Π-electron Energy Research Articles

Ab initiocalculations of the π-electronic structures of pyridine by valence-bond method

Ab initio valence-bond calculations of the π-electronic energy levels, π-electron densities and bond orders for pyridine have been carried out on the basis of the complete set of non-polar and polar structures. The atomic orbitals have been assumed to be Slater orbitals. The multiple exchange integrals have been taken into account completely by the orthogonalization of the π-atomic orbitals. The results are compared with those for benzene. The effects of the supplement of the multi-polar structures in pyridine on the molecular properties have been discussed.

ChemInform Abstract: THE ELECTRONIC STRUCTURE OF SOME HETEROCYCLES WITH BRIDGEHEAD NITROGEN‐ PHOTOELECTRON SPECTRA AND AB INITIO MOLECULAR ORBITAL CALCULATIONS

Abstract He(I) and He(II) photoelectron spectra are reported for the cycl[3,3,3]azine (1), cycl[3,2,2]azine (2), indolizine (6) and imidazo[1,2-a] pyridine (7), as well as He(I) spectra for related compounds (3–5). Ab initio molecular orbital calculations have been used to assign the spectra of 1, 2, 3, 6 and 7, and to give information about the nature of the π-electron energy levels. The first IP for 1 is singularly low (5.86 eV), and this has been interpreted in terms of occupancy of the 1a 1 '' orbital which is normally vacant in related compounds. In the cyclazines, the nitrogen lone pair seems to be split into two π-levels.

Polynomial matrix method for the calculation of charge densities and bond orders in linear conjugated π-electron systems

The polynomial matrix method (PMM) described earlier for evaluating the π-electron energies of linear conjugated polymers has been extended to calculate the charge densities and bond orders. The formulae used are those given by Heilbronner, and it is shown that the PMM enables the various terms in his equations to be calculated conveniently. The method has been applied to p-quaterphenyl. The values of charge densities and bond orders obtained by this method are in very good agreement with those obtained by solving the secular determinant directly by computer.

The electronic structure of some heterocycles with bridgehead nitrogen: photoelectron spectra and ab initio molecular orbital calculations

He(I) and He(II) photoelectron spectra are reported for the cycl[3,3,3]azine (1), cycl[3,2,2]azine (2), indolizine (6) and imidazo[1,2-a] pyridine (7), as well as He(I) spectra for related compounds (3–5). Ab initio molecular orbital calculations have been used to assign the spectra of 1, 2, 3, 6 and 7, and to give information about the nature of the π-electron energy levels. The first IP for 1 is singularly low (5.86 eV), and this has been interpreted in terms of occupancy of the 1a 1'' orbital which is normally vacant in related compounds. In the cyclazines, the nitrogen lone pair seems to be split into two π-levels.

The deprotonation and rearrangement of N-methyl methylphosphazenium quaternary salts: a novel synthetic route to cyclic azaphosphorins

The N-methyl methylphosphazenium salts (NPMe2)3,4•MeI and N3P3Ph4Me2•MeI can be deprotonated by a variety of bases to yield the novel azaphosphorins Me2n−1(NHMe)PnNn−1CH (n = 3,4) and Me(NHMe)Ph4P3N2CH, formed by a rearrangement in which the methylated nitrogen atom is displaced from the PN ring by the initially produced exocyclic methylene group. The 1H nmr spectra of the azaphosphorins indicate a rapid proton exchange between the endocyclic carbon and the exocyclic nitrogen, which can be slowed by the addition of an auxiliary base. When KO-t-Bu reacts with the quaternary salts, nucleophilic attack competes with proton removal, and the linear oxides (NHMe)(PMe2N)nPMe2O (n = 2−4) have been isolated from these reactions. The azaphosphorins Me2n−1(NHMe)PnNn−1CH (n = 3, 4) are hydrolysed in aqueous ethanol to give the cyclic oxides Me2n−1(O)PnNn−1CH2, and react with methyl iodide by a proton transfer reaction to give the hydroiodides Me2n−1(NHMe)PnNn−1CH•HI. Their reaction with benzoyl chloride leads to the derivatives Me7(NHMe)P4N3CCOPh and Me7(NMeCOPh)P3N2CCOPh, the initial substitution on carbon indicating that it is the primary basic centre. Model calculations of π-electron energies suggest that both the azaphosphorin rearrangement and the proton exchange reactions depend on the relative orbital electronegativity of the ring and exocyclic atoms, the less electronegative atom being more stable in the endocyclic position.

Bounds for total π-electron energy of polymethines

The introduction of a -CHCH- fragment into an arbitrary alternant α,ω-disubstituted polymethine increases the total Hückel π-electron energy at least by 2(√5 − 1) = 2.472 β and at most by 2(√3 + 1 − √2) = 2.636 β. These bounds are the best possible. With increasing length of the polymethine chain, the energy difference tends to 8/π = 2.546 β.

A Topological Formula for Total π-Electron Energy

Abstract Total π-electron energy E is presented as a sum of first-neighbour interaction terms λ and contributions of cycles ζ [Equation (2)]. The main conclusion of the work is that the total effect of λ's is a constant, independent of the molecular structure. Therefore, E is an additive function of ζ′s only.

A class of approximate topological formulas for total π-electron energy

A class of approximate topological formulas, Eqs. (12), (15), (25), and (27) for total π-electron energy E is derived. These formulas reflect the dependence of E on a number of structural details of the molecule: the number of atoms, bonds, rings, and nonbonding MO’s, the ring size, the algebraic structure count, and the branching. The formulas are obtained using analytical considerations and contain no fitting parameters.

Acyclic systems with extremal H�ckel ?-electron energy

The main result of the present work is the proof that among acyclic polyenes CnHn+2, the linear isomer H2C=(CH)n−2=CH2 has maximal HMO π-electron energy. The 1,1-divinyl isomer (H2C=CH)2C(CH)n−6=CH2 has maximal π-energy among branched acyclic systems. Among trees withn vertices, the star has minimal energy. A number of additional inequalities for HMO total π-electron energy of acyclic conjugated systems are proved.

Quantitative approach to hückel rule the relations between the cycles of a molecular graph and the thermodynamic stability of a conjugated molecule

Contribution of the rings to the total π-electron energy (CE) is calculated for a number of polycyclic conjugated hydrocarbons. The Hückel 4m+2 rule is tested quantitatively in this way. It is shown that (4m)-membered rings always destabilize, while (4m + 2)-membered rings almost always stabilize the molecule. The magnitude of this effect is, however, subject to considerable variations. The main factors which determine the magnitude of CE are discussed. Examples of the alternant hydrocarbons are found for which the (4m + 2)-membered cycles have a destabilizing effect, and therefore violate the Hückel rule. The odd membered cycles are shown to have a negligibly small effect on the stability of the conjugated molecules.

Polynomial matrix method for the calculation of π-electron energies for linear conjugated polymers

A new polynomial matrix method has been proposed to calculate the energy levels of the π-electrons of a linear conjugated polymer in the framework of the H.M.O. approximation. The polynomial matrix is a 2 × 2 matrix, one element of which is the secular polynomial for the building block, and the rest are obtained by eliminating one or both the atoms through which the building blocks are linked with each other. The secular polynomial for the polymeric molecule then happens to be one element of the polynomial matrix for the entire chain obtained by suitable multiplication of individual polynomial matrices. Linking of the chain through heteroatoms can be taken into account by introducing a k-matrix governed by the resonance integral for this bond. The secular polynomial for the polymer can be arrived at in a simple way provided it contains repetition of identical building units. For an infinite chain polymer, the energy bands are given by a single equation. This method is capable of handling disordered polymers.

Effect of a Ring on the Stability of Polycyclic Conjugated Molecules

Abstract A graph theoretical method is developed which enables to calculate the contribution of a partic­ular ring to the total π-electron energy of a conjugated molecule.

Topological studies on heteroconjugated molecules. The stability of alternant systems with one heteroatom

The stability of alternant conjugated molecules, containing one heteroatom, is studied by means of graph theory. The Coulson integral representation of total π-electron energy yields a formula for the difference between the π-energy of a heteroconjugated molecule and its parent hydrocarbon. The integral is calculated approximatively and a simple topological formula is derived, enabling the prediction of the stability of a given heteroconjugated molecule relative to its parent hydrocarbon.

A linear relationship between the total π-electron energy and the characteristic polynomial

A linear relationship between the total π-electron energy ( E π) and the coefficients of the characteristic polynomial of the molecular graph is analysed. It is deduced that (a) the main part of E π depends on the number of bonds, (b) the Hückel 4 m+2 rule holds generally, but corrections regarding the role of the size of the rings are to be added, (c) the perimeter rule can be justified, and (d) E π is increased proportionally to the number of Kekulé and Dewar resonance forms. A quantitative measure of all these topological factors is estimated.

ChemInform Abstract: PREDICTIONS OF MOLECULAR GEOMETRIES AND ELECTRONIC SPECTRA OF COMPLEX UNSATURATED MOLECULES FROM MC‐LCAO‐MO METHOD WITH PARTICULAR REFERENCE TO TRIPLET‐TRIPLET TRANSITIONS OF NAPHTHALENE

An MC-LCAO-MO approach which has been proposed for open-shell systems of unsaturated hydrocarbons having degenerate MO's is applied to naphthalene, calculating its molecular geometry and electronic spectrum. The results are compared with those obtained by the usual semi-empirical SCF-CI method and with experiment. As for benzene, anthracene, phenanthrene and triphenylene, the bond lengths and the π-electron energies in their ground states are calculated in the same manner. Most of the calculated bond lengths are in fairly good agreement with experiment. The total π-electron energies of the ground states obtained by the MC-LCAO-MO and SCF-CI methods agree within about 0.01 eV when CI is included and within about 0.1 eV when CI is not invoked. It is found that the electronic spectrum of naphthalene obtained by the present method is in good agreement with that derived from the SCF-CI method and also explains most part of experiments. A detailed discussion is given on the calculated triplet-triplet absorption spectrum and its intensity distribution of naphthalene.

On the Coulson integral formula for total π-electron energy

The Coulson integral formula for total π-electron energy ( E π) is analysed, and an elementary derivation of it is presented. Three novel Coulson-type formulae are obtained and one is used for deriving the McClelland (approximate) expression for E π. An approximation of a particular formula is proposed which results in a linear relationship between E π and the coefficients of the characteristic polynomial of the molecular graph.

The number of Kekulé structures and the thermodynamic stability of conjugated systems

The dependence of Hückel π-electron energies, E π, on the basic graph theoretical parameters N (the number of vertices), ν (the number of edges) and ASC (the algebraic structure count) is explored. The form with the ASC enters E π is established and an equation for E π is developed. It is shown how the early and apparent success of the (resonance) theory rested on the fortunate fact that all Kekulé structures for benzenoid hydrocarbons and acyclic polyenes have the same parity. The significance of ASC in determining chemical stability and reactivity is dicussed briefly.

Predictions of molecular geometries and electronic spectra of complex unsaturated molecules from MC-LCAO-MO method with particular reference to triplet-triplet transitions of naphthalene

An MC-LCAO-MO approach which has been proposed for open-shell systems of unsaturated hydrocarbons having degenerate MO's is applied to naphthalene, calculating its molecular geometry and electronic spectrum. The results are compared with those obtained by the usual semi-empirical SCF-CI method and with experiment. As for benzene, anthracene, phenanthrene and triphenylene, the bond lengths and the π-electron energies in their ground states are calculated in the same manner. Most of the calculated bond lengths are in fairly good agreement with experiment. The total π-electron energies of the ground states obtained by the MC-LCAO-MO and SCF-CI methods agree within about 0.01 eV when CI is included and within about 0.1 eV when CI is not invoked. It is found that the electronic spectrum of naphthalene obtained by the present method is in good agreement with that derived from the SCF-CI method and also explains most part of experiments. A detailed discussion is given on the calculated triplet-triplet absorption spectrum and its intensity distribution of naphthalene.

Aromatic substitution

It is demonstrated that a previously developed topological expression for the total π-electron energy of aromatic molecules provides a good qualitative account of localization energies. The logarithm of the ratio of the algebraic structure counts for the ground state and the localized reaction intermediate is the principle energy determining factor. This expression fails for hydrocarbons with unusually small HOMO-LUMO separations. An alternative topological expression that includes a correction for this situation provides an excellent non-empirical explanation for the successful empirical use of Dewar reactivity numbers in correlating exact localization energies. The present analysis provides an explanation for the success of the traditional resonance structure counting technique in predicting relative rates of aromatic substitution. The analysis develop applied only to alternant hydrocarbons.

Energy band structure of polymer chains with screw axes of symmetry

The general relations concerning the energy band structure of quasi-one-dimensional crystals possessing screw axes are obtained. The π-electron energy bands of an infinite polyene chain are considered within the SCF tight binding approximation.