Chemical graph theory density

El-Basil S (1990) Caterpillar (Gutman) Trees in Chemical Graph Theory. 153 273-290 Engel E (1996) Relativistic Density Functional Theory. 181 1-80... 

Edelmann, F.T. Rare Earth Complexes with Heteroallylic Ligands. 179, 113-148 (1996). Edelmann, F.T. Lanthanide Metallocenes in Homogeneous Catalysis. 7 79, 247-276(1996). El-Basil, S. Caterpillar (Gutman) Trees in Chemical Graph Theory. 153, 273-290 (1990). Engel, E. Relativistic Density Functional Theory.757, 1-80 (1996)... 

As discussed in Ref. [20], some matrix invariants within the context of chemical graph theory may occasionally be identical despite being derived from different molecular graphs. A known example is that of the characteristic polynomial of 1,4-divinylbenzene and that of 2-phenylbutadiene which are identical - lOx H- 33x - 44x" H- 24x - 4). This problem is extremely unlikely when the molecules are coded not by topological connectivity matrices consisting of ones and zeroes but rather by their respective LDMs (or electron density-weighted adjacency/connectivity matrices, discussed below) since these matrices cannot contain elements that are all of identical magnitudes. 

Chemical bonding models based on graph theory or tensor surface harmonic theory demonstrate the analogy between the aromaticity in two-dimensional planar polygonal hydrocarbons such as benzene and that in three-dimensional deltahedral borane anions of the type B F1 (6 < n < 12). Such models are supported both by diverse computational studies and experimental determinations of electron density distribution. Related methods can be used to study the chemical bonding in the boron polyhedra found in... 

QTAIM provides a definitive answer to the question of whether two atoms are bonded or not even in ambiguous cases [87, 88] and, as a consequence, the molecular graph, i.e., the chemical structure, is readily defined by this theory. Two atoms are bonded if their nuclei are linked in space by a line of maximal electron density termed the bond path [89, 90] (see Fig. 1). A single bond path links the nuclei of chemically bonded atoms irrespective of the mode of the bonding covalent (single or multiple), hydrogen, van der Waals, ionic, metallic, etc. The properties of the eleetron density determined at the point of lowest density along the bond path, where... 

The second approach to defining the absolute hardness rj has a companion parameter taken from density functional theory, called the electronic chemical potential ji. The value of pis essentially the same as the negative of %, as defined in Equation 3.2, and the value of rj is essentially the same as in the more approximate definition in Equation 3.3 but both are defined differently. If the total electronic energy of an atom or molecule is plotted as a function of the total number of electrons N, the graph takes the form of Fig. 3.2 in which the only experimental points are at integral values of but between them it is convenient to... 

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