Bounds for total π-electron energy of polymethines

The introduction of a -CH=CH- fragment into an arbitrary alternant ,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.     

Semiempirical Hamiltonians for spatially confined π-electron systems

A study of π-electron systems confined by impenetrable surfaces is presented. The study results in a nonempirical-based approach to obtain confinement-adapted semiempirical π-Hamiltonians including repulsive terms (PPP or Hubbard). The impenetrable surface confinement of a physical system involves changes in the boundary conditions that the eigenvectors of its differential Hamiltonian operator have to fulfill, while the Hamiltonian itself remains unchanged. However, if this Hamiltonian is written in second quantization language, then confinement only involves changes of the Hamiltonian scalar factors (integrals). Semiempirical Hamiltonian integrals are replaced by parameters; therefore, confinement involves only changes of these parameters. It is shown that confinement changes Coulomb (α_i) and exchange (β_ij), while repulsion (γ_ij) parameters remain unaffected. Next, the influence of confinement upon the electron correlation of (i) π-electron molecular systems, (ii) atoms, and (iii) an electron gas is discussed. The behaviour of the correlation energy vs. the confinement size is found to be different for each type of system. A neat explanation of this variety is given in terms of the Coulomb attractive fields of the systems. Some chemical confinement effects such as an increase in the reactivity of π-electron systems is also outlined. © 1996 John Wiley & Sons, Inc.     

Assessment of standard force field models against high‐quality ab initio potential curves for prototypes of π–π, CH/π, and SH/π interactions

Several popular force fields, namely, CHARMM, AMBER, OPLS‐AA, and MM3, have been tested for their ability to reproduce highly accurate quantum mechanical potential energy curves for noncovalent interactions in the benzene dimer, the benzene‐CH₄ complex, and the benzene‐H₂S complex. All of the force fields are semi‐quantitatively correct, but none of them is consistently reliable quantitatively. Re‐optimization of Lennard‐Jones parameters and symmetry‐adapted perturbation theory analysis for the benzene dimer suggests that better agreement cannot be expected unless more flexible functional forms (particularly for the electrostatic contributions) are employed for the empirical force fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

First π-electron transitions in finite polymethine chains

In the present article, polymethine and annulene electronic spectra are described in a unique way by means of the Pariser-Parr-Pople method. The analytical expressions were derived for the first π-electron transitions energies. The character of the annulene spectra, like the character of the open-chain spectra, was shown to be dependent on the ratio between electron and site numbers. The Dahne's triad theory and the existence of finite energy gap in polymethines are discussed. © 1996 John Wiley & Sons, Inc.     

Stable π-electron systems and new aromatic structures

Aromatic character, as expressed in the reactions of azulene and its derivatives, is correlated with the development, in the appropriate transition state, of a stable π-electron system (sextet) in the five- or the seven-membered ring.

The recognition that considerable stability is associated with the ions and radical derived from perinaphthene leads to the formulation of several new types of hydrocarbons which may be expected to show aromatic character. A brief theoretical consideration of these hydrocarbons is given.

The synthesis of carbocyclic and heterocyclic derivatives of one of these hydrocarbons, cyclopenta[a]perinaphthene, is outlined, and a detailed account of their properties is given.     

Ab initio studies on the electronic structures of certain 10π-electron six-membered ring compounds

By using ab initio methods of all-electron or effective core potential calculations, the electronic structures and the possible aromaticity of some 10π-electron systems, C₆H₆⁴⁻ (1), N₆⁴⁻ (2), P₆⁴⁻ (3), S₆²⁻ (4), Te₆²⁻ (5) and S₃N₃⁻ (6), have been studied at the SCF levels using 4-31G//4-31G and 6-31G^*//6-31G^* basis sets. The bonding characteristics of these systems are analysed in terms of the canonical molecular orbital and the Foster-Boys localized molecular orbital results. The application of the second-order Jahn-Teller theorem to the stability of these diamagnetical planar species is presented.     

Symmetry distortion of extended 1-D π-electron systems

It has been shown that a symmetry lowering from a state with higher symmetry to a state with lower symmetry (D_(2m)d → C_(2m)) occurs in 1-D polymers with polymethine fragments as elementary units when electron–vibration interaction is taken into account. The investigations are carried out using an extended Su–Schrieffer–Heeger method, where the electron–electron interaction is taken into account.     

Free-electron model for hyperpolarizability of the π-electron system in benzene

The hyperpolarizabilities of benzene have been calculated using a free-electron model for the π-electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γ_zzzz; γ_xxxx; γ_yyyy; γ_zzxx; γ_zzyy; γ_xxyy are non-zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π-electron system also shows similer dispersion.     

Variable ζ calculation for self-consistent screening parameters in ab initio molecular theory

A resolution of Roothaan's HF–SCF–LCAO–MO equations is proposed in which atomic orbital exponents (ζ) are made dependent on the molecular charge distribution and included in the self-consistent scheme. Screening parameters so obtained are self-consistent with the molecular orbital coefficients and compare closely to optimum orbital exponents found by other methods. The technique is applied to the ground, lowest positive, and lowest negative ion states of the hydride series LiH, BH, and HF. Calculated potential curves are used to define purely theoretical values for the vertical and adiabatic ionization energies and electron affinities. Predictions are compared to experimental values where available.     

Spin-projected EHF method. III. Applications to π-electron systems

The surely convergent procedure to obtain extended Hartree–Fock (EHF ) solutions of the spin-projected scheme, for which the equations are given in Part II, is applied to eleven π-electronic systems with 2–10 electrons at the PPP level of integral approximations. The method takes into account a considerable part of the correlation energy. The symmetry properties of the EHF wave functions obtained are discussed together with some computational details. A simplified algorithm is also described.     

Hydrogen bonding in simple π-electron systems II. Pyridine–pyrrol

Previous work in this laboratory concerning the properties of hydrogen bonds in the base pairs of DNA [1–6] has led to considerable interest in the properties of hydrogen bonds in π-electron systems. The first paper in this series [7] has investigated the usefulness of the LCAO –MO –SCF method and the Pariser–Parr–Pople approximation as applied to this problem, by calculation on the ideal pyridine–pyridinium complex. In this paper, a relation with experiment will be established by comparison of the results obtained from this method of calculation with the properties of the experimentally observable pyridine–pyrrol system.     

Hydrogen bonding in simple π-electron systems I. Pyridinium–pyridine

In this work, the application of the Pariser–Parr–Pople scheme to hydrogen-bonded systems containing π electrons has been examined. The potential energy curves for the movement of the hydrogen atom in the bond have been calculated, and the reliability of the results obtained from this method, applied in this manner, have been discussed.