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Prabhu S, Arulperumjothi M, Ghani MU, Imran M, Salu S, Jose BK. Computational Analysis of Some More Rectangular Tessellations of Kekulenes and Their Molecular Characterizations. Molecules 2023; 28:6625. [PMID: 37764401 PMCID: PMC10538234 DOI: 10.3390/molecules28186625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 08/31/2023] [Accepted: 09/02/2023] [Indexed: 09/29/2023] Open
Abstract
Cycloarene molecules are benzene-ring-based polycyclic aromatic hydrocarbons that have been fused in a circular manner and are surrounded by carbon-hydrogen bonds that point inward. Due to their magnetic, geometric, and electronic characteristics and superaromaticity, these polycyclic aromatics have received attention in a number of studies. The kekulene molecule is a cyclically organized benzene ring in the shape of a doughnut and is the very first example of such a conjugated macrocyclic compound. Due to its structural characteristics and molecular characterizations, it serves as a great model for theoretical research involving the investigation of π electron conjugation circuits. Therefore, in order to unravel their novel electrical and molecular characteristics and foresee potential applications, the characterization of such components is crucial. In our current research, we describe two unique series of enormous polycyclic molecules made from the extensively studied base kekulene molecule, utilizing the essential graph-theoretical tools to identify their structural characterization via topological quantities. Rectangular kekulene Type-I and rectangular kekulene Type-II structures were obtained from base kekulene molecules arranged in a rectangular fashion. We also employ two subcases for each Type and, for all of these, we derived ten topological indices. We can investigate the physiochemical characteristics of rectangular kekulenes using these topological indices.
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Affiliation(s)
- S. Prabhu
- Department of Mathematics, Rajalakshmi Engineering College, Chennai 602105, India
| | - M. Arulperumjothi
- Department of Mathematics, St. Joseph’s College of Engineering, Chennai 600119, India;
| | - Muhammad Usman Ghani
- Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan 64200, Pakistan;
| | - Muhammad Imran
- Department of Mathematical Sciences, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates
| | - S. Salu
- PG & Research Department of Mathematics, Sanatana Dharma College, Kerala University, Kerala 688003, India; (S.S.); (B.K.J.)
| | - Bibin K. Jose
- PG & Research Department of Mathematics, Sanatana Dharma College, Kerala University, Kerala 688003, India; (S.S.); (B.K.J.)
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Arockiaraj M, Paul D, Ghani MU, Tigga S, Chu YM. Entropy structural characterization of zeolites BCT and DFT with bond-wise scaled comparison. Sci Rep 2023; 13:10874. [PMID: 37407626 DOI: 10.1038/s41598-023-37931-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 06/29/2023] [Indexed: 07/07/2023] Open
Abstract
Entropy of a connected network is a quantitative measure from information theory that has triggered a plethora of research domains in molecular chemistry, biological sciences and computer programming due to its inherent capacity to explore the structural characteristics of complex molecular frameworks that have low structural symmetry as well as high diversity. The analysis of the structural order is greatly simplified through the topological indices based graph entropy metrics, which are then utilized to predict the structural features of molecular frameworks. This predictability has not only revolutionized the study of zeolitic frameworks but has also given rise to new generations of frameworks. We make a comparative study of two versatile framework topologies namely zeolites BCT and DFT, which have been widely utilized to create a new generation of frameworks known as metal organic frameworks. We discuss bond-additive topological indices and compute entropy measure descriptors for zeolites BCT and DFT using degree and degree-sum parameters. In addition, we perform bond-wise scaled comparative analysis between BCT and DFT which shows that zeolite BCT has greater entropy values compared to zeolite DFT.
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Affiliation(s)
| | - Daniel Paul
- Department of Mathematics, Sri Sairam Institute of Technology, Chennai, 600044, India
| | - Muhammad Usman Ghani
- Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan, 64200, Pakistan
| | - Sushil Tigga
- Department of Mathematics, Loyola College, Chennai, 600034, India
| | - Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, 313000, People's Republic of China.
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Paull D, Jacob K, Clement J, Arockiaraj M, Paul D, Balasubramanian K. Topological Characterization and Entropy Measures of Tetragonal Zeolite Merlinoites. J Mol Struct 2022. [DOI: 10.1016/j.molstruc.2022.134786] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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Prabhu S, Murugan G, Therese SK, Arulperumjothi M, Siddiqui MK. Molecular Structural Characterization of Cycloparaphenylene and its Variants. Polycycl Aromat Compd 2022. [DOI: 10.1080/10406638.2021.1942082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- S. Prabhu
- Department of Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, Tamil Nadu, India
| | - G. Murugan
- Department of Mathematics, Chennai Institute of Technology, Chennai, Tamil Nadu, India
| | - S. Kulandai Therese
- Department of Mathematics, St. Mary’s College, Thoothukudi, Tamil Nadu, India
| | - M. Arulperumjothi
- Department of Mathematics, Loyola College, University of Madras, Chennai, Tamil Nadu, India
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Antony D, Balasubramanian K, Yadav R. Experimental and computational studies of phytomediated selenium-CuO and ZnO nanoparticles-potential drugs for breast cancer. J Mol Struct 2022. [DOI: 10.1016/j.molstruc.2022.133113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Symmetry and Combinatorial Concepts for Cyclopolyarenes, Nanotubes and 2D-Sheets: Enumerations, Isomers, Structures Spectra & Properties. Symmetry (Basel) 2021. [DOI: 10.3390/sym14010034] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out.
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Huilgol MI, Sriram V, Balasubramanian K. Structure–activity relations for antiepileptic drugs through omega polynomials and topological indices. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1987542] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
| | - V. Sriram
- Department of Mathematics, School of Engineering and Technology, Jain University, Bengaluru, India
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Abstract
Symmetry forms the foundation of combinatorial theories and algorithms of enumeration such as Möbius inversion, Euler totient functions, and the celebrated Pólya’s theory of enumeration under the symmetric group action. As machine learning and artificial intelligence techniques play increasingly important roles in the machine perception of music to image processing that are central to many disciplines, combinatorics, graph theory, and symmetry act as powerful bridges to the developments of algorithms for such varied applications. In this review, we bring together the confluence of music theory and spectroscopy as two primary disciplines to outline several interconnections of combinatorial and symmetry techniques in the development of algorithms for machine generation of musical patterns of the east and west and a variety of spectroscopic signatures of molecules. Combinatorial techniques in conjunction with group theory can be harnessed to generate the musical scales, intensity patterns in ESR spectra, multiple quantum NMR spectra, nuclear spin statistics of both fermions and bosons, colorings of hyperplanes of hypercubes, enumeration of chiral isomers, and vibrational modes of complex systems including supergiant fullerenes, as exemplified by our work on the golden fullerene C150,000. Combinatorial techniques are shown to yield algorithms for the enumeration and construction of musical chords and scales called ragas in music theory, as we exemplify by the machine construction of ragas and machine perception of musical patterns. We also outline the applications of Hadamard matrices and magic squares in the development of algorithms for the generation of balanced-pitch chords. Machine perception of musical, spectroscopic, and symmetry patterns are considered.
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Liu J, Arockiaraj M, Arulperumjothi M, Prabhu S. Distance based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID-19. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2021; 121:e26617. [PMID: 33785968 PMCID: PMC7995035 DOI: 10.1002/qua.26617] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Revised: 01/09/2021] [Accepted: 01/22/2021] [Indexed: 06/12/2023]
Abstract
The entire world is struggling to control the spread of coronavirus (COVID-19) as there are no proper drugs for treating the disease. Under clinical trials, some of the repurposed antiviral drugs have been applied to COVID-19 patients and reported the efficacy of the drugs with the diverse inferences. Molecular topology has been developed in recent years as an influential approach for drug design and discovery in which molecules that are structurally related show similar pharmacological properties. It permits a purely mathematical description of the molecular structure so that in the development of identification of new drugs can be found through adequate topological indices. In this paper, we study the structural properties of the several antiviral drugs such as chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir and bevacizumab by considering the distance and bond measures of chemical compounds. Our quantitative values of the topological indices are extremely useful in the recent development of designing new drugs for COVID-19.
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Affiliation(s)
- Jia‐Bao Liu
- School of Mathematics and PhysicsAnhui Jianzhu UniversityHefeiChina
| | | | - M. Arulperumjothi
- Department of Mathematics, Loyola CollegeUniversity of MadrasChennaiTamil NaduIndia
| | - Savari Prabhu
- Department of MathematicsSri Venkateswara College of EngineeringSriperumbudurTamil NaduIndia
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Topological characterization of hexagonal and rectangular tessellations of kekulenes as traps for toxic heavy metal ions. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02733-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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Prabhu S, Murugan G, Arockiaraj M, Arulperumjothi M, Manimozhi V. Molecular topological characterization of three classes of polycyclic aromatic hydrocarbons. J Mol Struct 2021. [DOI: 10.1016/j.molstruc.2020.129501] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
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