Information Entropy in Chemistry: An Overview

Sabirov, Denis Sh.; Shepelevich, Igor S.

doi:10.3390/e23101240

Cited by 92 publications

(62 citation statements)

References 115 publications

(228 reference statements)

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“…Both CGCNN and ALIGNN can predict density, vpa (volume per atom), packing fraction, and natoms (number of atoms in the primitive cell; in this work, the "primitive cell" is defined as the Niggli reduced cell 37,38 ) with R 2 scores close to or higher than 0.8. However, they cannot predict struct_comp_cell (structural complexity per cell 39 ) and lattice constants (𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝛼𝛼, 𝛽𝛽, 𝛾𝛾; in this work, 𝑎𝑎 denotes the length of the longest lattice vector, 𝑐𝑐 the shortest, and 𝛼𝛼 denotes the largest lattice angle, 𝛾𝛾the smallest) well. Both structure-based models outperform the compositiononly model, and ALIGNN outperforms CGCNN, except for 𝛼𝛼 and 𝛾𝛾.…”

Section: Resultsmentioning

confidence: 96%

Examining graph neural networks for crystal structures: limitations and opportunities for capturing periodicity

Gong

Xie

Shao‐Horn

et al. 2022

Preprint

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Historically, materials informatics has relied on human-designed descriptors of materials structures. In recent years, graph neural networks (GNNs) have been proposed for learning representations of crystal structures from data end-to-end producing vectorial embeddings that are optimized for downstream prediction tasks. However, a systematic scheme is lacking to analyze and understand the limits of GNNs for capturing crystal structures. In this work, we propose to use human-designed descriptors as a bank of human knowledge to test whether black-box GNNs can capture the knowledge of crystal structures. We find that current state-of-the-art GNNs cannot capture the periodicity of crystal structures well, and we analyze the limitations of the GNN models that result in this failure from three aspects: local expressive power, long-range information, and readout function. We propose an initial solution, hybridizing descriptors with GNNs, to improve the prediction of GNNs for materials properties, especially phonon internal energy and heat capacity with 90% lower errors, and we analyze the mechanisms for the improved prediction. All the analysis can be extended easily to other deep representation learning models, human-designed descriptors, and systems such as molecules and amorphous materials.

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Section: Resultsmentioning

confidence: 96%

Examining graph neural networks for crystal structures: limitations and opportunities for capturing periodicity

Gong

Xie

Shao‐Horn

et al. 2022

Preprint

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“…Let

denote the neighborhood degree based topological index of a graph

, then we get,

where t is the functional characterizing the neighborhood degree-based topological index. The entropy measure [ 42 , 43 , 44 ] is denoted by

and is defined as,

…”

Section: Neighborhood Entropies Of Pent-heptagonal Nanosheetsmentioning

confidence: 99%

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

Xavier¹,

Ghani

Imran

et al. 2023

Molecules

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In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet C5C7(a,b) is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding, non-bonding and antibonding Ruckel molecular orbitals. They are demonstrated to be immediately determinable from their topological characteristics. The effort of chemical and pharmaceutical researchers is significantly increased by the need to conduct numerous chemical experiments to ascertain the chemical characteristics of such a wide variety of novel chemicals. In order to generate novel cellular imaging techniques and to accomplish the regulation of certain cellular mechanisms, scientists have utilized the attributes of nanosheets such as their flexibility and simplicity of modification, out of which carbon nanosheets stand out for their remarkable strength, chemical stability, and electrical conductivity. With efficient tools like polynomials and functions that can forecast compound features, mathematical chemistry has a lot to offer. One such approach is the M-polynomial, a fundamental polynomial that can generate a significant number of degree-based topological indices. Among them, the neighborhood M-polynomial is useful in retrieving neighborhood degree sum-based topological indices that can help in carrying out physical, chemical, and biological experiments. This paper formulates the unique M-polynomial approach which is used to derive and compare a variety of neighborhood degree-based molecular descriptors and the corresponding entropy measures of two variations of pent-heptagonal carbon nanosheets. Furthermore, a regression analysis on these descriptors has also been carried out which can further help in the prediction of various properties of the molecule.

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“…Molecular complexity is sometimes defined over the group of all the molecular graph automorphisms (AG) instead of the molecular symmetry group (a point group, PG), 26 and generally these groups differ (Table 2). AG is defined as the group of permutations of the vertices that preserve the connectivity of the graph by way of not making or breaking edges in a graph, 27 while PG is based on the invariance of the molecule under proper or improper rotational operations.…”

Section: The Complexity Of a Moleculementioning

confidence: 99%

On the origin of the combinatorial complexity of the crystal structures with 0D, 1D, or 2D primary motifs

et al. 2023

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Information Entropy in Chemistry: An Overview

Cited by 92 publications

References 115 publications

Examining graph neural networks for crystal structures: limitations and opportunities for capturing periodicity

Examining graph neural networks for crystal structures: limitations and opportunities for capturing periodicity

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

On the origin of the combinatorial complexity of the crystal structures with 0D, 1D, or 2D primary motifs

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