Huckel MO Research Articles

ChemInform Abstract: Variation of Aromaticity by Twisting or Expanding the Ring Content

AbstractReview: 105 refs.

New Pt(II)(dithiolate) Compounds Possessing an Energetically Accessible Diphosphine-Based LUMO: Syntheses, Redox Properties, and Solid-State Structures of PtCl2(pbpcd), Pt(tdt)(pbpcd), and Pt(tdt)(bpcd)

The new ligand 2-(pyren-1-ylidene)-4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (pbpcd) has been synthesized from the Knoevenagel condensation using 1-pyrenecarboxaldehyde with 4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (bpcd). Displacement of the cod ligand in PtCl2(cod) by pbpcd furnishes PtCl2(pbpcd) (2) in near quantitative yield. Treatment of 2 with the dipotassium salt of toluene-3,4-dithiol (K2tdt) affords the dithiolate compound Pt(tdt)(pbpcd) (3) as a 1:1 mixture of diastereomers. An alternative synthesis of 3 from Pt(tdt)(bpcd) (5) and 1-pyrenecarboxaldehyde also affords 3 in 23% yield. The pbpcd ligand and all new diphosphine-substituted compounds have been isolated and fully characterized in solution by IR and NMR spectroscopies, and the solid-state structures of 2·CH2Cl2, 3·toluene, and 5·CH2Cl2 established by X-ray diffraction analyses. The solid-state structure of each product exhibits a square-planar architecture at the metal center. The redox properties of the pbpcd ligand and the tdt-substituted compound 3 have been explored by cyclic and differential-pulse voltammetry, and these data are discussed with respect to extended Huckel MO calculations and the nature of the HOMO and LUMO levels in each compound. The synthesis of the new ligand 2-(pyren-1-ylidene)-4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (pbpcd) from the Knoevenagel condensation of 1-pyrenecarboxaldehyde with 4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (bpcd) is reported. Reaction of pbpcd with PtCl2(cod) affords PtCl2(pbpcd), which in turn reacts with the dipotassium salt of toluene-3,4-dithiol (K2tdt) to yield Pt(tdt)(pbpcd). The latter complex may also be synthesized from the Knoevenagel condensation of Pt(tdt)(bpcd) with 1-pyrenecarboxaldehyde. The spectroscopic and electrochemical properties of the pbpcd ligand and Pt(tdt)(pbpcd) have been investigated, and the solid-state structures of three of the new Pt(II) compounds are reported.

Variation of aromaticity by twisting or expanding the ring content

Generalization of the Hückel rule predicts that the (anti)aromaticity of a neutral ring is qualitatively reverted upon a single twist of the π-orbital array (Möbius interconversion), and is preserved upon expansion of all the bonds by singleC2units (ringcarbo-merization). These opposite effects are addressed from quantitative theoretical and experimental standpoints, respectively. (i) According to most resonance energy (RE) schemes, the RE value of a Möbius ring isnotthe opposite of that of the Hückel version. This also applies to the Aihara’s and Trinajstic’s topological resonance energy (TRE), where a non-aromatic reference in the topological limit is defined as being “as identical as possible” to the parent ring but just “acyclic”. In spite of its conceptual merits, the computing complexity and fictitious character of the TRE acyclic reference resulted in a disuse of TRE as a current energetic aromaticity index. Both the calculation and interpretation of TRE have been revisited in light of a cross-reference between the Hückel and Möbius rings within the Hückel molecular orbital (HMO) framework. Whereas the topological influence of triple bonds is currently neglected in the first-level HMO treatment of π-conjugated systems, a graph-theoretical analysis allows one to differentiate the TRE value of a [3n]annulene from those of the correspondingcarbo-[n]annulene. The C18ring ofcarbo-benzene is thus predicted to be slightly more topologically aromatic than that of [18]annulene. (ii) Recent experimental and density functional theory (DFT) theoretical studies of quadrupolarcarbo-benzene derivatives are presented. The results show that the “flexible aromaticity” of thep-C18Ph4bridge between donor anisyl substituents plays a crucial role in determining the intriguing chemical/spectroscopical/optical properties of thesecarbo-chromophores.

Phenomenological chemical reactivity theory for mobile electrons

We present herein a model to deal with the chemical reactivity, selectivity and site activation concepts of π electron systems derived by merging the classical Coulson–Longuet-Higgins response function theory based on the Huckel molecular orbital (HMO) theory and the conceptual density functional theory. HMO-like expressions for the electronic chemical potential, chemical hardness and softness, including their local counterparts, atomic and bond Fukui functions and non-local response functions are derived. It is shown that sophisticated non-local concepts as site activation may be cast into deeper physical grounds by introducing a simplified version of static response functions. In this way, useful quantities such as self and mutual polarizabilities originally defined through the HMO parameters can be redefined as self and mutual softnesses. The model is illustrated by discussing the classical Hammett free energy relationship describing inductive substituent effects on the reactivity of benzoic acids.

Communication-theory perspective on valence-bond theory

The information-theoretic (IT) approach to the electronic structure of molecules, called the Communication Theory of the chemical bond, is used to explore the entropy/information “bond-orders” of the system Valence-Bond (VB) structures, and their covalent/ionic composition. The molecular communication channel in atomic resolution is interpreted as the ensemble-average of the elementary information networks corresponding to the system elementary VB structures, with the probability-weights generated by the coefficients of the familiar VB expansion of the system wave-function. The elementary probability-scattering networks corresponding to a single ionic and covalent bonds of the system constituent diatomic fragments, to be used to construct the communication systems of any VB structure, are identified and their entropy/information descriptors are summarized. The overall bond multiplicities of VB structures are generated using the relevant grouping rules for the entropy/information quantities and the molecular IT bond-order and its covalent/ionic components are obtained as the ensemble averages of the corresponding descriptors of individual VB structures. Illustrative applications to the hydrogen molecule and π-bonds in allyl, butadiene and benzene are reported and discussed. Equating the VB-ensemble average quantities for these π-electron systems with those resulting from the Huckel Molecular Orbital (MO) theory then allows one to extract the VB relative covalency and ionicity measures for all chemical bonds in the molecule. The simple MO and VB descriptions of the hydrogen molecule are compared and the role of a strong overlap between the VB structures is investigated in a more detail. Finally, the entropy/information descriptors of the information distribution in the resultant promolecule → Atoms-in-H2 channel resulting from the sequential information cascade consisting of the promolecular and VB probability propagation stages is examined to determine the dependence of the flow of information on the adopted reference system.

Properties of Aromaticity Indices Based on the One-Electron Density Matrix

Proper normalization of two previously published indices yields aromaticity measures that, when computed within the Hückel molecular orbital (HMO) approximation, closely match the topological resonance energies per pi electron of aromatic annulenes and their ions. The normalized indices, which quantify aromaticity of individual rings in polycyclic systems, are equally applicable to homocyclic and heterocyclic compounds and can be readily computed from 1-matrices calculated at any level of electronic structure theory. However, only the index ING, derived from the Giambiagi formula, produces proper ordering of aromaticities of heterocyclic compounds, provided it is calculated from all-electron wavefunctions in conjunction with the atoms in molecule (AIM) partitioning. Its values are shown to be strongly affected by electron correlation effects. Because of its apparent inability to distinguish between anti- and nonaromatic systems, ING should only be employed for aromatic species.

The pseudo-π method examined for the computation of multicenter aromaticity indices

This paper examines the applicability of the so-called pseudo-π method for the calculation of multicenter indices. The pseudo-π method allows for substantial reductions in required computer time, without significant loss of chemical insight. It is found to be a good alternative for the Huckel MO approach and the full ab initio approach involving large basis sets.

Electron delocalization and aromaticity measures within the Hückel molecular orbital method

In this paper, we review the electronic aromaticity measures from the perspective of the Hückel molecular orbital (HMO) theory. The analysis of FLU, PDI, I ring and SCI in the framework of the HMO theory provides an interesting scenario for the interpretation of these indices. Within the Hückel theory the formulas for the Coulson bond orders are easily obtained in a closed form for annulenes, which enables the production of analytical expressions for some of the aromaticity measures. These analytical functions are used to study the ring size dependence of current aromaticity indices. Besides, HMO calculations of polycyclic benzenoids complete the analysis of the electronic aromaticity indices reviewed in this paper, by showing how HMO theory explains the changes in aromaticity due to annulation. All these results help grasping the meaning and the behavior of the electronic aromaticity indices.

What I like about Hückel theory

We start with some biographical notes on Erich Hückel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Hückel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Möbius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrödinger equation, but as a way towards the understanding of some aspects of the Chemical Bond.

Complexation of copper(II) with 3-(2-hydroxyphenylazo)pentadione-2,4

It is shown that 3-(2-hydroxyphenylazo)pentadione-2,4 (H2L) can exist in three tautomeric forms (enol-azo, keto-azo, and hydrazo). The effective atomic charges in the tautomeric forms of H2L are calculated by the Huckel MO LCAO method. The molar fractions and molar absorptivities of the tautomers at different pH are found. The complexation of copper(II) with H2L is studied by spectrophotometry. Beer’s law is obeyed for 0.51–5.12 µg/mL of copper. The assumed complex structure is given. The effect of foreign ions and masking agents on the complexation is studied. A procedure for the photometric determination of copper(II) in zinc-based alloys is proposed.

Density Functional Study of Methyl Chemisorption on Polycyclic Aromatic Hydrocarbons

The reactions of methyl radicals with large (up to C(96)H(24)) polycyclic aromatic hydrocarbons (PAHs) are studied by density functional calculations to shed light on the experimentally observed deposition of carbon on highly oriented pyrolytic graphite (HOPG), which occurs when hot HOPG (decorated by nanometre-sized defects) is exposed to methyl radicals. The equilibrium structures of the reaction products, together with transition structures for PAHs up to the size of phenanthroperylene, are determined using the density functionals B3LYP, TPSSh, BP86 and TPSS. The structures are analysed by computing the pi orbital axis vector (POAV) and the altitude of the reactive carbon above the molecular plane of the PAH. The strongest C-CH(3) bonds are found at the edges of the PAHs, where the s character of the C orbital involved in the bond is roughly 25 % (sp(3) hybrid orbital). Carbon atoms inside the PAH form bonds with the methyl radical through atomic orbitals with about 16 % s character in the POAV analysis. These bonds are much weaker than those at the edges of the PAH, while the reactive carbon has moved about 40 pm above the molecular plane. At the edges, the PAH carbon atoms do not leave the molecular plane to this extent. The computed barrier heights and geometrical parameters of the transition structures are in agreement with Hammond's postulate, and the relative energies of all of the equilibrium structures can be rationalized by Hückel molecular orbital (HMO) theory.

Fully-angular polyhex chains with minimal total π-electron energy

By Hückel molecular orbital (HMO) theory, the calculation of the total energy of all π -electrons in conjugated hydrocarbons can be reduced to that of E ( G ) = | λ 1 | + | λ 2 | + ⋯ + | λ n | , where λ i are the eigenvalues of the corresponding graph G . Denote by Ψ n the set of all fully-angular polyhex chains with n hexagons. In this paper, we show that H n has the minimum total π -electron energy among chains in Ψ n , where H n is the helicene chain.

The quantum in chemistry: an experimentalist's view

The quantum in chemistry: an experimentalist's view

Atomic branching in molecules

AbstractA graph theoretic measure of extended atomic branching is defined that accounts for the effects of all atoms in the molecule, giving higher weight to the nearest neighbors. It is based on the counting of all substructures in which an atom takes part in a molecule. We prove a theorem that permits the exact calculation of this measure based on the eigenvalues and eigenvectors of the adjacency matrix of the graph representing a molecule. The definition of this measure within the context of the Hückel molecular orbital (HMO) and its calculation for benzenoid hydrocarbons are also studied. We show that the extended atomic branching can be defined using any real symmetric matrix, as well as any Hermitian (self‐adjoint) matrix, which permits its calculation in topological, geometrical, and quantum chemical contexts. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Synthesis, X-ray diffraction structure, and redox chemistry of Re2(CO)8(bmf)

The reaction between Re2(CO)8(μ-H)(μ-η1,η2-CH=CHBu) (1) and the diphosphine ligand 3,4-bis(diphenylphosphino)-5-methoxy-2(5H)-furanone (bmf) proceeds at room temperature to give the dirhenium compound Re2(CO)8(bmf) (2) as the sole observable product in good yield after 24 h. Re2(CO)8(bmf) has been isolated and characterized in solution by IR and NMR (31P and 1H) spectroscopies, and the molecular structure of Re2(CO)8(bmf) has been determined by X-ray crystallography. The solid-state structure of 2 reveals a bridging bmf ligand that spans the Re=Re vector and whose Re(CO)4 moieties exhibit a staggered rotational geometry about the equatorial phosphine and CO groups. The redox properties of Re2(CO)8(bmf) have been explored by cyclic voltammetry in CH2Cl2, where an irreversible oxidation was found at Epa = 1.04 V, along with a reversible, one-electron reduction at E1/2 = −1.23 V. These redox couples have been assigned to the oxidation of the Re=Re σ bond and electron occupation of the π∗ system associated with the furanone ring of Re2(CO)8(bmf), respectively. The electrochemical behavior is discussed relative to the nature of the HOMO and LUMO levels in the model compound Re2(CO)8(H4-bmf), whose HOMO and LUMO compositions have been established by extended Huckel MO calculations. The electrochemistry and MO data from Re2(CO)8(bmf) are contrasted with the structurally similar dirhenium compound Re2(CO)8(bma).

Quantum mechanics: a conceptual approach

Preface. 1. The Discovery of Quantum Mechanics. I Introduction. II Planck and Quantization. III Bohr and the Hydrogen Atom. IV Matrix Mechanics. V The Uncertainty Relations. VI Wave Mechanics. VII The Final Touches of Quantum Mechanics. VIII Concluding Remarks. 2. The Mathematics of Quantum Mechanics. I Introduction. II Differential Equations. III Kummer's Function. IV Matrices. V Permutations. VI Determinants. VII Properties of Determinants. VIII Linear Equations and Eigenvalues. IX Problems. 3. Classical Mechanics. I Introduction. II Vectors and Vector Fields. III Hamiltonian Mechanics. IV The Classical Harmonic Oscillator. V Angular Momentum. VI Polar Coordinates. VII Problems. 4. Wave Mechanics of a Free Particle. I Introduction. II The Mathematics of Plane Waves. III The Schrodinger Equation of a Free Particle. IV The Interpretation of the Wave Function. V Wave Packets. VI Concluding Remarks. VII Problems. 5. The Schrodinger Equation. I Introduction. II Operators. III The Particle in a Box. IV Concluding Remarks. V Problems. 6. Applications. I Introduction. II A Particle in a Finite Box. III Tunneling. IV The Harmonic Oscillator. V Problems. 7. Angular Momentum. I Introduction. II Commuting Operators. III Commutation Relations of the Angular Momentum. IV The Rigid Rotor. V Eigenfunctions of the Angular Momentum. VI Concluding Remarks. VII Problems. 8. The Hydrogen Atom. I Introduction. II Solving the Schrodinger Equation. III Deriving the Energy Eigenvalues. IV The Behavior of the Eigenfunctions. V Problems. 9. Approximate Methods. I Introduction. II The Variational Principle. III Applications of the Variational Principle. IV Perturbation Theory for a Nondegenerate State. V The Stark Effect of the Hydrogen Atom. VI Perturbation Theory for Degenerate States. VII Concluding Remarks. VIII Problems. 10. The Helium Atom. I Introduction. II Experimental Developments. III Pauli's Exclusion Principle. IV The Discovery of the Electron Spin. V The Mathematical Description of the Electron Spin. VI The Exclusion Principle Revisited. VII Two--Electron Systems. VIII The Helium Atom. IX The Helium Atom Orbitals. X Concluding Remarks. XI Problems. 11 Atomic Structure. I Introduction. II Atomic and Molecular Wave Function. III The Hartree--Fock Method. IV Slater Orbitals. V Multiplet Theory. VI Concluding Remarks. VII Problems. 12 Molecular Structure. I Introduction. II The Born--Oppenheimer Approximation. III Nuclear Motion of Diatomic Molecules. IV The Hydrogen Molecular Ion. V The Hydrogen Molecule. VI The Chemical Bond. VII The Structures of Some Simple Polyatomic Molecules. VIII The Huckel Molecular Orbital Method. IX Problems. Index.

New polydentate sulfide ligands: Synthesis, redox properties, and molecular structure of 4,5-bis(p-tolylthio)-4-cyclopenten-1,3-dione

The reaction of p-toluenethiol with 4,5-dichloro-4-cyclopenten-1,3-dione in 1,2-dichloroethane with added DBU affords good yields of the new bidentate sulfide ligand 4,5-bis(p-tolylthio)-4-cyclopenten-1,3-dione. The title compound was isolated by column chromatography and characterized in solution by IR and NMR spectroscopies. The solid-state structure of RC=CRC(O)CH2C(O) (where R = p-tolylthio) was solved by X-ray crystallography. 4,5-Bis(p-tolylthio)-4-cyclopenten-1,3-dione crystallizes in the monoclinic space group P21/c, a = 14.203(3) A, b = 6.181(1) A, c = 20.372(4) A, β = 106.111(3)°, V = 1718.1(6) A3, Z = 4, and dcalc = 1.316 mg/m3; R = 0.0743, Rw = 0.1693 for 3958 reflections with I > 2σ(I). The redox properties of 4,5-bis(p-tolylthio)-4-cyclopenten-1,3-dione have been examined by cyclic voltammetry in CH2Cl2 solution, where a quasireversible reduction wave at −1.10 V was found. The reduction behavior is discussed relative to the nature of the LUMO level, which has been determined by extended Huckel MO calculations. The redox chemistry and the LUMO of our bidentate sulfide ligand are contrasted with the known redox chemistry and the LUMO composition of the corresponding bidentate phosphine ligand 4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (bpcd).

BACK TO BASICS: MODERN REACTIVITY CONCEPTS WITHIN THE HMO THEORY FRAMEWORK è..

We describe how modern concepts of chemical reactivity and selectivity, defined as response functions in the conceptual density functional theory (DFT), may be implemented within a simple Huckel Molecular Orbital (HMO) formalism. Concepts like electrophilicity may be easily explained using the electronic chemical potential. Intramolecular and intermolecular selectivity may in turn be conveniently described by the Fukui function, which is formulated in terms of single coefficients of the frontier molecular orbitals within the HMO frame. The conceptual value obtained by merging a powerful formalism based on response functions with a simple model of electronic structure is the transparent interpretation of modern concepts of reactivity in terms of classical chemical quantities. The model is illustrated for the reactivity and intermolecular selectivity of Diels-Alder reactions

X-ray structure and redox chemistry of the heptacobalt cluster Co 3 (CO) 9 [μ 3 -CCO 2 CH 2 CCH{Co 4 (CO) 10 }

The tetrahedrane cluster $${\text{Co}}_3 ({\text{CO}})_9 (\mu _3 {\text{ - CCO}}_{\text{2}} {\text{CH}}_{\text{2}} {\text{C}} \equiv {\text{CH)}}$$ reacts with Co4(CO)12 to furnish the heptacobalt compound Co3(CO)9[μ3-CCO2CH2CCH{Co4(CO)10}] in high yield. Substitution of the pendant alkyne group by the Co4(CO)10 moiety was ascertained by IR and 1H NMR spectroscopies, and the solid-state structure of Co3(CO)9[μ3-CCO2CH2CCH{Co4(CO)10}] was unequivocally determined by X-ray crystallography. Co3(CO)9[μ3-CCO3CH3CCH{Co4(CO)10}] crystallizes in the monoclinic space group P2 1/n, a = 12.895(13) A, b = 18.803(18) A, c = 13.748(13) A, β = 97.27(2)°, V = 3307(6) A3, Z = 4, d calc = 2.087 mg/m3; R = 0.0493, R w = 0.0989 for 4310 observed reflections with I > 2σ(I). The X-ray structure confirms the presence of an intact tetrahedral Co3 moiety and an alkyne-tethered Co4 butterfly cluster moiety. The cyclic voltammetric properties of Co3(CO)9[μ3-CCO2CH2CCH{Co4(CO)10}] were examined and three reduction waves were found. The first two reduction waves correspond to the regionally localized 0/1− redox couples on the tetra- and tricobalt moieties, respectively, while the third redox process is assigned to the 1−/2− reduction associated with the tetracobalt residue. Both 0/1− redox couples are reversible, while the 1−/2− reduction exhibits only quasi-reversible behavior. No evidence for electronic communication between the Co3 and Co4 portions of the complex was observed. Extended Huckel MO calculations support the site of the first reduction occurring solely on the tetracobalt moiety of this Co7 cluster.

Calculated geometries and charge distributions of 4n and 4n + 2 π‐ring systems linked with −CH: An asymmetric versus symmetric π‐delocalization

AbstractWith the assistance of quantum chemical calculations we discussed the geometrical and charge density differences between [4n]CH and [4n + 2]CH cations for [4n] and [4n + 2] π cyclic‐membered rings substituted with a CH group. In the case of [4n] and [4n + 2] membered rings we are dealing with antiaromaticity and aromaticity, respectively, in the ring systems. The calculations were performed with the Hückel molecular orbital (HMO) description including a variable bond‐length–dependent resonance integral. Furthermore, the HMO method was used with (limited) configuration interaction (CI) in combination with a valence bond (VB) formalism. We focused on the symmetry of π delocalization with respect to the different kind of cations. A symmetrical π delocalization was found for the [4n + 2] CH cations and an asymmetrical π delocalization for the [4n]CH cations. Via introduction of top symmetry cations as, for example, in [4n](CH)4n then the degeneracy of the highest‐occupied molecular orbitals (HOMOs) leads to symmetry lowering from D4nh into D2nh accompanied by alternating symmetrically localized π structures. As an example, the [4](CH)4 cation is given. In both cases, as the result of a Jahn–Teller distortion, the original geometry (D2h) and π contribution of the four‐membered ring is maintained. Several cations derived from the [4n] and [4n + 2] membered rings obtained by specific regio substitution of CH groups have been studied. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002