On conjugated molecules with identical topological spectra

Živković, Tomislav P.; Trinajstić, Nenad; Randić, Milan

doi:10.1080/00268977500102101

Cited by 51 publications

(56 citation statements)

References 17 publications

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“…It is also worth noting that the significance of second-order corrections to CBO matrices of PAHs is not limited to description of alterations in neighboring bond orders due to perturbation. This additional anticipation is based on the important role of the secondorder correction P (2) in the formation of the stabilization energy of any perturbed system revealed recently [20,21].…”

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confidence: 99%

“…In particular, the secondorder energy E (2) (which is responsible for stabilization (or destabilization) of perturbed systems vs. those desribed by the zero-order Hamiltonian matrices [21]) consists of the P (1) -containing component and of the P (2) -containing one [20,21], the absolute value of the former exceeding twice that of the latter. Just this result allowed the conclusion to be drawn about the role of the second-order correction P (2) being as important as that of the first-order one in the formation of the stabilization energy of the perturbed system. Finally, the above-mentioned interrelation between the absolute values of the two principal components of the second-order energy formed the basis for expressing the total correction either in terms of the P (1) -containing component or via the P (2) -containing one.…”

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confidence: 99%

“…[15] and Section 3). Hence, analysis of the respective second-order correction P (2) is required when looking for the similarity expected. To this end, an efficient method of derivation of members of the power series for the CBO matrix is required.…”

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confidence: 99%

“…We begin, in Section 2, with an overview of general conclusions concerning total energies and demonstrate their applicability to PAHs. In Section 3, expressions for the second-order corrections P (2) are analyzed and compared with the first-order corrections. Section 4 is devoted to exploration of corrections describing the PAHs of the same origin.…”

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confidence: 99%

“…Accordingly, specific concepts are usually introduced to distinguish these groups of molecules. For example, the concepts of isoconjugated systems [1] and of isospectral graphs [2][3][4] may be mentioned.…”

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confidence: 99%

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Second‐order effects in the Hückel model of perturbed alternant hydrocarbons and their coincidence for specific one‐ and two‐center perturbations

Gineitytė

2006

Int J of Quantum Chemistry

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Explicit algebraic expressions are derived and analyzed for the second-order corrections to the charge-bond order (CBO) matrix of perturbed alternant hydrocarbons (PAHs) in terms of entire blocks of the common Hamiltonian matrix of parent AHs in the framework of the simple Hückel model. The derivation is based on the direct means of solution of the commutation equation for the one-electron density matrix by means of passing to the basis of noncanonical molecular orbitals of parent AHs followed by application of the noncommutative Rayleigh-Schrödinger perturbation theory and retransformation of the results into the initial basis of 2p z AOs of carbon atoms. The second-order corrections obtained are shown to determine alterations in bond orders between chemically bound pairs of atoms under influence of the most popular types of perturbation, viz. changes in the Coulomb parameter(s) and emergence of new intermolecular resonance parameter(s). The same corrections are also demonstrated to play an important role in the formation of stabilization energies of PAHs vs. those of parent AHs. On this basis, an additional insight is given into the content of the classical formulae for total energies of PAHs in terms of self-polarizabilities of atoms and bonds, viz. an energy correction is shown to be made up of a difference between the primary stabilizing contribution of perturbation (which is twice as large as the final stabilization energy) and the destabilizing increment related to weakening of remaining chemical bonds. A detailed comparison of CBO matrices and stabilization energies is made for compounds originating from the same parent hydrocarbon (R) after perturbation of the Coulomb parameter of a certain AO χ r and after building up a composite AH R R by formation of a new bond between AOs χ r and χ r of two identical AHs R and R (e.g., pyridine and biphenyl). The first-order corrections to CBO matrices of these systems are shown to be expressible in terms of the same submatrices, whereas the respective GINEITYTE second-order corrections contain coinciding submatrices referring to parent fragments R and R . As a result, coincidences are established (i) between the self-polarizability of the rth atom of the parent AH R and that of the bond between atoms r and r of the composite AH R R , (ii) between alterations in orders of chemical bonds due to both types of perturbation, and (iii) between stabilization energies referring to a single fragment R or R under an assumption of coinciding perturbation parameters. On this basis, a nontrivial and intriguing similarity is concluded between respective electronic structures in general. Finally, two particular second-order effects are revealed for the same systems, viz. a destabilizing effect related mostly to a local weakening of bonds at the site of perturbation and an energy-free effect manifesting itself as emergence of changes in all bond orders of alternating nature.

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confidence: 99%