Structure and energetics of small gold nanoclusters and their positive ions

We performed density functional theory calculations at the PW91PW91/LANL2DZ, PW91PW91/Stuttgart 1997, PW91PW91/CRENBL, B3LYP/LANL2DZ, and SVWN5/LANL2DZ levels of theory to attain the minimum-energy structures of neutral and cationic gold clusters of up to nine gold atoms. We locate the 2D-to-3D (two-dimensional to three-dimensional) transition in cationic clusters as occurring between Au(8) (+) and Au(9) (+). We also demonstrate that we can correlate the 2D-to-3D transition in cationic clusters with a linear extrapolation of the energy differences of the lowest-lying 2D and 3D structures of cluster sizes below the transition. We then use the same approach to predict that the 2D-to-3D transition occurs in neutral clusters at Au(11); this is confirmed by locating 3D Au(11) structures that are lower in energy than the best 2D structures reported to date. We examine the effects of choice of basis sets and exchange-correlation functionals on the relative stabilities and other properties of the calculated structures. Finally we find that there is good agreement between calculated and experimental data for clusters with up to six constituent atoms. For clusters with more than seven atoms, there are significant differences observed between the calculated and experimental properties using SVWN5/LANL2DZ, but there is still good agreement for the other levels of theory used.     

Low-symmetry structures of Au32Z (Z = +1, 0, -1) clusters

In this work, we have explored new stable structures of the Au32Z (Z = +1, 0, -1) clusters. Theoretical calculations using density functional theory within the generalized-gradient approximation were performed. Our results show that, in the anion state (Au32-), low-symmetry (disordered) structures are preferred over the caged fullerene-like isomer. In addition, the cationic cluster (Au32+) also exhibits a disordered low-symmetry structure as its lowest energy configuration, but it is much closer in energy to the fullerene-like isomer. These results, obtained at T = 0 K, indicate that disordered structures for the Au32- and Au32+ clusters may be detected not only at room temperature, as was experimentally verified for the Au32- one, but also at much lower temperatures.     

Theoretical study of Al(n) and Al(n)O (n = 2-10) clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.     

Adsorption of molecular hydrogen and hydrogen sulfide on Au clusters

The authors present theoretical results describing the adsorption of H2 and H2S molecules on small neutral and cationic gold clusters (Au(n)((0/+1)), n=1-8) using density functional theory with the generalized gradient approximation. Lowest energy structures of the gold clusters along with their isomers are considered in the optimization process for molecular adsorption. The adsorption energies of H2S molecule on the cationic clusters are generally greater than those on the corresponding neutral clusters. These are also greater than the H2 adsorption energies on the corresponding cationic and neutral clusters. The adsorption energies for cationic clusters decrease with increasing cluster size. This fact is reflected in the elongations of the Au-S and Au-H bonds indicating weak adsorption as the cluster grows. In most cases, the geometry of the lowest energy gold cluster remains planar even after the adsorption. In addition, the adsorbed molecule gets adjusted such that its center of mass lies on the plane of the gold cluster. Study of the orbital charge density of the gold adsorbed H2S molecule reveals that conduction is possible through molecular orbitals other than the lowest unoccupied molecular orbital level. The dissociation of the cationic Au(n)SH2+ cluster into Au(n)S+ and H2 is preferred over the dissociation into Au(m)SH2+ and Au(n-m), where n=2-8 and m=1-(n-1). H2S adsorbed clusters with odd number of gold atoms are more stable than neighboring even n clusters.     

Low-energy isomer identification, structural evolution, and magnetic properties in manganese-doped gold clusters MnAu(n) (n = 1-16)

The size-dependent electronic, structural, and magnetic properties of Mn-doped gold clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. A number of new isomers are obtained for neutral MnAu(n) (n = 1-16) clusters to probe the structural evolution. The two-dimensional (2D) to three-dimensional (3D) transition occurs in the size range n = 7-10 with manifest structure competitions. From size n = 13 to n = 16, the MnAu(n) prefers a gold cage structure with Mn atom locating at the center. The relative stabilities of the ground-state MnAu(n) clusters show a pronounced odd-even oscillation with the number of Au atoms. The magnetic moments of MnAu(n) clusters vary from 3 μ(B) to 6 μ(B) with the different cluster size, suggesting that nonmagnetic Au(n) clusters can serve as a flexible host to tailor the dopant's magnetism, which has potential applications in new nanomaterials with tunable magnetic properties.     

Trends in structural, electronic and energetic properties of bimetallic vanadium-gold clusters Au(n)V with n = 1-14

A systematic quantum chemical investigation on the electronic, geometric and energetic properties of Au(n)V clusters with n = 1-14 in both neutral and anionic states is performed using BP86/cc-pVTZ-PP calculations. Most clusters having an even number of electrons prefer a high spin state. For odd-electron systems, a quartet state is consistently favoured as the ground state up to Au(8)V. The larger sized Au(10)V, Au(12)V and Au(14)V prefer a doublet state. The clusters prefer 2D geometries up to Au(8)V involving a weak charge transfer. The larger systems bear 3D conformations with a more effective electron transfer from Au to V. The lowest-energy structure of a size Au(n)V is built upon the most stable form of Au(n-1)V. During the growth, V is endohedrally doped in order to maximize its coordination numbers and augment the charge transfer. Energetic properties, including the binding energies, embedding energies and second-order energy differences, show that the presence of a V atom enhances considerably the thermodynamic stability of odd-numbered gold clusters but reduces that of even-numbered systems. The atomic shape has an apparently more important effect on the clusters stability than the electronic structure. Especially, if both atomic shape and electronic condition are satisfied, the resulting cluster becomes particularly stable such as the anion Au(12)V(-), which can thus combine with the cation Au(+) to form a superatomic molecule of the type [Au(12)V]Au. Numerous lower-lying electronic states of these clusters are very close in energy, in such a way that DFT computations cannot clearly establish their ground electronic states. Calculated results demonstrate the existence of structural isomers with comparable energy content for several species including Au(9)V, Au(10)V, Au(13)V and Au(14)V.     

Stability of small Pdn (n=1-7) clusters on the basis of structural and electronic properties: a density functional approach

Density functional calculations within the generalized gradient approximation have been used to investigate the lowest energy electronic and geometric structures of neutral, cationic, and anionic Pd(n) (n=1-7) clusters in the gas phase. In this study, we have examined three different spin multiplicities (M=1, 3, and 5) for different possible structural isomers of each neutral cluster. The calculated lowest energy structures of the neutral clusters are found to have multiplicities, M=1 for Pd(1), Pd(3), Pd(5), Pd(6), and Pd(7), while M=3 for Pd(2) and Pd(4). We have also determined the lowest energy states of cationic and anionic Pd(n) (n=1-7) clusters, formed from the most stable neutral clusters, in three spin multiplicities (M=2, 4, and 6). Bond length, coordination number, binding energy, fragmentation energy, bond dissociation energy, ionization potential, electron affinity, chemical hardness, and electric dipole moment of the optimized clusters are compared with experimental and other theoretical results available in the literature. Based on these criteria, we predict the four-atom palladium cluster to be a magic-number cluster.     

Binding of gold clusters with DNA base pairs: a density functional study of neutral and anionic GC-Aun and AT-Aun (n = 4, 8) complexes

Binding of clusters of gold atoms (Au) with the guanine-cytosine (GC) and adenine-thymine (AT) Watson-Crick DNA base pairs was studied using the density functional theory (DFT). Geometries of the neutral GC-Au(n) and AT-Au(n) and the corresponding anionic (GC-Au(n))(-1) and (AT-Au(n))(-1) (n = 4, 8) complexes were fully optimized in different electronic states, that is, singlet and triplet states for the neutral complexes and doublet and quartet states for the anionic complexes, using the B3LYP density functional method. The 6-31+G basis set was used for all atoms except gold. For gold atoms, the Los Alamos effective core potential (ECP) basis set LanL2DZ was employed. Vibrational frequency calculations were performed to ensure that the optimized structures corresponded to potential energy surface minima. The gold clusters around the neutral GC and AT base pairs have a T-shaped structure, which satisfactorily resemble those observed experimentally and in other theoretical studies. However, in anionic GC and AT base pairs, the gold clusters have extended zigzag and T-shaped structures. We found that guanine and adenine have high affinity for Au clusters, with their N3 and N7 sites being preferentially involved in binding with the same. The calculated adiabatic electron affinities (AEAs) of the GC-Au(n)complexes (n = 4, 8) were found to be much larger than those of the isolated base pairs.     

Far‐Infrared Spectra of Yttrium‐Doped Gold Clusters AunY (n=1–9)

The geometric, spectroscopic, and electronic properties of neutral yttrium‐doped gold clusters Au_nY (n=1–9) are studied by far‐infrared multiple photon dissociation (FIR‐MPD) spectroscopy and quantum chemical calculations. Comparison of the observed and calculated vibrational spectra allows the structures of the isomers present in the molecular beam to be determined. Most of the isomers for which the IR spectra agree best with experiment are calculated to be the energetically most stable ones. Attachment of xenon to the Au_nY cluster can cause changes in the IR spectra, which involve band shifts and band splittings. In some cases symmetry changes, as a result of the attachment of xenon atoms, were also observed. All the Au_nY clusters considered prefer a low spin state. In contrast to pure gold clusters, which exhibit exclusively planar lowest‐energy structures for small sizes, several of the studied species are three‐dimensional. This is particularly the case for Au₄Y and Au₉Y, while for some other sizes (n=5, 8) the 3D structures have an energy similar to that of their 2D counterparts. Several of the lowest‐energy structures are quasi‐2D, that is, slightly distorted from planar shapes. For all the studied species the Y atom prefers high coordination, which is different from other metal dopants in gold clusters.     

A photoelectron spectroscopic and computational study of sodium auride clusters, NanAun- (n = 1-3)

Negatively charged sodium auride clusters, NanAun- (n = 1-3), have been investigated experimentally using photoelectron spectroscopy and ab initio calculations. Well-resolved electronic transitions were observed in the photoelectron spectra of NanAun- (n = 1-3) at several photon energies. Very large band gaps were observed in the photoelectron spectra of the anion clusters, indicating that the corresponding neutral clusters are stable closed-shell species. Calculations show that the global minimum of Na2Au2- is a quasi-linear species with Cs symmetry. A planar isomer of D2h symmetry is found to be 0.137 eV higher in energy. The two lowest energy isomers of Na3Au3- consist of three-dimensional structures of Cs symmetry. The global minimum of Na3Au3- has a bent-flake structure lying 0.077 eV below a more compact structure. The global minima of the sodium auride clusters are confirmed by the good agreement between the calculated electron detachment energies of the anions and the measured photoelectron spectra. The global minima of neutral Na2Au2 and Na3Au3 are found to possess higher symmetries with a planar four-membered ring (D2h) and a six-membered ring (D3h) structure, respectively. The chemical bonding in the sodium auride clusters is found to be highly ionic with Au acting as the electron acceptor.     

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.     

Structural and electronic properties of Al12X+ (X=C, Si, Ge, Sn, and Pb) clusters

Using the first-principles method with the generalized gradient approximation, the authors have studied the structural and electronic properties of Al(12)X(+) (X=C, Si, Ge, Sn, and Pb) clusters in detail. The ground state of Al(12)C(+) is a low symmetry C(s) structure instead of an icosahedron. However, the Si, Ge, Sn, and Pb atom doped cationic clusters favor icosahedral structures. The ground states for Al(12)Si(+) and Al(12)Ge(+) are icosahedra, while the C(5nu) structures optimized from an icosahedron with a vertex capped by a tetravalent atom have the highest binding energy for Al(12)Sn(+) and Al(12)Pb(+) clusters. The I(h) structure and the C(5nu) structure are almost degenerate for Al(12)Ge(+), whose binding energy difference is only 0.03 eV. The electronic properties are altered much by removing an electron from the neutral cluster. The binding strength of a valence electron is enhanced, while the binding energy of the cluster is reduced much. Due to the open electronic shell, the band gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital are approximately 0.3 eV for the studied cationic clusters.     

Structures, rugged energetic landscapes, and nanothermodynamics of Al(n) (2 <or= n <or= 65) particles

Metal nanoparticles are important in several emerging technologies, but their size-selected thermodynamic properties are hard to obtain from experiment. We have characterized the energetic and structural properties of unsupported neutral Aln (2 相似文献   

Geometrical and electronic structures of Au(m)Ag(n) (2 < or = m + n < or = 8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.     

Gas phase synthesis, structure and unimolecular reactivity of silver iodide cluster cations, Ag(n)I(m)(+) (n = 2-5, 0 < m < n)

Multistage mass spectrometry (MS(n)) experiments reveal that gas phase silver iodide cluster cations, Ag(n)I(m)(+), are readily built up in a stepwise fashion via ion-molecule reactions between mass selected silver (Ag(3)(+) and Ag(5)(+)) or silver hydride (Ag(2)H(+) and Ag(4)H(+)) cluster cations and allyl iodide, in contrast to their reactions with methyl iodide, which solely result in ligation of the clusters. The stoichiometries of these clusters range from 1 < or = n < or = 5 and 1 < or = m < or = 4, indicating the formation of several new subvalent silver iodide clusters. Collision induced dissociation (CID) experiments were carried out on each of these clusters to shed some light on their possible structures. The products arising from CID of the Ag(n)I(m)(+) clusters are highly dependent on the stoichiometry of the cluster. Thus the odd-electron clusters Ag(4)I(2)(+) and Ag(5)I(+) fragment via loss of a silver atom. In contrast, the even-electron cluster ions all fragment via loss of AgI. In addition, Ag(2)I(2) loss is observed for the Ag(4)I(3)(+) and Ag(5)I(2)(+) clusters, while loss of Ag(3)I(3) occurs for the stoichiometric Ag(5)I(4)(+) cluster. DFT calculations were carried out on these Ag(n)I(m)(+) clusters as well as the neutrals associated with the ion-molecule and CID reactions. A range of different isomeric structures were calculated and their structures are described. A noteworthy aspect is that ligation of these silver clusters by I can have a profound effect on the geometry of the silver cluster. For example, D(3h) Ag(3)(+) becomes C(2v) Ag(3)I(+), which in turn becomes C(2h) Ag(3)I(2)(+). Finally, the DFT predicted thermochemistry supports the different types of reaction channels observed in the ion-molecule reactions and CID experiments.     

Dinuclear gold(I) dithiophosphonate complexes: synthesis,luminescent properties,and X-ray crystal structures of [AuS(2)PR(OR')](2) (R = Ph,R' = C(5)H(9); R = 4-C(6)H(4)OMe,R' = (1S,5R,2S)-(--)-menthyl; R = Fc,R' = (CH(2))(2)O(CH(2))(2)OMe)

2,4-Diaryl- and 2,4-diferrocenyl-1,3-dithiadiphosphetane disulfide dimers (RP(S)S)(2) (R = Ph (1a), 4-C(6)H(4)OMe (1b), FeC(10)H(9) (Fc) (1c)) react with a variety of alcohols, silanols, and trialkylsilyl alcohols to form new dithiophosphonic acids in a facile manner. Their corresponding salts react with chlorogold(I) complexes in THF to produce dinuclear gold(I) dithiophosphonate complexes of the type [AuS(2)PR(OR')](2) in satisfactory yield. The asymmetrical nature of the ligands allows for the gold complexes to form two isomers (cis and trans) as verified by solution (1)H and (31)P[(1)H] NMR studies. The X-ray crystal structures of [AuS(2)PR(OR')](2) (R = Ph, R' = C(5)H(9) (2); R = 4-C(6)H(4)OMe, R' = (1S,5R,2S)-(-)-menthyl (3); R = Fc, R' = (CH(2))(2)O(CH(2))(2)OMe (4)) have been determined. In all cases only the trans isomer is obtained, consistent with solid state (31)P NMR data obtained for the bulk powder of 3. Crystallographic data for 2 (213 K): orthorhombic, Ibam, a = 12.434(5) A, b = 19.029(9) A, c = 11.760(4) A, V = 2782(2) A(3), Z = 4. Data for 3 (293 K): monoclinic, P2(1), a = 7.288(2) A, b = 12.676(3) A, c = 21.826(4) A, beta = 92.04(3) degrees, V = 2015.0(7) A(3), Z = 2. Data for 4 (213 K): monoclinic, P2(1)/n, a = 11.8564(7) A, b = 22.483(1) A, c = 27.840(2) A, beta = 91.121(1) degrees, V = 7419.8(8) A(3), Z = 8. Moreover, 1a-c react with [Au(2)(dppm)Cl(2)] to form new heterobridged trithiophosphonate complexes of the type [Au(2)(dppm)(S(2)P(S)R)] (R = Fc (12)). The luminescence properties of several structurally characterized complexes have been investigated. Each of the title compounds luminesces at 77 K. The results indicate that the nature of Au...Au interactions in the solid state has a profound influence on the optical properties of these complexes.     

Structure evolution of gold cluster anions between the planar and cage structures by isoelectronic substitution: Au(n)- (n = 13-15) and MAu(n)- (n = 12-14; M = Ag, Cu)

The structural and electronic effects of isoelectronic substitution by Ag and Cu atoms on gold cluster anions in the size range between 13 and 15 atoms are studied using a combination of photoelectron spectroscopy and first-principles density functional calculations. The most stable structures of the doped clusters are compared with those of the undoped Au clusters in the same size range. The joint experimental and theoretical study reveals a new C(3v) symmetric isomer for Au(13)(-), which is present in the experiment, but has hitherto not been recognized. The global minima of Au(14)(-) and Au(15)(-) are resolved on the basis of comparison between experiment and newly computed photoelectron spectra that include spin-orbit effects. The coexistence of two isomers for Au(15)(-) is firmly established with convincing experimental evidence and theoretical calculations. The overall effect of the isoelectronic substitution is minor on the structures relative to those of the undoped clusters, except that the dopant atoms tend to lower the symmetries of the doped clusters.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Theoretical study of mixed silicon-lithium clusters Si(n)Li(p)(+) (n=1-6, p=1-2)

Theoretical study on the structures of neutral and singly charged Si(n)Li(p)((+)) (n=1-6, p=1-2) clusters have been carried out in the framework of the density functional theory (DFT) with the B3LYP functional. The structures of the neutral Si(n)Li(p) and cationic Si(n)Li(p)(+) clusters are found to keep the frame of the corresponding Si(n), Li species being adsorbed at the surface. The localization of the lithium cation is not the same one as that of the neutral atom. The Li(+) ion is preferentially located on a Si atom, while the Li atom is preferentially attached at a bridge site. A clear parallelism between the structures of Si(n)Na(p) and those of Si(n)Li(p) appears. The population analysis show that the electronic structure of Si(n)Li(p) can be described as Si(n)(p)(-)+pLi(+) for the small sizes considered. Vertical and adiabatic ionization potentials, adsorption energies, as well as electric dipole moments and static dipolar polarizabilities, are calculated for each considered isomer of neutral species.     

Gold as hydrogen. An experimental and theoretical study of the structures and bonding in disilicon gold clusters Si2Au(n)- and Si2Au(n) (n = 2 and 4) and comparisons to Si2H2 and Si2H4

In a previous communication, we showed that a single Au atom behaves like H in its bonding to Si in a series of Si-Au clusters, SiAu(n) (n = 2-4) (Kiran et al. Angew. Chem., Int. Ed. 2004, 43, 2125). In this article, we show that the H analogy of Au is more general. We find that the chemical bonding and potential energy surfaces of two disilicon Au clusters, Si(2)Au(2) and Si(2)Au(4), are analogous to Si(2)H(2) and Si(2)H(4), respectively. Photoelectron spectroscopy and ab initio calculations are used to investigate the geometrical and electronic structures of Si(2)Au(2)(-), Si(2)Au(4)(-), and their neutral species. The most stable structures for both Si(2)Au(2) and Si(2)Au(2)(-) are found to be C(2)(v), in which each Au bridges the two Si atoms. For Si(2)Au(4)(-), two nearly degenerate dibridged structures in a cis (C(2)(h)) and a trans (C(2)(v)) configuration are found to be the most stable isomers. However, in the neural potential energy surface of Si(2)Au(4), a monobridged isomer is the global minimum. The ground-state structures of Si(2)Au(2)(-) and Si(2)Au(4)(-) are confirmed by comparing the computed vertical detachment energies with the experimental data. The various stable isomers found for Si(2)Au(2) and Si(2)Au(4) are similar to those known for Si(2)H(2) and Si(2)H(4), respectively. Geometrical and electronic structure comparisons with the corresponding silicon hydrides are made to further establish the isolobal analogy between a gold atom and a hydrogen atom.