Magnetism in Thiolated Gold Model Junctions - The Journal of

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Magnetism in Thiolated Gold Model Junctions Matús ̌ Dubecký†,‡,§ and Haibin Su*,§ †

Institute of Electrical Engineering, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, SK-84104 Slovakia Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, SK-84511 Slovakia § Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore ‡

ABSTRACT: Three stable, neutral diradical model molecules with an even number of electrons, based on pairs of small thiolated Au clusters connected via Au−Au bonding, are studied within a broken symmetry unrestricted density functional theory involving a set of exchange-correlation functionals, including PBE, M06L, TPSS, B3LYP, M06, and TPSSh. The models, mostly with an antiferromagnetic ground state within the theory used, are analyzed in terms of the vertical spin−flip energy splitting, total spin expectation values, Heisenberg exchange coupling constant, magnetic orbitals and their overlap, diradical character, binding energies, natural bond-order analysis, and bond index of the central Au− Au bond. The spin-symmetry breaking is attributed to the open-shell nature of the dimerized monomer constituents and the structural feature of the facing S−Au−S edges, in combination with the attractive unsupported metallophilic d−d interaction of the incident Au atoms, allowing a weak coupling of the spins localized sideways. The modeling provides insight to AuI−AuI interactions, potentially useful in design of novel gold-based magnetic nanoscopic assemblies.

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INTRODUCTION Organometallic nanoparticles based on gold clusters protected by organic ligands (AuNPs) have received much attention in recent years due to their viable synthesis,1,2 their wide range of applications in photonic3,4 and electronic devices,5 sensors,6 biotechnology as labels7 and/or nanocarriers in drug delivery applications,8 and their potential to reveal rich physical phenomena such as enhanced photoemission,9 Coulomb blockade at room temperature,10 photomagnetic effect11 and ferromagnetism,12,13 unexpected in organometallic systems based solely on diamagnetic compounds such as gold and alkane-thiols.14−21 The observed spin polarization has been attributed to the size effect and localized d holes, induced in gold due to the strong interaction with sulfur acting as a bridge between gold and organic ligands.12,22−25 Nanoparticles revealing magnetism and their assemblies are of importance in nanotechnology and spintronics,26,27 in fundamental quantum-mechanical experiments,28 and potentially in quantum computing.28 To date, theoretical studies of thiol-capped AuNPs have been primarily devoted to neutral or charged nanoparticles containing a single gold core,22,25,29−40 but no magnetic state has been explicitly proven to exist in relatively small (e.g., 144 Au atoms35), simulated undoped systems with an even number of electrons. On the other hand, Okumura et al.41−43 studied the interaction of electrons localized on organic radical ligands attached to a small Au cluster, acting as a channel transmitting the magnetic interaction, revealing a high-spin ground state. In order to understand assembly and linking of nanoscopic magnetic AuNPs, a natural step forward is to study systems consisting of their pairs. Interlinking, cross-linking, and dimerization of AuNPs are becoming topics of great interest (e.g., refs 40, 44−46). Various linking/coupling scenarios are possible in © 2012 American Chemical Society

principle (e.g., linking via organic molecules anchored between AuNPs).47 Even though the magnetism has not yet been explicitly demonstrated in pure, neutral, and small thiolated AuNPs, it may be readily promoted by transition-metal doping of AuNP cores.48 It is thus beneficial to study model junctions resembling a contact of real AuNPs carrying a spin. The structures proposed in the present work focus on assessment of direct AuI−AuI bonding between facing S−Au−S edges/staple motifs,25,30,31,49,50 attached to small Au/thiolated Au clusters carrying a spin. The junctions represent minimalistic models of interactions that may take place between pairs of real thiol-capped open-shell AuNPs with weak steric repulsions. The AuI−AuI bonding, known as aurophilicity,51,52 is a weak attractive interaction of d10−d10 nature, giving rise to extended equilibrium Au−Au distances between 2.85 and 3.5 Å.52 The aurophilic bonding is of interest due to its ability to dimerize, or even polymerize,51,52 gold compounds, making it a versatile tool in materials science. The so-called staple motifs such as S− Au−S, S−Au−S−Au−S, or sometimes even longer ones typically cover surfaces of thiol-capped AuNPs in experiment, and since the sulfur-attached alkane chains are typically long,9,12,13 steric repulsions mask the weak attractive interactions of gold. The effect of aurophilicity may be tested using short ligand chains, as adopted in our study. Three simple, neutral dimerlike hybrid molecular models are investigated, namely, [(SCH 3 ) 2 Au 3 ] 2 denoted D1, [(SCH3)3Au4]2 denoted D2, and D3 with [(SCH3)2Au5]2 stoichiometry (cf. Figure 1). These models, with the even total number of electrons, are composed of Au−Au linked pairs Received: June 12, 2012 Revised: July 24, 2012 Published: July 24, 2012 17714

dx.doi.org/10.1021/jp305716m | J. Phys. Chem. C 2012, 116, 17714−17720

The Journal of Physical Chemistry C

Article

with a transition-metal bonding and small overlap between magnetic orbitals (MGO), contrary to the closed-shell geometry optimizations in such systems.69 The calculated electronic states were always forced to converge to the lowest possible solution within a given spin multiplicity/charge and were checked for stability.70 The LS states of the studied dimers were analyzed in terms of the vertical spin-flip energy splitting HS LS ε = Etot − Etot

(1)

HS from the respective total energies ELS tot and Etot of the low-spin and high-spin (HS) state, the total spin expectation values SLS2 and SHS2, Heisenberg exchange coupling constant71

J=−

(SHS

2

ε − SLS2)

(2)

and the overlap of MGOs, O, diradical character η=

∑ |ni(ni − 2)| i

(3)

of doublet monomers (M1, M2, and M3, indicated in Figure 1). The monomer subunits consist of 3−5 atoms of gold in twodimensional (2D) and three-dimensional (3D) arrangements. To avoid steric repulsions, methyl groups53 are used instead of the long alkyl chains used in the experiment.9,13 The models, revealing spin-symmetry breaking, are studied within the nonrelativistic broken symmetry (BS) density functional theory (DFT) as routinely used in studies of diradicals54−56 where the wave-function methods are prohibitively expensive. It turns out that the aurophilic bonding in the studied model junctions gives rise to a stabilization of dimers with respect to isolated monomers, and at the same time, the junctions allow only a weak coupling of the spins localized sideways, leading to formation of diradicals. The results provide insight to interactions between spin-carrying thiolated gold molecules, potentially useful in design of gold-based magnetic molecular and nanoparticle assemblies.

proportional to the number of unpaired electrons calculated from the natural orbital (NO) occupation numbers, 0 ≤ ni ≤ 2, and fragmentation energy, εfrag = Etot(Di) − 2Etot(Mi) (i.e., energy of the central Au−Au bond scission of the respective dimer i). Additionally, the same Au−Au bond linking the monomers is discussed in terms of its equilibrium bond distance, d, and Wiberg’s natural bond index,72 b, and compared with the bonding in Au2 in terms of the differences δbAu2 = bAu2 − b and δdAu2 = dAu2 − d. Some additional structural tests (see below), estimation of a basis-set superposition error (BSSE), natural bond-order (NBO) analysis (e.g., see Yang et al.73), assignment of formal natural atomic configurations, calculations of ionization potentials (IP), and electron affinities (EA) for model D2, were done using a TPSSh xc functional only. The quantity similar to η has been reported by Staroverov et al.74 Our value gives results very close to the more complicated definition.75 MGOs are obtained by biorthogonalization (i.e., unitary rotation of unrestricted orbitals giving maximal alignment of α and β sets; cf. Bachler et al.54), allowing for the identification of orbital pairs with a closed-shell character (O ≈ 1, here in all cases >0.99) and the remaining orbital pairs (O < 0.99), called MGOs due to their open-shell nature. MGOs contain information on the spin polarization and are directly related to the spin density.

MODELING The DFT57,58 modeling, involving pure, meta, hybrid, and meta-hybrid generalized-gradient (GGA) exchange-correlation (xc) functionals, namely, PBE,59 TPSS,60 M06L,61 B3LYP,62,63 M06,64 and TPSSh,60 was performed using Gaussian 09.65 The atoms of Au were represented by the energy-adjusted scalar relativistic effective-core potential of def2-type66 and def2TZVP basis set,67 also used to represent S, C, and H atoms. MOLDEN68 was used in part for analyses and production of the figures. The dimer structure models, D1, D2, and D3, depicted in Figure 1, and their monomer subunits, M1, M2, and M3, were fully relaxed without imposing any constraints to stable local minima, confirmed by frequency calculations. Geometry optimizations were performed in the BS low-spin (LS) state, known to follow the experimental trends in open-shell systems

RESULTS AND DISCUSSION The bond lengths and bond indexes of Au2 evaluated for reference (i.e., evaluation of differences δbAu2 and δdAu2) are reported in Table 1. The bond lengths range between 2.534 and 2.590 Å, overestimating the experimental value of 2.47 Å,76 with no clear correlation to the nature of the xc functional used. A similar behavior is observed for the bond indexes which all lie slightly above 1, indicating the presence of a single covalent bond between atoms of Au2. In addition, Table 1 contains the calculated lowest vertical singlet−triplet energy splittings, ε, compared to the experimental value,77 that may serve as a reference for assessment of the xc functionals used in future studies. The properties of interest calculated for dimers D1, D2, and D3, each optimized in the LS state, are summarized in Table 2.

Figure 1. Structures of the studied dimer models, D1, D2, and D3, and their monomer subunits, M1, M2, and M3 (indicated by line). Dimers are formed by linking monomers via Au−Au bonding in the middle. Yellow, Au; green, S; brown, C; white, H.

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Table 1. Summary of Bond Indexes, b, Equilibrium Bond Lengths, d, and Vertical Singlet−Triplet Energy Splittings, ε, Calculated for Au2 PBE TPSS M06L B3LYP M06 TPSSh exptl76 exptl77

b

d (Å)

ε (eV)

1.0367 1.0362 1.0311 1.0286 1.0248 1.0324

2.546 2.535 2.564 2.568 2.590 2.534 2.47

2.040 2.031 2.133 2.060 2.172 2.085

Table 3. Magnetic Orbitals (MGO) of the Dimer D1 and HOMO of the Corresponding Monomer M1, Obtained with Different DFT xc Functionalsa

2.062

The corresponding MGOs and monomer HOMOs are reported for D1, D2, and D3, in Tables 3, 4, and 5, respectively. Model D1, within the theory used, is characterized by the small, positive LS → HS spin-flip energy splitting ε. The BS singlet ground state is preferable except for the B3LYP revealing a vertical spin-flip triplet slightly below the LS state. In general, the tested hybrid xc functionals give values of ε about an order of magnitude smaller than the tested nonhybrids. Heisenberg exchange coupling constant, J, varies according to vanishing ε, typical for diradicals, and reveals stronger antiferromagnetic (AFM) coupling for PBE, TPSS, and M06L, around 100−200 cm−1. The xc functionals containing a fraction of the exact Hartree−Fock (HF) exchange, namely, B3LYP, M06, and TPSSh, give J values equal to +6, −12, and −66 cm−1, respectively. The diradical character, η, clearly identifies D1 as a diradical with 1.696− 1.998 unpaired electrons, depending on the nature of the xc functional used. The overlaps of MGOs, O, are correspondingly small (cf. Table 3); however, they are not negligible, in general,

a

MGOs weakly overlap and resemble well the HOMO of the monomer. The weak Au−Au bonding between the monomers does not strongly affect the original spin distributions and gives rise to a diradical character of the molecule.

and vary with contribution of HF exchange. Functionals PBE, TPSS, and M06L result in O ∼ 0.3, whereas for B3LYP and M06, O = 0.033 and 0.095, respectively. In the case of TPSSh, O = 0.183, falling between the values from nonhybrids and the

Table 2. Summary of Parameters Calculated for the LS-Optimized Dimer Models D1, D2, and D3a ε (eV)

SLS2

SHS2

J (cm−1)

PBE TPSS M06L B3LYP M06 TPSSh

0.0146 0.0312 0.0248 −0.0008 0.0014 0.0084

0.913 0.861 0.891 1.020 1.001 0.984

2.008 2.011 2.010 2.021 2.010 2.018

−107.1 −218.8 −178.2 6.1 −11.6 −65.8


0.2823 0.3117 0.2127 0.0118 0.0597 0.1907

0.000 0.000 0.000 0.977 0.859 0.379

2.003 2.003 2.005 2.011 2.009 2.007

−1135.8 −1253.2 −854.7 −91.9 −418.6 −943.3


0 0 0 0 0 0

1.005 1.007 1.006 1.011 1.004 1.010

2.005 2.007 2.006 2.011 2.004 2.010

−0.09 −0.13 −0.07 −0.29 −0.02 −0.11

η

O

model D1 1.808 0.307 1.696 0.386 1.769 0.343 1.998 0.033 1.980 0.095 1.935 0.183 model D2 0 1 0 1 0 1 1.935 0.184 1.696 0.385 0.752 0.790 model D3 2 0.003 2 0.001 2 0.000 2 0.002 2 0.000 2 0.001

εfrag(eV)

b

δbAu2

d(Å)

−δdAu2(Å)

0.470 0.472 0.641 0.202 0.594 0.412

0.318 0.323 0.276 0.229 0.240 0.286

0.718 0.714 0.755 0.799 0.785 0.747

2.797 2.768 2.838 2.971 2.901 2.810

0.251 0.232 0.275 0.403 0.311 0.276

0.769 0.800 0.851 0.222 0.463 0.619

0.381 0.380 0.334 0.246 0.287 0.357

0.656 0.657 0.697 0.783 0.738 0.675

2.684 2.668 2.719 2.917 2.882 2.679

0.137 0.132 0.156 0.349 0.292 0.145

0.410 0.396 0.587 0.088 0.569 0.369

0.284 0.280 0.242 0.168 0.231 0.263

0.753 0.756 0.789 0.861 0.794 0.770

2.862 2.843 2.908 3.230 2.928 2.857

0.316 0.307 0.344 0.662 0.339 0.322

Notation: ε is the vertical LS → HS spin-flip energy splitting, S2LS is the total spin expectation value of the LS state, S2HS is the total spin expectation value of the vertically spin-flipped HS state, J is the Heisenberg exchange coupling constant, η is the diradical character, O is the overlap of MGOs, εfrag is the fragmentation energy, b and d are the bond index and bond length of the central Au−Au bond, respectively, and δbAu2 and δdAu2 are the bond index and bond length differences, respectively, with respect to Au2. a

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that of an open-shell. Bond index b is found to be insensitive to the presence of HF exchange in xc functionals of TPSS nature, comparing TPSS and TPSSh. However, values of b differ significantly in D2 when comparing nonhybrid M06L, where b = 0.334, and hybrid M06, where b = 0.29. Apart from that, the qualitative trend of the weak bonding holds. NBO analysis again reveals no direct covalent bonding orbital. Only d-type lone pairs are identified that are responsible for the weak binding. The most pronounced differences between the used xc functionals are found for B3LYP, that should be used with care in organometallic systems, such as those studied here. Since the two qualitatively different sets of results were found when varying xc functionals for D2, namely, a diradical-indicating set and a closed-shell solution-giving set, an additional test has been performed. A possibility of artificial symmetry breaking, due to a small basis set, has been excluded by a fully optimized def2-QZVP/TPSSh calculation. Like the default def2-TZVP basis set, it leads to a BS solution. A BSSE correction calculated for the fragmentation D2 → 2M2 was found to be about 0.1 eV, an amount that does not change the overall picture. Evidence from literature suggests that the TPSSh xc functional describes the interactions between gold atoms well78−80 and between gold and organic ligands79,81,82 better than nonhybrid TPSS.83 In addition, TPSSh was found to describe aurophilicity better than TPSS from a comparison with the CCSD(T) data.84 On the other hand, meta-hybrid M06 was quoted to be the best from M06s for transition-metal energetics, revealing smaller mean errors than TPSS/TPSSh.64 Its performance was demonstrated by the right prediction of the 2D/3D structural transition in gold anionic clusters, not revealed by TPSS/ TPSSh.85 Both xc functionals, M06 and TPSSh, reveal a BS state in D2 and M06 even more pronounced than TPSSh. From the presented calculations, evidence from literature, and comparison with data for D1 and D3 that are found to be diradicals within all used xc functionals, we conclude that the model D2 is a diradical with an antiferromagnetic ground state with a higher probability than we attribute to a closed-shell solution. The final conclusion, however, remains to be answered by high-level methods able to describe both static and dynamic correlations in an accurate and balanced way. The data calculated for D3 reveal trends similar to D1, except for the diradical character, η, that is more pronounced here. The two magnetic electrons repel each other and stay localized in MGOs resembling the original HOMO orbitals of the corresponding monomer M3 (cf. Table 5) for all xc functionals (B3LYP converged to a different geometry with respect to all of the remaining xc functionals, cf. Table 5). The calculated spinflip energy splitting, ε = 0, overlap of MGOs, O = 0, and η = 2 imply that the junction of the facing S−Au−S edges in D3 does not efficiently transmit the interaction, leading to a vanishing J (see Table 2). D3 thus appears to be a 50/50 mixture of singlet and triplet states at the current level of theory. The binding of the monomers (M3) via the central Au−Au bond, measured by εfrag, still remains relatively strong, on the order of 0.4 eV (i.e., similar to the previous models where the coupling of spins was found to be small but not vanishing). The same is true for the bond index, b, on the order of 0.25 and negative δdAu2, corresponding to Au−Au bond elongation with respect to isolated Au2, slightly above 0.3 Å. The observations determined from the data obtained for the three studied dimer models, within the theory used, may be summarized as follows:

remaining hybrids, as apparent from MGOs (cf. Table 3). Delocalization of MGOs well correlates with the overlap O. Fragmentation energies ε frag reveal a relatively strong stabilization of D1 with respect to its monomers (M1), on the order of 0.4−0.65 eV, except for B3LYP giving ∼0.2 eV. The BSSE calculated for the monomer fragments is found to be ∼0.08 eV. Bond index b of the central Au−Au bond lies between 0.24 and 0.32 compared to ∼1 in Au2, and a bond length elongation, −δdAu2, of ∼0.3 Å versus Au2 falls to the range known for aurophilicity. Finally, the NBO analysis reveals no bonding orbital between the monomers, suggesting a noncovalent d−d bonding between the dimers. Model D2 is described in two qualitatively different ways, within the class of the functionals used. The nonhybrid xc functionals PBE, TPSS, and M06L converge to a closed-shell ground state, stabilized with respect to fragmentation by εfrag ∼ 0.8 eV. The corresponding closed-shell orbitals (CSO) are reported instead of MGOs in Table 4. The HF admixture Table 4. Closed-Shell Orbitals (CSO) and Magnetic Orbitals (MGO) of the Dimer D2 and HOMO of the Corresponding Monomer M2, Obtained with Different DFT xc Functionalsa

a

The nonhybrid functionals PBE, M06L, and TPSS reveal a closedshell singlet ground state, whereas the exact exchange containing xc functionals B3LYP, M06, and TPSSh reveal an open-shell singlet ground state.

containing xc functionals prefer a spin-symmetry broken LS ground state of diradical nature (cf. MGOs in Table 4) and smaller stabilization energy gain, εfrag, varying from case to case by tenths of electron volts between 0.2 and 0.6 eV. In general, the calculated quantities and tendencies are similar for PBE, TPSS, and M06L and separately for B3LYP and M06, and the data obtained with TPSSh lie between the two groups (similar trend as in the case of D1). The distinction between the xc functionals correlates well with the amount of exact exchange used. The positive ε pointing to the LS ground state is higher for nonhybrids, with η = 0, where ε is ∼0.2−0.3 eV, versus hybrids, where ε is ∼0.01−0.2 eV. As expected, more energy is required for the spin-flip of a closed-shell state compared to 17717



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In the following text, we discuss an additional analysis of the model D2, relying on the results obtained using the TPSSh xc functional only. The calculated first and second electron affinities, EA1 = 3.62 eV and EA2 = 0.58 eV, suggest D2 to be a highly reactive species with a high preference to attach one electron. The unstable nature of the molecule originates from its doublet monomer subunits. First and second ionization potentials were found to be IP1 = 6.65 eV and IP2 = 9.28 eV, implying a high stability of D2 with respect to electron detachment. For comparison, in M2, EA = 2.99 eV and IP = 7.36 eV. Similar trends are expected for the remaining models, D1 and D3. The natural atomic configurations of the interacting AuI atoms change from 6s(0.82)5d(9.72)6p(0.20)7p(0.01) in M2 to 6s(0.76)5d(9.65)6p(0.41)6d(0.02)7p(0.01) in D2. The interaction formally induces a charge transfer of ∼0.2e to the 6p channels of the atoms, coming mainly from their 6s/5d orbitals. Qualitatively similar bond properties were found in the weak/noncovalent metallophilic Pt−Pt interactions in the complex revealing antiferromagnetic ground state,88 providing additional support to metallophilicity in our models. An interesting finding in D2 is that with the removal of the terminal SCH3 acceptor group (not from the staple motif) from each monomer and subtraction of the two electrons from the system to maintain a formal doublet nature of the monomer counterparts, the final molecule (Au4(SCH3)2+)2 reveals a closed-shell singlet ground state. The presence of an SCH3 group is essential, in this respect, to promote a BS state. A more detailed investigation of the spin-symmetry breaking with respect to the ligand coverage and charge in small thiolated AuNPs will be addressed elsewhere. Finally, we tested the effect of additional steric hindrance on the bonding in D2 by substituting all terminal SCH3 ligand groups with various branched groups based on alkane-thiols, including ethanethiol, 1-butanethiol, 2-methyl-1-propanethiol, and 2-methyl-2-propanethiol. The qualitative picture, including the antiferromagnetic ground state in these systems, remained unchanged. The overall results lead us to theorize that if short alkanethiol-capped AuNPs with pronounced staple motifs on the surface (e.g., S−Au−S) come into close proximity (e.g., by mechanical means, overcoming steric repulsions), binding of surface-layer atoms may take place and possibly give rise to configurations where Au atoms in staple motifs, formally belonging to different AuNPs, interact directly via the aurophilic interactions, as in the studied models. The situation is schematically illustrated in Figure 2 (bottom) and compared to the standard situation when AuNPs are covered by longer ligand chains (top). If the AuNPs would carry a nonzero spin momentum,12,13 spins may possibly couple through weakly interacting AuI atoms and form a magnetic assembly, as the present model suggests, assuming that closure of the electronic shells of the individual AuNPs is avoided (e.g., by steric encapsulation of the whole dimers).

Table 5. Magnetic Orbitals (MGO) of the Dimer D3 and HOMO of the Corresponding Monomer M3, Obtained with Different DFT xc Functionalsa

a

MGOs overlap weakly and well resemble the HOMO of the monomer. The Au−Au bonding in the middle does not strongly affect the fingerprint of the spins located on monomers upon binding. In D3, B3LYP converged to a different structure with respect to the remaining xc functionals.

(i) The models are diradicals. Strong spin polarization, measuring a multiconfigurational character in DFT,86 suggests a complicated interplay of correlation effects and incomlete description of the near-degeneracies. The spins localized on monomer subunits (cf. MGOs in Tables 3, 4 , and 5) interact so that the systems prefer an open-shell singlet ground state (except for the nonhybrid xc functionals in D2). Magnetic orbitals resemble the singly occupied HOMOs of the original monomers (i.e., the identity of spins is not strongly affected by the binding). A spin coupling pathway is found to lie along the Au−Au bond of facing S−Au−S edges (cf. MGOs). (ii) The lengths of the central Au−Au bond connecting the monomers, in all studied models and functionals, fall well to the interval reported for the aurophilically interacting Au atoms.52 Aurophilicity here is also supported by the NBO analysis, revealing no direct bonding orbitals. The systems rather reveal d lone pair orbitals facing each other. The noncovalent metallophilic51,52,87 bonding efficiently stabilizes dimers with respect to corresponding isolated monomers. According to Schmidbaur and Schier,52 the interaction may be classified as unsupported aurophilic. (iii) The key features of the dimer molecules, allowing a weak coupling of the sideways spins required for magnetism, were found to be a doublet nature of the monomers and the weak AuI bonding of the gold atoms in the middle of the two facing S−Au−S edges. In D2, we have explicitly verified that if the S−Au−S edge of M2 interacts with the S−Au−Au−S side of the other monomer, reordering of Au atoms takes place, and the BS state is immediately lost. From the structural point of view, existence of a BS state in the models studied may be attributed to the facing S−Au−S motifs, providing aurophilic AuI−AuI contact.

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CONCLUSIONS In summary, interaction of spins in the model dimerlike thiolated gold-based molecules with a spin-symmetry broken antiferromagnetic ground state has been studied within the BS DFT. Analysis of the results obtained from various xc functionals proves that AuI−AuI bonding in the studied model junctions stabilizes dimer structures with respect to corresponding 17718



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Figure 2. Schemes of thiolated AuNPs with staple motifs on the surface and sulfur-attached alkyl chains (green). Typical AuNPs with long ligand chains (top), and AuNPs with short ligand chains interacting through aurophilic bonding (bottom, blue).

monomers and acts as a channel transmitting a weak spin−spin interaction. At the same time, the magnetic orbitals well resemble HOMO orbitals of the original monomers. A diradical nature of the model molecules is therefore preserved. From the structural point of view, the magnetism may be attributed to the close contact of AuI atoms belonging to the facing S−Au−S edges of the monomer subunits, allowing the sideways spins to interact along the aurophilic bond pathway. The modeling provides insight that may serve in design of novel gold-based magnetic nanoscopic assemblies. A more rigorous treatment of the studied and related systems, too expensive for the conventional wave-function methods and coupled-cluster, will be addressed by techniques of density matrix renormalization group and/or quantum Monte Carlo.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors are grateful to Xingyu Gao from NUS Singapore for discussions, in part motivating the presented work. Financial support from APVV, Grant COQI APVV-0646-10, is acknowledged. Work at NTU was supported in part by a MOE AcRF Tier-1 Grant (M52070060) and an A*STAR SERC Grant (M47070020).

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Magnetism in Thiolated Gold Model Junctions - The Journal of

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