Molecular topology and the<i>Aufbau</i>principle

Mallion, R. B.; Rouvray, Dennis H.

doi:10.1080/00268977800101451

Cited by 32 publications

(52 citation statements)

References 6 publications

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“…It has been argued [28][29][30][31][32] that the Aufbau process may itself be simulated by means of what may be considered as an entirely topological algorithm.…”

Section: ) -Thatmentioning

confidence: 99%

“…[28][29][30][31][32] Because of this (on grounds of differences in symmetry, for one thing), the corresponding rings of isoarithmic structures are by no means guaranteed to have associated with them identically the same topological π-electron ring-currents. That said, however, it is a remarkable fact that, in practice, the topological π-electron ring-currents in the respective rings of isoarithmic structures seem frequently to differ only in the third decimal-place.…”

Section: 62mentioning

confidence: 99%

“…We shall examine only two types of benzenoids: catafusenes (with no internal carbon atoms, a = 0), and perifusenes (with a > 0); moreover, we shall restrict the discussion to Kekuléan benzenoid structures 27 for which both n and a are even numbers and there are no odd electrons in their ground-state configurations built up by means of the Aufbau process. [28][29][30][31][32] In most of this paper, we shall confront two indices that characterise the individual rings of such benzenoid systems -namely, π-electron partitions 33,34 and topolog-ical π-electron ring-currents 35 -seeking possible correlations between them. Later, we shall also consider the recently defined 36 six-centre delocalisation-indices, Δ 6 .…”

Section: Introductionmentioning

confidence: 99%

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Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Balaban¹,

Mallion²

2012

Croat. Chem. Acta

119

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Abstract. Comparison is made between three different indices that characterise the individual rings of a wide range of condensed benzenoid hydrocarbons. Two of these ("π-electron partitions" and the six-centre delocalisation-indices that have been called "Δ 6 -values") have been introduced only recently as potential indicators of what might be called "local aromaticity", whilst the third ("topological π-electron ringcurrents") was suggested as a possible discriminator in this regard nearly fifty years ago. Whilst linear correlations between ring currents and π-electron partitions within certain restricted classes of ring types are good (with correlation coefficients of up to 0.998), agreement between the two indices over all classes of ring types is poor. Predictions arising from a consideration of π-electron partitions and Δ 6 -values seem, on the other hand, to be in somewhat better accord. It is therefore concluded that, despite its superficially intuitive appeal, the ring-current index is out of step both with π-electron partitions and Δ 6 -values as a general indicator of so-called "local aromaticity". (doi: 10.5562/cca1846)

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“…It has been argued [28][29][30][31][32] that the Aufbau process may itself be simulated by means of what may be considered as an entirely topological algorithm.…”

Section: ) -Thatmentioning

confidence: 99%

Section: 62mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Balaban¹,

Mallion²

2012

Croat. Chem. Acta

119

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“…The spectrum {4, 0 3 , −2 2 } of the octahedral graph (figure 1) has a threefold degenerate non-bonding level that is only partially occupied by four electrons (Mallion & Rouvray 1978). In chemistry, this is a classical case of the JT effect in an orbital triplet.…”

Section: Examples (A) the Octahedral Graphmentioning

confidence: 99%

“…Given a pair consisting of a graph G (of order n) and a number N of electrons (0 ≤ N ≤ n), a (ground state) electronic configuration can be determined as follows (Mallion & Rouvray 1978;Mallion 2009). The eigenvalues of the weighted adjacency matrix are arranged in non-increasing order.…”

Section: Introductionmentioning

confidence: 99%

Graph theory and the Jahn–Teller theorem

et al. 2011

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The Jahn-Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex-and edgeweighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons, then degeneracy of states can be resolved by a non-totally symmetric re-weighting of edges and, where necessary, vertices. This leads to the conjecture that whenever the spectrum of a graph contains a set of bonding or anti-bonding degenerate eigenvalues, the roots of the Hamiltonian matrix over this set will show a linear dependence on edge distortions, which has the effect of lifting the degeneracy. When the degenerate level is non-bonding, distortions of vertex weights have to be included to obtain a full resolution of the eigenspace of the degeneracy. Explicit treatments are given for examples of the octahedral graph, where the degeneracy to be lifted is forced by symmetry, and the phenalenyl graph, where the degeneracy is accidental in terms of the automorphism group.

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Computer generation of the characteristic polynomials of chemical graphs

Balasubramanian

1984

J Comput Chem

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A computer program based on the Frame method for the characteristic polynomials of graphs is developed. This program makes use of an efficient polynomial algorithm of Frame for generating the coefficients in the characteristic polynomials of graphs. This program requires as input only the set of vertices that are neighbors of a given vertex and with labels smaller than the label of that vertex. The program generates and stores only the lower triangle of the adjacency matrix in canonical ordering in a one-dimensional array. The program is written in integer arithmetic, and it can be easily modified to real arithmetic. The coefficients in the characteristic polynomials of several graphs were generated in less than a few seconds, thus solving the difficult problem of generating characteristic polynomials of graphs. The characteristic polynomials of a number of very complicated graphs are obtained including for the first time the characteristic polynomial of an honeycomb lattice graph containing 54 vertices.

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Molecular topology and theAufbauprinciple

Cited by 32 publications

References 6 publications

Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Graph theory and the Jahn–Teller theorem

Computer generation of the characteristic polynomials of chemical graphs

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