Cluster Molecular Orbitals Research Articles

The impact of anion electronic structure: similarities and differences in imidazolium based ionic liquids

In this paper the structural and energetic landscapes of ion-pair dimer conformers of 1,3-dimethylimidazolium based ionic liquids have been explored ([C1C1im][A])2, A = Cl–, [NO3]–, [MeSO4]–, [OTf]– and [BF4]–). A common low-energy conformer has been selected for full electronic structure analysis. We have compared and contrasted each cluster based on the relative hydrogen bonding ability (β-value) of the anion, which varies experimentally as Cl– > [NO3]– ≈ [MeSO4]– > [OTf]– ≈ [BF4]–. Correlations between experimental β-values, computed binding energies, charge transfer and various hydrogen bonding data have been made and outliers have been explained in terms of environmental effects present in the liquid phase. This is most evident in the structurally similar [MeSO4]– and [OTf]– anions that have very similar hydrogen bonding motifs, but significantly different β-values. Moreover, detailed analysis of the cluster molecular orbitals, for each anion, reveals a subtle interplay between two modes of interaction, an in-plane traditional H-bonding and inter-planar anion–π interaction. Inter-planar anion–π interactions are particularly prominent for the [NO3]– cluster. We have rationalized how the full range of interactions could impact on the structuring of ILs at surfaces and the effect these may have on viscosity.

Anomalous Diamagnetic Susceptibility in 13‐Atom Platinum Nanocluster Superatoms

We are used to being able to predict diamagnetic susceptibilities χD to a good approximation in atomic increments since there is normally little dependence on the chemical environment. Surprisingly, we find from SQUID magnetization measurements that the χD per Pt atom of zeolite-supported Pt13 nanoclusters exceeds that of Pt(2+) ions by a factor of 37-50. The observation verifies an earlier theoretical prediction. The phenomenon can be understood nearly quantitatively on the basis of a simple expression for diamagnetic susceptibility and the superatom nature of the 13-atom near-spherical cluster. The two main contributions come from ring currents in the delocalized hydride shell and from cluster molecular orbitals hosting the Pt 5d and Pt 6s electrons.

Electronic transport acrossS9sulfur clusters

The transport properties of ${\text{S}}_{9}$ clusters sandwiched between gold electrodes are investigated with a combination of density-functional theory and the nonequilibrium Green's-function method. In general we find a rather large conductance both when the cluster is oriented with its symmetry axis parallel to the transport direction and when it is perpendicular to it. In both cases the transmission is dominated by several closely spaced and extremely broad cluster molecular orbitals so that the transmission coefficient is almost flat around the gold Fermi level. This is only marginally affected by the external bias so that the $I\text{\ensuremath{-}}V$ characteristic remains almost linear at least up to 1 V and for both the orientations. Furthermore the electron transport is only little affected by the bond length between the cluster and the electrodes, with the largest sensitivity found for the perpendicular orientation. Our results are rationalized by analyzing the device density of states projected over the various molecular orbitals.

Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finite-temperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular orbitals in the vicinity of the Mott transition. In all cases studied, the charge transfer is found to be small, indicating weak Coulomb-induced orbital polarization despite sizable level splitting between orbitals. These results demonstrate that all cluster molecular orbitals take part in the Mott transition and that the insulating gap opens simultaneously across the entire Fermi surface. Thus, at half filling we do not find orbital-selective Mott transitions or a combination of band filling and Mott transition in different orbitals. Nevertheless, the approach toward the transition differs greatly between cluster orbitals, giving rise to a pronounced momentum variation along the Fermi surface, in agreement with previous works. The near absence of Coulomb-induced orbital polarization in these clusters differs qualitatively from single-site multiorbital studies of several transition-metal oxides, where the Mott phase exhibits nearly complete orbital polarization as a result of a correlation driven enhancement of the crystal-field splitting. The strong single-particle coupling among cluster orbitals in the single-band case is identified as the source of this difference.

INTERACTION BETWEEN TRANSITION METAL (TM) IONS AND LIGAND IONS IN TM: ZnSe CLUSTERS

A new approach for studying the electronic properties of the Ⅱ-Ⅵ compounds is presented , in which the atoms in a cluster is divided into the inner ones and boundary ones, the influence of the charge transfer on the environmental potential produced by the ion lattices outside the cluster is taken into account. The occupation number of the cluster molecular orbitals is calculated by a modified DV-SCC method with a new environmental potential. The net charges and the charge transfer of the clusters TM: ZnSe are investigated from the calculated electronic structure parameters. Some of new regularity, the behaviour and concept, due to the interaction between the transition-metal ions and ligand ions are discussed in brief.

High-T c superconductivity in potassium-doped fullerene, K xC 60, via coupled C 60 (pπ) cluster molecular orbitals and dynamic Jahn-Teller coupling

Recently observed superconductivity at 18 K in potassium-doped fullerene, K x C 60, may be due to Cooper pairing of partially occupied icosahedral C 60 cluster t 1u (pπ) molecular orbitals, induced by cooperative dynamic Jahn-Teller coupling of these orbitals to “soft-mode” vibrations of the C 60 molecules, leading to a BCS-like mechanism. Predicted are a nonvanishing isotope effect and T c increasing to 30 K or more with optimization of doping, and significant effects with pressure.

Ab initio cluster model approach to the chemisorption on mercury: Halogens and halides

The chemisorption of halogen atoms and halide anions on a mercury surface model has been studied at the ab initio level using non-empirical pseudo-potentials and moderately large basis sets. The main interactions are similar for halogens and halides although the former have smaller equilibrium distances and larger binding energies. These interactions are due to the mixing between the p atomic orbitais of the halogens and halides with the a lg and e lu cluster molecular orbitals with no evidence of back-bonding from the filled d mercury shell to the empty d shell of the halogen atoms or halides. The present ab initio results are compared with previous semi-empirical studies.

The multiple centre d pπ bond and its effects on the electronic structure of the transition metal clusters

In this paper, a new kind of chemical bond between metal atoms (M) and bridge (B) or terminal atoms (T), the multiple centre d pπ bond, has been found by calculating the electronic structure and by MO analysis of a series of 2–6 nuclear transition metal clusters. The MC d pπ bonding has a significant influence on the bond length R MB(T) and MM bond strength. The stronger the MC d pπ bonding, the shorter R MB(T) and the the stronger the MM bond. The calculation shows that M and B(T) orbital components of the d pπ bond are the main constituents of the frontier region of the cluster molecular orbitals, and the bonding leads to the transfer of energy levels of the MM interaction and the variation of the MM bonding character. Based on the MC d pπ bonding, an improved counting principle, which can be used to count CVE of the clusters with various oxidation states, is proposed and the electronic spectra of some binuclear and trinuclear Mo clusters are analysed.

Cluster molecular orbitals and an orbital symmetry view of solid phase transitions in perovskites

The molecular orbitals, normalization constants and energies of the M 8( O h ), M 4( T d ) and M 6( O h ) clusters are derived and tabulated through the d-atomic orbitals. A vector method, adapted to computer application, is devised to compute s, p and d overlap between variously oriented orbitals at atoms that do not have co-directional local axes. Mixing of σ, π and δ orbitals to give the same irreducible representation is also included. As illustrations, the orbitals of Sr 8, La 8, TiO 6 and AlO 6 clusters are computed by the Mulliken—Wolfsberg and Helmholz approximations. During solid phase transitions in the perovskite structures of SrTiO 3 and LaAlO 3, the TiO 6 octahedron rotates about the C 4 axis whereas the AlO 6 octahedron rotates about the C 3 axis. This difference is explained qualitatively in terms of the relative symmetries of the cluster HOMOs and LUMOs using the second-order Jahn—Teller effect. Allusions are made to the application of this cluster symmetry approach to other systems.

Novel tin(II) sites in X-ray crystal structures of the tin(II) halide sulphates K3Sn2(SO4)3X (X = Br or Cl)

The crystal structures of K3Sn2(SO4)3X (X = Br or Cl) have been determined by the heavy-atom method and refined by the full-matrix least-squares method to R= 0.0564 for the bromide and 0.0839 for the chloride. The crystals of both compounds are of the hexagonal space group P63(C66, no. 173) with a= 10.256(2), c= 7.582(4)A, and Z= 2 for K3Sn2(SO4)3Br, and a= 10.183(6), c= 7.540(2)A, and Z= 2 for K3Sn2(SO4)3Cl. The structures consist of three-dimensional networks of tin atoms and bridging sulphate groups with discrete potassium and halide ions in holes within the networks. The four tin atoms in the lattices are distributed together with two K+ ions in a six-fold general position and have three oxygen atoms at unusually long distances of 2.47, 2.57, and 2.63 A for the bromide and 2.45, 2.55, and 2.56 A for the chloride. The shortest tin–halogen contacts are 2.97 A for the chloride and 3.13 A for the bromide. The halide ion is surrounded in a distorted octahedron by tin(II) or potassium atoms. The arrangement of tin atoms, taken along with 119Sn Mossbauer data and the lengths of the Sn–O bonds in the structures, is consistent with cluster formation in which lone-pair electron density on the tin atoms is delocalised in cluster molecular orbitals.

Metal-metal bonds and metal-carbon bonds in the chemistry of molybdenum and tungsten alkoxides

Abstract : Metal-metal bonds are found in alkoxides of molybdenum and tungsten when the metal atoms are in oxidation states 2 through 5. Metal-metal bonds may be locailized and multiple or single in order, or may be delocalized in cluster molecular orbitals. The structures of these metal alkoxides are quite different from those seen previously. Metal-metal bonds provide a reservoir of electrons for redox reactions: the reservoir may be tapped in oxidative- addition reactions and filled in reductive-eliminatin reactions. Alkoxide ligands may act as four or two electron donor ligands and may readily change between terminal and bridging sites. This allows for the facile interconnversion of saturated and unsaturated metal centers. As strong Pi-donor ligands, they can enhance backbonding to pi-acid ligands on the same metal. By pi-donating to vacant metal d orbitals, they may suppress metal-hydride abstraction from coordinated alkyl, alkylidene and alkylidyne ligands and they stabilize metals in high oxidation states. A variety of steric control can be engineered by choice of alkyl (RO0 groups and this may greatly influence structure, M-M bonding and reactivity of coordinated ligands.