Quantum chemistry of quantum size‐effects in semiconductors: Small clusters electronic structure calculations

Ab initio RHF SCF calculations are used for some small clusters M_xX_y, where M=Cd, Ag; X=S, I; and x, y≤7. Variation of electronic structure with size for some clusters with the bulklike tetrahedral coordination and with the lower symmetry allows one to predict their possible geometries which are compared with experimental data on the existence of the clusters. The chemical‐bonding factor (the chemical nature of bounded atoms, coordination number for metal and nonmetal atoms, hybridization, etc.) is of more importance for properties of the clusters than is the familiar quantum confinement effect of semiconductor clusters. The essential difference in regularities of small cluster formation is analyzed for CdS‐ and AgI‐based structures. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 337–341, 1999     

Nickel and copper doped palladium clusters from a first-principles perspective

A complete study on the evolution of structures and the variation of the energy properties of MPd_n−1 (M = Ni and Cu; n = 2-13) clusters is presented. The study was performed employing auxiliary density functional theory. The obtained results were compared with the results of Pd_n clusters studied with the same methodology. For each cluster size, several structures were studied to determine the lowest energy structures. The initial structures for the geometry optimization were taken along ab initio Born-Oppenheimer molecular dynamics trajectories. Different potentials energy surfaces were studied. All cluster structures were fully optimized without any symmetry restriction. Stable structures, frequencies, spin multiplicities, averaged bond lengths, spin density plots, different energy properties, dipole and magnetic moments as well as charge transfers are reported. This investigation indicates that the palladium clusters doped with a Ni atom are the most stable and potentially the most chemical active ones.     

Ab initio study of electronic structures of Ptn clusters (n = 2–12)

Electronic structures of a series of Pt_n clusters (n = 2–12) have been calculated by ab initio method (SCF/MP2). The result shows that compared to that at the saturated coordination site, Pt at the unsaturated coordination site has lower Pt₆₅ electron occupancies, and the relationship between the electronic structure and the cluster size has been discussed. It is found that when the number of Pt in cluster reaches 7, electronic structures become more like the metallic ones. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62 : 427–436, 1997     

Structural electric dipole in small ionic nanocrystals

We present the results of gas phase electric dipole measurements for a series of M₁₈X₁₇ alkali–halide clusters. This cluster has a large structural dipole, which is due to the periodic arrangement of the ions in the nanocrystal and is directly related to the size of the particle. Experimental values are compared to the prediction of a Born Mayer model and to ab initio calculations. The results for the various salts are reproduced by our calculations.     

Nitrile Cluster Compounds [(M6X12)X2(RCN)4] (M=Nb, Ta; X=Cl, Br; R=Et, n-Pr, n-Bu)

Three new series of mixed-ligand clusters of the [(M₆X₁₂)X₂(RCN)₄] (M=Nb, Ta; X=Cl, Br; R=Et, n-Pr, n-Bu) composition have been prepared. It is supposed that four nitrile molecules and two halogen atoms are coordinated to the terminal octahedral coordination sites of the [M₆X₁₂]²⁺ unit.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

Modeling of self-organization of silicate systems: Precursor nanoclusters and self-assembly of Na<Subscript>3</Subscript>MSi<Subscript>3</Subscript>O<Subscript>9</Subscript> (M = Y,Eu-Lu; oP256) crystal structures producing two interpenetrating diamond-type frameworks

In the M-T-O model system (M is a polyvalent metal with CN ≥ 4; T is Si), cyclic clusters have been deduced as graphs in the T/M range from one to three. The case is considered when monocyclic cluster M₂T₂ is modified by T-tetrahedra that form diortho groups T₂. The M sites of the cluster have either topologically different local MT structures (four types) or identical local MT structures (two types). The cluster types for T/M = 3 obtained by modeling were used in analysis of one of the most complicated types of silicate crystal structures Na₃MSi₃O₉ (M = Y; Eu-Lu; T/M = 3) with the Pearson index oP256 and 64 independent atoms. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of the crystal structure: suprapolyhedral precursor nanocluster → primary chain → microlayer → microframework (supraprecursor) → ... three-dimensional framework. The calculation of the coordination sequences of site atoms in the 3D network of the MT framework MT₃O₉ revealed topological symmetry related to a three-dimensional separation of the framework into two interpenetrating frameworks. Each framework structure is generated by topologically equivalent cyclic precursor clusters Na₂M₂T₆ consisting of two YO₆ octahedra comprising three diortho groups Si₂O₇ and two Na atoms located above and below the ring center. The 3D graphs characterizing the connectivity of the centers of crystallographically equivalent clusters in the frameworks correspond to diamond-type networks.     

An ab initio investigation on (CO2)n and CO2(Ar)m clusters: geometries and IR spectra

An ab initio investigation on CO(2) homoclusters is done at MPWB1K6-31++G(2d) level of theory. Electrostatic guidelines are found to be useful for generating initial structures of (CO(2))(n) clusters. The ab initio minimum energy geometries of (CO(2))(n) with n=2-8 are T shaped, cyclic, trigonal pyramidal, tetragonal pyramidal, tetragonal bipyramidal, pentagonal bipyramidal, and pentagonal bipyramid with one CO(2) molecule attached to it. A test calculation on (CO(2))(20) cluster is also reported. The geometric parameters of the energetically most favored (CO(2))(n) clusters match quite well their experimental counterparts (wherever available) as well as those derived from molecular dynamics studies. The effect of clustering is quantified through the asymmetric C-O stretching frequency shift relative to the single CO(2) molecule. (CO(2))(n) clusters show an increasing blueshift from 1.8 to 9.6 cm(-1) on increasing number of CO(2) molecules from n=2 to 8. The energetics and geometries of CO(2)(Ar)(m) clusters have also been explored at the same level of theory. The geometries for m=1-6 show a predominant T type of the argon-CO(2) molecule interaction. Higher clusters with m=7-12 show that the argon atoms cluster around the oxygen atom after the saturation of the central carbon atom. The CO(2)(Ar)(m) clusters exhibit an increasing redshift in the C-O asymmetric stretch relative to CO(2) molecule of 0.7-5.6 cm(-1) with increasing number of argon atoms through m=1-8.     

Bond energies and structures of ammonia-sulfuric acid positive cluster ions

New particle formation in the atmosphere is initiated by nucleation of gas-phase species. The small molecular clusters that act as seeds for new particles are stabilized by the incorporation of an ion. Ion-induced nucleation of molecular cluster ions containing sulfuric acid generates new particles in the background troposphere. The addition of a proton-accepting species to sulfuric acid cluster ions can further stabilize them and may promote nucleation under a wider range of conditions. To understand and accurately predict atmospheric nucleation, the stabilities of each molecular cluster within a chemical family must be known. We present the first comprehensive measurements of the ammonia-sulfuric acid positive ion cluster system NH(4)(+)(NH(3))(n)(H(2)SO(4))(s). Enthalpies and entropies of individual growth steps within this system were measured using either an ion flow reactor-mass spectrometer system under equilibrium conditions or by thermal decomposition of clusters in an ion trap mass spectrometer. Low level ab initio structural calculations provided inputs to a master equation model to determine bond energies from thermal decomposition measurements. Optimized ab initio structures for clusters up through n = 3, s = 3 are reported. Upon addition of ammonia and sulfuric acid pairs, internal proton transfer generates multiple NH(4)(+) and HSO(4)(-) ions within the clusters. These multiple-ion structures are up to 50 kcal mol(-1) more stable than corresponding isomers that retain neutral NH(3) and H(2)SO(4) species. The lowest energy n = s clusters are composed entirely of ions. The addition of acid-base pairs to the core NH(4)(+) ion generates nanocrystals that begin to resemble the ammonium bisulfate bulk crystal starting with the smallest n = s cluster, NH(4)(+)(NH(3))(1)(H(2)SO(4))(1). In the absence of water, this cluster ion system nucleates spontaneously for conditions that encompass most of the free troposphere.     

Hexatellurium Rings in Coordination Polymers and Molecular Clusters: Synthesis and Crystal Structures of [M(Te6)]X3 (M = Rh,Ir; X = Cl,Br, I) and [Ru2(Te6)](TeBr3)4(TeBr2)2

The reaction of an electron‐rich transition metal M (M = Ru, Rh, Ir), tellurium and TeX₄ (X = Cl, Br, I) resulted in black crystals of five ternary coordination polymers with the general composition [M^III(Te₆)]X₃ (M = Rh, Ir) and of the molecular cluster compound [Ru^II₂(Te₆)](Te^IIBr₃)₄(Te^IIBr₂)₂. X‐ray diffraction on single‐crystals revealed that the compounds [M(Te₆)]X₃ crystallize isostructurally in the trigonal space group type R$\bar{3}$ c. In their crystal structures linear, positively charged [M^III(Te₆)] chains form the motif of a hexagonal rod packing. In the chain, each of the formally uncharged Te₆ molecules with chair conformation acts as a bis‐tridentate bridging ligand to two M atoms. The octahedrally coordinated M atoms are spiro atoms in the chain of trans vertices sharing heterocubane fragments. Including the isolated halide ions, which provide charge balance, the entire arrangement resembles a cut‐out of the α‐polonium structure type.In the monoclinic compound Ru₂Te₁₂Br₁₆ (space group P2₁/n), the ruthenium atoms of the hetero‐cubane core of the molecular cluster [Ru₂(Te₆)](TeBr₃)₄(TeBr₂)₂ are saturated by terminal bromidotellurate(II) groups. Again, the Te₆ ring is formally uncharged. With the tellurium atoms acting as electron‐pair donors the 18 electron rule is fulfilled for the M atoms in all compounds.     

Quantum-chemical modeling of the electronic structure and chemical bond of Sn<Subscript>0.875</Subscript>M<Subscript>0.125</Subscript>O<Subscript>2</Subscript> (M = Cr,Mn, Co)

The electronic structure of the Sn_0.875M_0.125O₂ compounds (M = Cr, Mn, Co) with a rutile structure and magnetic moments of the transition metal atoms in them were calculated by the ab initio spin-polarized linear muffin-tin orbital method. The electron density and electron localization function maps for these compounds were constructed. Based on these data, the effect of the composition of these phases on the electronic spectrum, chemical bond, and magnetic and transport properties were analyzed.     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Solvation of Na+ in argon clusters

The structures and stabilities of Ar(n)Na+ clusters (n < or = 54) are investigated using atomistic potentials fitted to reproduce ab initio calculations performed at the coupled-cluster level on the smaller clusters. Polarization effects are described using either the interaction between dipoles induced by the sodium ion, or a small charge transfer in the framework of a fluctuating charges model. In both models, extra three-body contributions of the Axilrod-Teller type are also included between the sodium ion and all pairs of argon atoms. The two models predict essentially similar growth patterns, and a transition in the metal ion coordination from 8 (square antiprism) to 12 (icosahedron) is seen to occur near n = 50, in response to the intrasolvent constraints.     

Silicon clusters: chemistry and structure

The chemical reactions of size selected silicon cluster ions (containing up to 70 atoms) have been studied with a number of different reagents using injected ion drift tube techniques. Both kinetic and equilibrium measurements have been performed as a function of temperature, and the influence of cluster annealing on chemical reactivity explored. Unlike metal clusters, where bulk behavior appears to be approached with around 30 atoms, large silicon clusters (n up to 70) are much less reactive than bulk silicon surfaces. These results suggest that the clusters in the size range examined here are not small crystals of bulk silicon, but have compact, high coordination number structures with few dangling bonds.     

Size resolved infrared spectroscopy of Na(CH3OH)n (n = 4-7) clusters in the OH stretching region: unravelling the interaction of methanol clusters with a sodium atom and the emergence of the solvated electron

Size resolved IR action spectra of neutral sodium doped methanol clusters have been measured using IR excitation modulated photoionisation mass spectroscopy. The Na(CH(3)OH)(n) clusters were generated in a supersonic He seeded expansion of methanol by subsequent Na doping in a pick-up cell. A combined analysis of IR action spectra, IP evolutions and harmonic predictions of IR spectra (using density functional theory) of the most stable structures revealed that for n = 4, 5 structures with an exterior Na atom showing high ionisation potentials (IPs) of ~4 eV dominate, while for n = 6, 7 clusters with lower IPs (~3.2 eV) featuring fully solvated Na atoms and solvated electrons emerge and dominate the IR action spectra. For n = 4 simulations of photoionisation spectra using an ab initio MD approach confirm the dominance of exterior structures and explain the previously reported appearance IP of 3.48 eV by small fractions of clusters with partly solvated Na atoms. Only for this cluster size a shift in the isomer composition with cluster temperature has been observed, which may be related to kinetic stabilisation of less Na solvated clusters at low temperatures. Features of slow fragmentation dynamics of cationic Na(+)(CH(3)OH)(6) clusters have been observed for the photoionisation near the adiabatic limit. This finding points to the relevance of previously proposed non-vertical photoionisation dynamics of this system.     

Geometrical and electronic properties of neutral and charged cesium clusters Cs(n) (n=2-10): a theoretical study

We have investigated the structure and electronic properties of cesium clusters following all electron ab initio theoretical methods based on configuration interaction, second-order Moller-Plesset (MP2) perturbation theory, and density-functional theory. Becke's three-parameter nonlocal hybrid exchange-correlation functional (B3LYP) is found to perform best on the present systems with a split valence 3-21G basis function. We have calculated the optimized geometries of neutral and singly charged cesium clusters having up to ten atoms, their binding energy per atom, ionization potentials (IPs), and adiabatic electron affinity (EA). Geometry optimizations for all the clusters are carried out without imposing any symmetry restriction. The neutral clusters having up to six atoms prefer planar structure and three-dimensional structure is preferred only when the number of atoms in a cluster is more than six. There is a good agreement between the present theoretical and reported experimental IP values for the neutral clusters with cluster size n相似文献   

Electronic structure and bonding in clusters: Theoretical studies

The electronic structures of small Al _n ,n=5, 9, 13, clusters with bulk geometry are studied using the ab initio Hartree-Fock-LCAO method. The cluster ground states have always multiplicity higher than the lowest possible value. However, the energy difference between ground and lowest low spin state decreases with increasing cluster size. The energy range of the Al _n cluster valence levels is comparable with the width of the occupied part of the 3sp band in bulk Al. The different binding mechanisms that arise when a CO molecule interacts with Al _n clusters in different coordination sites are analyzed in detail with the constrained space orbital variation (CSOV) method. Electrostatic and polarization contributions to the interaction are found to be important. Among charge transfer (donation) contributions π electron transfer from Al _n to CO corresponding to π backbonding is energetically more important than σ electron transfer from CO to Al _n characterizing the σ bond.     

Structure and stability of the mixed polymolecular complexes of nitrogen and carbon nonooxide: A quantum chemical study

The structure and stability of heteromolecular van der Waals clusters (N₂) _n CO _m ( _n = 1–7; m = 1–3) was studied using ab initio MP2(full)/6-311+G* and CCSD(full)/6-311+G* methods. For clusters with (n + m) > 3 the polyhedron structures are the most preferable, whose stability increases with the number of interacting molecules. Incorporation of CO molecules results in weakening of binding in the cluster and lowering the stereochemical rigidity relative to homomolecular systems. Increase of percentage of CO is followed by a decrease of stability of the clusters.     

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.