Density functional theory study of small nickel clusters

The stable geometries and atomization energies for the clusters Ni _n (n = 2–5) are predicted with all-electron density functional theory (DFT), using the BMK hybrid functional and a Gaussian basis set. Possible isomers and several spin states of these nickel clusters are considered systematically. The ground spin state and the lowest energy isomers are identified for each cluster size. The results are compared to available experimental and other theoretical data. The molecular orbitals of the largest cluster are plotted for all spin states. The relative stabilities of these states are interpreted in terms of superatom orbitals and no-pair bonding.     

Architecture, electronic structure and stability of TM@Ge(n) (TM = Ti, Zr and Hf; n = 1-20) clusters: a density functional modeling

The present study reports the geometry, electronic structure and properties of neutral and anionic transition metal (TM = Ti, Zr and Hf)) doped germanium clusters containing 1 to 20 germanium atoms within the framework of linear combination of atomic orbitals density functional theory under spin polarized generalized gradient approximation. Different parameters, like, binding energy (BE), embedding energy (EE), energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO), ionization energy (IP), electron affinity (EA), chemical potential etc. of the energetically stable clusters (ground state cluster) in each size are calculated. From the variation of these parameters with the size of the clusters the most stable cluster within the range of calculation is identified. It is found that the clusters having 20 valence electrons turn out to be relatively more stable in both the neutral and the anionic series. The sharp drop in IP as the valence electron count increases from 20 to 21 in neutral cluster is in agreement with predictions of shell models. To study the vibrational nature of the clusters, IR and Raman spectrum of some selected TM@Ge_n (n = 15,16,17) clusters are also calculated and compared. In the end, relevance of calculated results to the design of Ge-based super-atoms is discussed.     

Mixing s orbitals into p and d orbitals. An attempt at bridging the angular overlap model and the valence shell electron pair repulsion model. Critique of the cellular ligand-field model

The stereochemistries of main group molecules have been discussed by using the angular overlap model in its molecular orbital oriented form (MO-AOM). Either ligand-field stabilisation of the ground state s²p^q−2 configuration, or s-p mixing, or both, provide a consistent bonding model for the stereochemistries. The transformation of the non-bonding orbitals into equivalent orbitals leads invariably to agreement with the lone-pair locations of the valence shell electron pair repulsion (VSEPR) model. The concepts of Hamiltonian-generated hybrids and pseudohemispherical molecular systems are found useful in this context. The MO-AOM formalism is also used for discussing s-d mixing in transition metal systems, and the energetic consequences within the ligand-field AOM (LF-AOM) are included. This is a second-order effect, which depends on squares and cross-products of radial parameters. It may still be quite large for tetragonal systems and for systems that deviate strongly from orthoaxiality. The usual ligand-additive property of the AOM is lost when the symmetry is lower than tetragonal and so is the energy separability into angular and radial factors. The cellular ligand-field model is found to be identical with the LF-AOM, except that its users consider it important not to acknowledge the formal hierarchy, MO-AOMLF-AOM, as relevant. The unintelligible concept of an active coordination void is found to be unnecessary and insufficient.     

Tuning the properties of M(diimine)(dithiolate) complexes - The role of the metal and solvent effect. A combined experimental, DFT and TDDFT study

A combined experimental and DFT/TDDFT study on a series of seven M(diimine)(dithiolate) complexes of Group VIII metals has been performed. This analysis focuses mainly on three aspects: (a) the role of the metal, (b) the connection of NLO properties, through the intrinsic hyperpolarizability, with the slope of solvatochromic plots and (c) the effect of solvation on the valence orbitals of the complexes. Besides, the molecular and the electronic structure as well as the bonding scheme of these complexes are also explored. The three aforementioned aspects were not satisfactorily clarified in the literature up to now. Moreover, as it is proved, they possess a central role in the experimental design of the reactions in which these complexes take place or in the design of the synthesis of compounds with pre-required properties.     

Electronic structure theory based study of proline interacting with gold nano clusters

Interaction between metal nanoparticles and biomolecules is important from the view point of developing and designing biosensors. Studies on proline tagged with gold nanoclusters are reported here using density functional theory (DFT) calculations for its structural, electronic and bonding properties. Geometries of the complexes are optimized using the PBE1PBE functional and mixed basis set, i. e., 6-311++G for the amino acid and SDD for the gold clusters. Equilibrium configurations are analyzed in terms of interaction energies, molecular orbitals and charge density. The complexes associated with cluster composed of an odd number of Au atoms show higher stability. Marked decrease in the HOMO-LUMO gaps is observed on complexation. Major components of interaction between the two moieties are: the anchoring N-Au and O-Au bond; and the non covalent interactions between Au and N-H or O-H bonds. The electron affinities and vertical ionization potentials for all complexes are calculated. They show an increased value of electron affinity and ionization potential on complexation. Natural bond orbital (NBO) analysis reveals a charge transfer between the donor (proline) and acceptor (gold cluster). The results indicate that the nature of interaction between the two moieties is partially covalent. Our results will be useful for further experimental studies and may be important for future applications.     

Metal cluster topology. 2. Gold clusters

Previously developed methods for the treatment of polyhedral boranes, carboranes, and metal clusters are extended to the treatment of gold clusters, which present a variety of new problems. In most cases gold atoms in such cluster compounds do not employ the usual 9-orbital sp³d⁵ spherical bonding orbital manifold. Instead almost all non-tetrahedral gold clusters consist of a center gold atom surrounded by a puckered polygonal belt of peripheral gold atoms generally with one or more additional peripheral gold atoms in distal positions above and/or below the belt. The peripheral gold atoms in such clusters use a 7-orbital spd⁵ cylindrical bonding orbital manifold, but their residual two orthogonal anti- bonding p orbitals can receive electron density from the filled d orbitals of adjacent peripheral gold atoms through dσ → pσ^* and/or dπ → pπ^* backbonding leading to bonding distances between adjacent peripheral gold atoms. Centered gold clusters can be classified into either spherical or toroidal clusters depending upon whether the center gold atom uses a 9-orbital sp³d⁵ spherical bonding orbital manifold or an 8-orbital sp²d⁵ toroidal bonding orbital manifold, respectively. The topology of the core bonding in gold clusters is generally not that of the K_n complete graph found in other clusters but instead mimics the topology of the polyhedron formed by the surface atoms. This apparently is a consequence of the poor lateral overlap of the cylindrical spd⁵ manifolds of the peripheral gold atoms. Examples of non-centered gold clusters treated in this paper include the squashed pentagonal bipyramidal Au₇(PPh₃)₇⁺ and the edge-fused bitetrahedral (Ph₃P)₄Au₆[Co(CO)₄]₂ which may be regarded as a ‘perauraethylene’ in which the six cluster gold atoms correspond to the six atoms of ethylene including a double bond between the two gold atoms corresponding to the two ethylene carbon atoms.     

Metal-sulfur dπ-pπ buffering of the oxidations of metal-thiolate complexes: Photoelectron spectroscopy of (η-C5H5)Fe(CO)2SR (SR = SCH3, SBu) and (η-C5H5)Re(NO)(PR3)SCH3 (PR3 = PPr3, PPh3)

The metal-sulfur bonding present in the transition metal-thiolate complexes CpFe(CO)₂SCH₃, CpFe(CO)₂S^tBu, CpRe(NO)(PⁱPr₃)SCH₃, and CpRe(NO)(PPh₃)SCH₃ (Cp = η⁵-C₅H₅) is investigated via gas-phase valence photoelectron spectroscopy. For all four complexes a strong dπ-pπ interaction exists between a filled predominantly metal d orbital of the [CpML₂]⁺ fragment and the purely sulfur 3pπ lone pair of the thiolate. This interaction results in the highest occupied molecular orbital having substantial M-S π^∗ antibonding character. In the case of CpFe(CO)₂SCH₃, the first (lowest energy) ionization is from the Fe-S π^∗ orbital, the next two ionizations are from predominantly metal d orbitals, and the fourth ionization is from the Fe-S π orbital. The pure sulfur pπ lone pair of the thiolate fragment is less stable than the filled metal d orbitals of the [CpFe(CO)₂]⁺ fragment, resulting in a Fe-S π^∗ combination that is higher in sulfur character than the Fe-S π combination. Interestingly, substitution of a tert-butyl group for the methyl group on the thiolate causes little shift in the first ionization, in contrast to the shift observed for related thiols. This is a consequence of the delocalization and electronic buffering provided by the Fe-S dπ-pπ interaction. For CpRe(NO)(PⁱPr₃)SCH₃ and CpRe(NO)(PPh₃)SCH₃, the strong acceptor ability of the nitrosyl ligand rotates the metal orbitals for optimum backbonding to the nitrosyl, and the thiolate rotates along with these orbitals to a different preferred orientation from that of the Fe complexes. The initial ionization is again the M-S π^∗ combination with mostly sulfur character, but now has considerable mixing among several of the valence orbitals. Because of the high sulfur character in the HOMO, ligand substitution on the metal also has a small effect on the ionization energy in comparison to the shifts observed for similar substitutions in other molecules. These experiments show that, contrary to the traditional interpretation of oxidation of metal complexes, removal of an electron from these metal-thiolate complexes is not well represented by an increase in the formal oxidation state of the metal, nor by simple oxidation of the sulfur, but instead is a variable mix of metal and sulfur content in the highest occupied orbital.     

Valence orbital response to conformers of n-butane

Individual outer valence orbital responses to rotations of the C–C central bond of butane (C₄H₁₀) are explored on the torsional potential energy surface. Orbital ionization energies, topologies and momentum distributions for the four most significant butane conformation are presented, as snapshots of the conformational variations. The analysis is based on quantum mechanically generated information from coordinate space and momentum space, a technique called dual space analysis (DSA). By comparison with experimental measurements of photo-electron spectra (PES) for energies and of electron momentum spectra (EMS) for energies and Dyson orbitals, we demonstrate that the individual outer valence orbitals of these conformers response differently to the rotations of the central C–C bond of n-butane. Orbital signatures of other higher energy conformations, such as orbitals la ₂ and 5a ₁ of conformation D (C_2v ), are identified. This finding indicates a co-existence of butane conformations, although the global minimum structure of anti-butane, A (C_2h ), is dominant. Orbital topology and electron charges redistribution during the transformation provide useful information on the chemical bonding and related chemical reactions.     

Effect of solvent environment on the CO band position in the infrared spectrum of trans-[Fe(CN)4(CO)2]

Density functional theory (DFT) is used to understand the effect of hydrogen bonding solvents on the CO band position in the infrared (IR) spectrum of a mono-iron complex, trans-[Fe^II(CN)₄(CO)₂]²⁻. This mono-iron complex has received much attention recently due its potential relation to the biosynthesis of Fe-only hydrogenase enzymes. Our calculations show that the polar solvent molecules preferentially hydrogen bond to the cyano ligands in this complex. The effect of such hydrogen bonding on the electron density distribution is analyzed in terms of the population in natural bond orbitals (NBO). Our results show that the presence of hydrogen bonding to the cyano ligands decreases the extent of back bonding from the metal to the carbonyl ligand. This results in decreased electron density in the π^∗ orbitals of the carbonyl bond leading to a strengthening of the CO bond and a consequent blue shift in the IR band position of the carbonyl group. We also show that the extent of blue shift correlates with the number of nearest neighbor solvent molecules.     

Principles of bonding and reactivity in transition metal cluster compounds

The bonding in transition metal cluster compounds is examined by partitioning the system into the component parts suggested by expressions for the total energy. The nature of MM (metal-metal) interactions, ML (metal-ligand) interactions and LL (ligand-ligand) interactions are examined, and their effect on the stability and hence structure of the system considered. The processes by which one structure can rearrange into another are discussed. Some consideration is given to the partitioning of a cluster into ML_j fragments, and the interactions between these fragments. Isolobal analogies are discussed in this context. The emphasis of this work is on the general principles behind the structure and reactivity of transition metal cluster compounds, rather than focusing on specific systems.     

Computational investigation of a new ion-pair receptor for calix[4]pyrrole

Theoretical studies of a new ion-pair receptor, meso-octamethylcalix[4]pyrrole (OMCP), and its interactions with the halide anions F(-), Cl(-), and Br(-) and the cesium halides CsF, CsCl, and CsBr have been performed. Geometries, binding energies, and binding enthalpies were evaluated with the restricted hybrid Becke three-parameter exchange functional (B3LYP) method using the 6-31+G(d) basis set and relativistic effective core potentials. The optimized geometric structures were used to perform natural bond orbital (NBO) analysis. The two typical types of hydrogen bonds, N-H…X(-) and C-H…X(-), were investigated. The results indicate that hydrogen bonding interactions are dominant, and that the halide anions (F(-), Cl(-), and Br(-)) offer lone pair electrons to the σ*(N-H) or σ*(C-H) antibonding orbitals of OMCP. In addition, electrostatic interactions between the lone pair electrons of the halide anion and the LP* orbitals of Cs(+) as well as cation-π interactions between the metal ion and π-orbitals of the pyrrole rings have important roles to play in the Cs(+)?OMCP?X(-) complexes. The current study further demonstrates that this easy-to-make OMCP host compound functions as not only an anion receptor but also an ion-pair receptor.     

The Electronic Structure and Chemicai Bonding of (η5 -C5H5)2LuCl·OC4H8: a localized INDO study

A localized INDO study revealed that the monomeric (η₅-C₅H₅)₂LuCl·OC₄H₈ is covalent in character. The main contribution of the metal to bonding is due to the 5d orbitals while the 4f orbitals are strongly localized. The stability of the monomer may be attributed to the great energy gap between the HOMO and the LUMO and the steric hindrance of the THF group. The possible dimerization of dicyclopentadienyl lanthanide chlorides and the complexing activation of LnCl bond are discussed.     

Ab initio calculations of electron distributions in heme-CO models

We have, by the use of ab initio calculations, found a back-bonding state of pi symmetry close to the Fermi level for CO bound to FeN5C14. We thus find it likely that small shifts of the redox potential magnitude of EF - EV magnitude of will cause relatively large changes of the CO vibrational frequency. The separation of Fe 3d orbitals in our heme model is found to agree with what is predicted by ligand field theory for Oh symmetry. This paper presents nonrelativistic Hartree-Fock-Slater calculations of the 5 sigma bonding and 2 pi back-bonding between CO and Fe. The effects of up to 19 additional atoms are discussed for models of heme (COFe to COFeN5C14). The filled back-bonding state is found to be strongly influenced by second nearest neighbor atoms. By use of symmetry orbitals we have resolved the Fe 3d orbitals into the T2g and Eg representations of the Oh point group and find the former states to be occupied whereas the latter are unoccupied. The difference in occupancy is reduced when the CO ligand is removed which also causes an increased density of states at the Fermi level, i.e., the highest occupied and lowest unoccupied orbitals. Possible correlations between our data and experimental results are discussed for heme proteins as well as for metal surfaces.     

Metal cluster topology. 1. Osmium carbonyl clusters

Important theoretical approaches to metal cluster bonding including the Wade-Mingos skeletal electron pair method, the Teo topological electron count, the King-Rouvray graph theory derived method, and Lauher's extended Hückel calculations are shown to agree in their apparent skeletal electron counts for the most prevalent metal cluster polyhedra including the tetrahedron, the trigonal bipyramid (both ordinary and elongated), square pyramid, octahedron, bicapped tetrahedron, pentagonal bipyramid, and capped octahedron. The graph theory derived method is used to treat osmium carbonyl clusters containing from five to eleven osmium atoms. In this connection most osmium carbonyl clusters can be classified into the following types: (1) Clusters exhibiting edge- localized bonding containing multiple tetrahedral chambers (e.g., Os₅(CO)₁₆, Os₆(CO)₁₈, H₂Os₇(CO)₂₀ and HOs₈(CO)₂₂⁻); (2) Capped octahedral clusters derived from osmium carbonyl fragments of the type Os_6+p(CO)_19+2p (p = 0, 1, 2, and 4) (e.g., Os₆- (CO)₁₈²⁻, Os₇(CO)₂₁, Os₈(CO)₂₂²⁻, and H₄Os₁₀- (CO)₂₄²⁻). Other more unusual osmium carbonyl clusters such as the planar Os₆(CO)₁₇ [P(OCH₃)₃]₄, the Os₉ cluster [Os₉(CO)₂₁C₃H₂R]⁻, and the Os₁₁ cluster Os₁₁C(CO)₂₇²⁻ can also be treated satisfactorily by these methods. The importance of the number of ligands around isoelectronic Os_n systems in determining the cluster polyhedron is illustrated by the different cluster polyhedra found for each member of the following isoelectronic pairs: HOs₆- (CO)₁₈⁻/H₂Os₆(CO)₁₈. Os₇(CO)₂₁/H₂Os₇(CO)₂₀, Os₈(CO)₂₂²⁻/HOs₈(CO)₂₂⁻. The tendency for osmium carbonyl clusters frequently to form polyhedra exhibiting edge-localized rather than globally delocalized bonding relates to the facility for osmium carbonyl vertices to contribute more than three internal orbitals to the cluster bonding. In this way Wade's well-known analogy between boron hydride clusters and metal clusters, which assumes exactly three internal orbitals for each vertex atom, is frequently no longer followed in the case of osmium carbonyl clusters.     

Orbital based electronic structural signatures of the guanine keto G-7H/G-9H tautomer pair as studied using dual space analysis

Electronic structural signatures of the guanine-7H and guanine-9H tautomers have been investigated on an orbital by orbital basis using dual space analysis. A combination of density functional theory (B3LYP/TZVP), the statistical average of model orbital potentials (SAOP/TZ2P) method and outer valence Green's function theory (OVGF/TZVP) has been used to generate optimal tautomer geometries and accurate ionization energy spectra for the guanine tautomer pair. The present work found that the non-planar form for both of the guanine keto pair possesses lower energies than their corresponding planar counterparts, and that the canonical form of the guanine-7H tautomer has slightly lower total energy than guanine-9H. This latter result is in agreement with previous experimental and theoretical findings. In the planar guanine pair the geometric parameters and anisotropic molecular properties are compared, focusing on changes caused by the mobile proton transfer. It is demonstrated that the mobile proton only causes limited disturbance to isotropic properties, such as geometry and the energetics, of the guanine keto tautomer pair. The exception to this general statement is for related local changes such as the N((7))-C((8)) and C((8))-N((9)) bond length resonance between the single and double bonds, reflecting the nitrogen atom being bonded with the mobile proton in the tautomers. The mobile proton distorts the electron distribution of the tautomers, which leads to significant changes in the molecular anisotropic properties. The dipole moment of guanine-7H is altered by about a factor of three, from 2.23 to 7.05 D (guanine-9H), and the molecular electrostatic potentials also reflect significant electron charge distortion. The outer valence orbital momentum distributions, which were obtained using the plane wave impulse approximation (PWIA), have demonstrated quantitatively that the outer valence orbitals of the tautomer pair can be divided into three groups. That is orbitals 1a'-7a' and 18a', which do not have visible alternations in the tautomeric process (which consist of either pi orbitals or are close to the inner valence shell); a second group comprising orbitals 19a'-22a', 25a', 26a', 28a', 29a' and 31a', which show small perturbations as a result of the mobile hydrogen locations; and group three, orbitals 23a', 24a', 27a', 30a' and 32a', which demonstrate significant changes due to the mobile proton transfer and are therefore considered as signature orbitals of the G-7H/G-9H keto tautomeric process.     

Valence-tautomerism in high-valent iron and manganese porphyrins

Iron and manganese hemes are "high-valent" when the valence state of the metal exceeds III. Redox chemistry of the high valent metal complexes involves redistribution of holes and electrons over the metal ion and the porphyrin and axial ligands, defined as valence tautomerism. Thus, catalytic pathways of heme-containing biomolecules such as peroxidases, catalases and cytochromes P450 involve valence tautomerism, as do pathways of biomimetic oxygen transfer catalysis by manganese porphyrins, robust catalysts with potential commercial value. Determinants of the site of electron abstraction are key to understanding valence tautomerism. In model systems, metal-centered oxidation is supported by hard anionic axial ligands that are also strongly pi-donating, such as oxo, aryl, bix-methoxy and bis-fluoro groups. Manganese(IV) is more stable than iron(IV) and metal-centered one-electron oxidations occur with weaker pi-donating axial ligands such as bisazido, -isocyanato, -hypochlorito and bis chloro groups. Virtually all known high-valent iron porphyrin complexes oxidized by two-electrons above the ferric state are coordinated by the strongly pi-donating oxo or nitrido ligands. In all well-characterized oxo complexes, iron is in the ferryl state and the second oxidizing equivalent resides on the porphyrin. Complexes with iron(V) have not been definitively characterized. One-electron oxidation of oxomanganese(IV) porphyrin complexes gives the oxomanganese(IV) porphyrin pi-cation redicals. In aqueous solution, oxidation of Mn(III) complexes of tetra cationic N-methylpyridiniumylporphyrin isomers by monooxygen donors yields a transient oxomanganese(V) species.     

A theoretical and comparative CNDO study of chlorophylls a and b and their beryllium homologs

CNDO/II calculations of chlorophylls a and b and their beryllium homologs show that the 3d atomic orbitals of the metal atoms contribute significantly to the σ and π bonding energies. In both chlorophylls a and b replacement of magnesium by beryllium stabilizes the total molecular energy by 40 kcal/mol.