Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess confi...

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Tipo de recurso:
Fecha de publicación:
2017
Institución:
Universidad de Medellín
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Repositorio UDEM
Idioma:
eng
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oai:repository.udem.edu.co:11407/4282
Acceso en línea:
http://hdl.handle.net/11407/4282
Palabra clave:
Potential energy functions
Quantum chemistry
Stochastic systems
Equilibrium structures
Gradient Descent method
Initial configuration
Metal nanoclusters
Molecular quantum chemistry
Nuclear positions
Stochastic search
Valence shell electron pair repulsion
Nanoclusters
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id REPOUDEM2_bbd2921fa3c7846dee6eefd2254359ef
oai_identifier_str oai:repository.udem.edu.co:11407/4282
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.spa.fl_str_mv Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
title Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
spellingShingle Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
Potential energy functions
Quantum chemistry
Stochastic systems
Equilibrium structures
Gradient Descent method
Initial configuration
Metal nanoclusters
Molecular quantum chemistry
Nuclear positions
Stochastic search
Valence shell electron pair repulsion
Nanoclusters
title_short Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
title_full Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
title_fullStr Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
title_full_unstemmed Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
title_sort Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters
dc.contributor.affiliation.spa.fl_str_mv Arias, E., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
Florez, E., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
Pérez-Torres, J.F., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia, Escuela de Qumica, Universidad Industrial de Santander, Bucaramanga, Colombia
dc.subject.keyword.eng.fl_str_mv Potential energy functions
Quantum chemistry
Stochastic systems
Equilibrium structures
Gradient Descent method
Initial configuration
Metal nanoclusters
Molecular quantum chemistry
Nuclear positions
Stochastic search
Valence shell electron pair repulsion
Nanoclusters
topic Potential energy functions
Quantum chemistry
Stochastic systems
Equilibrium structures
Gradient Descent method
Initial configuration
Metal nanoclusters
Molecular quantum chemistry
Nuclear positions
Stochastic search
Valence shell electron pair repulsion
Nanoclusters
description A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported. © 2017 Author(s).
publishDate 2017
dc.date.accessioned.none.fl_str_mv 2017-12-19T19:36:44Z
dc.date.available.none.fl_str_mv 2017-12-19T19:36:44Z
dc.date.created.none.fl_str_mv 2017
dc.type.eng.fl_str_mv Article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 219606
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/4282
dc.identifier.doi.none.fl_str_mv 10.1063/1.4984049
dc.identifier.reponame.spa.fl_str_mv reponame:Repositorio Institucional Universidad de Medellín
dc.identifier.instname.spa.fl_str_mv instname:Universidad de Medellín
identifier_str_mv 219606
10.1063/1.4984049
reponame:Repositorio Institucional Universidad de Medellín
instname:Universidad de Medellín
url http://hdl.handle.net/11407/4282
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021646266&doi=10.1063%2f1.4984049&partnerID=40&md5=94f83345cd96396ea9a0d8ae262a6bf4
dc.relation.ispartofes.spa.fl_str_mv Journal of Chemical Physics
Journal of Chemical Physics Volume 146, Issue 24, 28 June 2017
dc.relation.references.spa.fl_str_mv Apsel, S. E., Emmert, J. W., Deng, J., & Bloomfield, L. A. (1996). Surface-enhanced magnetism in nickel clusters. Physical Review Letters, 76(9), 1441-1444. doi:10.1103/PhysRevLett.76.1441
Assadollahzadeh, B., Bunker, P. R., & Schwerdtfeger, P. (2008). The low lying isomers of the copper nonamer cluster, Cu9. Chemical Physics Letters, 451(4-6), 262-269. doi:10.1016/j.cplett.2007.12.024
Barrón, C., Gómez, S., Romero, D., & Saavedra, A. (1999). A genetic algorithm for lennard-jones atomic clusters. Applied Mathematics Letters, 12(7), 85-90.
Cai, W., Feng, Y., Shao, X., & Pan, Z. (2002). Optimization of lennard-jones atomic clusters. Journal of Molecular Structure: THEOCHEM, 579, 229-234. doi:10.1016/S0166-1280(01)00730-8
Calaminici, P., Köster, A. M., & Gómez-Sandoval, Z. (2007). Density functional study of the structure and properties of Cu9 and Cu9-. Journal of Chemical Theory and Computation, 3(3), 905-913. doi:10.1021/ct600358a
Calaminici, P., Pérez-Romero, M., Vásquez-Pérez, J. M., & Köster, A. M. (2013). On the ground state structure of neutral cun (n=12,14,16,18,20) clusters. Computational and Theoretical Chemistry, 1021, 41-48. doi:10.1016/j.comptc.2013.06.014
Chaves, A. S., Rondina, G. G., Piotrowski, M. J., Tereshchuk, P., & Da Silva, J. L. F. (2014). The role of charge states in the atomic structure of cun and ptn (n = 2-14 atoms) clusters: A DFT investigation. Journal of Physical Chemistry A, 118(45), 10813-10821. doi:10.1021/jp508220h
Császár, A. G., Fábri, C., Szidarovszky, T., Mátyus, E., Furtenbacher, T., & Czakó, G. (2012). The fourth age of quantum chemistry: Molecules in motion. Physical Chemistry Chemical Physics, 14(3), 1085-1106. doi:10.1039/c1cp21830a
Doye, J. P. K., & Wales, D. J. (1998). Global minima for transition metal clusters described by sutton-chen potentials. New Journal of Chemistry, 22(7), 733-744.
Doye, J. P. K., Wales, D. J., & Berry, R. S. (1995). The effect of the range of the potential on the structures of clusters. The Journal of Chemical Physics, 103(10), 4234-4249.
Ferraro, F., Pérez-Torres, J. F., & Hadad, C. Z. (2015). Selective catalytic activation of acetylene by a neutral gold cluster of experimentally known gas-phase geometry. Journal of Physical Chemistry C, 119(14), 7755-7764. doi:10.1021/jp512989q
Geudtner, G., Domínguez-Soria, V. D., Calaminici, P., & Köster, A. M. (2015). Molecular graphs of lin, nan and cun (n=6-9) clusters from the density and the molecular electrostatic potential. Computational and Theoretical Chemistry, 1053, 337-342. doi:10.1016/j.comptc.2014.07.021
Gillespie, R. J. (2008). Fifty years of the VSEPR model. Coordination Chemistry Reviews, 252(12-14), 1315-1327. doi:10.1016/j.ccr.2007.07.007
Gillespie, R. J. (1970). The electron-pair repulsion model for molecular geometry. Journal of Chemical Education, 47(1), 18-23.
Gillespie, R. J., & Nyholm, R. S. (1957). Inorganic stereochemistry. Quarterly Reviews, Chemical Society, 11(4), 339-380.
Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning.
Gruene, P., Rayner, D. M., Redlich, B., Van Der Meer, A. F. G., Lyon, J. T., Meijer, G., & Fielicke, A. (2008). Structures of neutral Au7, Au19, and Au20 clusters in the gas phase. Science, 321(5889), 674-676. doi:10.1126/science.1161166
Guan, G., Liu, S., Cai, Y., Low, M., Bharathi, M. S., Zhang, S., . . . Han, M. -. (2014). Destabilization of gold clusters for controlled nanosynthesis: From clusters to polyhedra. Advanced Materials, 26(21), 3427-3432. doi:10.1002/adma.201306167
Gupta, R. P. (1981). Lattice relaxation at a metal surface. Physical Review B, 23(12), 6265-6270. doi:10.1103/PhysRevB.23.6265
Guzmán-Ramírez, G., Aguilera-Granja, F., & Robles, J. (2010). DFT and GEGA genetic algorithm optimized structures of cun ν (ν=±1,0,2; N=3-13) clusters. European Physical Journal D, 57(1), 49-60. doi:10.1140/epjd/e2010-00001-4
Jin, M., Hao, G., Sun, X., & Chen, W. (2012). Nanoparticle-based positron emission tomography and single photon emission computed tomography imaging of cancer. Rev.Nanosci.Nanotechnol. 1.
Jin, R., Zeng, C., Zhou, M., & Chen, Y. (2016). Atomically precise colloidal metal nanoclusters and nanoparticles: Fundamentals and opportunities. Chemical Reviews, 116(18), 10346-10413. doi:10.1021/acs.chemrev.5b00703
Jug, K., Zimmermann, B., Calaminici, P., & Köster, A. M. (2002). Structure and stability of small copper clusters. Journal of Chemical Physics, 116(11), 4497-4507. doi:10.1063/1.1436465
Kabir, M., Mookerjee, A., & Bhattacharya, A. K. (2004). Structure and stability of copper clusters: A tight-binding molecular dynamics study. Physical Review A - Atomic, Molecular, and Optical Physics, 69(4), 043203-1-043203-10. doi:10.1103/PhysRevA.69.043203
Lewis, G. N. (1916). The atom and the molecule. Journal of the American Chemical Society, 38(4), 762-785. doi:10.1021/ja02261a002
Luo, C. (2000). Structure of small nickel clusters: Ni2-Ni19. Modelling and Simulation in Materials Science and Engineering, 8(2), 95-102. doi:10.1088/0965-0393/8/2/301
Mátyus, E., Hutter, J., Müller-Herold, U., & Reiher, M. (2011). Extracting elements of molecular structure from the all-particle wave function. Journal of Chemical Physics, 135(20) doi:10.1063/1.3662487
Mátyus, E., Hutter, J., Müller-Herold, U., & Reiher, M. (2011). On the emergence of molecular structure. Physical Review A - Atomic, Molecular, and Optical Physics, 83(5) doi:10.1103/PhysRevA.83.052512
Mátyus, E., & Reiher, M. (2012). Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated gaussian functions and the global vector representation. Journal of Chemical Physics, 137(2) doi:10.1063/1.4731696
Mehta, D., Chen, J., Chen, D. Z., Kusumaatmaja, H., & Wales, D. J. (2016). Kinetic transition networks for the thomson problem and smale's seventh problem. Physical Review Letters, 117(2) doi:10.1103/PhysRevLett.117.028301
Mehta, D., Chen, T., Hauenstein, J. D., & Wales, D. J. (2014). Communication: Newton homotopies for sampling stationary points of potential energy landscapes. Journal of Chemical Physics, 141(12) doi:10.1063/1.4896657
Mehta, D., Chen, T., Morgan, J. W. R., & Wales, D. J. (2015). Exploring the potential energy landscape of the thomson problem via newton homotopies. Journal of Chemical Physics, 142(19) doi:10.1063/1.4921163
Mitchell, M. (1996). An Introduction to Genetic Algorithms.
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Parks, E. K., Zhu, L., Ho, J., & Riley, S. J. (1994). The structure of small nickel clusters. I. Ni3-Ni15. The Journal of Chemical Physics, 100(10), 7206-7222.
Perdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77(18), 3865-3868. doi:10.1103/PhysRevLett.77.3865
Péreza, J. F., Florez, E., Hadad, C. Z., Fuentealba, P., & Restrepo, A. (2008). Stochastic search of the quantum conformational space of small lithium and bimetallic lithium-sodium clusters. Journal of Physical Chemistry A, 112(25), 5749-5755. doi:10.1021/jp802176w
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dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv American Institute of Physics Inc.
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 2017-12-19T19:36:44Z2017-12-19T19:36:44Z2017219606http://hdl.handle.net/11407/428210.1063/1.4984049reponame:Repositorio Institucional Universidad de Medellíninstname:Universidad de MedellínA new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported. © 2017 Author(s).engAmerican Institute of Physics Inc.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85021646266&doi=10.1063%2f1.4984049&partnerID=40&md5=94f83345cd96396ea9a0d8ae262a6bf4Journal of Chemical PhysicsJournal of Chemical Physics Volume 146, Issue 24, 28 June 2017Apsel, S. E., Emmert, J. W., Deng, J., & Bloomfield, L. A. (1996). Surface-enhanced magnetism in nickel clusters. Physical Review Letters, 76(9), 1441-1444. doi:10.1103/PhysRevLett.76.1441Assadollahzadeh, B., Bunker, P. R., & Schwerdtfeger, P. (2008). The low lying isomers of the copper nonamer cluster, Cu9. Chemical Physics Letters, 451(4-6), 262-269. doi:10.1016/j.cplett.2007.12.024Barrón, C., Gómez, S., Romero, D., & Saavedra, A. (1999). A genetic algorithm for lennard-jones atomic clusters. Applied Mathematics Letters, 12(7), 85-90.Cai, W., Feng, Y., Shao, X., & Pan, Z. (2002). Optimization of lennard-jones atomic clusters. Journal of Molecular Structure: THEOCHEM, 579, 229-234. doi:10.1016/S0166-1280(01)00730-8Calaminici, P., Köster, A. M., & Gómez-Sandoval, Z. (2007). Density functional study of the structure and properties of Cu9 and Cu9-. Journal of Chemical Theory and Computation, 3(3), 905-913. doi:10.1021/ct600358aCalaminici, P., Pérez-Romero, M., Vásquez-Pérez, J. M., & Köster, A. M. (2013). On the ground state structure of neutral cun (n=12,14,16,18,20) clusters. Computational and Theoretical Chemistry, 1021, 41-48. doi:10.1016/j.comptc.2013.06.014Chaves, A. S., Rondina, G. G., Piotrowski, M. J., Tereshchuk, P., & Da Silva, J. L. F. (2014). The role of charge states in the atomic structure of cun and ptn (n = 2-14 atoms) clusters: A DFT investigation. Journal of Physical Chemistry A, 118(45), 10813-10821. doi:10.1021/jp508220hCsászár, A. G., Fábri, C., Szidarovszky, T., Mátyus, E., Furtenbacher, T., & Czakó, G. (2012). The fourth age of quantum chemistry: Molecules in motion. Physical Chemistry Chemical Physics, 14(3), 1085-1106. doi:10.1039/c1cp21830aDoye, J. P. K., & Wales, D. J. (1998). Global minima for transition metal clusters described by sutton-chen potentials. New Journal of Chemistry, 22(7), 733-744.Doye, J. P. K., Wales, D. J., & Berry, R. S. (1995). The effect of the range of the potential on the structures of clusters. The Journal of Chemical Physics, 103(10), 4234-4249.Ferraro, F., Pérez-Torres, J. F., & Hadad, C. Z. (2015). Selective catalytic activation of acetylene by a neutral gold cluster of experimentally known gas-phase geometry. Journal of Physical Chemistry C, 119(14), 7755-7764. doi:10.1021/jp512989qGeudtner, G., Domínguez-Soria, V. D., Calaminici, P., & Köster, A. M. (2015). Molecular graphs of lin, nan and cun (n=6-9) clusters from the density and the molecular electrostatic potential. Computational and Theoretical Chemistry, 1053, 337-342. doi:10.1016/j.comptc.2014.07.021Gillespie, R. J. (2008). Fifty years of the VSEPR model. Coordination Chemistry Reviews, 252(12-14), 1315-1327. doi:10.1016/j.ccr.2007.07.007Gillespie, R. J. (1970). The electron-pair repulsion model for molecular geometry. Journal of Chemical Education, 47(1), 18-23.Gillespie, R. J., & Nyholm, R. S. (1957). Inorganic stereochemistry. Quarterly Reviews, Chemical Society, 11(4), 339-380.Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning.Gruene, P., Rayner, D. M., Redlich, B., Van Der Meer, A. F. G., Lyon, J. T., Meijer, G., & Fielicke, A. (2008). Structures of neutral Au7, Au19, and Au20 clusters in the gas phase. Science, 321(5889), 674-676. doi:10.1126/science.1161166Guan, G., Liu, S., Cai, Y., Low, M., Bharathi, M. S., Zhang, S., . . . Han, M. -. (2014). Destabilization of gold clusters for controlled nanosynthesis: From clusters to polyhedra. Advanced Materials, 26(21), 3427-3432. doi:10.1002/adma.201306167Gupta, R. P. (1981). Lattice relaxation at a metal surface. Physical Review B, 23(12), 6265-6270. doi:10.1103/PhysRevB.23.6265Guzmán-Ramírez, G., Aguilera-Granja, F., & Robles, J. (2010). DFT and GEGA genetic algorithm optimized structures of cun ν (ν=±1,0,2; N=3-13) clusters. European Physical Journal D, 57(1), 49-60. doi:10.1140/epjd/e2010-00001-4Jin, M., Hao, G., Sun, X., & Chen, W. (2012). Nanoparticle-based positron emission tomography and single photon emission computed tomography imaging of cancer. Rev.Nanosci.Nanotechnol. 1.Jin, R., Zeng, C., Zhou, M., & Chen, Y. (2016). Atomically precise colloidal metal nanoclusters and nanoparticles: Fundamentals and opportunities. Chemical Reviews, 116(18), 10346-10413. doi:10.1021/acs.chemrev.5b00703Jug, K., Zimmermann, B., Calaminici, P., & Köster, A. M. (2002). Structure and stability of small copper clusters. Journal of Chemical Physics, 116(11), 4497-4507. doi:10.1063/1.1436465Kabir, M., Mookerjee, A., & Bhattacharya, A. K. (2004). Structure and stability of copper clusters: A tight-binding molecular dynamics study. Physical Review A - Atomic, Molecular, and Optical Physics, 69(4), 043203-1-043203-10. doi:10.1103/PhysRevA.69.043203Lewis, G. N. (1916). The atom and the molecule. Journal of the American Chemical Society, 38(4), 762-785. doi:10.1021/ja02261a002Luo, C. (2000). Structure of small nickel clusters: Ni2-Ni19. Modelling and Simulation in Materials Science and Engineering, 8(2), 95-102. doi:10.1088/0965-0393/8/2/301Mátyus, E., Hutter, J., Müller-Herold, U., & Reiher, M. (2011). Extracting elements of molecular structure from the all-particle wave function. Journal of Chemical Physics, 135(20) doi:10.1063/1.3662487Mátyus, E., Hutter, J., Müller-Herold, U., & Reiher, M. (2011). On the emergence of molecular structure. Physical Review A - Atomic, Molecular, and Optical Physics, 83(5) doi:10.1103/PhysRevA.83.052512Mátyus, E., & Reiher, M. (2012). Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated gaussian functions and the global vector representation. Journal of Chemical Physics, 137(2) doi:10.1063/1.4731696Mehta, D., Chen, J., Chen, D. Z., Kusumaatmaja, H., & Wales, D. J. (2016). Kinetic transition networks for the thomson problem and smale's seventh problem. Physical Review Letters, 117(2) doi:10.1103/PhysRevLett.117.028301Mehta, D., Chen, T., Hauenstein, J. D., & Wales, D. J. (2014). Communication: Newton homotopies for sampling stationary points of potential energy landscapes. Journal of Chemical Physics, 141(12) doi:10.1063/1.4896657Mehta, D., Chen, T., Morgan, J. W. R., & Wales, D. J. (2015). Exploring the potential energy landscape of the thomson problem via newton homotopies. 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Physical Chemistry Chemical Physics, 17(37), 24173-24181. doi:10.1039/c5cp04060dScopusAlgorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclustersArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Arias, E., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaFlorez, E., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaPérez-Torres, J.F., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia, Escuela de Qumica, Universidad Industrial de Santander, Bucaramanga, ColombiaArias E.Florez E.Pérez-Torres J.F.Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaEscuela de Qumica, Universidad Industrial de Santander, Bucaramanga, ColombiaPotential energy functionsQuantum chemistryStochastic systemsEquilibrium structuresGradient Descent methodInitial configurationMetal nanoclustersMolecular quantum chemistryNuclear positionsStochastic searchValence shell electron pair repulsionNanoclustersA new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported. © 2017 Author(s).http://purl.org/coar/access_right/c_16ec11407/4282oai:repository.udem.edu.co:11407/42822020-05-27 16:36:46.087Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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