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mploying Virial Coefficients for Optimal Solutions in Variational Calculations

Year 2024, Volume: 45 Issue: 3, 604 - 608, 30.09.2024

Mahmut Özgür Sezer

https://doi.org/10.17776/csj.1510611

Abstract

In this study, virial coefficients for one and two-electron hydrogen and helium-like quantum dot structures confined in an infinite potential well were calculated. The virial coefficients were determined based on the dot radius using the Quantum Genetic Algorithm (QGA) method. Calculations were performed using Fernandez's expression; however, due to calculation errors in confined systems, this equivalent expression was found unsuitable as a direct stopping criterion. Instead, virial coefficients were calculated using the ⟨T⟩/⟨V⟩ relationship, and the results were plotted. The fitting function obtained for the virial coefficients is proposed as an effective cutoff criterion for electronic structure calculations of quantum dot systems.

Keywords

Quantum Genetic Algorithm (QGA) Variational calculations Virial coefficients quantum dots.

References

  • [1] Özmen, A., Yakar, Y., Çakır, B., Atav, Ü., Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot, Opt. Commun., (2009) 282, 3999.
  • [2] Çakır, B., Yakar, Y., Özmen, A., Sezer, M.Ö., Şahin, M., Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot, Superlattices Microstruct., (2010) 47, 556.
  • [3] Çakır, B., Yakar, Y., Özmen, A., Linear and nonlinear optical absorption coefficients of spherical quantum dot inside external magnetic field. Physica B, (2017) 510, 86-91.
  • [4] Rahimi, F., Ghaffary, T., Naimi, Y., Khajehazad, H., Effect of magnetic field on energy states and optical properties of quantum dots and quantum antidots, Optical and Quantum Electronics, (2021) 53 (47).
  • [5] Çakır, B., Yakar, Y., Özmen, A., Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential, Journal of luminescence, (2012) 132, 10, 2659.
  • [6] Çakır, B., Özmen, A., Atav, Ü., Yüksel, H., Yakar, Y., Investigation of electronic structure of a quantum dot using Slater-type orbitals and Quantum Genetic Algorithm, Int. J. Mod. Phys. C, (2007)18, 61-72.
  • [7] Rayleigh, Lord, Scientific Papers (1905), Vol. 5: 1902-1910. Cambridge: University Press.
  • [8] Poincaré, H., Lectures on Cosmological Theories, (1911) Paris: Hermann.
  • [9] Zwicky, F. "Die Rotverschiebung von extragalaktischen Nebeln", Helvetica Physica Acta (1933) 6: 110–127.
  • [10] Ledoux, P., On the radial pulsation of gaseous stars, Astrophysical Journal, (1945) 102, 143–153.
  • [11] Kohn, W., Two applications of the variational method to quantum mechanics, Physical Review, (1947), 71(10), 635-636.
  • [12] Cottrell, T. L., & Paterson, S., The virial theorem in quantum mechanics, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, (1951) 42(327), 391-395.
  • [13] Parker, E. N., Tensor Virial Equations. Physical Review, (1954) 96(6), 1686–1689.
  • [14] Hoover, W. G., & Ree, F. H., Calculation of Virial Coefficients., J. Chem. Phys., (1965) 43(2), 375-392.
  • [15] Fernandez F. M., Castro, E., Hypervirial theorems and enclosed quantum-mechanical systems, Phy. Rev. A, (1981) 24(5), 2344.
  • [16] Fernandez F. M., Castro, E., Virial theorem and boundary conditions for approximate wave functions, Int. J. Quantum. Chem., (1982) 11, 741.
  • [17] Mukhopadhyay, S., Bhattacharyya, K., Confined systems and the modified virial theorem from semiclassical considerations, Int. J. Quantum Chem., (2005) 101, 27.
  • [18] Demir, C., Yakar, Y., Çakır, B., Özmen, A., Excited state energies, orbital energies and virial coefficients in confined multi-electron systems, J. Lumin., 251, 119185, 2022.
  • [19] Hirschfelder, J. O., Classical and Quantum Mechanical Hypervirial Theorems, J. Chem. Phys., (1960) 33 (5), 1462-1466.
  • [20] Fernandez, F. M., Castro, E., The virial theorem for systems subjected to sectionally defined potentials, J. Chem. Phys., 75 (6), 2908, 1981.
  • [21] J. H. Holland, Adaptation in Natural and Artificial Systems (1975) University of Michigan Press, Ann Arbor, MI.
  • [22] Çakir, B., Özmen, A., & Yakar, Y., Investigation of electronic structure of a Quantum Dot using Slater-Type Orbitals and Quantum Genetic Algorithm, Int. J. of Modern Physics C, (2007) 8(1), 61-72.
  • [23] Çakır, B., Özmen, A., Atav, Ü., Yakar, Y., Yüksel, H., Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree Fock Roothaan method, Int. J. of Modern Physics C, (2008) 19(4), 599-609.
  • [24] Demir, C., Yakar, Y., Çakır, B., Özmen, A., Energies of the ground and excited states of confined two-electron atom in finite potential well, Physica B, (2023) 662, 414967.

Year 2024, Volume: 45 Issue: 3, 604 - 608, 30.09.2024

Mahmut Özgür Sezer

https://doi.org/10.17776/csj.1510611

Abstract

References

  • [1] Özmen, A., Yakar, Y., Çakır, B., Atav, Ü., Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot, Opt. Commun., (2009) 282, 3999.
  • [2] Çakır, B., Yakar, Y., Özmen, A., Sezer, M.Ö., Şahin, M., Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot, Superlattices Microstruct., (2010) 47, 556.
  • [3] Çakır, B., Yakar, Y., Özmen, A., Linear and nonlinear optical absorption coefficients of spherical quantum dot inside external magnetic field. Physica B, (2017) 510, 86-91.
  • [4] Rahimi, F., Ghaffary, T., Naimi, Y., Khajehazad, H., Effect of magnetic field on energy states and optical properties of quantum dots and quantum antidots, Optical and Quantum Electronics, (2021) 53 (47).
  • [5] Çakır, B., Yakar, Y., Özmen, A., Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential, Journal of luminescence, (2012) 132, 10, 2659.
  • [6] Çakır, B., Özmen, A., Atav, Ü., Yüksel, H., Yakar, Y., Investigation of electronic structure of a quantum dot using Slater-type orbitals and Quantum Genetic Algorithm, Int. J. Mod. Phys. C, (2007)18, 61-72.
  • [7] Rayleigh, Lord, Scientific Papers (1905), Vol. 5: 1902-1910. Cambridge: University Press.
  • [8] Poincaré, H., Lectures on Cosmological Theories, (1911) Paris: Hermann.
  • [9] Zwicky, F. "Die Rotverschiebung von extragalaktischen Nebeln", Helvetica Physica Acta (1933) 6: 110–127.
  • [10] Ledoux, P., On the radial pulsation of gaseous stars, Astrophysical Journal, (1945) 102, 143–153.
  • [11] Kohn, W., Two applications of the variational method to quantum mechanics, Physical Review, (1947), 71(10), 635-636.
  • [12] Cottrell, T. L., & Paterson, S., The virial theorem in quantum mechanics, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, (1951) 42(327), 391-395.
  • [13] Parker, E. N., Tensor Virial Equations. Physical Review, (1954) 96(6), 1686–1689.
  • [14] Hoover, W. G., & Ree, F. H., Calculation of Virial Coefficients., J. Chem. Phys., (1965) 43(2), 375-392.
  • [15] Fernandez F. M., Castro, E., Hypervirial theorems and enclosed quantum-mechanical systems, Phy. Rev. A, (1981) 24(5), 2344.
  • [16] Fernandez F. M., Castro, E., Virial theorem and boundary conditions for approximate wave functions, Int. J. Quantum. Chem., (1982) 11, 741.
  • [17] Mukhopadhyay, S., Bhattacharyya, K., Confined systems and the modified virial theorem from semiclassical considerations, Int. J. Quantum Chem., (2005) 101, 27.
  • [18] Demir, C., Yakar, Y., Çakır, B., Özmen, A., Excited state energies, orbital energies and virial coefficients in confined multi-electron systems, J. Lumin., 251, 119185, 2022.
  • [19] Hirschfelder, J. O., Classical and Quantum Mechanical Hypervirial Theorems, J. Chem. Phys., (1960) 33 (5), 1462-1466.
  • [20] Fernandez, F. M., Castro, E., The virial theorem for systems subjected to sectionally defined potentials, J. Chem. Phys., 75 (6), 2908, 1981.
  • [21] J. H. Holland, Adaptation in Natural and Artificial Systems (1975) University of Michigan Press, Ann Arbor, MI.
  • [22] Çakir, B., Özmen, A., & Yakar, Y., Investigation of electronic structure of a Quantum Dot using Slater-Type Orbitals and Quantum Genetic Algorithm, Int. J. of Modern Physics C, (2007) 8(1), 61-72.
  • [23] Çakır, B., Özmen, A., Atav, Ü., Yakar, Y., Yüksel, H., Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree Fock Roothaan method, Int. J. of Modern Physics C, (2008) 19(4), 599-609.
  • [24] Demir, C., Yakar, Y., Çakır, B., Özmen, A., Energies of the ground and excited states of confined two-electron atom in finite potential well, Physica B, (2023) 662, 414967.
There are 24 citations in total.

Details

Primary Language English
Subjects Atomic and Molecular Physics
Journal Section Natural Sciences
Authors

Mahmut Özgür Sezer 0000-0002-8415-8440

Publication Date September 30, 2024
Submission Date July 4, 2024
Acceptance Date September 3, 2024
Published in Issue Year 2024Volume: 45 Issue: 3

Cite

APA Sezer, M. Ö. (2024). mploying Virial Coefficients for Optimal Solutions in Variational Calculations. Cumhuriyet Science Journal, 45(3), 604-608. https://doi.org/10.17776/csj.1510611
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