Complete graph conjecture for inner‐core electrons: Homogeneous index case

Pogliani, Lionello

doi:10.1002/jcc.10277

Cited by 14 publications

(30 citation statements)

References 15 publications

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“…4 This conjecture, which is based on the concept of a complete graph, has been successfully tested with several classes of compounds. 5,6 A graph is complete if every two of its vertices are adjacent. A complete graph of order p is denoted by K p and is r-regular, where r is its regularity and r ) p-1.…”

Section: Methodsmentioning

confidence: 99%

Encoding the Core Electrons with Graph Concepts

Pogliani¹

2004

J. Chem. Inf. Comput. Sci.

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The core electron problem of atoms in chemical graph studies has always been considered as a minor problem. Usually, chemical graphs had to encode just a small set of second row atoms, i.e., C, N, O, and F, thus, graph and, in some cases, pseudograph concepts were enough to "graph" encode the molecules at hand. Molecular connectivity theory, together with its side-branch the electrotopological state, introduced two "ad hoc" algorithms for the core electrons of higher-row atoms based, mainly, on quantum concepts alike. Recently, complete graphs, and, especially, odd complete graphs have been introduced to encode the core electrons of higher-row atoms. By the aid of these types of graphs a double-valued algorithm has been proposed for the valence delta, deltav, of any type of atoms of the periodic table with a principal quantum number n > or =2. The new algorithm is centered on an invariant suggested by the hand-shaking theorem, and the values it gives rise to parallel in some way the values derived by the aid of the two old "quantum" algorithms. A thorough comparative analysis of the newly proposed algorithms has been undertaken for atoms of the group 1A-7A of the periodic table. This comparative study includes the electronegativity, the size of the atoms, the first ionization energy, and the electron affinity. The given algorithm has also been tested with sequential complete graphs, while the even complete graphs give rise to conceptual difficulties. QSAR/QSPR studies do not show a clear-cut preference for any of the two values the algorithm gives rise to, even if recent results seem to prefer one of the two values.

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Section: Methodsmentioning

confidence: 99%

Encoding the Core Electrons with Graph Concepts

Pogliani¹

2004

J. Chem. Inf. Comput. Sci.

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“…The overall model of these three properties with the given set of basis indices uncovers some interesting points: (i) the best basis indices are, unequivocally, those derived with the K p − ( pp − seq) description; (ii) no good terms of any type could be found; and (iii) a pseudo‐connectivity, 1 ψ I , index has the lion's share throughout the model of this property. A comparison with a previous model of the polarizability of organic compounds shows that these two different classes of compound have different features 2, 3. It should be noted that polarizability is found to be quite useful for the prediction of unknown boiling points 32.…”

Section: Resultsmentioning

confidence: 84%

“…The choice of a K 7 for iodine is based on the fact that, to date, only odd complete graphs, K p with p = 1, 3, 5, 7, 9 have been successful in QSPR studies. The K p representation for the core electrons allows us to define the following general algorithm for δ v 1–6: Parameter p · r equals the sum of all vertex degrees in a complete graph. The handshaking theorem states that this sum for every type of graph, and pseudo‐graphs, complete graphs inclusive, equals twice the number of connections 21, 22.…”

Section: Methodsmentioning

confidence: 99%

“…This choice would introduce K 2 vertices for n = 2 atoms, thus redefining all graphs made up of second‐row atoms. Previous work 1–6 has shown that in Eq. (1), q = 1, and p , even if other values cannot be excluded a priori.…”

Section: Methodsmentioning

confidence: 99%

“…The complete K p graph representation for the core electrons of any atom with principal quantum number n ≥ 2 has recently been used to model many properties of different classes of compounds, 1–6. To date, the preferred “graph” representation for the core electrons was the odd complete graph representation, which gave rise to a two‐valued algorithm for the valence delta number, δ v .…”

Section: Introductionmentioning

confidence: 99%

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Model of the physical properties of halides with complete graph‐based indices

Pogliani¹

2004

Int J of Quantum Chemistry

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ABSTRACT:Complete graph-based molecular connectivity indices are used to model different theoretical and experimental properties of a class of 20 alkali halides, as well as a theoretical quantum property of a class of fluorides and chlorides. The experimental properties are the lattice enthalpy, the binding enthalpy, and the polarizability in three different media of the alkali halides. The experimental lattice and binding enthalpy are used as training set to evaluate the other sets of theoretical energies, with which the two enthalpies have, finally, been "reconstructed." The theoretical energies are Coulomb energy, polarization energy, van der Waals energy, repulsion energy, and zero-point energy. The lattice enthalpy descriptors are rather good descriptors of its constituent energies: Coulomb, van der Waals, repulsion, and zero-point. The descriptors of the binding enthalpies, instead, fail to model some of its constituent energies: Coulomb, polarization, van der Waals, and repulsion energies. All types of energies are described by basis molecular connectivity indices based on odd complete graph algorithms, which allow an optimal description of the "reconstructed" calculated enthalpies. A common description of the experimental lattice and binding enthalpies with a descriptor trained on the binding enthalpies alone has also been possible. The model of three sets of polarization values of the metal halides with a descriptor trained with one set of polarization values compares positively with a previous study on the polarization of organic compounds. The model of this property requires molecular connectivity basis indices based on a sequential complete graph algorithm. The model of the quantum theoretical property, the electron density at the bond critical point of a class of fluorides and chlorides, allows an interesting comparison with density functional theory calculations.

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The hydrogen perturbation in molecular connectivity computations

Pogliani

2006

J Comput Chem

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A new algorithm for the delta(v) number, the basic parameter of molecular connectivity indices, is proposed. The new algorithm, which is centered on graph concepts like complete graphs and general graphs, encodes the information of the bonded hydrogen on different atoms through a perturbation parameter that makes use of no new graph concepts. The model quality of the new algorithm is tested with 13 properties of seven different classes of compounds, as well as with composite classes of compounds with the same property and with composite properties of the same class of compounds. Chosen properties and classes of compounds display different percentage of bonded hydrogen atoms, which allow a checking of the importance of this parameter. A comparison is drawn with previous results with zero contribution for the hydrogen perturbation as well as among results obtained by changing the number of compounds of a property but keeping constant the percentage of hydrogen atoms. Results underline the importance of the property as well as the importance of the number of compounds in determining the level of the hydrogen perturbation. Molecular connectivity terms are in some cases more critical than the combination of indices in detecting the perturbation introduced by the hydrogen atoms.

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Complete graph conjecture for inner‐core electrons: Homogeneous index case

Cited by 14 publications

References 15 publications

Encoding the Core Electrons with Graph Concepts

Encoding the Core Electrons with Graph Concepts

Model of the physical properties of halides with complete graph‐based indices

The hydrogen perturbation in molecular connectivity computations

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