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Evaluation of restricted probabilistic cellular automata on the exploration of the potential energy surface of Be6B11

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Abstract

Herein the performance of a modification within the hybrid algorithm implemented in the AUTOMATON program is introduced and evaluated. For the creation of the initial population, AUTOMATON combines a probabilistic automata procedure with a genetic algorithm used to evolve this population. The proposed modification is addressed to efficiently identify the minimum energy structures of systems composed of more than one type of atom and with a low computational cost. The effectiveness of this approach is evaluated in the determination of the minimum energy structures of Be6B11. The modification, aimed to explore the potential energy surface, consisted of filling the cells first with Be atoms in the process of creating the initial population. This order obeys the structural pattern established in the Be–B clusters reported to date. The results show that this variation not only identifies a more significant number of viable isomers but also to find a better putative global minimum than those previously reported in the literature. Therefore, it is recommended to be used as a complement to the standard searching process.

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References

  1. Jortner J (1992) Clusters as a key to the understanding of properties as a function of size and dimensionality. In: Jena P, Khanna SN, Rao BK (eds) Physics and chemistry of finite systems: from clusters to crystals. Springer, Netherlands, pp 1–17

    Google Scholar 

  2. Alexandrova AN, Boldyrev AI, Zhai H-J, Wang L-S (2006) All-boron aromatic clusters as potential new inorganic ligands and building blocks in chemistry. Coord Chem Rev 250:2811–2866. https://doi.org/10.1016/J.CCR.2006.03.032

    Article  CAS  Google Scholar 

  3. Malinowski N, Schaber H, Bergmann T, Martin TP (1989) Electronic shell structure in NaO clusters. Solid State Commun 69:733–735. https://doi.org/10.1016/0038-1098(89)90820-X

    Article  CAS  Google Scholar 

  4. Wade K (1976) Structural and bonding patterns in cluster chemistry. Adv Inorg Chem Radiochem 18:1–66. https://doi.org/10.1016/S0065-2792(08)60027-8

    Article  CAS  Google Scholar 

  5. Wang L, Cheng H, Fan J (1995) Photoelectron spectroscopy of size-selected transition metal clusters: Fen − , n = 3–24. J Chem Phys 102:9480–9493. https://doi.org/10.1063/1.468817

    Article  CAS  Google Scholar 

  6. León I, Yang Z, Liu H-T, Wang L-S (2014) The design and construction of a high-resolution velocity-map imaging apparatus for photoelectron spectroscopy studies of size-selected clusters. Rev Sci Instrum 85:083106. https://doi.org/10.1063/1.4891701

    Article  CAS  PubMed  Google Scholar 

  7. Li X, Kuznetsov AE, Zhang H-F, Boldyrev AI, Wang L-S (2001) Observation of all-metal aromatic molecules. Science 291(80):859. https://doi.org/10.1126/science.291.5505.859

    Article  CAS  PubMed  Google Scholar 

  8. Li J, Li X, Zhai H-J, Wang L-S (2003) Au20: a tetrahedral cluster. Science 299(80):864. https://doi.org/10.1126/science.1079879

    Article  CAS  PubMed  Google Scholar 

  9. Ji M, Gu X, Li X, Gong X, Li J, Wang L-S (2005) Experimental and theoretical investigation of the electronic and geometrical structures of the Au32 cluster. Angew Chemie Int Ed 44:7119–7123. https://doi.org/10.1002/anie.200502795

    Article  CAS  Google Scholar 

  10. Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic, and kinetic effects. Rev Mod Phys 77:371–423. https://doi.org/10.1103/RevModPhys.77.371

    Article  CAS  Google Scholar 

  11. Ferrando R, Jellinek J, Johnston RL (2008) Nanoalloys: from theory to applications of alloy clusters and nanoparticles. Chem Rev 108:845–910. https://doi.org/10.1021/cr040090g

    Article  CAS  PubMed  Google Scholar 

  12. Metropolis N, Ulam S (1949) The monte carlo method. J Am Stat Assoc 44:335–341. https://doi.org/10.1080/01621459.1949.10483310

    Article  CAS  PubMed  Google Scholar 

  13. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092. https://doi.org/10.1063/1.1699114

    Article  CAS  Google Scholar 

  14. Vanderbilt D, Louie SG (1984) A Monte carlo simulated annealing approach to optimization over continuous variables. J Comput Phys 56:259–271. https://doi.org/10.1016/0021-9991(84)90095-0

    Article  Google Scholar 

  15. Van Laarhoven PJM, Aarts EHL (1987) Simulated annealing. In: Hwang CR (ed) Simulated annealing: theory and applications. Springer, Berlin, pp 7–15

    Chapter  Google Scholar 

  16. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(80):671–680. https://doi.org/10.1126/science.220.4598.671

    Article  CAS  PubMed  Google Scholar 

  17. Hartke B (2002) Global geometry optimization of clusters using genetic algorithms. J Phys Chem 97:9973–9976. https://doi.org/10.1021/j100141a013

    Article  Google Scholar 

  18. Hartke B (1995) Global geometry optimization of clusters using a growth strategy optimized by a genetic algorithm. Chem Phys Lett 240:560–565. https://doi.org/10.1016/0009-2614(95)00587-T

    Article  CAS  Google Scholar 

  19. Rabanal-León WA, Tiznado W, Osorio E, Ferraro F (2018) Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects. RSC Adv 8:145–152. https://doi.org/10.1039/C7RA11449D

    Article  Google Scholar 

  20. Deaven DM, Ho KM (1995) Molecular geometry optimization with a genetic algorithm. Phys Rev Lett 75:288–291. https://doi.org/10.1103/PhysRevLett.75.288

    Article  CAS  PubMed  Google Scholar 

  21. Daven DM, Tit N, Morris JR, Ho KM (1996) Structural optimization of Lennard–Jones clusters by a genetic algorithm. Chem Phys Lett 256:195–200. https://doi.org/10.1016/0009-2614(96)00406-X

    Article  Google Scholar 

  22. Alexandrova AN, Boldyrev AI, Fu Y-J, Yang X, Wang X-B, Wang L-S (2004) Structure of the NaxClx+1  (x = 1–4) clusters via ab initio genetic algorithm and photoelectron spectroscopy. J Chem Phys 121:5709–5719. https://doi.org/10.1063/1.1783276

    Article  CAS  PubMed  Google Scholar 

  23. Davis JBA, Shayeghi A, Horswell SL, Johnston RL (2015) The Birmingham parallel genetic algorithm and its application to the direct DFT global optimisation of IrN (N = 10–20) clusters. Nanoscale 7:14032–14038. https://doi.org/10.1039/C5NR03774C

    Article  CAS  PubMed  Google Scholar 

  24. Shayeghi A, Götz D, Davis JBA, Schäfer R, Johnston RL (2015) Pool-BCGA: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters. Phys Chem Chem Phys 17:2104–2112. https://doi.org/10.1039/C4CP04323E

    Article  CAS  PubMed  Google Scholar 

  25. Johnston RL, Mortimer-Jones TV, Roberts C, Darby S, Manby FR (2002) Application of genetic algorithms in nanoscience: cluster geometry optimization BT. In: Cagnoni S, Gottlieb J, Hart E, Middendorf M, Raidl GR (eds) Applications of evolutionary computing. Springer, Berlin, pp 92–101

    Chapter  Google Scholar 

  26. Vargas JA, Buendía F, Beltrán MR (2017) New AuN (N = 27–30) lowest energy clusters obtained by means of an improved DFT—genetic algorithm methodology. J Phys Chem C 121:10982–10991. https://doi.org/10.1021/acs.jpcc.6b12848

    Article  CAS  Google Scholar 

  27. Kanters PFR, Donald KJ (2014) Cluster: searching for unique low energy minima of structures using a novel implementation of a genetic algorithm. J Chem Theory Comput 10:5729–5737. https://doi.org/10.1021/ct500744k

    Article  CAS  PubMed  Google Scholar 

  28. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science, pp 39–43

  29. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1:33–57. https://doi.org/10.1007/s11721-007-0002-0

    Article  Google Scholar 

  30. Zhan Z, Zhang J, Li Y, Chung HS (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man, Cybern Part B 39:1362–1381. https://doi.org/10.1109/TSMCB.2009.2015956

    Article  Google Scholar 

  31. Call ST, Zubarev DY, Boldyrev AI (2007) Global minimum structure searches via particle swarm optimization. J Comput Chem 28:1177–1186. https://doi.org/10.1002/jcc.20621

    Article  CAS  PubMed  Google Scholar 

  32. Jana G, Mitra A, Pan S, Sural S, Chattaraj PK (2019) Modified particle swarm optimization algorithms for the generation of stable structures of carbon clusters, Cn (n = 3–6, 10). Front Chem 7:485

    Article  CAS  Google Scholar 

  33. Li Z, Scheraga HA (1987) Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proc Natl Acad Sci 84:6611–6615. https://doi.org/10.1073/pnas.84.19.6611

    Article  CAS  PubMed  Google Scholar 

  34. Wales JD, Doye PKJ (1997) Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116. https://doi.org/10.1021/jp970984n

    Article  CAS  Google Scholar 

  35. White RP, Mayne HR (1998) An investigation of two approaches to basin hopping minimization for atomic and molecular clusters. Chem Phys Lett 289:463–468. https://doi.org/10.1016/S0009-2614(98)00431-X

    Article  CAS  Google Scholar 

  36. Liberti L, Maculan N (2006) Global optimization: from theory to implementation. Springer, Berlin

    Book  Google Scholar 

  37. Zhao Y, Chen X, Li J (2017) TGMin: a global-minimum structure search program based on a constrained basin-hopping algorithm. Nano Res 10:3407–3420. https://doi.org/10.1007/s12274-017-1553-z

    Article  CAS  Google Scholar 

  38. Saunders M (1987) Stochastic exploration of molecular mechanics energy surfaces: hunting for the global minimum. J Am Chem Soc 109:3150–3152. https://doi.org/10.1021/ja00244a051

    Article  CAS  Google Scholar 

  39. Bera PP, Schleyer PV, Schaefer HFR III (2007) Periodane: a wealth of structural possibilities revealed by the Kick procedure. Int J Quantum Chem 107:2220–2223. https://doi.org/10.1002/qua.21322

    Article  CAS  Google Scholar 

  40. Averkiev B (2009) Geometry and electronic structure of doped clusters via the Coalescence Kick method. Utah State University, Logan

    Google Scholar 

  41. Addicoat MA, Metha GF (2009) Kick: constraining a stochastic search procedure with molecular fragments. J Comput Chem 30:57–64. https://doi.org/10.1002/jcc.21026

    Article  CAS  PubMed  Google Scholar 

  42. Cabellos JL, Ortiz-Chi F, Ramirez A, Merino G (2013) GLOMOS 1.0, Cinvestav, Mérida

  43. Heiles S, Johnston RL (2013) Global optimization of clusters using electronic structure methods. Int J Quantum Chem 113:2091–2109. https://doi.org/10.1002/qua.24462

    Article  CAS  Google Scholar 

  44. Zhang J, Dolg M (2016) Global optimization of clusters of rigid molecules using the artificial bee colony algorithm. Phys Chem Chem Phys 18:3003–3010. https://doi.org/10.1039/C5CP06313B

    Article  CAS  PubMed  Google Scholar 

  45. Jackson KA, Horoi M, Chaudhuri I, Frauenheim T, Shvartsburg AA (2004) Unraveling the shape transformation in silicon clusters. Phys Rev Lett 93:13401. https://doi.org/10.1103/PhysRevLett.93.013401

    Article  CAS  Google Scholar 

  46. Avaltroni F, Corminboeuf C (2012) Identifying clusters as low-lying mimina—efficiency of stochastic and genetic algorithms using inexpensive electronic structure levels. J Comput Chem 33:502–508. https://doi.org/10.1002/jcc.22882

    Article  CAS  PubMed  Google Scholar 

  47. Zhao J, Shi R, Sai L, Huang X, Su Y (2016) Comprehensive genetic algorithm for ab initio global optimisation of clusters. Mol Simul 42:809–819. https://doi.org/10.1080/08927022.2015.1121386

    Article  CAS  Google Scholar 

  48. Tiznado W, Perez-Peralta N, Islas R, Toro-Labbe A, Ugalde J, Merino G (2009) Designing 3-D molecular stars. J Am Chem Soc 131:9426–9431. https://doi.org/10.1021/ja903694d

    Article  CAS  PubMed  Google Scholar 

  49. Perez-Peralta N, Contreras M, Tiznado W, Stewart J, Donald KJ, Merino G (2011) Stabilizing carbon-lithium stars. Phys Chem Chem Phys 13:12975–12980. https://doi.org/10.1039/C1CP21061K

    Article  CAS  PubMed  Google Scholar 

  50. Torres-Vega JJ, Vásquez-Espinal A, Beltran MJ, Ruiz L, Islas R, Tiznado W (2015) Li7(BH)+5 : a new thermodynamically favored star-shaped molecule. Phys Chem Chem Phys 17:19602–19606. https://doi.org/10.1039/c5cp02006a

    Article  CAS  PubMed  Google Scholar 

  51. Contreras M, Osorio E, Ferraro F, Puga G, Donald KJ, Harrison JG, Merino G, Tiznado W (2013) Isomerization energy decomposition analysis for highly ionic systems: case study of starlike E5Li7+ clusters. Chem Eur J 19:2305–2310. https://doi.org/10.1002/chem.201203329

    Article  CAS  PubMed  Google Scholar 

  52. Vásquez-Espinal A, Palacio-Rodríguez K, Ravell E, Orozco-Ic M, Barroso J, Pan S, Tiznado W, Merino G (2018) E5M7+ (E = C–Pb, M = Li–Cs): a source of viable star-shaped clusters. Chem Asian J 13:1751–1755. https://doi.org/10.1002/asia.201800654

    Article  CAS  PubMed  Google Scholar 

  53. Yañez O, Garcia V, Garza J, Orellana W, Vásquez-Espinal A, Tiznado W (2019) (Li6Si5)2–5: the smallest cluster-assembled materials based on aromatic Si56− rings. Chem Eur J 25:2467–2471. https://doi.org/10.1002/chem.201805677

    Article  CAS  PubMed  Google Scholar 

  54. Vassilev-Galindo V, Pan S, Donald KJ, Merino G (2018) Planar pentacoordinate carbons. Nat Rev Chem 2:114

    Article  CAS  Google Scholar 

  55. Ravell E, Jalife S, Barroso J, Orozco-Ic M, Hernández-Juárez G, Ortiz-Chi F, Pan S, Cabellos JL, Merino G (2018) Structure and bonding in CE5− (E = Al–Tl) clusters: planar tetracoordinate carbon versus pentacoordinate carbon. Chem Asian J 13:1467–1473. https://doi.org/10.1002/asia.201800261

    Article  CAS  PubMed  Google Scholar 

  56. Yañez O, Vasquez-Espinal A, Pino-Rios R, Ferraro F, Pan S, Osorio E, Merino G, Tiznado W (2017) Exploiting electronic strategies to stabilize a planar tetracoordinate carbon in cyclic aromatic hydrocarbons. Chem Commun 53:12112–12115. https://doi.org/10.1039/C7CC06248F

    Article  Google Scholar 

  57. Yañez O, Vásquez-Espinal A, Báez-Grez R, Rabanal-León WA, Osorio E, Ruiz L, Tiznado W (2019) Carbon rings decorated with group 14 elements: new aromatic clusters containing planar tetracoordinate carbon. New J Chem 43:6781–6785. https://doi.org/10.1039/C9NJ01022J

    Article  Google Scholar 

  58. García J-J, Hernández-Esparza R, Vargas R, Tiznado W, Garza J (2019) Formation of small clusters of NaCl dihydrate in the gas phase. New J Chem 43:4342–4348. https://doi.org/10.1039/C8NJ06315J

    Article  Google Scholar 

  59. Fuentealba P, Cardenas C, Pino-Rios R, Tiznado W (2016) Topological analysis of the fukui function BT. In: Chauvin R, Lepetit C, Silvi B, Alikhani E (eds) Applications of topological methods in molecular chemistry. Springer, Cham, pp 227–241

    Chapter  Google Scholar 

  60. Vásquez-Espinal A, Torres-Vega JJ, Alvarez-Thon L, Fuentealba P, Islas R, Tiznado W (2016) Boron avoids cycloalkane-like structures in the LinBnH2n series. New J Chem 40:2007–2013. https://doi.org/10.1039/c5nj02051d

    Article  Google Scholar 

  61. Mondal S, Cabellos JL, Pan S, Osorio E, Torres-Vega JJ, Tiznado W, Restrepo A, Merino G (2016) 10-π-Electron arenes à la carte: structure and bonding of the [E–(CnHn)–E]n−6 (E = Ca, Sr, Ba; n = 6–8) complexes. Phys Chem Chem Phys 18:11909–11918. https://doi.org/10.1039/C6CP00671J

    Article  CAS  PubMed  Google Scholar 

  62. Dong X, Jalife S, Vásquez-Espinal A, Barroso J, Orozco-Ic M, Ravell E, Cabellos JL, Liang WY, Cui ZH, Merino G (2019) Li2B24: the simplest combination for a three-ring boron tube. Nanoscale 11:2143–2147. https://doi.org/10.1039/c8nr09173k

    Article  CAS  PubMed  Google Scholar 

  63. Liang W, Barroso J, Jalife S, Orozco-Ic M, Zarate X, Dong X, Cui Z-H, Merino G (2019) B10M2 (M = Rh, Ir): finally a stable boron-based icosahedral cluster. Chem Commun 55:7490–7493. https://doi.org/10.1039/C9CC03732B

    Article  CAS  Google Scholar 

  64. Guo J-C, Feng L-Y, Wang Y-J, Jalife S, Vásquez-Espinal A, Cabellos JL, Pan S, Merino G, Zhai H-J (2017) Coaxial triple-layered versus helical Be6B11 clusters: dual structural fluxionality and multifold aromaticity. Angew Chem Int Ed 56:10174–10177. https://doi.org/10.1002/anie.201703979

    Article  CAS  Google Scholar 

  65. Dong X, Jalife S, Vásquez-Espinal A, Ravell E, Pan S, Cabellos JL, Liang WY, Cui ZH, Merino G (2018) Li2B12 and Li3B12: prediction of the smallest tubular and cage-like boron structures. Angew Chem Int Ed 57:4627–4631. https://doi.org/10.1002/anie.201800976

    Article  CAS  Google Scholar 

  66. Yanez O, Báez-Grez R, Inostroza D, Rabanal-León WA, Pino-Rios R, Garza J, Tiznado W (2019) AUTOMATON: a program that combines a probabilistic cellular automata and a genetic algorithm for global minimum search of clusters and molecules. J Chem Theory Comput 15:1463–1475. https://doi.org/10.1021/acs.jctc.8b00772

    Article  CAS  PubMed  Google Scholar 

  67. Fernández R, Louis P-Y, Nardi FR (2018) Overview: PCA models and issues. In: Probabilistic cellular automata. Springer, pp 1–30

  68. Zhai H-J, Alexandrova AN, Birch KA, Boldyrev AI, Wang L-S (2003) Hepta- and octacoordinate boron in molecular wheels of eight- and nine-atom boron clusters: observation and confirmation. Angew Chem Int Ed 42:6004–6008. https://doi.org/10.1002/anie.200351874

    Article  CAS  Google Scholar 

  69. Huang W, Sergeeva AP, Zhai H-J, Averkiev BB, Wang L-S, Boldyrev AI (2010) A concentric planar doubly π-aromatic B19 cluster. Nat Chem 2:202–206. https://doi.org/10.1038/nchem.534

    Article  CAS  PubMed  Google Scholar 

  70. Averkiev BB, Zubarev DY, Wang L-M, Huang W, Wang L-S, Boldyrev AI (2008) Carbon avoids hypercoordination in CB6, CB62−, and C2B5 planar carbon − boron clusters. J Am Chem Soc 130:9248–9250. https://doi.org/10.1021/ja801211p

    Article  CAS  PubMed  Google Scholar 

  71. Romanescu C, Galeev TR, Li W-L, Boldyrev AI, Wang L-S (2011) Aromatic metal-centered monocyclic boron rings: co©B8 and Ru©B9. Angew Chemie Int Ed 50:9334–9337. https://doi.org/10.1002/anie.201104166

    Article  CAS  Google Scholar 

  72. Báez-Grez R, Garza J, Vásquez-Espinal A, Osorio E, Rabanal-León WA, Yañez O, Tiznado W (2019) Exploring the potential energy surface of trimetallic deltahedral zintl ions: lowest-energy [Sn6Ge2Bi]3– and [(Sn6Ge2Bi)2]4– structures. Inorg Chem 58:10057–10064. https://doi.org/10.1021/acs.inorgchem.9b01206

    Article  CAS  PubMed  Google Scholar 

  73. Grande-Aztatzi R, Martínez-Alanis PR, Cabellos JL, Osorio E, Martínez A, Merino G (2014) Structural evolution of small gold clusters doped by one and two boron atoms. J Comput Chem 35:2288–2296. https://doi.org/10.1002/jcc.23748

    Article  CAS  PubMed  Google Scholar 

  74. Ramirez-Manzanares A, Peña J, Azpiroz JM, Merino G (2015) A hierarchical algorithm for molecular similarity (H-FORMS). J Comput Chem 36:1456–1466. https://doi.org/10.1002/jcc.23947

    Article  CAS  PubMed  Google Scholar 

  75. Feng L-Y, Guo J-C, Li P-F, Zhai H-J (2018) Boron-based binary Be6B102− cluster: three-layered aromatic sandwich, electronic transmutation, and dynamic structural fluxionality. Phys Chem Chem Phys 20:22719–22729. https://doi.org/10.1039/C8CP04332A

    Article  CAS  PubMed  Google Scholar 

  76. Kang D, Sun W, Shi H, Lu C, Kuang X, Chen B, Xia X, Maroulis G (2019) Probing the structure and electronic properties of beryllium doped boron clusters: a planar BeB16 cluster motif for metallo-borophene. Sci Rep 9:14367. https://doi.org/10.1038/s41598-019-50905-7

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Wang Y-J, Miao C-Q, Xie J-J, Wei Y-R, Ren G-M (2019) Be2B6 and Be2B7+: two double aromatic inverse sandwich complexes with spin-triplet ground state. New J Chem 43:15979–15982. https://doi.org/10.1039/C9NJ02819F

    Article  CAS  Google Scholar 

  78. Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158–6170

    Article  CAS  Google Scholar 

  79. Bergner A, Dolg M, Küchle W, Stoll H, Preuss H (1993) Ab initio energy-adjusted pseudopotentials for elements of groups 13–17. Mol Phys 80:1431–1441. https://doi.org/10.1080/00268979300103121

    Article  CAS  Google Scholar 

  80. Igel-Mann G, Stoll H, Preuss H (1988) Pseudopotentials for main group elements (IIIa through VIIa). Mol Phys 65:1321–1328. https://doi.org/10.1080/00268978800101811

    Article  CAS  Google Scholar 

  81. Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys Chem Chem Phys 7:3297–3305. https://doi.org/10.1039/B508541A

    Article  CAS  Google Scholar 

  82. Gaussian 09, Revision D.01, Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Petersson GA, Nakatsuji H, Li X, Caricato M, Marenich A, Bloino J, Janesko BG, Gomperts R, Mennucci B, Hratchian HP, Ortiz JV, Izmaylov AF, Sonnenberg JL, Williams-Young D, Ding F, Lipparini F, Egidi F, Goings J, Peng B, Petrone A, Henderson T, Ranasinghe D, Zakrzewski VG, Gao J, Rega N, Zheng G, Liang W, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Throssell K, Montgomery Jr. JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Millam JM, Klene M, Adamo C, Cammi R, Ochterski JW, Martin RL, Morokuma K, Farkas O, Foresman JB, Fox DJ (2013) Gaussian, Inc., Wallingford CT

  83. CYLview, 1.0b; Legault, C. Y., Université de Sherbrooke, 2009 (http://www.cylview.org)

  84. Jiménez-Halla JOC, Islas R, Heine T, Merino G (2010) B19: an aromatic wankel motor. Angew Chem Int Ed 49:5668–5671. https://doi.org/10.1002/anie.201001275

    Article  CAS  Google Scholar 

  85. Sergeeva AP, Popov IA, Piazza ZA, Li W-L, Romanescu C, Wang L-S, Boldyrev AI (2014) Understanding boron through size-selected clusters: structure, chemical bonding, and fluxionality. Acc Chem Res 47:1349–1358. https://doi.org/10.1021/ar400310g

    Article  CAS  PubMed  Google Scholar 

  86. Cervantes-Navarro F, Martínez-Guajardo G, Osorio E, Moreno D, Tiznado W, Islas R, Donald KJ, Merino G (2014) Stop rotating! One substitution halts the B19 motor. Chem Commun 50:10680–10682. https://doi.org/10.1039/C4CC03698K

    Article  CAS  Google Scholar 

  87. Martínez-Guajardo G, Sergeeva AP, Boldyrev AI, Heine T, Ugalde JM, Merino G (2011) Unravelling phenomenon of internal rotation in B13+ through chemical bonding analysis. Chem Commun 47:6242–6244. https://doi.org/10.1039/C1CC10821B

    Article  Google Scholar 

  88. Merino G, Heine T (2012) And yet it rotates: the starter for a molecular wankel motor. Angew Chem Int Ed 51:10226–10227. https://doi.org/10.1002/anie.201206188

    Article  CAS  Google Scholar 

  89. Moreno D, Pan S, Zeonjuk LL, Islas R, Osorio E, Martínez-Guajardo G, Chattaraj PK, Heine T, Merino G (2014) B182−: a quasi-planar bowl member of the Wankel motor family. Chem Commun 50:8140–8143. https://doi.org/10.1039/C4CC02225D

    Article  CAS  Google Scholar 

  90. Jalife S, Liu L, Pan S, Cabellos JL, Osorio E, Lu C, Heine T, Donald KJ, Merino G (2016) Dynamical behavior of boron clusters. Nanoscale 8:17639–17644. https://doi.org/10.1039/C6NR06383G

    Article  CAS  PubMed  Google Scholar 

  91. Pan S, Barroso J, Jalife S, Heine T, Asmis KR, Merino G (2019) Fluxional boron clusters: from theory to reality. Acc Chem Res 52:2732–2744. https://doi.org/10.1021/acs.accounts.9b00336

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

The authors are grateful for financial support from Fondecyt Grant 1181165. The authors are thankful for the facilities provided by the Laboratorio de Supercómputo y Visualización en Paralelo at Universidad Autónoma Metropolitana-Iztapalapa. The work in Mérida was supported by Conacyt (Grant CB–2015–252356) and Cinvestav (Grant SEP-Cinvestav-2018-57). J. B. thanks Conacyt for his Ph. D. fellowship. D. I. thanks Conicyt for his Ph.D fellowship (CONICYT PFCHA/BECAS DOCTORADO NACIONAL/2019−21190427).

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Correspondence to Gabriel Merino or William Tiznado.

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Yañez, O., Inostroza, D., Usuga-Acevedo, B. et al. Evaluation of restricted probabilistic cellular automata on the exploration of the potential energy surface of Be6B11. Theor Chem Acc 139, 41 (2020). https://doi.org/10.1007/s00214-020-2548-5

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