Density functional theory investigation of benzenethiol adsorption on Au(111)

We have studied the adsorption of benzenethiol molecules on the Au(111) surface by using first principles total energy calculations. A single thiolate molecule is adsorbed at the bridge site slightly shifted toward the fcc-hollow site, and is tilted by 61 degrees from the surface normal. As for the self-assembled monolayer (SAM) structures, the (2 square root of 3 x square root of 3)R30 degrees herringbone structure is stabilized against the (square root 3 x square root 3)R30 degrees structure by large steric relaxation. In the most stable (2 square root 3 x square root 3)R30 degrees SAM structure, the molecule is adsorbed at the bridge site with the tilting angle of 21 degrees, which is much smaller compared with the single molecule adsorption. The van der Waals interaction plays an important role in forming the SAM structure. The adsorption of benzenethiolates induces the repulsive interaction between surface Au atoms, which facilitates the formation of surface Au vacancy.     

Molecular dynamics investigation into the effect of temperature on the structure and properties of methyl methacrylate thin films on a Au(111) surface

An atomistic modeling approach is performed to investigate the effect of temperature on the structural properties of the MMA (methyl methacrylate) thin film and a Au(111) surface. The density profile and orientation of the MMA molecule in the thin film have been analyzed. We found that there is a significant effect on the density profile and orientation of the MMA molecule in the region near the interface between the thin film and the Au substrate. As the temperature increases, the density clearly decreases in this region; in addition, the orientation of the MMA molecule also changes. Next, we calculated and examined the relationships between the stress, surface tension, and free energy and the density profile. Finally, we analyzed the influence of temperature on the interaction strength between the MMA molecules and between the MMA molecules and the Au(111) surface. We found that the influence of the interaction strength is more significant between MMA molecules than between MMA molecules and the Au(111) surface.     

The dynamics of noble metal atom penetration through methoxy-terminated alkanethiolate monolayers

We have studied the interaction of vapor-deposited Al, Cu, Ag, and Au atoms on a methoxy-terminated self-assembled monolayer (SAM) of HS(CH(2))(16)OCH(3) on polycrystalline Au[111]. Time-of-flight secondary ion mass spectrometry, infrared reflection spectroscopy, and X-ray photoelectron spectroscopy measurements at increasing coverages of metal show that for Cu and Ag deposition at all coverages the metal atoms continuously partition into competitive pathways: penetration through the SAM to the S/substrate interface and solvation-like interaction with the -OCH(3) terminal groups. Deposited Au atoms, however, undergo only continuous penetration, even at high coverages, leaving the SAM "floating" on the Au surface. These results contrast with earlier investigations of Al deposition on a methyl-terminated SAM where metal atom penetration to the Au/S interface ceases abruptly after a approximately 1:1 Al/Au layer has been attained. These observations are interpreted in terms of a thermally activated penetration mechanism involving dynamic formation of diffusion channels in the SAM via hopping of alkanethiolate-metal (RSM-) moieties across the surface. Using supporting quantum chemical calculations, we rationalized the results in terms of the relative heights of the hopping barriers, RSAl > RSAg, RSCu > RSAu, and the magnitudes of the metal-OCH(3) solvation energies.     

Density Functional Theory Study of Pd Aggregation on a Pyridine-Terminated Self-Assembled Monolayer

By using density functional theory calculations, the initial steps towards Pd metal cluster formation on a pyridine-terminated self-assembled monolayer (SAM) consisting of 3-(4-(pyridine-4-yl)phenyl)propane-1-thiol on an Au(1 1 1) surface are investigated. Theoretical modelling allows the investigation of structural details of the SAM surface and the metal/SAM interface at the atomic level, which is essential for elucidating the nature of Pd–SAM and Pd–Pd interactions at the liquid/solid interface and gaining insight into the mechanism of metal nucleation in the initial stage of electrodeposition. The structural flexibility of SAM molecules was studied first and the most stable conformation was identified, planar molecules in a herringbone packing, as the model for Pd adsorption. Two binding sites are found for Pd atoms on the pyridine end group of the SAM. The strong interaction between Pd atoms and pyridines illustrates the importance of SAM functionalisation in the metal nucleation process. Consistent with an energetic driving force of approximately −0.3 eV per Pd atom towards Pd aggregation suggested by static calculations, a spontaneous Pd dimerisation is observed in ab initio molecular dynamic studies of the system. Nudged elastic band calculations suggest a potential route with a low energy barrier of 0.10 eV for the Pd atom diffusion and then dimerisation on top of the SAM layer.     

Reaction of 5-40 eV ions with self-assembled monolayers

The reaction of 5-40 eV O(+) and Ne(+) ions with alkanethiolate and semifluorinated alkanethiolate self-assembled monolayers (SAMs) is studied under ultrahigh vacuum (UHV) conditions. Whereas Ne(+) simply sputters fragments from the surface, O(+) can also abstract surface atoms and break C-C bonds in both the hydrocarbon and fluorocarbon SAM chains. Isotopic labeling experiments reveal that O(+) initially abstracts hydrogen atoms from the outermost two carbon atoms on an alkanethiolate SAM chain. However, the position of the isotopic label quickly becomes scrambled along the chain as the SAM is damaged through continuous ion bombardment. Scanning tunneling microscopy (STM) monitors changes in the SAM conformational structure at various stages during 5 eV ion bombardment. STM images indicate that O(+) reacts less efficiently with dodecanethiolate molecules packed internally within a structural domain than it does with molecules adsorbed at domain boundaries or near defect sites. STM images recorded after Ne(+) bombardment suggest that Ne(+) attacks the SAM exclusively near the domain boundaries. Taken collectively, these experiments advance our understanding of the degradation pathways suffered by polymeric satellite materials in the low-earth orbit (LEO) space environment.     

Pinning mononuclear Au on the surface of titania

We have deposited Au atoms on the surface of titania without sintering or surface damage. Mass-selected Au+ atoms were deposited from the gas phase at room temperature with kinetic energies from <3 to 190+/-3.5 eV. Scanning tunneling microscopy reveals island formation following deposition at <3 eV, while mainly atomic features are observed for energies between approximately 35 and approximately 190 eV. A mixture of islands and atomic features is observed at a landing energy of 20+/-3.5 eV, suggesting a critical energy above which pinning occurs. Cluster size is also probed as a function of coverage in the deposition of Au+ with 100 eV of energy, revealing that sintering begins at a coverage of only 0.06 ML. These observations suggest a mechanism in which high-energy collision leads to the annealing of any impact-created surface damage and the pinning of Au atoms to the surface. We provide a new method of preparing isolated Au atoms on an oxide surface, which can serve as a platform for catalytic studies.     

Efficient transport of gold atoms with a scanning tunneling microscopy tip and a linker molecule

A thiophene-containing molecule attached to a scanning tunneling microscopy (STM) tip is used to transport gold atoms on a Au(111) surface. The molecule contains eight thiophene rings and therefore has sulfur atoms that are known to bind to gold atoms. Using a gold-coated tip, the molecules previously deposited on the surface bind to the lower-coordination gold atoms of the tip. When that tip is used to scan the surface, the still free thiophene rings (not all of the sulfur atoms bind to the tip) can attach to gold atoms from the surface and drag them along the scanning direction, depositing them either at the position where the tip changes its scanning direction or where the tip encounters an "up step", whichever event occurs first.     

Bond insertion, complexation, and penetration pathways of vapor-deposited aluminum atoms with HO- and CH(3)O-terminated organic monolayers

The interaction of vapor-deposited Al atoms with self-assembled monolayers (SAMs) of HS-(CH(2))(16)-X (X = -OH and -OCH(3)) chemisorbed at polycrystalline Au[111] surfaces was studied using time-of-flight secondary-ion mass spectrometry, X-ray photoelectron spectroscopy, and infrared reflectance spectroscopy. Whereas quantum chemical theory calculations show that Al insertion into the C-C, C-H, C-O, and O-H bonds is favorable energetically, it is observed that deposited Al inserts only with the OH SAM to form an -O-Al-H product. This reaction appears to cease prior to complete -OH consumption, and is followed by formation of a few overlayers of a nonmetallic type of phase and finally deposition of a metallic film. In contrast, for the OCH(3) SAM, the deposited Al atoms partition along two parallel paths: nucleation and growth of an overlayer metal film, and penetration through the OCH(3) SAM to the monolayer/Au interface region. By considering a previous observation that a CH(3) terminal group favors penetration as the dominant initial process, and using theory calculations of Al-molecule interaction energies, we suggest that the competition between the penetration and overlayer film nucleation channels is regulated by small differences in the Al-SAM terminal group interaction energies. These results demonstrate the highly subtle effects of surface structure and composition on the nucleation and growth of metal films on organic surfaces and point to a new perspective on organometallic and metal-solvent interactions.     

Solvation of Au+ versus Au0 in aqueous solution: electronic structure governs solvation shell patterns

The solvation behavior of Au(+) and Au(0) in liquid water under ambient conditions has been studied using ab initio molecular dynamics. The Au(+) aqua ion forms a rigid and well-defined quasi-linear structure in the sense of ligand field theory, where two water molecules are tightly bound to the gold cation through oxygen atoms ("cationic solvation"). Yet, transient charge accumulation in the direction perpendicular to the O-Au(+)-O linear core structure leads occasionally to the formation of a short Au(+)-H contact within the distance range of the first solvation shell, which is typical of "anionic solvation". Upon adding an electron to Au(+), the resulting solvation pattern of Au(0)(aq) has nothing in common with that of Au(+)(aq). Quite surprisingly we discover that the first solvation shell of Au(0)(aq) consists of a single water molecule and features both "anionic" and "cationic" solvation patterns depending on fluctuation and polarization effects. Thus, charging/decharging of metals dissolved in water, M(0)? M(+) + e(-), as occurring e.g. during elementary electrochemical steps, is expected to change dramatically their solvation behavior in the sense of re-solvation processes.     

A spectroscopic study of self-assembled monolayer of porphyrin-functionalized oligo(phenyleneethynylene)s on gold: the influence of the anchor moiety

Porphyrin-functionalized oligo(phenyleneethynylene)s (OPE) are promising molecules for molecular electronics applications. Three such molecules () with the common structure P-OPE-AG (P and AG are a porphyrin and anchor group, respectively) and different anchor groups, viz. an acetyl protected thiol, -S-COCH(3) (), an acetyl protected thiol with methylene linker, -CH(2)-S-COCH(3) (), and a trimethylsilylethynyl group, -C[triple bond, length as m-dash]C-Si(CH(3))(3) () have been synthesized and the corresponding self-assembled monolayers (SAMs) on Au(111) substrates have been prepared. The integrity and structural properties of these films were studied by X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy. The results suggest that the films formed from have a high orientational order with an almost upright orientation and dense packing of the molecular constituents, i.e. represent a high quality SAM. In contrast, molecule formed disordered molecular layers on Au, even though the molecule-surface bonding (thiolate) is the same as in the case of molecule . This suggests that the methylene linker in molecule has a strong impact on the quality of the resulting film, so that a well-ordered SAM cannot be formed. The silane system, , is also able to bind to the gold surface but the resulting SAM has a poor quality, being significantly disordered and/or comprised of strongly inclined molecules. The above results suggest that the nature of the anchor group along with a possible linker is an important parameter which, to a high extent, predetermines the entire quality of OPE-based molecular layers.     

Electronic structure and luminescence of [AuS2PPh(OCH2CHCH2)]2 complex

The complex [AuS₂PPh(OCH₂CHCH₂)]₂ (1) presents an Au(I)–Au(I) intramolecular and intermolecular bonding with luminescence properties. To understand the nature of these features, fully optimized geometries were obtained by three computational methods, DFT/B3LYP, MPW1B95 and MP2. An Au(I)–Au(I) intramolecular bond was found in the ground state, at the three levels of theory, exhibiting an aurophilic interaction between the two gold atoms. Two molecules of the complex were optimized using DFT/B3LYP, in order to analyze the intermolecular interaction between them. The resulting intermolecular bonding distance between the two adjacent gold atoms on each molecule is 3.16 Å, indicating a strong aurophilic attraction. Time dependent calculations indicate that the first excited state with nonzero oscillator strength is a singlet, with an excitation energy equal to 3.16 eV. This should correspond to the absorption band seen experimentally at 3.10 eV. The lowest energy emission of (1) was obtained at 2.73 eV, which corresponds to the emission peak resulting from phosphorescence and located at 2.53 eV. This transition comes from an excited electron on the p orbitals of the ligands that is transferred to the d orbitals of the gold atoms on the HOMO. This interaction may be attributed to Ligand to Ligand–Metal Charge Transfer (LL–MCT).     

Evolution of the interface and metal film morphology in the vapor deposition of Ti on hexadecanethiolate hydrocarbon monolayers on Au

The combination of in situ X-ray photoelectron spectroscopy, infrared reflection spectroscopy, atomic force microscopy, and time-of-flight secondary ion mass spectrometry are used to probe the nature of the evolving interface chemistry and metal morphology arising from Ti vapor deposition onto the surface of a CH(3)(CH(2))(15)S/Au{111} self-assembled monolayer (SAM) at ambient temperature. The results show that for a deposition rate of approximately 0.15 Ti atom.nm(-2).s(-1) a highly nonuniform Ti overlayer is produced via a process in which a large fraction of impinging Ti atoms do not stick to the bare SAM surface. The adsorbed atoms form isolated Ti clusters and react with CH(3) groups to form carbide products at the cluster-SAM interfaces. Further growth of Ti clusters appears to be concentrated at these scattered reaction centers. The SAM molecules in the local vicinity are subsequently degraded to inorganic products, progressing deeper into the monolayer as the deposition proceeds to give an inorganic/organic nanocomposite. A continuous overlayer does not form until metal coverage approaches approximately 50 Ti atoms per SAM molecule. These data indicate that for applications such as molecular device contacts the use of Ti may be highly problematic, suffering from both a highly nonuniform contact area and the presence of extensive inorganic products such as nonstoichiometric carbides and hydrides.     

Interaction of low-energy ions and atoms of light elements with a fluorinated carbon molecular lattice

The mechanism of interaction of low-energy atoms and ions of light elements (H, H+, He, Li, the kinetic energy of the particles 2-40 eV) with C6H6, C6F12, C60, and C60F48 molecules was studied by ab initio MD simulations and quantum-chemical calculations. It was shown that starting from 6 A from the carbon skeleton for the "C6H6 + proton" and "C60 + proton" systems, the electronic charge transfer from the aromatic molecule to H+ occurs with a probability close to 1. The process transforms the H+ to a hydrogen atom and the neutral C6H6 and C60 molecules to cation radicals. The mechanism of interaction of low-energy protons with C6F12 and C60F48 molecules has a substantially different character and can be considered qualitatively as the interaction between a neutral molecule and a point charge. The Coulomb perturbation of the system arising from the interaction of the uncompensated proton charge with the Mulliken charges of fluorine atoms results in an inversion of the energies of the electronic states localized on the proton and on the C6F12 and C60F48 molecules and makes the electronic charge transfer energetically unfavorable. On the different levels of theory, the barriers of the proton penetration for the C6F12 and C60F48 molecules are from two to four times lower than those for the corresponding parent systems (C6H6 and C60). The penetration barriers of the He atom and Li+ ion depend mainly on the effective radii of the bombarding particles. The theoretical penetration and escaped barriers for the "Li+ + C60" process qualitatively explain the experimental conditions of synthesis of the Li@C60 complex.     

Enhanced adsorption energy of Au1 and O2 on the stoichiometric TiO2(110) surface by coadsorption with other molecules

During heterogeneous catalysis the surface is simultaneously covered by several adsorbed molecules. The manner in which the presence of one kind of molecule affects the adsorption of a molecule of another kind has been of interest for a long time. In most cases the presence of one adsorbate does not change substantially the binding energy of another adsorbate. The calculations presented here show that the stoichiometric rutile TiO(2)(110) surface, on which one of the compounds -OH, Au(3), Au(5), Au(7), Na, K, or Cs or two different gold strips was preadsorbed, behaves differently: the binding energy of Au(1) or O(2) to such a surface is much stronger than the binding to the clean stoichiometric TiO(2)(110) surface. Moreover, the binding energy of Au(1) or O(2) and the amount of charge they take from the surface when they adsorb are the same, regardless of which of the above species is preadsorbed. The preadsorbed species donate electrons to the conduction band of the oxide, and these electrons are used by Au(1) or O(2) to make stronger bonds with the surface. This suggests that adding an electron to the conduction band of the clean stoichiometric TiO(2)(110) slab used in the calculation will affect similarly the adsorption energy of Au(1) or O(2). Our calculations show that it does. We have also studied how the preadsorption of Au(4) or Au(6) affects the binding of Au(1) or O(2) to the surface. These two gold clusters do not donate electrons to the surface when they bind to it and therefore should not influence substantially the binding energy of Au(1) or O(2) to the surface. However, adsorbing O(2) or Au(1) on the surface forces the clusters to change their structure into that of isomers that donate charge to the oxide. This charge is used by Au(1) or O(2) to bind to the surface and the energy of this bond exceeds the isomerization energy. As a result the surface with the isomerized cluster is the lowest energy state of the system. We believe that these results can be generalized as follows. The molecules that we coadsorbed with Au(1) or O(2) donate electrons to the oxide and are Lewis bases. By giving the surface high energy electrons, they turn it into a Lewis base and this increases its ability to bind strong Lewis acids such as Au(1) and O(2). We speculate that this kind of interaction is general and may be observed for other oxides and for other coadsorbed Lewis base-Lewis acid pairs.     

Electrochemically controlled assembly and logic gates operations of gold nanoparticle arrays

The reversible assembly of β-cyclodextrin-functionalized gold NPs (β-CD Au NPs) is studied on mixed self-assembled monolayer (SAM), formed by coadsorption of redox-active ferrocenylalkylthiols and n-alkanethiols on gold surfaces. The surface coverage and spatial distribution of the β-CD Au NPs monolayer on the gold substrate are tuned by the self-assembled monolayer composition. The binding and release of β-CD Au NPs to and from the SAMs modified surface are followed by surface plasmon resonance (SPR) spectroscopy. The redox state of the tethered ferrocene in binary SAMs controls the formation of the supramolecular interaction between ferrocene moieties and β-CD-capped Au NPs. As a result, the potential-induced uptake and release of β-CD Au NPs to and from the surface is accomplished. The competitive binding of β-CD Au NPs with guest molecules in solution shifted the equilibrium of the complexation-decomplexation process involving the supramolecular interaction with the Fc-functionalized surface. The dual controlled assembly of β-CD Au NPs on the surface enabled to use two stimuli as inputs for logic gate activation; the coupling between the localized surface plasmon, associated with the Au NP, and the surface plasmon wave, associated with the thin metal surface, is implemented as readout signal for "AND" logic gate operations.     

Electronic and structural properties of oligophenylene ethynylenes on Au(111) surfaces

The interaction of oligophenylene ethynylene (OPE) on the (111) surface of a gold slab resembling a self-assembled monolayer (SAM) is investigated using ab initio density functional theory calculations. The authors performed a full optimization including all atoms in the OPE and in the slab to better understand OPE adsorption on the surface. It is found that OPE has two energetically favorable adsorption sites on the Au surface with relatively different molecular geometries: the nontop site adsorption greatly modifies the (111) surface structure; however, the extensive electron interactions enable a delocalized electron density distribution, implying an improved conductivity between OPE and Au, and the top site which is 0.9 eV higher in energy than the nontop and features weaker Au-S bonds. Interestingly the on top configuration shows a strong spin imbalance along the molecule and the nontop shows a small spin imbalance on the surface. This feature is of strong interest for the development of resonators for the detection of chemical and biological agents. They have also calculated the frequency spectrum of these SAMs, which yield deformations in the gold surface yielding peak frequency shifts specific to each absorption site.     

Mechanistic study of proton transfer and HD exchange in ice films at low temperatures (100-140 K)

We have examined the elementary molecular processes responsible for proton transfer and HD exchange in thin ice films for the temperature range of 100-140 K. The ice films are made to have a structure of a bottom D(2)O layer and an upper H(2)O layer, with excess protons generated from HCl ionization trapped at the D(2)OH(2)O interface. The transport behavior of excess protons from the interfacial layer to the ice film surface and the progress of the HD exchange reaction in water molecules are examined with the techniques of low energy sputtering and Cs(+) reactive ion scattering. Three major processes are identified: the proton hopping relay, the hop-and-turn process, and molecular diffusion. The proton hopping relay can occur even at low temperatures (<120 K), and it transports a specific portion of embedded protons to the surface. The hop-and-turn mechanism, which involves the coupling of proton hopping and molecule reorientation, increases the proton transfer rate and causes the HD exchange of water molecules. The hop-and-turn mechanism is activated at temperatures above 125 K in the surface region. Diffusional mixing of H(2)O and D(2)O molecules additionally contributes to the HD exchange reaction at temperatures above 130 K. The hop-and-turn and molecular diffusion processes are activated at higher temperatures in the deeper region of ice films. The relative speeds of these processes are in the following order: hopping relay>hop and turn>molecule diffusion.     

The "staple" motif: a key to stability of thiolate-protected gold nanoclusters

Recently obtained single-crystal structure of a thiolate-protected gold cluster shows that all thiolate groups form "staple" motifs on the cluster surface. To find out the driving force for such a formation, we use first-principles density functional theory simulations to model formation of "staple" motifs on an Au38 cluster from zero to full coverage. By geometry optimization, molecular dynamics, and simulated annealing, we show that formation of "staples" is strongly preferred on a cluster surface and helps stabilize the cluster by pinning the surface Au atoms and increasing the HOMO-LUMO gap. We devise a method to generate initial structural models for thiolate-protected gold clusters by adding "staples" to the cluster surface. Using this method, we obtain a staple-covered, low-energy structure for Au38(SCH3)24, a much studied cluster whose structure is not yet known. Optical band-edge energy computed from time-dependent DFT for our Au38(SCH3)24 structure shows good agreement with experiment.     

Gold cluster formation on a fullerene surface

The growth of Au clusters on a fullerene thin film was investigated by in situ photoelectron spectroscopy in the ultraviolet (UPS) and x-ray (XPS) regime. Due to its highly corrugated surface fullerene films provide a wide range of bonding sites which could be exploited as molecular templates and serve to create a cluster superstructure. To gain insight into the fullerene-Au interaction two types of experiments were performed: (i) the deposition of Au on a fullerene surface, and (ii) the deposition of fullerenes on a Au surface. In both experiments an island growth mode is observed. The deposition of submonolayer amounts of C60 onto a gold film showed that the main interaction of the two species is due to chemisorption of the first C60 monolayer. In addition a constant band bending in the fullerene film is detected, but the UPS valence-band spectra show that there is no charge transfer from the Au to the C60 lowest unoccupied molecular orbital. In the reverse experiment, the cluster growth of Au on the corrugated C60 surface, the analysis of the Au core level does not reveal a specific bonding or nucleation site for Au atoms and clusters. This is in contrast to observations with Si clusters, which prefer to reside in the troughs between the fullerene molecules. The Au clusters grow continually from a size of about 55 atoms for the early stages of growth up to 150 atoms for the deposition of a nominal coverage of 1.5 nm. These data are derived from an analysis of the d-band splitting and the Au 4f core-level shift due to delayed photohole relaxation. The thermal stability of the Au-clusters-covered fullerene film was investigated by annealing in situ up to temperatures of 650 degrees C. For temperatures up to 450 degrees C a continuous growth of the clusters is detected, which is accompanied by a slight drop in Au concentration in the range of XPS for annealing temperatures higher than 350 degrees C. This may be due to a ripening of the clusters. The presence of Au apparently delays fullerene sublimation. The film shows a very good thermal stability and even after annealing at 650 degrees C there is still a fullerene film detectable in the photoelectron spectroscopy spectra.     

How cationic gold clusters respond to a single sulfur atom

Results describing the interaction of a single sulfur atom with cationic gold clusters (Au(n) (+), n=1-8) using density functional theory are described. Stability of these clusters is studied through their binding energies, second order differences in the total energies, fragmentation behavior, and atom attachment energies. The lowest energy structures for these clusters appear to be three dimensional right from n=3. In most cases the sulfur atom in the structure of Au(n)S(+) is observed to displace the gold atom siting at the peripheral site of the Au(n) (+) cluster. The dissociation channels of Au(n)S(+) clusters follow the same trend as Au(n) (+) cluster, based on the even/odd number of gold atoms in the cluster, with the exception of Au(3)S(+). This cluster dissociates into Au and Au(2)S(+), signifying the relative stability of Au(2)S(+) cluster regardless of having an odd number of valence electrons. Clusters with an even number of gold atoms dissociate into Au and Au(n-1)(S)(+) and clusters with an odd number of gold atoms dissociate into Au(2) and Au(n-2)(S)(+) clusters. An empirical relation is found between the conduction molecular orbital and the number of atoms in the Au(n)S(+) cluster.