Author(s):
K. B. Handage, S. S. Jadhav, P. R. More, A. D. Matere, P. R. Pote, V. R. Jadhav
Email(s):
mevikramjadhav@gmail.com
DOI:
10.52711/0974-4150.2023.00054
Address:
K. B. Handage, S. S. Jadhav, P. R. More, A. D. Matere, P. R. Pote, V. R. Jadhav*
Department of Chemistry, K. K. Wagh Art’s, Commerce and Science College, Pimpalgaon (B), 422209, Tal Niphad, Nashik, Maharashtra (India)
*Corresponding Author
Published In:
Volume - 16,
Issue - 5,
Year - 2023
ABSTRACT:
In this study, we exploit the distinctive attributes of the Hückel method to gain valuable insights into the Cyclopropene system. Alongside quantifying the delocalization energy within the conjugated Cyclopropene ring framework, we employ a theoretical framework to derive secular equations, total energy values, wave functions, electron density, and charge density for the C3H3+ (cation), C3H3- (anion), and C3H3* (Radical) species. By applying the Hückel methods secular determinant, we ascertain orbital energies, electron and charge densities, thus comprehensively characterizing this stable configuration. Our approach offers an accessible means for graduate and post-graduate students to understanding the stable systems configuration analysis and associated parameters. It rests upon assumptions of local comparability such as coulomb integrals, exchange integrals, and overlap integrals. The Cyclopropene system can be thoroughly investigated through our simplified hypothetical approach, facilitating an in-depth understanding of its intrinsic electrical properties.
Cite this article:
K. B. Handage, S. S. Jadhav, P. R. More, A. D. Matere, P. R. Pote, V. R. Jadhav. Cyclopropene System: A Theoretical Investigation into Secular Determinants, π-Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density. Asian Journal of Research in Chemistry. 2023; 16(5):337-3. doi: 10.52711/0974-4150.2023.00054
Cite(Electronic):
K. B. Handage, S. S. Jadhav, P. R. More, A. D. Matere, P. R. Pote, V. R. Jadhav. Cyclopropene System: A Theoretical Investigation into Secular Determinants, π-Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density. Asian Journal of Research in Chemistry. 2023; 16(5):337-3. doi: 10.52711/0974-4150.2023.00054 Available on: https://ajrconline.org/AbstractView.aspx?PID=2023-16-5-4
REFERENCES:
1. Hückel, E. Quantum-theoretical contributions to the benzene problem. I. The electron configuration of benzene and related compounds. Z. Physic. 1931; 70(3-4): 204-286.
2. Longuet-Higgins, H. C., McDowell, C. A., Bawn, C. E. H., Lawrence, A. S. C., and Mills, O. S. General and physical chemistry. Annual Reports on the Progress of Chemistry. 1951; 48:7-86. https://doi.org/10.1039/AR9514800007
3. Kutzelnigg, W. What I like about Hückel theory. Journal of Computational Chemistry. 2007; 28(1): 25-34. https://doi.org/10.1002/jcc.20470
4. Kopf, A., and Saalfrank, P. Electron transport through molecules treated by LCAO-MO Green’s functions with absorbing boundaries. Chemical Physics Letters. 2004; 386(1-3): 17-24. https://doi.org/10.1016/j.cplett.2003.12.118
5. Hoffmann, R. (1963). An extended Hückel theory. I. hydrocarbons. The Journal of Chemical Physics. 1963; 39(6): 1397-1412. https://doi.org/10.1063/1.1734456
6. Jug, K., Hiberty, P. C., Shaik, S. σ− π Energy separation in modern electronic theory for ground states of conjugated systems. Chemical Reviews. 2005; 101(5): 1477-1500. https://doi.org/10.1021/cr990328e
7. Jadhav, V. R., Aher, J. S., Bhagare, A. M., Jamdhade, M. S., and Wadhawane, P. B. Cyclobutadiene System (C4H3+, C4H3-, and C4H3): A Theoretical Study for Solving Secular Determinant, Delocalization Energy, Electron Density, and Charge Density. 2020. 10.5958/0974-4150.2020.00076.0
8. Jadhav, Vikram, Theoretical Approach to Understanding an Electron Density, Charge Density and Most Stable Configuration of H3 System (March 15, 2020). International Journal of Research and Review. 2020; 7(3): SSRN: https://ssrn.com/abstract=3684255
9. Nagaoka, S. I., Yamasaki, Y., Teramae, H., Nagashima, U., and Kokubo, T. Addition to Practical Training in Simple Hückel Theory: Matrix Diagonalization via Tridiagonalization, Cyclobutadiene, and Visualization of Molecular Orbitals. Journal of Chemical Education. 2020; 97(8): 2373-2374. https://doi.org/10.1021/acs.jchemed.0c00857
10. McKee, W. C., Wu, J. I., Rzepa, H. S., Schleyer, P. V. R. (2013). A Hückel Theory Perspective on Möbius Aromaticity. Organic letters. 2013; 15(13): 3432-3435. https://doi.org/10.1021/ol401491s
11. Pedersen, K. G., Borges, A., Hedegård, P., Solomon, G. C., and Strange, M. Illusory connection between cross-conjugation and quantum interference. The Journal of Physical Chemistry C.n 2015; 119(48): 26919-26924. https://doi.org/10.1021/acs.jpcc.5b10407
12. El Bakouri, O., Szczepanik, D. W., Jorner, K., Ayub, R., Bultinck, P., Solà, M., and Ottosson, H. Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?. Journal of the American Chemical Society. 2022; 144(19): 8560-8575. https://doi.org/10.1021/jacs.1c13478
13. Wypych, K., Dimitrova, M., Sundholm, D., Pawlicki, M. Diagnosing Ring Current (s) in Figure-Eight Skeletons: A 3D Through-Space Conjugation in the Two-Loops Crossing. Organic Letters. 2022; 24(27): 4876-4880. https://doi.org/10.1021/acs.orglett.2c01625
14. Jadhav, V. R., Madhuri, J., Pooja, W., Baste, Y. R. Cyclopentadienyl System: Solving the Secular Determinant, π Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density. Journal of Chemistry, Environmental Sciences and its Applications. 2020; 6(2): 21-26. https://doi.org/10.15415/jce.2020.62002
15. Kuldeep B. Handage, Snehal S. Jadhav, Vikram R. Jadhav. Benzene System: A Theoretical Exploration of its Secular Determinant, π-Energy, Delocalization Energy, Wave Functions, Electron Density, and Charge Density. Asian Journal of Research in Chemistry. 2023; 16(4):265-0. doi: 10.52711/0974-4150.2023.00044.
16. Zhu, Z. B., Wei, Y., Shi, M. Recent developments of cyclopropene chemistry. Chemical Society Reviews. 2011; 40(11): 5534-5563. https://doi.org/10.1039/C1CS15074J
17. Tapia, O., Andres, J., Aullo, J. M., Cardenas, R. Electronic aspects of the hydride transfer mechanism: Part 2. Ab-initio analytical gradient studies of the pyridinium cation/1, 4-dihydropyridine, cyclopropenyl-cation/cyclopropene and formaldehyde/methanolate model reactant systems. Journal of Molecular Structure: Theochem. 1988; 167(3-4): 395-412. https://doi.org/10.1016/0166-1280(88)80240-9
18. Allen, Annette D., and Thomas T. Tidwell. Antiaromaticity in open-shell cyclopropenyl to cycloheptatrienyl cations, anions, free radicals, and radical ions. Chemical Reviews. 2001; 101(5): 1333-1348. https://doi.org/10.1021/cr990316t
19. Glukhovtsev, M. N., Laiter, S., Pross, A. Thermochemical assessment of the aromatic and antiaromatic characters of the cyclopropenyl cation, cyclopropenyl anion, and cyclopropenyl radical: A high-level computational study. The Journal of Physical Chemistry. 1996; 100(45): 17801-17806. https://doi.org/10.1021/jp961882k
20. D'yakonov, I. A., Kostikov, R. R. The cyclopropenyl cation. Russian Chemical Reviews. 1967; 36(8): 557. 10.1070/RC1967v036n08ABEH001671