Conjugated Circuits Model Research Articles

The conjugated-circuit model: application to nonalternant hydrocarbons and a comparison with some other theoretical models of aromaticity

The conjugated-circuit model with an improved set of Q n parameters is applied to non-alternant hydrocarbons. The resonance energy per π electron (REPE) model (with a corrected set of parameters) and the hardness model are also applied to the same group of non-alternants. It is found that the RE/e (the resonance energy per π electron calculated using the conjugated-circuit model) and the REPE are intercorrelated quantities, whereas RE/e or REPE do not correlate with absolute hardness at all for non-alternants. Therefore RE/e was selected as the criterion for aromatic stability, and hardness as the reactivity criterion because it is defined in terms of the frontier orbitals. The stability (high aromaticity and low reactivity) of a non-alternant molecule is then judged by both the RE/e and the hardness. In most cases the stability predictions were in agreement with the available experimental evidence. Buckminsterfullerene, which is a spherical non-alternant structure, is found to be a hard molecule, but not as hard as benzene.

The conjugated-circuit model: The optimum parameters for benzenoid hydrocarbons

A search for the optimum set of parameters for the conjugated-circuit computations on benzenoid hydrocarbons in reported. The SCFπ-MO resonance energies (REs) of Dewar and de Llano were used as standards for the determination ofRn (n= l,2,3) parameters, which correspond to 4n + 2 conjugated circuits. The following set of parameters:R1 = 0.827 eV.R2 = 0.317 andR3 = 0.111 eV produced the best agreement between the REs calculated by the conjugated-circuit model and the REs calculated using the SCF π-MO model.

Quantum-mechanical and computational aspects of the conjugated-circuit model

The current level of the development of the conjugated-circuit model, which is a simple valence bond resonance-theoretic model, is reviewed. The concept of conjugated circuits is presented and the resonance energy expression based on conjugated circuits is given. The quantum mechanical foundations of the conjugated-circuits model are discussed. The selection of parameters for several kinds of conjugated circuits is described in some detail. The computational scheme for making conjugated-circuit calculations is delineated and several approaches to key combinatorial problems in the scheme, i.e. the enumeration of Kekulé structures and conjugated circuits, are outlined. The polycyclic systems studied so far by using the conjugated-circuit model are tabulated and this reveals a wide variety of structurally rather diverse molecular systems ranging from benzenoid hydrocarbons to high temperature superconductors.

The conjugated-circuit model

Several annelated [n]annulenes are examined from a graph-theoretical point of view. It is shown how a new interpretation of the conjugated circuit model can be used in order to study the geometries of such compounds. The work illustrates which energetical factors determine whether a structure with alternating bond lengths, or with reduced symmetry is more stable than one with full double bond delocalization or full symmetry.

The conjugated-circuit model: application to benzenoid hydrocarbons

The conjugated-circuit model is presented and its application to benzenoid hydrocarbons is described. The set of conjugated circuits is truncated at those around three hexagons and these are used for computing the resonance energies (RE) of benzenoids. The concept of benzenoidicity defined in terms of conjugated circuits is also presented. Clar's concept of fully benzenoid hexagonal structures is extended to fully naphthalenoid structures and is further generalized to the concept of fully arenoid hexagonal structures. A comparison is given between the conjugated-circuit model and several other theoretical models for computing the REs of benzenoid hydrocarbons.

ChemInform Abstract: Aromatic Stabilities of Thiophene Analogues of Helicenes.

AbstractThe conjugated circuits model is applied to thia‐helicenes such as (I)‐(IV).

Aromaticity in polycyclic conjugated hydrocarbon dianions

Dianions of polycyclic conjugated hydrocarbons are classified into aromatic, partially aromatic and anti-aromatic types. The classification has been based on a single structural concept: the conjugated circuits model. The negative charge in dianions is formally treated as a “double” bond contracted to a single carbon atom. Most dianions have been found to belong to the type “partially aromatic”, the degree of aromaticity being rather small, even zero or corresponding to weakly antiaromatic systems. The degree of aromaticity has been determined by the relative roles of RE (4 n + 2) and RE (4 n) which represent the positive and the negative contributions to molecular resonance energy, respectively. Our approach is contrasted to the still occasionally used peripheral model, the limitations of which are more serious than generally recognized. Its premise is that large (peripheral) conjugation is dominant, whilst in fact small conjugated cycles (circuits) play the dominant role in aromaticity and conjugation.

Foundations of conjugated circuit models

Abstract

On the aromatic stabilities of thiophene analogues of helicenes

The conjugated circuits model is used to predict the relative aromatic stabilities of a variety of thia-helicenes, i.e., thiophene analogues of helicenes. All studied thia-helicenes are predicted to be aromatic structures. The parent helicenes are always found to be more aromatic than the corresponding daughter thia-helicenes. The theoretical predictions are supported by modest experimental evidence.

The conjugated circuits model

Several annelated [n]annulenes are examined from a graph-theoretical point of view. It is shown how a new interpretation of the conjugated circuit model can be used in order to study the geometries of such compounds. The work illustrates which energetical factors determine whether a structure with alternating bond lengths, or with reduced symmetry is more stable than one with full double bond delocalization or full symmetry.

Aromaticity in heterocyclic molecules containing divalent sulfur

The conjugated circuits model is applied to heterocycles containing divalent sulfur. A novel parametrization is introduced for 4n + 2 and 4n conjugated circuits containing a single sulfur atom. The relative aromatic stabilities of a number of heterocyclic systems containing divalent sulfur are studied. Comparison is made whenever possible with earlier reported resonance energies of these compounds, obtained by using Huckel MO and SCF π-MO models, and appropriate reference structures. Special attention is given to positional isomers. An explanation of the differences amongst such isomers is given.

On the Relative Stabilities of Conjugated Heterocycles Containing Divalent Sulfur

Abstract We have examined the relative stabilities of a number of heterocyclic systems containing divalent sulfur by applying the conjugated circuit model. Comparison is made with earlier reported resonance energies of these compounds, obtained by employing the HMO and SCF π-MO models and appropriate reference structures, indicating a fair parallelism. The approach is then extended to numerous polycyclic sulfur-containing systems synthesized in the last decade and is used for discussing the relative stabilities of positional isomers producing the qualitative explanation for the differences amongst such isomers. Finally, we made predictions on yet unknown structures with divalent sulfur, extending the study to polycyclic systems involving fused rings other than benzene.