Structure, bonding, and linear optical properties of a series of silver and gold nanorod clusters: DFT/TDDFT studies

DFT/TDDFT calculations have been carried out for a series of silver and gold nanorod clusters (Ag(n), Au(n), n = 12-120) whose structures are of cigar-type. Pentagonal Ag(n) clusters with n = 49-121 and hexagonal Au(n) clusters with n = 14-74 were also calculated for comparison. Metal-metal distances, binding energies per atom, ionization potentials, and electron affinities were determined, and their trends with cluster size were examined. The TDDFT calculated excitation energies and oscillator strengths were fit by a Lorentz line shape modification, which gives rise to the simulated absorption spectra. The significant features of the experimental spectra for actual silver and gold nanorod particles are well reproduced by the calculations on the clusters. The calculated spectral patterns are also in agreement with previous theoretical results on different-type Ag(n) clusters. Many differences in the calculated properties are found between the Ag(n) and Au(n) clusters, which can be explained by relativistic effects.     

Electronic excitation energies of Zn(i)O(i) clusters

Time-dependent density-functional theory (TDDFT) is used to study the excitation energies of the global minima of small Zn(i)O(i) clusters, i = 1-15. The relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch, and Jasien (SKBJ), systematically enlarged with extra functions, were used throughout this work. In general, the calculated excitations occur from the nonbonding p orbitals of oxygen. These orbitals are perpendicular to the molecular plane in the case of the rings and normal to the spheroid surface for 3D clusters. The calculated excitation energies are larger for ringlike clusters as compared to 3D clusters, with the excitation energies of the latter structures lying close to the visible spectrum. The difference between Kohn-Sham eigenvalues of the orbitals involved in the electronic excitations studied have also been compared to the TDDFT results of the corresponding excitations for two approximate density functionals, that is, MPW1PW91 and B3LYP, the latter being more accurate. Moreover, they approach the TDDFT value as the cluster size increases. Therefore, this might be a practical method for estimating excitation energies of large Zn(i)O(i) clusters.     

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.     

Solidification of small p-H2 clusters at zero temperature

We have determined the ground-state energies of para-H(2) clusters at zero temperature using the diffusion Monte Carlo method. The liquid or solid character of each cluster is investigated by restricting the phase through the use of proper importance sampling. Our results show inhomogeneous crystallization of clusters, with alternating behavior between liquid and solid phases up to N = 55. From there on, all clusters are solid. The ground-state energies in the range N = 13-75 are established, and the stable phase of each cluster is determined. In spite of the small differences observed between the energy of liquid and solid clusters, the corresponding density profiles are significantly different, a feature that can help to solve ambiguities in the determination of the specific phase of H(2) clusters.     

Fragmentation Behavior and Ionization Potentials of Lead Clusters Pb_n(n≤30)

The properties of Pbn(n=2―30) clusters including binding energies,second differences in energy,and HOMO-LUMO gaps,especially fragmentation energies and ionization potentials,have been studied by ab initio calculation.The main fragmentation products of Pbn+ are shown to be Pb+Pbn-1+ for n≤14 and two small cluster fragments for larger ones with n14.The Pb13+ appears frequently as the products in the fragmentations of large clusters.Also,the calculated ionization potentials of the clusters are consistent with the experiment data.     

Structures, energetics and vibrational spectra of CO2 clusters through molecular tailoring and cluster building algorithm

Clusters of CO(2) are a subject of detailed experimental as well as theoretical investigations due to their interesting applications. In the present article, CO(2) clusters (n = 6 to 13) are studied at the MP2 level of theory. The clusters are grown using a cluster building algorithm developed by our group and the larger ones are optimized at the MP2/aug-cc-pVDZ level by employing a Molecular Tailoring Approach (MTA). Vibrational spectra of these clusters are also calculated at this level of theory within MTA. The computed vibrational frequencies for an asymmetric C-O stretch generally exhibit a blue shift with increasing cluster size. This observation is in agreement with the experimental results. MTA-single point energies for each cluster size at the MP2/aug-cc-pVTZ level are also calculated for estimating the interaction energies at the complete basis set limit.     

On the statistical nature of collision and surface-induced dissociation: a theoretical investigation of aluminum clusters

The unimolecular dissociation dynamics of aluminum clusters following collision with either a rare gas atom or a surface is investigated by classical trajectory simulations with model potentials. Two conformers of Al(6) with very distinct shapes, i.e., the spherical O(h) and planar C(2)(h) clusters, are considered in this work. The initial vibrational energy and angular momentum distributions resulting from collision, as well as the energy and angular momentum resolved lifetime distributions, of excited clusters were determined for both collision-induced dissociation (CID) and surface-induced dissociation (SID) processes. The partitioning of excitation energy acquired upon collision was found to depend on the excitation mechanism (CID or SID), as well as on the cluster molecular shape, especially in the case of CID. For both types of processes, the energy and angular momentum resolved excited cluster lifetime distributions were found to decay exponentially, in agreement with statistical theories of chemical reactions, suggesting intrinsic Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. Moreover, the simulated microcanonical rate constants determined from the cluster lifetime distributions are in good agreement with the predictions of the orbiting transition state model of phase space theory (OTS/PST), which further supports the statistical character of cluster CID and SID. Thus, in the CID and SID of highly fluxional systems such as aluminum clusters, the rate of intramolecular vibrational energy redistribution (IVR) is much faster than the dissociation rate, which validates one of the key assumptions, i.e., post-collision statistical behavior, underlying the models that are routinely used to determine cluster binding energies from experimental CID/SID cross sections.     

The spectra of mixed 3He-4He droplets

The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of 3He atoms bound to a cluster of 4He atoms by using a previously determined optimum filling of single-fermion orbits with well-defined orbital angular momentum L, spin S, and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum L or maximum S states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects, whose binding and excitation energies are essentially determined by averages over configuration at fixed number of particles and spin, i.e., by the monopole properties of an effective Hamiltonian.     

Theoretical Study of the Structural,Electronic, and Magnetic Properties of Zirconium-doped Aluminum Clusters:Al_nZr(n = 1～14)

The geometrical structures, stabilities, electronic and magnetic properties of Al_nZr(n = 1~14) clusters have been systematically investigated using density functional theory. It is found that for the optimized clusters the zirconium atom prefers to remain on the surface, and the growth patterns are organized as follows: Zr substituted Al_(n+1) clusters or Zr capped Aln clusters as well as Al added Al_(n-1)Zr clusters. All doped clusters exhibit relatively larger average binding energies and magnetic behaviors compared with pure Al_(n+1) counterpart. The calculated fragmentation energies and second-order difference of energies exhibit pronounced odd-even alternation behavior as a function of the cluster size when n = 3~13. In all Al_nZr clusters, there exits internal hybridization in both Al and Zr atoms and charge transfer from Al to Zr atom, which reflects the strong interactions between the two kinds of atoms. The magnetic property analysis shows that the 4d electrons of Zr atom are the main origin for cluster magnetism.     

Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

The TaSi(n) (n=1-13) clusters with doublet, quartet, and sextet spin configurations have been systematically investigated by a relativistic density functional theory with the generalized gradient approximation available in Amsterdam density functional program. The total bonding energies, equilibrium geometries, Mulliken populations as well as Hirshfeld charges of TaSi(n) (n=1-13) clusters are calculated and presented. The emphasis on the stabilities and electronic properties is discussed. The most stable structures of the small TaSi(n) (n=1-6) clusters and the evolutional rule of low-lying geometries of the larger TaSi(n) (n=7-13) clusters are obtained. Theoretical results indicate that the most stable structure of TaSi(n) (n=1-6) clusters keeps the similar framework as the most stable structure of Si(n+1) clusters except for TaSi(3) cluster. The Ta atom in the lowest-energy TaSi(n) (n=1-13) isomers occupies a gradual sinking site, and the site moves from convex, to flatness, and to concave with the number of Si atom varying from 1 to 13. When n=12, the Ta atom in TaSi(12) cluster completely falls into the center of the Si frame, and a cagelike TaSi(12) geometry is formed. Meanwhile, the net Mulliken and Hirsheld populations of the Ta atom in the TaSi(n) (n=1-13) clusters vary from positive to negative, manifesting that the charges in TaSi(n) (n>/=12) clusters transfer from Si atoms to Ta atom. Additionally, the contribution of Si-Si and Si-Ta interactions to the stability of TaSi(n) clusters is briefly discussed. Furthermore, the investigations on atomic averaged binding energies and fragmentation energies show that the TaSi(n) (n=2,3,5,7,10,11,12) clusters have enhanced stabilities. Compared with pure silicon clusters, a universal narrowing of highest occupied molecular orbital-lowest unoccupied molecular orbital gap in TaSi(n) clusters is found.     

Nitric oxide decomposition on small rhodium clusters, Rh(n)+/-

The decomposition of nitric oxide on small charged rhodium clusters Rh(n)(+/-) (6 < n < 30) has been investigated by Fourier transform ion cyclotron resonance mass spectrometry. For both cationic and anionic naked clusters, the rates of reaction with NO increase smoothly with cluster size in the range studied without the dramatic size-dependent fluctuations often associated with the reactions of transition-metal clusters. The cationic clusters react significantly faster than the anions and both exhibit rate constants exceeding collision rates calculated by average dipole orientation theory. Both the approximate magnitude and the trends in reactivity are modeled well by the surface charge capture model recently proposed by Kummerl?we and Beyer. All clusters studied here exhibit pseudo-first-order kinetics with no sign of biexponential kinetics often interpreted as evidence for multiple isomeric structures. Experiments involving prolonged exposure to NO have revealed interesting size-dependent trends in the mechanism and efficiency of NO decomposition: For most small clusters (n < 17), once two NO molecules are coadsorbed on a cluster, N(2) is evolved, generating the corresponding dioxide cluster. By analogy with experiments on extended surfaces, this observation is interpreted in terms of the dissociative adsorption of NO in the early stages of reaction, generating N atoms that are mobile on the surface of the cluster. For clusters where n < 13, this chemistry, which occurs independently of the cluster charge, repeats until a size-dependent, limiting oxygen coverage is achieved. Following this, NO is observed to adsorb on the oxide cluster without further N(2) evolution. For n = 14-16 no single end-point is observed and reaction products are based on a small range of oxide structures. By contrast, no evidence for N(2) production is observed for clusters n = 13 and n > 16, for which simple sequential NO adsorption dominates the chemistry. Interestingly, there is no evidence for the production of N(2)O or NO(2) on any of the clusters studied. A simple general mechanism is proposed that accounts for all observations. The detailed decomposition mechanisms for each cluster exhibit size (and, by implication, structure) dependent features with Rh(13)(+/-) particularly anomalous by comparison with neighboring clusters.     

银团簇结构与特性的分子动力学研究

用分子动力学方法模拟了银团簇的结构与力能学.计算模拟中使用了一种基于第一性原理的原子间互作用多体势函数.通过分子动力学模拟确定了银微团簇(原子个数3～13)的稳态结构;模拟了原子个数为13～141的银FCC晶体结构理想球形团簇的力能学,发现球形银团簇形成三雏紧密结构;计算了平均结合能,给出了结合能随团簇原子数N的变化图,发现随N增大团簇结合能逐渐接近块材的数值.     

Core-to-Rydberg band shift and broadening of hydrogen bonded ammonia clusters studied with nitrogen K-edge excitation spectroscopy

Nitrogen 1s (N 1s) core-to-Rydberg excitation spectra of hydrogen-bonded clusters of ammonia (AM) have been studied in the small cluster regime of beam conditions with time-of-flight (TOF) fragment-mass spectroscopy. By monitoring partial-ion-yield spectra of cluster-origin products, "cluster" specific excitation spectra could be recorded. Comparison of the "cluster" band with "monomer" band revealed that the first resonance bands of clusters corresponding to N 1s → 3sa(1)/3pe of AM monomer are considerably broadened. The changes of the experimental core-to-Rydberg transitions ΔFWHM (N 1s → 3sa(1)/3pe) = ~0.20/~0.50 eV compare well with the x ray absorption spectra of the clusters generated by using density functional theory (DFT) calculation. The broadening of the core-to-Rydberg bands in small clusters is interpreted as being primarily due to the splitting of non-equivalent core-hole N 1s states caused by both electrostatic core-hole and hydrogen-bonding (H(3)N···H-NH(2)) interactions upon dimerization. Under Cs dimer configuration, core-electron binding energy of H-N (H-donor) is significantly decreased by the intermolecular core-hole interaction and causes notable redshifts of core-excitation energies, whereas that of lone-pair nitrogen (H-acceptor) is slightly increased and results in appreciable blueshifts in the core-excitation bands. The result of the hydrogen-bonding interaction strongly appears in the n-σ* orbital correlation, destabilizing H-N donor Rydberg states in the direction opposite to the core-hole interaction, when excited N atom with H-N donor configuration strongly possesses the Rydberg component of anti-bonding σ* (N-H) character. Contributions of other cyclic H-bonded clusters (AM)(n) with n ≥ 3 to the spectral changes of the N 1s → 3sa(1)/3pe bands are also examined.     

Structures and energetics of helium cluster cations: equilibrium geometries revisited through the genetic algorithm approach

Equilibrium geometries and dissociation energies of He(N)(+) clusters have been calculated for N=3-35 using an extended genetic algorithm approach and a semiempirical model of intracluster interactions [P. J. Knowles, J. N. Murrell, and E. J. Hodge, Mol. Phys. 85, 243 (1995)]. A general aufbau principle is formulated for both ionic cores and neutral solvation shells, and the results are thoroughly compared with other theoretical data available for helium cluster cations in literature.     

Structures and dissociation channels of protonated mixed clusters around a small magic number: infrared spectroscopy of ((CH3)3N)n-H(+)-H2O (n = 1-3)

The magic number behavior of ((CH(3))(3)N)(n)-H(+)-H(2)O clusters at n = 3 is investigated by applying infrared spectroscopy to the clusters of n = 1-3. Structures of these clusters are determined in conjunction with density functional theory calculations. Dissociation channels upon infrared excitation are also measured, and their correlation with the cluster structures is examined. It is demonstrated that the magic number cluster has a closed-shell structure, in which the water moiety is surrounded by three (CH(3))(3)N molecules. The ion core (protonated site) of the clusters is found to be (CH(3))(3)NH(+) for n = 1-3, but coexistence of an isomer of the H(3)O(+) ion core cannot be ruled out for n = 3. Large rearrangement of the cluster structures of n = 2 and 3 before dissociation, which has been suggested in the mass spectrometric studies, is confirmed on the basis of the structure determination by infrared spectroscopy.     

The optical extinction of ligand-stabilized Au13- and Au55-clusters: The vanishing of the Mie-resonance

We present optical extinction spectra of ligand-stabilized Au-clusters Au_N with sizes of N=13 and N=55. They are compared to larger, embedded clusters up to N=5·10³ (diameter 5nm). The Mie resonance due to excitation of the dipole plasmon polariton vanishes with decreasing cluster size. For N>55, this effect has recently been interpreted as caused by smearing out of the interband transition edge of Au.     

Nonergodicity in electron capture dissociation investigated using hydrated ion nanocalorimetry

Hydrated divalent magnesium and calcium clusters are used as nanocalorimeters to measure the internal energy deposited into size-selected clusters upon capture of a thermally generated electron. The infrared radiation emitted from the cell and vacuum chamber surfaces as well as from the heated cathode results in some activation of these clusters, but this activation is minimal. No measurable excitation due to inelastic collisions occurs with the low-energy electrons used under these conditions. Two different dissociation pathways are observed for the divalent clusters that capture an electron: loss of water molecules (Pathway I) and loss of an H atom and water molecules (Pathway II). For Ca(H(2)O)(n)(2+), Pathway I occurs exclusively for n >or= 30 whereas Pathway II occurs exclusively for n 相似文献   

Time-dependent density functional theory as a tool for isomer assignments of hydrogen-bonded solute.solvent clusters

Can isomer structures of hydrogen-bonded solute x solvent clusters be assigned by correlating gas-phase experimental S0 <--> S1 transitions with vertical or adiabatic excitation energies calculated by time-dependent density functional theory (TD-DFT)? We study this question for 7-hydroxyquinoline (7HQ), for which an experimental database of 19 complexes and clusters is available. The main advantage of the adiabatic TD-B3LYP S0 <--> S1 excitations is the small absolute error compared to experiment, while for the calculated vertical excitations, the average offset is +1810 cm(-1). However, the empirically adjusted vertical excitations correlate more closely with the experimental transition energies, with a standard deviation of sigma = 72 cm(-1). For the analogous correlation with calculated adiabatic TD-DFT excitations, the standard deviation is sigma = 157 cm(-1). The vertical and adiabatic TD-DFT correlation methods are applied for the identification of isomers of the 7-hydroxyquinoline.(MeOH) n , n = 1-3 clusters [Matsumoto, Y.; Ebata, T.; Mikami, N. J. Phys. Chem. B 2002, 106, 5591]. These confirm that the vertical TD-DFT/experimental correlation yields more effective isomer assignments.     

Structural and electronic properties of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13): Theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13) have been investigated using the ab initio molecular orbital theory formalism. The hybrid exchange-correlation energy functional (B3LYP) and a standard split-valence basis set with polarization functions (6-31+G(d)) were employed to optimize geometrical configurations. The total energies of the lowest energy isomers thus obtained were recalculated at the MP2/aug-cc-pVTZ level of theory. Unlike positively charged clusters, which showed similar structural behavior as that of neutral clusters [Nigam et al., J. Chem. Phys. 121, 7756 (2004)], significant geometrical changes were observed between Si(n) and Si(n)- clusters for n = 6, 8, 11, and 13. However, the geometries of P substituted silicon clusters show similar growth as that of negatively charged Si(n) clusters with small local distortions. The relative stability as a function of cluster size has been verified based on their binding energies, second difference in energy (Delta2 E), and fragmentation behavior. In general, the average binding energy of Si(n)- clusters is found to be higher than that of Si(n) clusters. For isoelectronic PSi(n-1) clusters, it is found that although for small clusters (n < 4) substitution of P atom improves the binding energy of Si(n) clusters, for larger clusters (n > or = 4) the effect is opposite. The fragmentation behavior of these clusters reveals that while small clusters prefer to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size. The adiabatic electron affinities of Si(n) clusters and vertical detachment energies of Si(n)- clusters were calculated and compared with available experimental results. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.     

The elastic scattering on jellium clusters

The following calculations are based on the local density approximation potential (LDA) of W. Ekardt for the spherical jellium-background model (SJBM). Taking into account the smooth shape of the potential, the WKB approximation was used to calculate the energy and angular dependence of the electron scattering cross-sections fo rsmall Na clusters. The number of phase shifts needed to describe the scattering in the range of energies <4.5 eV increases with the size of cluster. The calculated elastic electron scattering cross-sections for the Na clusters, corresponding to the shell closings (8, 20, 40), are exhibiting a pronounced peak structure, correlated with resonance states. The computed peaks of the angular dependences of the cross-sections on energy are shifted to small angles with increasing the cluster size. The absence of fragmentation at these small electron energies presents a challenge for the experimentalists.