Extended Huckel Molecular Orbital Research Articles

Extended Hückel Calculations on Solids Using the Avogadro Molecular Editor and Visualizer

The “Yet Another extended Huckel Molecular Orbital Package” (YAeHMOP) has been merged with theAvogadro open-source molecular editor and visualizer. It is now possible to perform YAeHMOP calculations directly from the Avogadro graphical user interface for materials that are periodic in one, two, or three dimensions, and to visualize band structures, total and projected density of states, and crystal orbital overlap/Hamilton populations (COOPs/COHPs). Calculations on graphite, silicon, sodium, and a one-dimensional hydrogen chain are provided to illustrate the functionality. Similar exercises have been carried out in an upper-level undergraduate quantum theory course.

Geometric structure, electronic structure and optical absorption properties of one-dimensional thiolate-protected gold clusters containing a quasi-face-centered-cubic (quasi-fcc) Au-core: a density-functional theoretical study

Based on the recently reported atomic structures of thiolate-protected Au28(SR)20, Au36(SR)24, Au44(SR)28, and Au52(SR)32 clusters, a family of homogeneous, linear, thiolate-protected gold superstructures containing novel quasi-face-centered-cubic (quasi-fcc) Au-cores is theoretically envisioned, denoted as the Au20+8N(SR)16+4N cluster. By means of density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations, a unified view of the geometric structure, electronic structure, magic stable size and size-dependent NIR absorption properties of Au20+8N(SR)16+4N clusters is provided. We find that the Au20+8N(SR)16+4N clusters demonstrate oscillating transformation energies dependent on N. The odd-N clusters show more favorable (negative) reaction energies than the even-N clusters. The magic stability of recently reported Au28(SR)20, Au36(SR)24, Au44(SR)28, Au52(SR)32 and Au76(SR)44 clusters can be addressed from the relative reaction energies and geometric distortion of Au-cores. A novel 4N + 4 magic electron-number is suggested for the Au20+8N(SR)16+4N cluster. Using the polyhedral skeletal electron pair theory (PSEPT) and the extended Hückel molecular orbital (EHMO) calculations, we suggest that the magic 4N + 4 electron number is correlated with the quasi-fcc Au-cores, which can be viewed as double helical tetrahedron-Au4 chains. The size-dependent optical absorption properties of Au20+8N(SR)16+4N clusters are revealed based on TD-DFT calculations. We propose that these clusters are potential candidates for the experimental synthesis of atomically precise one-dimensional ligand protected gold superstructures with tunable NIR absorption properties.

English

Extended Huckel Molecular Orbital (EHMO) calculations were carried out on octahedral transition metal clusters with general formula (M6X8 iY6 a) (M = Molybdenum; X and Y = π-Donor Ligands) in order to rationalize their electronic structure. In these species the opti- mal metallic electron (ME) count is of 24 but for many clusters experimentally synthesized, the ME count can vary from 20 to 48 without dramatically altering the architecture of the octahedral cluster. Herein are reported the geometrical parameters and electronic properties, of a series of clusters with 20 to 24 valence electrons per cluster. The calculated characteristics for all the considered structures are in excel- lent agreement with the experimental ones and requires to learn more about the relationships that exist between their structural arrangement and electronic properties especially the number of electrons available for metal-metal bonding in M6 octahedral clusters. Keywords- Cluster Compounds, Molybdenum, Electron counting, Extended Huckel Molecular Orbital (EHMO) calculations, Electronic Struc- ture, Frontier orbitals.

Nickel poly-acetylide carbonyl clusters: structural features, bonding and electrochemical behaviour

The reactions of [NEt(4)](2)[Ni(6)(CO)(12)] with miscellaneous carbon halides (e.g. CCl(4), C(4)Cl(6)) in CH(2)Cl(2) have been extensively investigated particularly focusing on the stoichiometric ratio of the reagents and reaction temperature. This allowed the preparation of the previously known acetylide clusters [Ni(16)(C(2))(2)(CO)(23)](4-), [HNi(25)(C(2))(4)(CO)(32)](3-) and [Ni(22)(C(2))(4)(CO)(28)Cl](3-), as well as isolation and full characterisation of the closely related [Ni(17)(C(2))(2)(CO)(24)](4-) and [Ni(25)(C(2))(4)(CO)(32)](4-) tetraanions. From a structural point of view, all these clusters are based on a Ni(16) square orthobicupola which contain interstitial C(2), Ni(η(2)-C(2))(4) or Ni(2)(μ-η(2)-C(2))(4) moieties, displaying rather short C-C bonds. Electrochemical studies reveal that all these species undergo different redox processes, even if their stability is rather limited. This is corroborated by an extensive analysis of the interaction between interstitial C(2) acetylide units and the metal cluster cage by Extended Huckel Molecular Orbital (EHMO) calculations, which indicates that tightly bonded C-C units are less effective than isolated C-atoms in stabilising the cluster cage.

Synthesis, Molecular Structure and Properties of the [H6−nNi30C4(CO)34(CdCl)2]n− (n=3–6) Bimetallic Carbide Carbonyl Cluster: A Model for the Growth of Noncompact Interstitial Metal Carbides

Reaction of the [Ni(9)C(CO)(17)](2-) dianion with CdCl(2)2.5 H(2)O in THF affords the novel bimetallic Ni--Cd carbide carbonyl clusters [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) (n=3-6), which undergo several protonation-deprotonation equilibria in solution depending on the basicity of the solvent or upon addition of acids or bases. Although the occurrence in solution of these equilibria complicates the pertinent electrochemical studies on their electron-transfer activity, they clearly indicate that the clusters [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) (n=3-6), as well as the structurally related [H(6-n)Ni(34)C(4)(CO)(38)](n-) (n=4-6), undergo reversible or partially reversible redox processes and provide circumstantial and unambiguous evidence for the presence of hydrides for n=3, 4 and 5. Three of the [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) anions (n=4-6) have been structurally characterized in their [NMe(3)(CH(2)Ph)](4)[H(2)Ni(30)C(4)(CO)(34)(CdCl)(2)]2 COMe(2), [NEt(4)](5)[HNi(30)C(4)(CO)(34)(CdCl)(2)]2 MeCN and [NMe(4)](6)[Ni(30)C(4)(CO)(34)(CdCl)(2)]6 MeCN salts, respectively. All three anions display almost identical geometries and bonding parameters, probably because charge effects are minimized by delocalization over such a large metal carbonyl anion. Moreover, the Ni(30)C(4) core in these Ni-Cd carbide clusters is identical within experimental error to those present in the [HNi(34)C(4)(CO)(38)](5-) and [Ni(35)C(4)(CO)(39)](6-) species, suggesting that the stepwise assembly of their nickel carbide cores may represent a general pathway of growth of nickel polycarbide clusters. The fact that the [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-)(n=4-6) anions display two valence electrons more than the structurally related [H(6-n)Ni(34)C(4)(CO)(38)](n-) (n=4-6) species has been rationalized by extended Hückel molecular orbital (EHMO) analysis.

Substituent Effects in the Iron 2p and Carbon 1s Edge Near-Edge X-ray Absorption Fine Structure (NEXAFS) Spectroscopy of Ferrocene Compounds

The iron 2p and carbon 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of substituted ferrocene compounds (Fe(Cp-(CH3)5)2, Fe(Cp)(Cp-COOH), Fe(Cp-COOH)2, and Fe(Cp-COCH3)2) are reported and are interpreted with the aid of extended Hückel molecular orbital (EHMO) theory and density functional theory (DFT). Significant substituent effects are observed in both the Fe 2p and C 1s NEXAFS spectra. These effects can be related to the electron donating/withdrawing properties of the cyclopentadienyl ligands and their substituents as well as the presence of pi* conjugation between the cyclopentadienyl ligand and unsaturated substituents.

Importance of Orbital Complementarity in Spin Coupling through Two Different Bridging Groups in Dicopper(II) Complexes of Endogenous Alkoxo Bridging Ligand with Exogenous Carboxylate: Ab-initio and Semi-Empirical Calculations

The influence of overlap interactions between the bridging ligands and the metal d orbitals on the super-exchange coupling constant are studied by means of ab-initio restricted Hartree-Fock molecular orbital calculations. The interaction between the magnetic d orbitals and the HOMOs of the carboxylate oxygen atoms are investigated in homologous asymmetrically dibridged dicopper(II) complexes which have significantly different - 2J values (the energy separation between the spin-triplet and spin-singlet states). In order to determine the nature of the fronter orbitals, extended Hückel molecular orbital (EHMO) calculations are also reported. The differences in the magnitude of the coupling constants and magnetic behaviour are rationalized in terms of the bridging ligand orbital complementary / countercomplementary concept.

Electronic structures, chemical bonding, and defect formation in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs)

The effect of the alkali metal nature on the electronic structures and chemical bonding in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs) was studied by ab initio tight-binding linear muffin-tin orbital (TB-LMTO) method (in the spin-polarized implementation) and the extended Huckel molecular orbital (EHMO) method. It was found that the X-ray photoelectron spectra of the ferrimagnetic compounds Na2Cu[Fe(CN)6] (I), K2Cu[Fe(CN)6] (II), Rb2Cu[Fe(CN)6] (III), and Cs2Cu[Fe(CN)6] (IV) are similar. The magnetic moments on Cu2+ and iron ions remain virtually constant in compounds I–IV (μ(Cu) = 0.9 μB, μ(Fe) < −0.06 μB). Analyses of the electron density maps and the bond overlap populations showed that the cubic frameworks of cyanoferrates are built from stable fragments ⋯-Fe-C≡N-Cu-⋯. The bond strength in these fragments decreases substantially in the order C-N → Fe-C → Cu-N and only slight in the order IV → III → II → I. The calculated total energies of the cyanoferrates Cs2−x Cu[Fe(CN)6], CsHCu[Fe(CN)6], and NaHCu[Fe(CN)6] for different concentrations and configurations of defects (cesium vacanices and hydrogen substitution defects) suggest mutual repulsion of defects. This repulsion is responsible for the experimentally observed lowering of the ionic conductivity with an increase in the defect concentration in the mixed cyanoferrates.

Super-Exchange Interaction in a Chair-Piperazine Bridged Dicopper(II/II) Complex: Synthesis, Crystal Structure, Magnetic Properties and Molecular Orbital Calculations

Abstract Reaction of the /i-bis(tridentate) ligand H3L' (L' = 1,3-bis[N-(5-cliloro-2-hydroxybenzylidene)- 2-ainiiioetliylene]-2-(5-cliloro-2-hydroxy!phenyl)iniidazoliduie) with eopper(II) chlonde diliydrate gives the chair-piperazine bridged complex [Cu2(μ-L)Cl2]. The halves of the binuclear complex are related by crystallographic inversion symmetry. The intramolecular Cu ・・・Cu separation is 6.954(3) Å. Temperature-dependent magnetic susceptibility measurements of the complex show a weak intramolecular antiferromagnetic eouphng. The super-exchange coupling constant (J) is - 10.5 cm-1. Semi-empirical extended Huckel molecular orbital (EHMO) calculations have been performed in order to gain msight into the molecular orbitals that participate in the super-exchange pathway.

Crystal Structure and Magnetic Exchange Interaction in a Binuclear Copper(II) Schiff Base Complex with a Bridging m-Phenylenediamine Ligand

Condensation of 2-hydroxy-3-methoxybenzaldehyde with m-phenylenediamine (1,3-diaminobenzene) (m-pda) gives the ligand [N,N′-bis(2-hydroxy-3-methoxybenzylidene)-1,3-diaminobenzene] which reacts with cupric acetate to give the complex [Cu2(L-m-pda)2]·2H2O, [L = 2-hydroxy-3- methoxybenzaldehyde)]. The molecular structure of the complex [Cu2(L-m-pda)2]·2H2O has been determined by single-crystal X-ray analysis. (C44H40Cu2N4O8)·2H2O, triclinic, space group P1̄. Two [Cu(L-m-pda)] fragments, related by an inversion center, are connected by m-phenylene groups to form a binuclear unit. The coordination geometry around each copper(II) can be described as a distorted tetrahedron formed by the N2O2 donor set of the Schiff base ligands. The intramolecular Cu···Cu separation is 7.401(6) Å. The magnetic susceptibility of the complex in the 5 - 301 K temperature range can be rationalized by the parameters J = −0.4 cm−1 and g = 2.17. This indicates a weak intramolecular antiferromagnetic interaction. Extended Hückel molecular orbital (EHMO) calculations have been performed in order to gain insight into the molecular orbitals that participate in the super-exchange pathway.

Surface-enhanced Raman scattering of thiourea adsorbed on the silver electrode: bond polarizability derivatives as elucidated from the Raman intensities

Surface-enhanced Raman scattering (SERS) was employed to investigate the adsorption of thiourea (TU) on the silver electrode at different applied electrode potentials. The SER intensities were interpreted by an algorithm originally proposed by Wu et al. [J. Chem. Phys. 87 (1987) 7300] to elucidate the bond polarizability derivatives. The results showed that TU is adsorbed on the electrode via the S atom with a tilted orientation. An extended Huckel molecular orbital (EHMO) calculation was employed to explain the charge transfer between TU and the silver electrode surface.

Relation between Magnetic, Spectroscopic and Structural Properties of Binuclear Copper(II) Complexes of Pentadentate Schiff-base Ligand, Semi-empirical and ab-initio Calculations

The synthesis and characterization of [Cu2(L1)(3,5 prz)] (L1=1,3-Bis(2-hydroxy-3,5-chlorosalicylideneamino) propan-2-ol) 1 and of [Cu2(L2)(3,5 prz)] (L2=1,3-Bis(2-hydroxy-bromosalicylideneamino) propan-2-ol) 2 are reported. The compounds were studied by elemental analysis, infrared and electronic spectra. The structure of the Cu2(L1)(3,5 prz)] complex was determined by x-ray diffraction. The magnetochemical characteristics of these compounds were determined by temperaturedependent magnetic susceptibility measurements, revealing their antiferromagnetic coupling. The superexchange coupling constants are 210 cm−1 for 1 and 440 cm−1 for 2. The difference in the magnitude of the coupling constants was explained by the metal-ligand orbital overlaps and confirmed by ab-initio restricted Hartree-Fock (RHF) calculations. In order to determine the nature of the frontier orbitals, Extended Hückel Molecular Orbital (EHMO) calculations are also reported.

Synthesis, electrochemistry and structural characterization of luminescent rhenium(I) monoynyl complexes and their homo- and hetero-metallic binuclear complexes

A series of luminescent rhenium(I) monoynyl complexes, [Re(NN)(CO) 3(CCR)] (NN=bpy, t Bu 2bpy; R=C 6H 5, C 6H 4Cl-4, C 6H 4OCH 3-4, C 6H 4C 8H 17-4, C 6H 4C 6H 5, C 8H 17, C 4H 3S, C 4H 2SC 4H 3S, C 5H 4N), together with their homo- and hetero-metallic binuclear complexes, {Re(NN)(CO) 3(CCC 5H 4N)[M]} (NN=bpy, t Bu 2bpy; [M]=[Re{(CF 3) 2-bpy}(CO) 3]ClO 4, [Re(NO 2-phen)(CO) 3]ClO 4, W(CO) 5) have been synthesized and their electrochemical and photoluminescence behaviors determined. The structural characterization and electronic structures of selected complexes have also been studied. The luminescence origin of the rhenium(I) alkynyl complexes has been assigned as derived states of a [dπ(Re)→π*(NN)] metal-to-ligand charge transfer (MLCT) origin mixed with a [π(CCR)→π*(NN)] ligand-to-ligand charge transfer (LLCT) character. The assignments are further supported by extended Hückel molecular orbital (EHMO) calculations, which show that the LUMO mainly consists of π*(NN) character while the HOMO is dominated by the antibonding character of the ReCCR moiety resulted from the overlap of the dπ(Re) and π(CCR) orbitals.

A Proposed Mechanism for Olefin Polymerization, 2. EHMO and MM2 Study

This paper reports the results about the model presented in Part 1 for olefin polymerization with metallocenes, using semiempirical extended Huckel molecular orbital (EHMO) and MM2 methods The main aspects of the model are analyzed. These are bipyramidal or octahedral coordination, two different olefins coordination and the possibility of different active sites. A model of polymerization for a C 2 catalyst, prototypical and with steric hindrance, and for a C s catalyst was analyzed with MM2 to evaluate steric effects. The electronic effects were modeled using MAO to determine the feasibility of the model. Models for ethylene and propylene coordination and insertion were considered. The insertion models were only of qualitative value and they were designed to evaluate the effect of a triggering second olefin. A third olefin coordination (polymerizable or not) was considered for C 2 and C s catalysts. Experimental evidence was analyzed with the different aspects of the model.

Copper Concentration inside Guinier-Preston I Zones Formed in an Al–Cu Alloy

Abstract The copper concentration inside a Guinier-Preston (GPI) zone was studied by means of an extended Huckel molecular orbital (EHMO) calculation. The present EHMO calculation revealed that the Cu concentration inside a GPI zone depends on the size of the zone. The GPI zone comprises both Cu and Al in a small GPI zone, whereas the Cu concentration inside the GPI zone increases to nearly 100 at.% Cu in a large GPI zone. A compressive lattice distortion, which is associated with the zone, increases the stability, but when a GPI zone is 5 nm in diameter, the stabilizing effect of the zone is estimated to be not higher than 10% of the chemical energy due to Cu coalescence.

A π-Stacked Organometallic Propeller: Experimental and Theoretical Studies on Reactivity and Bonding in the π-Arene-Bridged Nickel Triple-Decker [{(η5-Me4EtC5)Ni}2(μ-η3:η3-decacyclene)

Synthesis, structure, reactivity, and theoretical studies of a new type of Ni triple-decker complexes are reported. A prominent feature of its molecular structure is the (η3:η3)-bis(enyl) coordination of two [(η5-Me4EtC5)Ni] fragments to the central arene ring of the polycondensed π-perimeter decacyclene. The central arene ring of decacyclene displays a distinct chair conformation with significant tilt angles of 25.5 and 26.1°. The three naphthalene units are twisted in a propeller-like fashion with torsion angles of 16°, 16.6°, and 19°, which is twice the twisting observed for the free decacyclene ligand. According to Extended Huckel Molecular Orbital (EHMO) calculations, a qualitative measure for arene lability in the title compound and a number of related arene-bridged metal complexes can be attributed to a subsequent filling of metal−arene antibonding orbitals. The experimentally observed reactivities of π-arene exchange in these complexes are reproduced nicely by the EHMO calculations. The title compound offers access to a number of organonickel chalcogenato complexes under mild conditions by cleavage of the S−S, Se−Se, or Te−Te bonds of diorganyl dichalcogenides R−E−E−R. The title compound is also capable of C−H activation of azobenzene and [(dimethylamino)methyl]ferrocene resulting in orthometallated complexes containing five-membered metallacycles. PES and semi-empirical ZINDO/S calculations were used to study the product of the orthometallation of the title compound with azobenzene. These studies reveal that the HOMO of the metallacycle (IE = 6.45 eV) has dominant Ni−Cp and Ni−Caryl π-antibonding character.

Structural rearrangements in triple-decker-like complexes with mixed group 15/16 ligands: synthesis and characterization of the redox couple.

The reaction of As4Se4 with stoichiometric amounts of [Cp*Fe2(CO)4] (Cp* = C5Me5) in boiling toluene forms [Cp2*Fe2As2Se2] (1) in good yield. X-ray crystallography shows 1 to have a triple-decker structure which comprises a tetraatomic mu,eta4:4-As2Se2 ligand. Density functional theory (DFT) and extended Hückel molecular orbital (EHMO) calculations confirm that the As2Se2 ligand behaves as a four-electron pi donor. Oxidation of 1 with equimolar amounts of [(C5H5)2Fe]PF6, Br2 and I2, respectively, gave compounds 2-4. According to X-ray crystallographic investigations that were carried out on 2 and 4, the oxidation state has a considerable influence on the structure of the Fe2As2Se2 core: significant shortening of the Fe-Fe distance (deltad(Fe-Fe)> 0.3 A) and weakening of the As-As bond length ((deltad(As-As) > 0.3 A) suggests the formal presence of two diatomic AsSe ligands and a Fe-Fe bond. DFT and EHMO calculations confirm that an electron is removed from an occupied Fe-Fe orbital of antibonding character during oxidation. All molecular orbitals lower their energies upon oxidation, but the energy drop is relatively small for those involving the As-As bond. An additional structural feature in 4 consists of an electronic interaction of the iodide with both As atoms which suggests a formally neutral ion pair. Electrochemical studies confirm that the oxidation of 1 is a reversible one-electron process with E(1/2)= +0.07 V (in THF). These studies also reveal that 4 dissociates in polar solvents, such as THF, into [1]+ and I-, which is followed by transformation into 1 and I3.

A theoretical and experimental study of the possible phenytriethoxysilane species found on treated silica

A modified extended Hückel molecular orbital (EHMO) method, which includes core–core repulsion terms, was used to study the silane adsorption on SiO 2 surfaces. The SiO 2 treated at 300°C was chemically modified with an alcoxysilane, phenyltriethoxysilane (PTES). Therefore, we study the possible adsorption of PTES on two planes (with isolated and geminal silanols) and the possible species formed once the reaction with a SiO 2 surface is finished. Starting from this analysis, it is possible to evaluate the PTES selectivity to the different anchoring points on the SiO 2 surface.

拡張Ｈｕｅｃｋｅｌ法を用いた原子変位のあるグラファイト表面の電子密度分布計算

We calculated electron density distribution of the graphite surface with an atomic displacement, in order to analyze scanning tunneling microscope (STM) images of ion irradiated graphite surface.The calculation is based on the extended Huckel molecular orbital (EHMO) method. We found that an electronic perturbation in threefold-symmetry which was observed on the ion irradiated graphite surface is reproduced either by the displacement or by the removal of a β atom at the surface. This result shows that a bright spot of STM image does not always locate at the place where an atom exists.

(Silox)3Nb(η2-N,C-4-picoline) as a source of (silox)3Nb: structure of [(silox)3Nb]2(μ-η2,η2-C6H6) (silox= Bu3SiO)

Abstract Electrochemical and chemical reductions of (silox)3NbCl2 (1, −1.42 V versus Ag/Ag+) and (silox)3TaCl2 (2, −2.18 V) generated [(silox)3NbCl2]− (1−) and [(silox)3TaCl2]− (2−). The anions were subject to Cl− loss, leading to (silox)3NbCl (3) and probable disproportionation (Ta). Complex 3 formed reversible solvent adducts (silox)3ClNbL (3-L, L=THF, py). Na/Hg reduction of (silox)3NbCl2 (1) in the presence of 4-picoline afforded (silox)3Nb(η2-N,C-4-NC5H4CH3) (6), which can be considered a source of ‘(silox)3Nb’, analagous to (silox)3Ta (4). Adducts such as (silox)3Nb(η2-H2CCHR) (R=H, 7; Ph, 8) may be formed upon addition of olefins, and 6 abstracted an oxygen from N2O, NO or ethylene oxide to give (silox)3NbO (9) and N2 or C2H4, respectively, which are reactions also observed for 4. 4-Picoline may be abstracted from 6 by 4 to give {(silox)3Nb}2(μ:η2,η2-C6H6) (11) and (silox)3Ta(η2-N,C-4-NC5H4CH3) (12). An X-ray structure determination of 11 revealed a disordered bridge that was modeled as a μ:η2,η2-benzene. Extended Huckel molecular orbital (EHMO) calculations showed that the μ:η2,η2-configuration was energetically better than a μ:η6,η6-alternative, but about the same as a plausible μ:η3,η3-arrangement.