-induced magnetism that occurs in gold nanoparticles may be locali zed in a shell below the surface, and can be controlled by modifying the coverage of the thiolates.

Nanoparticles consisting of metals and oxides have been shown to exhibit magnetic behavior even when they are made only of non-magnetic compounds [1][2][3][4][5]. When organic molecules are attached to Au via thiol bonds, Au nanoparticles (NPs) with a size of 1.6 nm show a kind of ferromagnetic response, even at room temperature. The saturation magnetization is very low, being typically in the range 10 −1 -10 −2 Bohr magnetons per atom, and is weakly dependent on temperature in the range from 4K up to room temperature.
The low magnitude of the magnetic moment is not caused by the few magnetic impurities present, because any increase in the number of impurities causes the magnetic signal to disappears [3]. The results of both X-ray magnetic circular dichroism (XMCD) and Au Mössbauer spectroscopy have shown that the Au atom possses a magnetic moment [4,5], which was previously thought to be due to the spins of Au d-holes introduced by the ligands [6]. However, the observed saturation at room temperature and the shape of the magnetization curve still lack convincing explanation. A more detailed understanding of the nature of the gold-alkenethiol bond is therefore required. In particular, understanding of the interaction between alkenethiols and Au NPs is currently one of the main challenges in the study of their magnetic structure.
The contribution of the sp levels in Au NPs is particularly significant, and it is the filling of these levels that explains the effects of the electronic shells in noble metal clusters in general and in gold clusters in particular [7]. Using a theoretical approach, it has been shown that the coverage of the gold clusters by thiols that have well-defined compositions is rather disordered, and that the charge transfer depends strongly on the coordination of sulphur atoms [8]. A range of different coordination numbers must therefore be taken into account in any investigation. Alkenethiols with longer chains on Au surfaces have been the focus of detailed theoretical studies [9] and the presence of several different metastable states in energy have been shown. The sulphur atoms in the gold layers becomes arranged in a bridge configuration for the ground state, and this must then be primarily considered in assesing their magnetic signal. Other NPs such as ZnO capped with a range of different organic molecules, e.g. amine, thiol and topo, also exhibit ferromagnetism at room temperature [10].
The results of XMCD show that the magnetic signal of ZnO NPs is due to the conduction band, which is mainly formed from empty 4sp Zn surface states [11]. The d-electrons of Zn are too far away in terms of energy and clearly make no contribution to the magnetic signal. It has been shown theoretically that a carbon oxide CO molecule on ZnO surface donates a single electron to the 4sp surface orbitals, which are initially empty [12]. Although there have been a number of studies of the changes in the geometrical structure induced by alkenethiols in gold surfaces and clusters, to our knowledge no studies have yet focused on the magnetism of the NPs covered by such molecules. The results of such a study would be of particular interest when considered toghether the effect of magnetism on the electronic properties of gold nanoparticles covered by thiols.
An all-electron local-orbitals scheme, namely the ADF (Amsterdam Density Functional) method [13], was used herein for calculations involving density-functional-theory (DFT). The valence basis set was composed of the d gold, sulphur, carbon and hydrogen states, which were expanded in triple zeta with two polarization functions at each atom. The relativistic effects of gold were modeled using the Zeroth Order Regular Approximation (ZORA) and its scalar relativistic version was used for the structural optimizations. The data presented herein were obtained using generalized gradient density approximations (GGA) with the parametrized exchange-correlation functional of Perdew-Burke-Ernzerhof according to Ref. [14]. The optimization of the geometry was carried out until the forces were all smaller than 0.02 eV/Å. The magnetic anisotropy (MAE) was obtained by means of self-consistent ZORA relativistic calculations, including spin-orbit. The resulting GGA data were regarded as a lower estimate for the MAE. In order to obtain an upper estimate, an orbital polarization correction (OPC) [15] should be considered, but this work is beyond the scope of the present study.
The singly or doubly occupied levels of the Au clusters are responsible for the odd-even oscillations. These oscillations do not vary strongly much with the number of atoms in the cluster. We have herein therefore chosen to investigate the interaction between alkenethiols −SCH 3 and minimal gold clusters. The interactions of gold clusters with thiols are considered to be a suitable model of adsorption of thiols onto larger nanoparticles [8].
We begin our analysis with a cluster of Au 3 , which allows us to investigate a number of different coordination numbers for the sulphur atom. Au 3 SCH 3 has an even number of electrons, and thus has a spin moment equivalent to an even number of Bohr magnetons.
In order to determine the lowest-energy geometry and the spin magnetic state, four possible high-symmetry structures were optimized for each of the possible values of low spin µ S =0, 1, 2 etc. We only compared the data for µ S =0 and 1 in Fig. 1, because the other spin states produce an even higher total energy. The point group symmetries were fixed in our calculations to reproduce those of the geometries in the surfaces of the nanoparticles. The geometry of the gold atoms was not fixed because the adsorbates of thiols on gold can alter the atomic distances of Au-sulphur and Au-Au binding.
Calculations using DFT yield energies that depend on the exchange-correlation approach used. In order to confirm the qualitative validity of the calculated energies, structural sequence, and spin states of Fig. 1, we performed calculations with many other functionals, as implemented in ADF, using the fixed geometry obtained with the previous GGA approach.
We obtain that the energetic difference between the different spin states was sometimes higher [though never lower] than that obtained from the previous GGA values using the PBE approach. The other functionals produced energetic differences of about 1.4 eV between the non-and spin-polarized structure. These supporting calculations therefore confirm the main findings obtained using PBE, in that the bonds of an SCH 3 molecule with a three-atom cluster form the structure depicted in the bottom of Fig. 1 which has a total spin of zero.
Our findings show a gain in total energy of 0.12 eV for the −SCH 3 adsorbate with the gold cluster in a bridge position, this being the ground-state structure with respect to the molecule in the Au 3 plane. We are not aware of any previous investigation of this structural form of Au 3 SCH 3 . Although other molecules of Au-thiols have been studied previously [16], no report has been made of a model of the surface of gold nanoparticles. Evidence for such 'tilt' arrangement for the molecule was previously provided by Ref. [9] for thiols on gold surfaces. Furthermore, thiols have theoretically been predicted [9] to form a mat on a gold surface with perpendicularly oriented molecules. This is given by the bridge position with all the atoms bonded to S in the same plane, as shown in the third geometry of Fig. 1.
However, this form has a larger energy than the tilt case, because it is a metastable position by 0.56 eV. Althought this form has a similar coordination number to that of the studied case of C 6 H 5 − S − Au 13 [17], is not considered in the results that follow, despite its spin polarization for alkanethiols.
The structural forms of other gold cluster structures are given in Fig. 2. The panel on the far right hand side shows the structures of S=0, as previously discussed for the ground state of Au 3 -thiol, while the left-hand panel refers to clusters with spin polarization (S=1). The numbers shown below the structures give the spin polarization energy in each case, which are almost independent of the size of the cluster. The related energy differences ∆E are around 0.5 eV and -0.2 eV for the odd and even cases, respectively. These values should be considered to be lower estimates for the polarization, because they were evaluated without the so-called orbital polarization. The most important characteristic is the shift between odd-even oscillations, by a single gold atom, with respect to bare gold clusters. The structure is spin compensated for an even number of gold atoms in the thiol-cluster, while it is spin polarized otherwise.
It is perhaps somewhat surprisingly that the bonding of thiols on gold clusters does not lead to the elimination of the spin magnetic moment, but rather to a new paradigm, i.e. the spin moments induced by the thiols are unchanged, as in free particles. It is noteworthy that our spin polarized state can be more stable in energy, by >0.2 eV, than the state withouth spin polarization. In consequence, the level of the highest occupied molecular orbital HOMO is singly occupied, and follows the local magnetization on atoms. Further analysis of this characteristic for Au n SCH 3 clusters that contain an even number of gold atoms, as also seen in Fig. 2 Although some of the gold-thiol molecules described herein were investigated both experimentally [1], by quantum mechanical calculations [16], and using spin-polarized GGA [8], their behaviour in terms of their magnetic moment merits further study. Figure 3 shows the bonding mechanism of thiolates on metal clusters. A sulphur atom is shown here joined to two Au atoms with sp 3 hybridization. The spin population is smaller in these sulphur and bonded gold atoms than in that of the next nearest neighbors below the sulphur-gold bonds. There are five sulphur electrons in total: the two bonds with gold atoms share two electrons, an electron is shared in the bond with the carbon atom, and two more form the lone pair in the sp 3 hybridization. Because each sulphur atom contributes with a total of six electrons, a single electron is left over and is passed to the gold cluster. It is this sp electron that contributes to the spin polarization.
A related discussion that supports the back-donation of a sp electron from the thiols to gold arises from a comparison between the eletronegativities of thiols and those of their gold counterparts. We calculated the ionization potentials (IPs) and eletroaffinities (EAs), thereby obtaining the Mulliken electronegativities M = (IP + EA)/2. This M value is the the negative of the electrochemical potential. The electronegativity of the SCH 3 unit is slightly higher (5.43 eV) [18] than the work function of around 5.22 eV for the Au surface [19] and is comparable with the M value for gold nanostructures ( 6 eV) [20]. The SCH 3 unit behaves rather differently from the sulphur atom (M=6.21 eV). In consecuence, the transfer of charge from gold to sulfur cannot be assumed a priori. In fact, we stress that independently of the partition scheme used, the calculated transfer of charge between the thiols and the gold clusters is less than 0.1 e. Such a charge neutrality is also seen in other systems, even in those assumed to be highly ionic [21], and supports the previously commented mechanism of back-donation.
We now compare our findings with those obtained from experiments on thiols and gold nanoparticles. To this end, it must be stressed that the sulphur atom is not negatively charged, even though XANES experiments have shown that the 5d orbitals of gold are slightly open. The sp contribution to the magnetic signal is larger than that of the d orbitals. The back-donated electron from sulphur to gold also sits in the sp states of the Au bond, and cannot be differentiated by the previous results using XANES method. These sp electrons are almost free in the second gold layer and could orbit, and it is these that are responsible for the magnetism. These findings are consistent with experimental results in which a number of gold layers are needed in order to engender thiol induced magnetism.
This general picture is in agreement with the donor mechanism of carbon monoxide to Zn atoms on a ZnO surface [12], in that there is donation of a single electron from the molecule to the 4sp surface orbitals of Zn, which are initially empty. More importantly, it is also in agreement with the 4sp magnetism observed by XMCD in thiol capped ZnO nanoparticles [11].
The method of application of thiols is via their deposition in layers on the surface of gold nanoparticles. The magnetism that results should be that of the electrons donated by the capping molecules, which are confined to a thin layer below the surface, and form a two-dimensional electron gas. We have herein determined the means by which this surface layer is unfilled, thereby giving rise to a permanent magnetic moment [22]. Orbital and spin angular moments are formed at the generally unfilled Fermi level of the system, which is confined to a spherical shell at the surface. The unfilled Fermi level of the surface band is characterized by a collective magnetic moment that is rather similar to an atomic orbital, but with a much larger quantum number. The order of magnitude (0.1 or 0.01 µ B per atom) is in agreement with that measured experimentally [1][2][3][4][5].
Among all the possible combinations of thiol and noble metals, we have herein described our investigation of Au clusters, but it should be mentioned that copper shows similarly good bonding behavior with thiols. The related magnetic ground states have the same spin state (1 µ B ) and lie at similar energies with respect to the state with zero moment. This finding is similar to recent experimental work carried out for these nanoparticles [5] and deserves further investigation.
By including spin-orbit coupling, we find that thiols attached ot Au 4 and Au 6 show a magnetic anisotropies MAE of 1.43 and 0.98 meV per SCH 3 molecule, respectively, while the change of MAE in the plane parallel to the surface is less than an order of magnitude smaller. These figures are comparable with the giant magnetic anisotropy of single cobalt atoms on a Pt surface (9 meV per Co atom) [23]. Such large values of MAE demonstrate the stability of the magnetism discussed herein at room temperature, and are a factor of ten times larger than the equivalent values for tetragonal Ni (0.2 meV). The results of a recent experiment [1] showed that the magnetism of gold nanoparticles covered by thiols can indeed survive almost unchanged at room temperature, and it could therefore be used in hyperthermic applications.
In summary, we predict that the bonding of alkanethiols on gold clusters (i.e.SCH 3 Au n ) results in a bridge arrangement with a deviated axis in a polarised ground state for even n values of n. This structure is characterized by a division of functions, in that while the sulphur atom and the close pair of atoms are responsible for the chemical bonding, it is the outer gold atoms that host the larger part of the magnetic moment. The large magnetic moment is preserved in the structure of the nanoparticles because they have lower