DOI: 10.1063/1.463486. A global optimization approach for Lennard-Jones microclusters

A global optimization approach for Lennard-Jones microclusters

10.1063/1.463486

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A global optimization approach is proposed for finding the global minimum energy configuration of Lennard-Jones microclusters. First, the original nonconvex total potential energy function, composed by rational polynomials, is transformed to the difference of two convex functions (DC transformation) via a novel procedure performed for each pair potential that constitute the total potential energy function. Then, a decomposition strategy based on the global optimization (GOP) algorithm [C. A. Floudas and V. Visweswaran, Comput. Chem. Eng. 14, 1397 (1990); V. Visweswaran and C. A. Floudas, ibid. 14, 1419 (1990); Proc. Process Systems Eng. 1991, I.6.1; C. A. Floudas and V. Visweswaran, J. Opt. Theory Appl. (in press)] is designed to provide tight bounds on the global minimum through the solutions of a sequence of relaxed dual subproblems. A number of theoretical results are included which expedite the computational effort by exploiting the special mathematical structure of the problem. The proposed approach attains ε convergence to the global minimum in a finite number of iterations. Based on this procedure, global optimum solutions are generated for small microclusters n≤7. For larger clusters 8≤N≤24 tight lower and upper bounds on the global solution are provided serving as excellent initial points for local optimization approaches. Finally, improved lower bounds on the minimum interparticle distance at the global minimum are provided.

Bibliography

Maranas, C. D., & Floudas, C. A. (1992). A global optimization approach for Lennard-Jones microclusters. The Journal of Chemical Physics, 97(10), 7667â7678.

Authors 2

Costas D. Maranas (first)
Christodoulos A. Floudas (additional)

References 48 Referenced 124

10.1002/9780470142592.ch2 / Adv. Chem. Phys. (1979)
10.1080/00018738300101611 / Adv. Phys. (1983)
10.1088/0305-4470/18/8/003 / J. Phys. A (1985)
{'key': '2024020517010699700_r4'}
{'key': '2024020517010699700_r5', 'first-page': '303', 'volume': '7', 'year': '1953', 'journal-title': 'Philips Res. Rep.'} / Philips Res. Rep. (1953)
{'key': '2024020517010699700_r6'}
{'key': '2024020517010699700_r7'}
{'key': '2024020517010699700_r8', 'first-page': '5', 'volume': '230', 'year': '1971', 'journal-title': 'Nature Phys. Sci.'} / Nature Phys. Sci. (1971)
10.1080/00018737100101231 / Adv. Phys. (1971)
10.1016/0022-0248(72)90234-5 / J. Cryst. Growth (1972)
{'key': '2024020517010699700_r11', 'first-page': '12', 'volume': '61', 'year': '1972', 'journal-title': 'Faraday Discuss. Chem. Soc.'} / Faraday Discuss. Chem. Soc. (1972)
{'key': '2024020517010699700_r12', 'first-page': '46', 'volume': '34', 'year': '1986', 'journal-title': 'Nature'} / Nature (1986)
10.1021/j100345a090 / J. Phys. Chem. (1989)
10.1007/BF01011658 / J. Stat. Phys. (1988)
10.1063/1.452436 / J. Chem. Phys. (1987)
10.1063/1.450303 / J. Chem. Phys. (1986)
10.1021/j100303a014 / J. Phys. Chem. (1987)
10.1007/BF01426910 / Z. Phys. D (1989)
10.1016/0009-2614(88)85011-5 / Chem. Phys. Lett. (1988)
10.1063/1.1699114 / J. Chem. Phys. (1953)
10.1016/0039-6028(78)90134-6 / Surf. Sci. (1978)
10.1016/0009-2614(84)80147-5 / Chem. Phys. Lett. (1984)
{'key': '2024020517010699700_r23', 'first-page': '462', 'volume': '82', 'year': '1984', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1984)
10.1016/0009-2614(87)87091-4 / Chem. Phys. Lett. (1987)
{'key': '2024020517010699700_r25', 'first-page': '3905', 'volume': '42', 'year': '1990', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1990)
{'key': '2024020517010699700_r26', 'first-page': '6880', 'volume': '96', 'year': '1992', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1992)
10.1063/1.462583 / J. Chem. Phys. (1992)
{'key': '2024020517010699700_r28', 'first-page': '8826', 'volume': '136', 'year': '1992', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1992)
10.1063/1.455356 / J. Chem. Phys. (1988)
10.1063/1.458306 / J. Chem. Phys. (1990)
10.1016/0097-8485(90)80037-3 / Comput. Chem. (1990)
{'key': '2024020517010699700_r32', 'first-page': '281', 'volume': '3', 'year': '1992', 'journal-title': 'J. Global Optimization'} / J. Global Optimization (1992)
{'key': '2024020517010699700_r33'}
10.1063/1.445375 / J. Chem. Phys. (1983)
10.1016/0039-6028(85)90596-5 / Surf. Sci. (1985)
10.1063/1.450235 / J. Chem. Phys. (1986)
10.1063/1.453492 / J. Chem. Phys. (1987)
{'key': '2024020517010699700_r38'}
{'key': '2024020517010699700_r39'}
{'key': '2024020517010699700_r40'}
{'key': '2024020517010699700_r41'}
10.1016/0098-1354(90)80020-C / Comput. Chem. Eng. (1990)
10.1016/0098-1354(90)80021-3 / Comput. Chem. Eng. (1990)
{'key': '2024020517010699700_r44'}
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Dates

Type	When
Created	23 years ago (July 26, 2002, 8:22 a.m.)
Deposited	1 year, 6 months ago (Feb. 5, 2024, 12:33 p.m.)
Indexed	1 month, 3 weeks ago (July 1, 2025, 7:06 a.m.)
Issued	32 years, 9 months ago (Nov. 15, 1992)
Published	32 years, 9 months ago (Nov. 15, 1992)
Published Print	32 years, 9 months ago (Nov. 15, 1992)

Funders 0

None

BibTeX

@article{Maranas_1992, title={A global optimization approach for Lennard-Jones microclusters}, volume={97}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.463486}, DOI={10.1063/1.463486}, number={10}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Maranas, Costas D. and Floudas, Christodoulos A.}, year={1992}, month=nov, pages={7667–7678} }

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