Some New Trends in Chemical Graph Theory

García-Domènech, Ramón; Gálvez, Jorge; Julián-Ortiz, Jesús Vicente de; Pogliani, Lionello

doi:10.1021/cr0780006

Cited by 226 publications

(169 citation statements)

References 163 publications

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“…This intuitive object is formally defined by lists of vertices (V) and edges (E); together V and E contain all of the pairwise relationships that define G. In graph theory, the concept of an edge is generalized to be compatible with any dimension of comparison. For example, if the vertices represent atoms, then the edges could represent bonds, nearest neighbors, or like elements, depending on the problem of interest (19,20). All vertex and edge relationships are succinctly contained within the weighted adjacency matrix, A, for the graph ( Fig.…”

Section: Significancementioning

confidence: 99%

Mesoscale molecular network formation in amorphous organic materials

Savoie

Kohlstedt

Jackson

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

104

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High-performance solution-processed organic semiconductors maintain macroscopic functionality even in the presence of microscopic disorder. Here we show that the functional robustness of certain organic materials arises from the ability of molecules to create connected mesoscopic electrical networks, even in the absence of periodic order. The hierarchical network structures of two families of important organic photovoltaic acceptors, functionalized fullerenes and perylene diimides, are analyzed using a newly developed graph methodology. The results establish a connection between network robustness and molecular topology, and also demonstrate that solubilizing moieties play a large role in disrupting the molecular networks responsible for charge transport. A clear link is established between the success of mono and bis functionalized fullerene acceptors in organic photovoltaics and their ability to construct mesoscopically connected electrical networks over length scales of 10 nm.soft materials | disordered properties | charge generation T he discovery that organic semiconductors can complement, or even replace, more expensive/less processable inorganic semiconductors in many applications has spurred intense research for several decades (1). This led to the realization of devices where organics act as one, or all, of the components in transistor, battery, light-emitting diode, photovoltaic, and artificial photosynthetic technologies (2). All of these applications rely on the efficient mesoscopic (10-1,000 nm length scale) transport of charge or energy through space, whereas the fundamental design unit for these systems is the single molecule (∼1 nm length scale). The successful function of these devices thus lies in the ability to bridge these length scales through the construction of efficient electrical molecular networks in the condensed phase. In this context, the challenge for materials scientists is to develop molecular descriptors that are predictive for macroscopic observables, such as charge mobility (3), exciton diffusion (4), or charge generation (5).To close this understanding gap, it will be necessary to develop methodologies that go beyond the traditional formulation of quantum chemistry, which begins with accurate single-molecule properties and extrapolates outward, to frameworks that establish the hierarchical importance of the many possible intermolecular interactions in structurally disordered materials (6-9). In this work, we show how network theory can be combined with quantum chemistry to describe the mesoscopic percolative behavior of technologically relevant organic electron acceptors. The network framework enables the connectivity of the quantum transport states in these materials to be described on the 10-1,000 nm length scale as a function of molecular identity and structural disorder. By evaluating how the transport networks transform with structural disorder and molecular identity, we elucidate the connection between network robustness and molecular topology.Nature offers a template fo...

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Section: Significancementioning

confidence: 99%

Mesoscale molecular network formation in amorphous organic materials

Savoie

Kohlstedt

Jackson

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

104

View full text Add to dashboard Cite

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“…The application of graphs in various fields, particularly in molecules, has been extremely productive, demonstrating to be a very effective tool for predicting molecular properties [25][26][27].…”

Section: Resultsmentioning

confidence: 99%

A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems

Gálvez¹

2012

OJPC

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One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum systems such as the particle in a box and the vibrational frequencies of diatomic molecules, such as hydrogen. The results shown here open a suggestive pathway for the use of graph-theoretical approaches in predicting properties of elementary particles and other physical systems, which seem to match similar topological patterns.

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“…When summarizing data, statistics including analyses of systematic error, correlation, or associations must be combined with simple visualizations such as heat maps (70). Before performing additional data analysis it is important to consider molecular descriptors that are encoded representation of molecules and useful for construction of QSAR/QSPR models (67) and (71). Unlike high throughput data analysis for inorganic materials, analysis of chemical data has distinct features in the development of descriptors.…”

Section: Figurementioning

confidence: 99%