Login Register Cart 0
Generic placeholder image

Nanoscience & Nanotechnology-Asia

Editor-in-Chief

ISSN (Print): 2210-6812
ISSN (Online): 2210-6820

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Research Article

A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms

Author(s): Samuel A. Surulere*, Michael Y. Shatalov, Andrew C.P.G. Mkolesia and Adejimi A. Adeniji

Volume 10, Issue 3, 2020

Page: [356 - 363] Pages: 8

DOI: 10.2174/2210681209666190220125249

Price: $65

Abstract

Background: The knowledge of parameter estimation for interatomic potentials is useful in the computation of the vibrational structure of van der Waals molecules.

Methods: On the estimation of the Generalized Morse and Classical Lennard-Jones potential energy functions, complex conjugates eigenvalues may be obtained. Different approaches can be used to solve this resulting problem. A method that uses the objective least squares function method to estimate parameters of the interatomic potentials is employed.

Results: Numerical simulation of the systems using metal atoms yields complex conjugates eigenvalues at some initial point.

Conclusion: Other approaches of solving the complex conjugates eigenvalues problem are discussed comprehensively.

Keywords: Interatomic potentials, least squares, potential parameters, objective functions, van der Waals molecule, conjugate.

Graphical Abstract

[1]
Steele, D.; Lippincott, E.R.; Vanderslice, J.T. Comparative study of empirical internuclear potential functions. Rev. Mod. Phys., 1962, 34(2), 239.
[2]
Matsumoto, A. Parameters of the Morse potential from second virial coefficients of gases. Zeitschrift für. Naturforschung A., 1987, 42(5), 447-450.
[3]
Oobatake, M.; Ooi, T. Determination of energy parameters in Lennard-Jones potentials from second virial coefficients. Prog. Theor. Phys., 1972, 48(6), 2132-2143.
[4]
Morse, P.M. Diatomic molecules according to the wave mechanics. Phys. Rev., 1929, 34(1), 57.
[5]
Kozlov, E.; Popov, L.; Starostenkov, M. Calculation of the Morse potential for solid gold. Russian Phys. J., 1972, 15(3), 395-396.
[6]
Lim, T-C.; Udyavara, R. Relations between Varshni and Morse potential energy parameters. Open Phys., 2009, 7(1), 193-197.
[7]
Biswas, R.; Hamann, D. Interatomic potentials for silicon structural energies. Phys. Rev. Lett., 1985, 55(19), 2001.
[8]
Rafii-Tabar, H.; Mansoori, G. Interatomic potential models for nanostructures. In: Encyclopedia of Nanoscience and Nanotechnology; American Scientific Publishers: USA, 2004.
[9]
Kikawa, C.; Shatalov, M.; Kloppers, P. A method for computing initial approximations for a 3-parameter exponential function. Phys. Sci. Int. J., 2015, 6, 203-208.
[10]
Kloppers, P.; Kikawa, C.; Shatalov, M. A new method for least squares identification of parameters of the transcendental equations. Int. J. Phys. Sci., 2012, 7(31), 5218-5223.
[11]
Olsson, P.A. Transverse resonant properties of strained gold nanowires. J. Appl. Phys., 2010, 108(3) 034318
[12]
Surulere, S.; Shatalov, M.; Mkolesia, A.; Fedotov, I. A modern approach for the identification of the Classical and Modified Generalized Morse potential. Nanosci. Nanotechnol. Asia, 2020, 10(2), 142-151.
[13]
Shatalov, M.; Surulere, S.; Mkolesia, A.; Malange, T. Estimation of potentials that are solutions of some second order ordinary differential equation; Russian J. Mathe. Phys, 2018. [Epub ahead of print]
[14]
Zope, R.R.; Mishin, Y. Interatomic potentials for atomistic simulations of the Ti-Al system. Phys. Rev. B., 2003, 68(2) 024102

Rights & Permissions Print Cite
Article Metrics
3
© 2024 Bentham Science Publishers | Privacy Policy