Small, nonstoichiometric zinc sulfide clusters

Recent experiments indicated that the formation of small, nonstoichiometric clusters Zn(n)S(m) and Zn(n)S(m)+ was possible. In this work, the ground states of these clusters, where 1 < or = n, m < or = 4, were studied using density functional theory. Global minima were found to be primarily cyclic structures in which the S-Zn-S preference for large bond angles was preserved. Ionization was shown to lead to structural relaxation and occasionally major changes in conformation. Cohesive energies are reported as a function of cluster composition. Qualitative comparisons were extracted from the energetics resulting from structural optimizations, and such comparisons appear to be consistent with the experiment. The computational data for the ZnS(n) and Zn(n)S(m) (where m > n) clusters indicated that sulfur-sulfur bonding in larger ZnS clusters could be feasible without significant energetic cost and that such structures should at least be considered.     

Photoionization studies of free sodium ammonia clusters

Free sodium ammonia clusters Na(NH₃) _n up ton=45 were generated in a pickup source by injecting a beam of neutral sodium atoms into the expansion zone of a piezo driven pulsed nozzle. The clusters thus formed are studied by one-photon ionisation in the region of 266 nm to 520 nm, time-of-flight mass spectrometry as well as photoelectron spectrometry. Ionisation thresholds for clusters up ton=18 and dissociation energies for the neutral Na(NH₃) _n up ton=6 are reported.     

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.     

Computational studies of small (AlP)N clusters

We have carried out extensive LDA calculations to investigate the structures of small (AlP)_N clusters.We find that the polarity of the Al-P bond has a significant effect on the cluster geometries and that the need to minimize electrostatic repulsion between relatively diffuse lone pair electrons on phosphorous atoms is a dominant energetic consideration in the structural arrangement.     

Computational studies of nucleophilic attack and protonation of electron-deficient benzoheterocycle triosmium clusters

The density functional theory method has been applied to gain insights into the regioselectivity of nucleophilic attack and protonation of electron-deficient benzoheterocycle triosmium clusters. We report our computational results on the reaction of the green 46-electron triosmium clusters Os3(CO)(9)(mu3-eta2-(LH))(mu-H) (L = benzoxazole, 1a; benzothiazole, 1b; dihydroquinoline, 1c; 1,3-dehydroindoline, 1d; 4H-3,1-benzoxazine, 1e) with hydride (H-) and proton (H+) in order to elucidate factors affecting the observed differences in the structure of the kinetic products of these reactions. Transition-state calculations for the interconversion of the anionic tautomers resulting from H- attack on the clusters 1a-e show that the activation energies of these anionic clusters are considerably lower than the previously reported barriers for related neutral clusters. Calculations also reveal that the structures of the kinetic products resulting from sequential H-/H+ attack are determined by the protonation process.     

Computational studies of aqueous-phase photochemistry and the hydrated electron in finite-size clusters

A survey of recent ab initio calculations on excited electronic states of water clusters and various chromophore-water clusters is given. Electron and proton transfer processes in these systems have been characterized by the determination of electronic wave functions, minimum-energy reaction paths and potential-energy profiles. It is pointed out that the transfer of a neutral hydrogen atom (leading to biradicals) rather than the transfer of a proton (leading to ion pairs) is the generic excited-state reaction mechanism in these systems. The hydrated hydronium radical, (H3O)(aq), plays a central role in this scenario. The electronic and vibrational spectra of H3O(H2O)(n) clusters and the decay mechanism of these metastable species have been investigated in some detail. The results suggest that (H3O)(aq) could be the carrier of the characteristic spectroscopic properties of the hydrated electron in liquid water.     

Computational study of phenolic compounds-water clusters

Structural Chemistry - Eight molecules (phenol, o-cresol, m-cresol, p-cresol, pyrocatechol, guaiacol, syringol, and vanillin) were investigated in their one water complex clusters by quantum...     

Vibrational frequencies of sodium clusters

The vibrational frequencies of Na_N clusters (2 ? N ? 72) are calculated by direct diagonalization of the dynamical matrix. Density functional theory with a spherically averaged pseudopotential is used to compute the total energy. The geometry is optimized by the simulated annealing technique. Contributions to the Hessian matrix due to electron relaxation following the ionic displacements are calculated in linear response theory. The frequencies are in the range 0-220 cm^?1 and the electron relaxation strongly modifies those of the modes dominated by radial oscillations, particularly the breathing mode frequencies that are proportional to N?1/3 . The filling of atomic shells produces a stepwise behavior of the highest frequencies. The giant dipole resonance energies are obtained as a byproduct of the calculation. © 1995 John Wiley & Sons, Inc.     

Triaxial shapes of sodium clusters

A modified Nilsson-Clemenger model is combined with Strutinsky's shell correction method. For spherical clusters, the model potential is fitted to the single-particle spectra obtained from selfconsistent Kohn-Sham calculations. The deformation energy surfaces of sodium clusters with sizes of up toN=270 atoms are calculated for a combination of triaxial, quadrupole and hexadecapole deformations. The ground state shapes and energies are determined by simultaneous minimization with respect to the three shape parameters. A significant fraction of the clusters is predicted to be triaxial. The deviations from the axial shape do not generate any systematic odd-even staggering of the binding energies.     

Spectroscopy of size-selected sodium clusters

The method of angular resolved elastic scattering has been used to achieve a size selection of neutral sodium clusters. After the scattering process the clusters are ionized by single photon ionization with various laser energies and detected by a time-of-flight mass spectrometer. The elastic scattering of Na₂ by Ne serves as a test for the experimental setup. Angular dependence of scattered sodium clusters ionized with 308 nm shows a significant amount of fragmentation of the neutral Na₆ to Na₉ clusters which are observed in the Na ₅ ⁺ and Na ₆ ⁺ ion channels.     

Spin dynamics in sodium clusters

We investigate the dynamics of the electron cloud in a metal cluster from the regime of small oscillations up to high excitations in the multi-plasmon regime. Particular attention is paid to the effect of spin modes. Test cases are a spin saturated cluster, Na₉ ⁺, and a strongly spin polarized cluster, the spherical isomer of Na₆ ⁺. The spectral distributions are dominated by the Mie plasmon resonance and a strong collective spin mode in all cases considered. Nonlinear effects as cross talk between multi-plasmon states or chaotic pattern cannot be observed in the investigated energy range.     

Evaporation rates of hot sodium clusters

A scheme based in density functional theory with pseudopotentials is used to obtain the normal modes of vibration of Na _n clusters (4 ≤n ≤ 22). The monomer and dimer evaporation rates from thermally excited clusters are obtained in this harmonic approximation. The time evolution of the abundance spectra from an initial uniform mass distribution of hot clusters is studied and its influence in the experimentally observed spectra is discussed.     

Potential energy surfaces of sodium clusters

We have calculated multidimensional Born- Oppenheimer energy surfaces of singly charged and neutral sodium clusters with quadrupole, octupole, and hexadecapole deformed shapes in a particle range from 8 ≤ N ≤ 58. We use the local-density approximation (LDA) and solve the Kohn-Sham equations on a cylindrical mesh for axially symmetric shapes. Employing the structure-averaged jellium model (SAJM), we ascertain that the correct empirical bulk properties and surface tension are reproduced. Besides a pronounced isomerism in the β ₂/β ₄ plane we also find super-deformed shapes. We compare the PES data with shape transitions deduced from experimental splittings of the dipole. photoabsorption cross sections. The influence of large octupole moments reverts the scheme of prolate-oblate shape transitions above the filled 2p-shell (N = 42, 44) which is wrongly predicted in spheroidal models.     

Ionization of sodium in water clusters

Structures of Na(H₂O)_n and Na⁺(H₂O)_n clusters with n = 1?6, 19, and 28 are determined in the second order of the Møller-Plesset perturbation theory with the use of extended atomic basis set 6–31++G^**. It is found that when the number of molecules is sufficient for the formation of two solvation shells around sodium, a continuous hydrogen-bond network is formed in both neutral and charged clusters, and the orientation of each molecule is determined by the balance between interactions with the neighboring water molecules and with the field of the central particle. In the cations, this field is stronger, and up to the third solvation shell, molecules have a predominant orientation with respect to sodium. In the neutral clusters, with an increase in the number of water molecules, the maximum of the electron density distribution of the highest occupied molecular orbital becomes more distant from the sodium nucleus, being shifted toward the cluster surface. The energy of this orbital accordingly decreases in absolute value approaching 22 kcal/mol inmicroparticles. In the charged clusters, the distribution of the positive charge generally correlates with the character of the highest occupied orbital in the neutral systems, so that with an increase in the number of molecules, the atomic charge of sodium decreases and tends to zero as n → ∞. The ionization potential of sodium changes in inverse proportion to the linear size of the cluster, and should not exceed 1.1 eV in watermicroparticles.     

Computational spectroscopy of carbon monoxide isotopomers in helium clusters

The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.     

Atom desorption energies for sodium clusters

The desorption energies of supported sodium clusters have been determined as a function of cluster size. Na _n clusters were formed by surface diffusion of sodium atoms adsorbed from a thermal atomic beam on a LiF(100) single crystal. Measurements have been performed by temperature programmed thermal desorption. The signals reflect fractional order desorption kinetics. The average cluster size could be controlled by varying the total number of sodium atoms on the surface. It was determined from scattering experiments. We find that the binding energies vary between 0.55 and 0.8 eV and only approach a constant value for clusters with diameters as large as 1,000 Å.     

Ring currents in polycyclic sodium clusters

In the recent work by Khatua et al. (Khatua, S.; Roy, D. R.; Bultinck, P.; Bhattacharjee, M.; Chattaraj, P. K. Phys. Chem. Chem. Phys.2008, 10, 2461-2474) the synthesis and structure of a fac-trioxo molybdenum metalloligand and its sodium complex containing 1D hexagonal chains of sodium ions was reported. In the same paper, the aromaticity of hexagonal Na clusters was quantified by means of the nucleus-independent chemical shift and electronic multicenter indices. It was shown that the aromaticity of hexagonal Na-clusters is of the same order as the aromaticity of analogous benzenoid hydrocarbons. In the present study current density maps are used to rationalize the aromaticity of polycyclic Na clusters. It is shown that although polycyclic Na systems sustain a diatropic ring current, the induced current density is several times weaker than in analogous benzenoid hydrocarbons. A detailed analysis indicates that the current density in hexagonal Na systems is almost completely determined by four HOMO σ electrons.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Optical response of small closed-shell sodium clusters

Absorption spectra of closed-shell Na(2), Na(3) (+), Na(4), Na(5) (+), Na(6), Na(7) (+), and Na(8) clusters are calculated using a complex Bethe-Salpeter equation derived using a conserving linear response method. In the framework of a quasiparticle approach, we determine electron-hole correlations in the presence of an external field. The calculated results are in excellent agreement with experimental spectra, and some possible cluster geometries that occur in experiments are analyzed. The position and the broadening of the resonances in the spectra arise from a consistent treatment of the scattering and dephasing contributions in the linear response calculation. Comparison between the experimental and the theoretical results yields information about the cluster geometry, which is not accessible experimentally.