Computational studies of nonstoichiometric sodium auride clusters

The molecular structures of low-lying isomers of anionic and neutral sodium auride clusters have been studied computationally at the second-order M?ller-Plesset perturbation theory level using quadruple-ζ basis sets augmented with a double set of polarization functions. The first vertical detachment energies were calculated at the M?ller-Plesset level as the energy difference between the cluster anion and the corresponding neutral cluster. The photodetachment energies of higher-lying ionization channels were calculated by adding electronic excitation energies of the neutral clusters to the first vertical detachment energy. The excitation energies were calculated at the linear response approximate coupled-cluster singles and doubles level using the anionic cluster structures. The obtained ionization energies for NaAu(-), NaAu(2)(-), NaAu(3)(-), NaAu(4)(-), Na(2)Au(2)(-), Na(2)Au(3)(-), Na(3)Au(3)(-), and Na(2)Au(4)(-) were compared to values deduced from experimental photoelectron spectra. Comparison of the calculated photoelectron spectra for a few energetically low-lying isomers shows that the energetically lowest cluster structures obtained in the calculations do not always correspond to the clusters produced experimentally. Spin-component-scaled second-order M?ller-Plesset perturbation theory calculations shift the order of the isomers such that the observed clusters more often correspond to the energetically lowest structure, whereas the spin-component-scaled approach does not improve the photodetachment energies of the sodium aurides. The potential energy surface of the sodium aurides is very soft, with several low-lying isomers requiring an accurate electron correlation treatment. The calculations show that merely the energetic criterion is not a reliable means to identify the structures of the observed sodium auride clusters; other experimental information is needed to ensure a correct assignment of the cluster structures. The cluster structures of nonstoichiometric anionic sodium aurides have been determined by comparing calculated ionization energies for low-lying structures of the anionic clusters with experimental data.     

Comparison of the growth patterns of Si(n) and Ge(n) clusters (n = 25-33)

We performed an unbiased search for low-energy structures of medium-sized neutral Si n and Ge n clusters ( n = 25-33) using a genetic algorithm (GA) coupled with tight-binding interatomic potentials. Structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Si n and Ge n clusters of n = 25-29 compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Si n and Ge n ( n = 29-33) and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Si n ( n = 25-33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE-calculated results. In the size range of 25-33, the corresponding Ge n clusters hold the prolate growth pattern. The relative stabilities and different structural motifs of Si n and Ge n ( n = 25-33) clusters were studied, and the changes of small cluster structures, when acting as building blocks of large clusters, were also discussed.     

Appearance of the bulk motif in Al clusters

We have performed an unbiased search for the lowest-energy structures of medium-sized aluminum clusters Al(n) (n=19-26) using a genetic algorithm (GA) coupled with a tight-binding interatomic potential. Structural candidates obtained from our GA search were further optimized using density functional theory. It is found that the double icosahedron is not the most stable structure for Al(19) but serves as the core for Al(20) and Al(21). The lowest-energy structures of Al(n) are found to undergo a transition to an aluminum bulk motif above Al(23). In particular, the lowest-energy structure of Al(26) is almost a fragment of the bulk face-centered-cubic crystal except for the stacking fault at the bottom layer. Anion clusters were also studied.     

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.     

Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80)

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80). We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si(39), we examined six endohedral fullerene structures using all six homolog C(34) fullerene isomers as cage motifs. We found that the Si(39) constructed based on the C(34)(C(s):2) cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches (combined with tight-binding optimization). The C(34)(C(s):2) cage motif also leads to a new candidate for the lowest-energy structure of Si(40) whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C(34)(C(1):1). Low-lying structures of larger silicon clusters Si(50) and Si(60) are also obtained on the basis of preconstructed endohedral fullerene structures. For Si(50), Si(60), and Si(80), the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger-Weber potential of silicon. Additionally, we found that the binding energy per atom (or cohesive energy) increases typically >10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si(50).     

Search for global minimum geometries for medium sized germanium clusters: Ge12-Ge20

We have performed an unbiased search for the global minimum geometries of small-to-medium sized germanium clusters Gen(12< or =n< or =18) as well as a biased search (using seeding method) for Gen(17< or =n< or =20). We employed the basin-hopping algorithm coupled with the plane-wave pseudopotential density functional calculations. For each size, we started the unbiased search with using several structurally very different initial clusters, or we started the biased search with three different seeds. Irrespective of the initial structures of clusters we found that the obtained lowest-energy clusters of the size n=12-16 and 18 are the same. Among them, the predicted global minima of Gen(12< or =n< or =16) are identical to those reported previously [Shvartsburg et al., Phys. Rev. Lett. 83, 167 (1999)]. For n=17-20, we have identified two or three nearly isoenergetic low-lying isomers (for each size) that compete for the global minimum. Nearly all the low-lying clusters in the size range of 12< or =n< or =20 contain the tri-caped trigonal prism motif and are all prolate in geometry, in agreement with the experiment.     

Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si12-Si20

Ab initio all-electron molecular-orbital calculations are carried out to study the structures and relative stability of low-energy silicon clusters (Si(n),n = 12-20). Selected geometric isomers include those predicted by Ho et al. [Nature (London) 392, 582 (1998)] based on an unbiased search with tight-binding/genetic algorithm, as well as those found by Rata et al. [Phys. Rev. Lett. 85, 546 (2000)] based on density-functional tight-binding/single-parent evolution algorithm. These geometric isomers are optimized at the M?ller-Plesset (MP2) MP2/6-31G(d) level. The single-point energy at the coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] CCSD(T)/6-31G(d) level for several low-lying isomers are further computed. Harmonic vibrational frequency analysis at the MP2/6-31G(d) level of theory is also undertaken to assure that the optimized geometries are stable. For Si12-Si17 and Si19 the isomer with the lowest-energy at the CCSD(T)/6-31G(d) level is the same as that predicted by Ho et al., whereas for Si18 and Si20, the same as predicted by Rata et al. However, for Si14 and Si15, the vibrational frequency analysis indicates that the isomer with the lowest CCSD(T)/6-31G(d) single-point energy gives rise to imaginary frequencies. Small structural perturbation onto the Si14 and Si15 isomers can remove the imaginary frequencies and results in new isomers with slightly lower MP2/6-31G(d) energy; however the new isomers have a higher single-point energy at the CCSD(T)/6-31G(d) level. For most Si(n) (n = 12-18,20) the low-lying isomers are prolate in shape, whereas for Si19 a spherical-like isomer is slightly lower in energy at the CCSD(T)/6-31G(d) level than low-lying prolate isomers.     

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.     

Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45

We have performed unconstrained search for low-lying structures of medium-sized silicon clusters Si(31)-Si(40) and Si(45), by means of the minimum-hopping global optimization method coupled with a density-functional based tight-binding model of silicon. Subsequent geometric optimization by using density-functional theory with the PBE, BLYP, and B3LYP functionals was carried out to determine the relative stability of various candidate low-lying silicon clusters obtained from the unconstrained search. The low-lying characteristics of these clusters can be affirmed by comparing the binding energies per atom of these clusters with previously determined lowest-energy clusters(Si(n)) in the size range of 21相似文献   

Electronic and structural investigations of gold clusters doped with copper: Aun-1Cu- (n=13-19)

We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.     

Glutathione-protected gold clusters revisited: bridging the gap between gold(I)-thiolate complexes and thiolate-protected gold nanocrystals

Small gold clusters (approximately 1 nm) protected by molecules of a tripeptide, glutathione (GSH), were prepared by reductive decomposition of Au(I)-SG polymers at a low temperature and separated into a number of fractions by polyacrylamide gel electrophoresis (PAGE). Chemical compositions of the fractionated clusters determined previously by electrospray ionization (ESI) mass spectrometry (Negishi, Y. et al. J.Am. Chem. Soc. 2004, 126, 6518) were reassessed by taking advantage of freshly prepared samples, higher mass resolution, and more accurate mass calibration; the nine smallest components are reassigned to Au10(SG)10, Au15(SG)13, Au18(SG)14, Au22(SG)16, Au22(SG)17, Au25(SG)18, Au29(SG)20, Au33(SG)22, and Au39(SG)24. These assignments were further confirmed by measuring the mass spectra of the isolated Au:S(h-G) clusters, where h-GSH is a homoglutathione. It is proposed that a series of the isolated Au:SG clusters corresponds to kinetically trapped intermediates of the growing Au cores. The relative abundance of the isolated clusters was correlated well with the thermodynamic stabilities against unimolecular decomposition. The electronic structures of the isolated Au:SG clusters were probed by X-ray photoelectron spectroscopy (XPS) and optical spectroscopy. The Au(4f) XPS spectra illustrate substantial electron donation from the gold cores to the GS ligands in the Au:SG clusters. The optical absorption and photoluminescence spectra indicate that the electronic structures of the Au:SG clusters are well quantized; embryos of the sp band of the bulk gold evolve remarkably depending on the number of the gold atoms and GS ligands. The comparison of these spectral data with those of sodium Au(I) thiomalate and 1.8 nm Au:SG nanocrystals (NCs) reveals that the subnanometer-sized Au clusters thiolated constitute a distinct class of binary system which lies between the Au(I)-thiolate complexes and thiolate-protected Au NCs.     

Probing the structures of neutral boron clusters using infrared/vacuum ultraviolet two color ionization: B11, B16, and B17

The structures of neutral boron clusters, B(11), B(16), and B(17), have been investigated using vibrational spectroscopy and ab initio calculations. Infrared absorption spectra in the wavelength range of 650 to 1550 cm(-1) are obtained for the three neutral boron clusters from the enhancement of their near-threshold ionization efficiency at a fixed UV wavelength of 157 nm (7.87 eV) after resonant absorption of the tunable infrared photons. All three clusters, B(11), B(16), and B(17), are found to possess planar or quasi-planar structures, similar to their corresponding anionic counterparts (B(n) (-)), whose global minima were found previously to be planar, using photoelectron spectroscopy and theoretical calculations. Only minor structural changes are observed between the neutral and the anionic species for these three boron clusters.     

Interlocked catenane-like structure predicted in Au24(SR)20: implication to structural evolution of thiolated gold clusters from homoleptic gold(I) thiolates to core-stacked nanoparticles

Atomic structure of a recently synthesized ligand-covered cluster Au(24)(SR)(20) [J. Phys. Chem. Lett., 2010, 1, 1003] is resolved based on the developed classical force-field based divide-and-protect approach. The computed UV-vis absorption spectrum and powder X-ray diffraction (XRD) curve for the lowest-energy isomer are in good agreement with experimental measurements. Unique catenane-like staple motifs are predicted for the first time in core-stacked thiolate-group (RS-) covered gold nanoparticles (RS-AuNPs), suggesting the onset of structural transformation in RS-AuNPs at relatively low Au/SR ratio. Since the lowest-energy structure of Au(24)(SR)(20) entails interlocked Au(5)(SR)(4) and Au(7)(SR)(6) oligomers, it supports a recently proposed growth model of RS-AuNPs [J. Phys. Chem. Lett., 2011, 2, 990], that is, Au(n)(SR)(n-1) oligomers are formed during the initial growth of RS-AuNPs. By comparing the Au-core structure of Au(24)(SR)(20) with other structurally resolved RS-AuNPs, we conclude that the tetrahedral Au(4) motif is a prevalent structural unit for small-sized RS-AuNPs with relatively low Au/SR ratio. The structural prediction of Au(24)(SR)(20) offers additional insights into the structural evolution of thiolated gold clusters from homoleptic gold(I) thiolate to core-stacked RS-AuNPs. Specifically, with the increase of interfacial bond length of Au(core)-S in RS-AuNPs, increasingly larger "metallic" Au-core is formed, which results in smaller HOMO-LUMO (or optical) gap. Calculations of electronic structures and UV-vis absorption spectra of Au(24)(SR)(20) and larger RS-AuNPs (up to ~2 nm in size) show that the ligand layer can strongly affect optical absorption behavior of RS-AuNPs.     

Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21-Si30

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21-30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin (n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin (n=6, 7, 9, or 10). For Si21-Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral cagedlike structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26-Si30, we construct a new (fourth) family of low-lying clusters which have "Y-shaped" three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families.     

Structure and energetics of two- and three-dimensional neutral, cationic, and anionic gold clusters Au(5< or = n < or =9)Z (Z=0,+/-1)

Low-energy structures are found on the potential energy surfaces of the neutral, cationic, and anionic gold clusters Au(5< or = n < or =9)Z (Z=0,+/-1) and on the neutral potential energy surface of Au(9). These structures provide insights on the two to three dimensional (2D-->3D) transition in small neutral and charged gold clusters. It is demonstrated that the size threshold for the 2D-3D coexistence is lower for cationic than neutral gold clusters: the 2D-3D coexistence develops for Au(5) (+) and Au(7) (+) on the cationic potential energy surfaces while only for Au(9) on the neutral. Two metastable long-lived dianions of gold clusters are also reported.     

Evolution of the geometrical and electronic structures of Gan(n=2-26) clusters: a density-functional theory study

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the lowest-energy geometries and electronic structure of neutral gallium clusters containing up to 26 atoms. Harmonic vibrational frequency analysis is undertaken to assure that the lowest-energy geometries are real local minima. With increasing cluster size, we find that the gallium clusters tend to adopt compact structures. The structures comprise triangular units that connect each other with different dihedral angles. The lowest-energy structure can be obtained by capping an atom on the structure of smaller one. The capping site occurs at a site where interactions with more atoms are available. The binding energy evolves monotonically with size, but Ga(8), Ga(14), and Ga(20) exhibit particularly higher stability. Except Ga(2) and Ga(4), all even-numbered gallium clusters we studied are closed-shell singlet states with a substantial highest occupied and lowest unoccupied molecular orbitals gap. The odd-numbered clusters are open shell with a small gap. The size dependence of cluster's ionization potentials and electron affinities is discussed and compared with available experiment.     

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.     

Structural and energetic properties of Ni-Cu bimetallic clusters

The lowest-energy structures for all compositions of Ni n Cu m bimetallic clusters with N = n + m up to 20 atoms, N = 23, and N = 38 atoms have been determined using a genetic algorithm for unbiased structure optimization in combination with an embedded-atom method for the calculation of the total energy for a given structure. Comparing bimetallic clusters with homoatomic clusters of the same size, it is shown that the most stable structures for each cluster size are composed entirely of Ni atoms. Among the bimetallic clusters in the size range N = 2-20, the Ni N-1 Cu 1 clusters possess the highest stability. Further, it has been established that most of the bimetallic cluster structures have geometries similar to those of pure Ni clusters. The size N = 38 presents a special case, as the bimetallic clusters undergo a dramatic structural change with increasing atom fraction of Cu. Moreover, we have identified an icosahedron, a double, and a triple icosahedron with one, two, and three Ni atoms at the centers, respectively, as particularly stable structures. We show that in all global-minimum structures Ni atoms tend to occupy mainly high-coordination inner sites, and we confirm the segregation of Cu on the surface of Ni-Cu bimetallic clusters predicted in previous studies. Finally, it is observed that, in contrast to the bulk, the ground-state structures of the 15-, 16-, and 17-atom bimetallic clusters do not experience a smooth transition between the structures of the pure copper and the pure nickel clusters as a function of the relative number of the two types of atoms. For these sizes, the concentration effect on energy is more important than the geometric one.     

First-principles study of intermediate size silver clusters: Shape evolution and its impact on cluster properties

Low-energy isomers of Ag(N) clusters are studied within gradient-corrected density functional theory over the size range of N = 9-20. The candidate conformations are drawn from an extensive structural database created in a recent exploration of Cu(N) clusters [M. Yang et al., J. Chem. Phys. 124, 24308 (2006)]. Layered configurations dominate the list of the lowest-energy isomers of Ag(N) for N < 16. The most stable structures for N > 16 are compact with quasispherical shapes. The size-driven shape evolution is similar to that found earlier for Na(N) and Cu(N). The shape change has a pronounced effect on the cluster cohesive energies, ionization potentials, and polarizabilities. The properties computed for the most stable isomers of Ag(N) are in good agreement with the available experimental data.     

On the structure of the Au18(SR)14 cluster

First principles calculations are used for a systematic search of the lowest-energy (most-stable) structure of the recently synthesized Au(18)(SR)(14) cluster. A comparison of the calculated optical absorption and electronic circular dichroism spectra, which are highly sensitive to the cluster structure and chirality, with the experimental spectra of the glutathione-protected gold cluster, Au(18)(SG)(14), is used to discriminate between low-energy isomers of the Au(18)(SR)(14) (R = CH(3)) cluster. From the good agreement between calculated and measured spectra, it is predicted that the structure of the Au(18)(SR)(14) cluster consists of a prolate Au(8) core covered with two dimer (SR-Au-SR-Au-SR) and two trimer (SR-Au-SR-Au-SR-Au-SR) motifs. These results provide additional evidence on the existence of longer trimer motifs as protecting units of small thiolated gold clusters.