Evolution of superhalogen properties in PtCl(n) clusters

We have systematically calculated the ground state geometries, relative stability, electronic structure, and spectroscopic properties of PtCl(n) (n = 1-7) clusters. The bonding in these clusters is dominated by covalent interaction. In neutral clusters, chlorine atoms are chemically bound to Pt up to n = 5. However, in neutral PtCl(6) and PtCl(7) clusters, two of the chlorine atoms bind molecularly while the remaining bind as individual atoms. In the negative ions, this happens only in the case of PtCl(7) cluster. The geometries of both neutral and anionic clusters can be considered as fragments of an octahedron and are attributed to the stabilization associated with splitting of partially filled d orbitals under the chloride ligand field. The electron affinity of PtCl(n) clusters rises steadily with n, reaching a maximum value of 5.81 eV in PtCl(5). PtCl(n) clusters with n ≥ 3 are all superhalogens with electron affinities larger than that of chlorine. The accuracy of our results has been verified by carrying out photoelectron spectroscopy experiments on PtCl(n)(-) anion clusters.     

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.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Structure and vibrations of Ga(n)N(n) (n = 3-10) clusters

The structure and harmonic vibrations of Ga(n)N(n) (n = 3-10) clusters have been investigated using the B3LYP (Becke 3-parameter-Lee-Yang-Parr) density functional theory. All structures are found to be cumulenic D(nh) rings (equal bonds, alternating angles), with one intense out of plane mode and three infrared-active degenerate modes, of which the highest one is extremely intense and asymptotically increases to 1029 cm(-1) for n = 10. Comparisons with C2n, B(n)N(n), and Al(n)N(n) clusters, the structure and bonding type for the Ga(n)N(n) (n=3-10) clusters are consistent with those of the C2n (n = 3, 5, 7, ...) clusters, the B(n)N(n) (n = 3-10), and Al(n)N(n) (n = 3-9) clusters.     

Fragmentation by electron impact ionization and intracluster reactions of size selected (N2H4) n and (OCS) n clusters

The hydrogen-bonded (N₂H₄) _n clusters and the van der Waals (OCS) _n clusters are size selected in a scattering experiment with a He beam up to the cluster sizen=6. By measuring the angular distributions of the scattered clusters the complete fragmentation pattern of electron impact ionization is obtained. For Hydrazine the two main fragment masses are the protonated species (N₂H₄) _n?1H⁺ and with somewhat weaker intensities also the nominal ion mass (N₂H₄) _n ⁺ . The largest intensity is observed for the monomer ion N₂H ₄ ⁺ to which clusters up ton=5 fragment. For carbonylsulfide, completely different results are obtained. Aside from the fragments of the OCS monomer and the van der Waals cluster fragments (OCS) ₂ ⁺ and (OCS) ₃ ⁺ signals at mass S ₂ ⁺ , S ₃ ⁺ and S₂OCS⁺ are detected. This indicates a fast chemical reaction in the cluster according to: S + OCS → CO + S₂ which occurs for clusters of sizen ≥ 2. Peaks at S ₃ ⁺ and S₂OCS⁺ are seen for the first time forn ≥ 5 according to a further reaction of S₂ in the cluster.     

Optical properties of (GaAs)n clusters (n = 2-16)

The electronic and geometrical structures of the lowest triplet states of (GaAs) n clusters ( n = 2-16) are studied using density functional theory with generalized gradient approximation (DFT-GGA). It is found that the triplet-state geometries are different from the corresponding singlet-state geometries; for n = 2-8, 10, and 11, the triplets and singlets have different topologies, while the (GaAs) 9, (GaAs) 12, (GaAs) 15, and (GaAs) 16 triplets possess a reduced symmetry, due to Jahn-Teller distortions. Except for GaAs, the singlet states are the ground states. Excitation energies and oscillator strengths are computed for excitations from the ground state to ten singlet states of all (GaAs) n clusters using time-dependent density functional theory. The adiabatic singlet-triplet gap is compared to the vertical gap, and the difference in the eigenvalues of the highest-occupied and lowest-unoccupied molecular orbitals (the HOMO-LUMO gap). While these three values show large oscillations for small n, they approach each other as the cluster size grows. Thus, the HOMO-LUMO gap computed using the DFT-GGA approach presents a rather reliable estimate of the adiabatic singlet-triplet gap.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Structure and stability of (A1N)n clusters

AIN and AI₂N₂ have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)_n (n = 1—15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists Al-N bond in the ground state structures of (AIN)_n clusters; and the “magical number” regularity of (AIN)_n is those whose atom number is 4, 8, 12, 16, 20, etc, all of which are times of four.     

Evolution of the electronic properties of Snn- clusters (n=4-45) and the semiconductor-to-metal transition

The electronic structure of Sn(n) (-) clusters (n=4-45) was examined using photoelectron spectroscopy at photon energies of 6.424 eV (193 nm) and 4.661 eV (266 nm) to probe the semiconductor-to-metal transition. Well resolved photoelectron spectra were obtained for small Sn(n) (-) clusters (n< or =25), whereas more congested spectra were observed with increasing cluster size. A distinct energy gap was observed in the photoelectron spectra of Sn(n) (-) clusters with n< or =41, suggesting the semiconductor nature of small neutral tin clusters. For Sn(n) (-) clusters with n> or =42, the photoelectron spectra became continuous and no well-defined energy gap was observed, indicating the onset of metallic behavior for the large Sn(n) clusters. The photoelectron spectra thus revealed a distinct semiconductor-to-metal transition for Sn(n) clusters at n=42. The spectra of small Sn(n) (-) clusters (n< or =13) were also compared with those of the corresponding Si(n) (-) and Ge(n) (-) clusters, and similarities were found between the spectra of Sn(n) (-) and those of Ge(n) (-) in this size range, except for Sn(12) (-), which led to the discovery of stannaspherene (the icosahedral Sn(12) (2-)) previously [L. F. Cui et al., J. Am. Chem. Soc. 128, 8391 (2006)].     

Correlations between bonding, size, and second hyperpolarizability (gamma) of small semiconductor clusters: ab initio study on Al(n)P(n) clusters with n=2, 3, 4, 6, and 9

A comprehensive investigation of the correlation between the second hyperpolarizability and the bonding and structural characteristics of stoichiometric aluminum phosphide clusters up to 18 atoms is presented. Several aluminum phosphide species displaying different types of configurations and bonding have been studied. The obtained ab initio and density functional finite field results suggest that the ionic AlP clusters are considerably less hyperpolarizable than the covalent bonded species. Other structural features such as symmetry, atoms' arrangement, and shape also play an important role on the hyperpolarizabilities of those species. However, they are only noticeable among clusters characterized by the same bonding patterns. Furthermore, the results of this study demonstrate that the bonding which is determined by the atoms' arrangement of a cluster has a more profound effect on the second hyperpolarizability than the cluster's composition or size. In addition, the mean second hyperpolarizability increases with the increasing number of atoms, assuming that the bonding characteristics among the clusters of increasing size are similar. On the other hand, the hyperpolarizability per atom rapidly decreases with the increase of atoms' number in the cluster and converges to values of approximately 900e(4)a(0)(4) and approximately 1300e(4)a(0)(4)E(h) (-3) at the HF/cc-pVDZ and MP2/cc-pVDZ levels of theory respectively. Lastly, this work provides the first systematic study on the hyperpolarizabilities of small aluminum phosphide clusters which, in their covalent forms, exhibit larger second order hyperpolarizabilities than the well studied small gallium arsenide clusters.     

Electron affinities of Al(n) clusters and multiple-fold aromaticity of the square Al4(2-) structure

The concept of aromaticity was first invented to account for the unusual stability of planar organic molecules with 4n + 2 delocalized pi electrons. Recent photoelectron spectroscopy experiments on all-metal MAl(4)(-) systems with an approximate square planar Al(4)(2-) unit and an alkali metal led to the suggestion that Al(4)(2-) is aromatic. The square Al(4)(2-) structure was recognized as the prototype of a new family of aromatic molecules. High-level ab initio calculations based on extrapolating CCSD(T)/aug-cc-pVxZ (x = D, T, and Q) to the complete basis set limit were used to calculate the first electron affinities of Al(n)(), n = 0-4. The calculated electron affinities, 0.41 eV (n = 0), 1.51 eV (n = 1), 1.89 eV (n = 3), and 2.18 eV (n = 4), are all in excellent agreement with available experimental data. On the basis of the high-level ab initio quantum chemical calculations, we can estimate the resonance energy and show that it is quite large, large enough to stabilize Al(4)(2-) with respect to Al(4). Analysis of the calculated results shows that the aromaticity of Al(4)(2-) is unusual and different from that of C(6)H(6). Particularly, compared to the usual (1-fold) pi aromaticity in C(6)H(6), which may be represented by two Kekulé structures sharing a common sigma bond framework, the square Al(4)(2-) structure has an unusual "multiple-fold" aromaticity determined by three independent delocalized (pi and sigma) bonding systems, each of which satisfies the 4n + 2 electron counting rule, leading to a total of 4 x 4 x 4 = 64 potential resonating Kekulé-like structures without a common sigma frame. We also discuss the 2-fold aromaticity (pi plus sigma) of the Al(3)(-) anion, which can be represented by 3 x 3 = 9 potential resonating Kekulé-like structures, each with two localized chemical bonds. These results lead us to suggest a general approach (applicable to both organic and inorganic molecules) for examining delocalized chemical bonding. The possible electronic contribution to the aromaticity of a molecule should not be limited to only one particular delocalized bonding system satisfying a certain electron counting rule of aromaticity. More than one independent delocalized bonding system can simultaneously satisfy the electron counting rule of aromaticity, and therefore, a molecular structure could have multiple-fold aromaticity.     

Structure and properties of the aluminum borates Al(BO2)n and Al(BO2)n(-), (n = 1-4)

The geometrical and electronic structures of Al(BO(2))(n) and Al(BO(2))(n)(-) (n = 1-4) clusters are computed at different levels of theory including density functional theory (DFT), hybrid DFT, double-hybrid DFT, and second-order perturbation theory. All aluminum borates are found to be quite stable toward the BO(2) and BO(2)(-) loss in the neutral and anion series, respectively. Al(BO(2))(4) belongs to the class of hyperhalogens composed of smaller superhalogens, and should possess a large adiabatic electron affinity (EA(ad)) larger than that of its superhalogen building block BO(2). Indeed, the aluminum tetraborate possesses the EA(ad) of 5.6 eV, which, however, is smaller than the EA(ad) of 7.8 eV of the AlF(4) supehalogen despite BO(2) is more electronegative than F. The EA(ad) decrease in Al(BO(2))(4) is due to the higher thermodynamic stability of Al(BO(2))(4) compared to that of AlF(4). Because of its high EA and thermodynamic stability, Al(BO(2))(4) should be capable of forming salts with electropositive counter ions. We optimized KAl(BO(2))(4) as corresponding to a unit cell of a hypothetical KAl(BO(2))(4) salt and found that specific energy and energy density of such a salt are competitive with those of trinitrotoluol (TNT).     

Structure and stability of Al13H(n) (n=1-13) clusters: exceptional stability of Al13H13

We have performed density functional calculations for the structure and stability of Al(13)H(n) (n=1-13) clusters. Population analysis has shown significant charge transfer occurring from the Al cluster to the H atoms. The population for Al(13) varies from 0.24 (Al(13)H) to 2.83 (Al(13)H(13)). The shape of Al(13) moieties in the Al(13)H(n) (n>/=8) clusters is significantly distorted from the icosahedral structure of Al(13) and is a "cagelike" form. Al(13)H(13) has a capped icosahedron as the ground-state structure, similar to B(13)H(13), while the shape of B(13) (planar) is different from Al(13) (icosahedral). The Al(13)H(13) cluster is predicted to be exceptionally stable on the basis of the high stabilization energy and the negative nucleus independent chemical shift value.     

Density functional calculation of the structure and electronic properties of Cu(n)O(n) (n = 1-8) clusters

Ab initio simulations and calculations were used to study the structures and stabilities of copper oxide clusters, Cu(n)O(n) (n = 1-8). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. For n ≥ 4, the clusters are nonplanar. Selected electronic properties including atomization energies, ionization energies, electron affinities, and Bader charges were calculated and examined as a function of n.     

Density-functional study of structural and electronic properties of Si(n)C(n) (n=1-10) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic structure of Si(n)C(n) (n=1-10) clusters. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster size n equals 4. Cagelike structures are favored as the cluster size increases. A distinct segregation between the silicon and carbon atoms is observed for these clusters. It is found that the C atoms favor to form five-membered rings as the cluster size n increases. However, the growth motif for Si atoms is not observed. The Si(n)C(n) clusters at n=2, 6, and 9 are found to possess relatively higher stability. On the basis of the lowest-energy geometries obtained, the size dependence of cluster properties such as binding energy, HOMO-LUMO gap, Mulliken charge, vibrational spectrum, and ionization potential has been computed and analyzed. The bonding characteristics of the clusters are discussed.     

Infrared spectra of V(n)Bz(n+1) sandwich clusters: a theoretical study of size evolution

Results of density functional theory computations of infrared (IR) spectra of linear sandwich V(n)Bz(n+1), n = 1-6, complexes are presented. It is shown that the systematic changes in the spectra as a function of the complex size can be categorized and understood in terms of responses of the "parent" modes of the Bz molecule and the VBz complex. The analysis presented should be applicable to a broad class of linear sandwich systems.     

Theoretical investigation of the large nonlinear optical properties of (HCN)n clusters with Li atom

Two new classes of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) clusters with the electride characteristic are formed in theory by the metal Li atom attaching to the (HCN)(n) (n = 1, 2, 3) clusters. Because of the interaction between the Li atom and the (HCN)(n) part, the 2s valence electron of the Li atom becomes a loosely bound excess electron. Our high-level ab initio calculations show that these new clusters with the excess electron have large first hyperpolarizabilities, for example, beta(0) = -15,258 au for (HCN)...Li and beta(0) = -3401 au for Li...(HCN) at the QCISD/6-311++G(3df,3pd) level (only beta(0) = -2.8 au for HCN monomer(26)). Obviously, the excess electron from the Li atom plays a crucial role in the large first hyperpolarizabilities of these clusters. The beta(0) value of (HCN)(n)...Li (beta(0) > 10(4) au, from sigma --> pi* transition) is larger than that of Li...(HCN)(n) (beta(0) > 10(3) au, from sigma --> sigma* transition) for n = 1, 2, or 3. In addition, two interesting rules have been observed. They are that |beta(0)| decreases with lengthening of the HCN chain for (HCN)(n)...Li clusters and that |beta(0)| increases as n increases for Li...(HCN)(n) clusters. In this paper, we discuss two classes of clusters that are highly similar to the electride structure model, of which the structural characteristics are that alkali metal atoms ionize to form cations and trapped electrons under the action of other polar molecules. Thus, the investigation on the large first hyperpolarizabilities of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) may prompt one to study the unusual nonlinear optical responses of some electrides.     

Structures and electronic properties of small FeB n (n=1-10) clusters

The geometries, stabilities, electronic properties, and magnetism of FeB(n) clusters up to n=10 are systematically studied with density functional theory. We find that our optimized structures of FeB(2), FeB(3), FeB(4), and FeB(5) clusters are more stable than those proposed in previous literature. The results show that it is favorable for the Fe atom to locate at the surface, not at the center of the cluster, and that FeB(4) and FeB(9) clusters exhibit high stability. For all the FeB(n) clusters studied, we find the charge transfer from Fe to B site and the coexistence of ionic and covalent bonding characteristics. The computed total magnetic moments of the lowest-energy structures oscillate with the cluster size and are quenched at n=4, 6, 8, and 10.     

Structure and properties of Mn(n), Mn(n)-, and Mn(n)+ clusters (n = 3-10)

Electronic and geometrical structures of Mn(3)-Mn(10) together with their singly negatively and positively charged ions are computed using density functional theory with generalized gradient approximation. The ground-state spin multiplicities in the neutral series are 16, 21, 4, 9, 6, 5, 2, and 5, for Mn(3)-Mn(10), respectively. Thus, there is a transition from a ferromagnetic ground state to a ferrimagnetic ground state at Mn(5). The energy difference between ferrimagnetic and ferromagnetic states in Mn(n) grows rapidly with increasing n and exceeds 2 eV in Mn(10). The corresponding change from ferro- to ferrimagnetic ground state occurs at Mn(6)(-) and Mn(3)(+) in the anionic and cationic series, respectively. Beginning with Mn(6), the ion spin multiplicities differ from that of the neutral by +/-1 (i.e., they obey the empirical "+/-1 rule"). We found that the energy required to remove an Mn atom is nearly independent of the charge state of an Mn(n) cluster and the number of atoms in the cluster, except for Mn(3). The results of our calculations are in reasonable agreement with experiment, except for the experimental data on the magnetic moments per atom, where, in general, we predict smaller values than the experiment.