Structures and energetics of helium cluster cations: Equilibrium geometries revisited through the genetic algorithm approach

Journal of Chemical Physics

Volumn 133, Issue 16, 2010, Pages

  Oleksy, Karel ^a   Karlick, František ^b   Kalus, René ^a  

^a UNIVERSITY OF OSTRAVA   (Czech Republic)

^b PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

DISSOCIATION ENERGIES; EQUILIBRIUM GEOMETRIES; GENETIC ALGORITHM APPROACH; HELIUM CLUSTERS; INTRA-CLUSTER; SEMIEMPIRICAL MODELS; SOLVATION SHELL;

HELIUM; POSITIVE IONS;

GENETIC ALGORITHMS;

EID: 78149371051     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3489346     Document Type: Article

References (60)

1. F. Grandinetti, Int. J. Mass. Spectrom. IMSPF8 1387-3806 237, 243 (2004). 10.1016/j.ijms.2004.07.012
2. F. Stienkemeier and K. K. Lehmann, J. Phys. B JPAMA4 0022-3700 39, R127 (2006). 10.1088/0953-4075/39/8/R01
3. M. Barranco, R. Guardiola, S. Hernández, R. Mayol, J. Navarro, and M. Pi, J. Low Temp. Phys. JLTPAC 0022-2291 142, 1 (2006). 10.1007/s10909-005- 9267-0
4. W. K. Lewis, C. M. Lindsay, R. J. Bemish, and R. E. Miller, J. Am. Chem. Soc. JACSAT 0002-7863 127, 7235 (2005). 10.1021/ja042489s (Pubitemid 40676748)
5. A. Boatwright, J. Jeffs, and A. J. Stace, J. Phys. Chem. A JPCAFH 1089-5639 111, 7481 (2007). 10.1021/jp0713965 (Pubitemid 47280491)
6. S. Denifl, F. Zappa, I. Mähr, F. F. da Silva, A. Aleem, A. Mauracher, M. Probst, J. Urban, P. Mach, A. Bacher, O. Echt, T. D. Märk, and P. Scheier, Angew. Chem., Int. Ed. ACIEF5 1433-7851 48, 8940 (2009). 10.1002/anie.200904381
7. P. J. Kuntz and J. Valldorf, Z. Phys. D: At., Mol. Clusters ZDACE2 0178-7683 8, 195 (1988). 10.1007/BF01384514
8. M. Amarouche, G. Durand, and J. P. Malrieu, J. Chem. Phys. JCPSA6 0021-9606 88, 1010 (1988). 10.1063/1.454267
9. F. O. Ellison, J. Am. Chem. Soc. JACSAT 0002-7863 85, 3540 (1963). 10.1021/ja00905a002
10. F. Y. Naumkin, P. J. Knowles, and J. N. Murrell, Chem. Phys. CMPHC2 0301-0104 193, 27 (1995). 10.1016/0301-0104(94)00414-6
11. F. X. Gad́a and I. Paidarová, Chem. Phys. CMPHC2 0301-0104 209, 281 (1996). 10.1016/0301-0104(96)00107-3 (Pubitemid 126123399)
12. M. Rosi and C. W. Bauschlicher, Chem. Phys. Lett. CHPLBC 0009-2614 159, 479 (1989). 10.1016/0009-2614(89)87519-0
13. V. Staemmler, Z. Phys. D: At., Mol. Clusters ZDACE2 0178-7683 16, 219 (1990). 10.1007/BF01437335
14. V. Staemmler, Z. Phys. D: At., Mol. Clusters ZDACE2 0178-7683 22, 741 (1992). 10.1007/BF01437257
15. P. J. Knowles, J. M. Murrell, and E. J. Hodge, Mol. Phys. MOPHAM 0026-8976 85, 243 (1995). 10.1080/00268979500101081
16. E. Scifoni and F. A. Gianturco, Eur. Phys. J. D EPJDF6 1434-6060 21, 323 (2002). 10.1140/epjd/e2002-00211-3 (Pubitemid 36185296)
17. E. Scifoni, G. Dellepiane, and F. A. Gianturco, Eur. Phys. J. D EPJDF6 1434-6060 30, 353 (2004). 10.1140/epjd/e2004-00108-1 (Pubitemid 39315651)
18. D. T. Chang and G. L. Gellene, J. Chem. Phys. JCPSA6 0021-9606 119, 4694 (2003). 10.1063/1.1594711
19. I. Paidarová, R. Polák, B. Paulíková, F. Karlick, K. Oleksy, D. Hrivák, F. X. Gad́a, and R. Kalus, Chem. Phys. CMPHC2 0301-0104 342, 64 (2007). 10.1016/j.chemphys.2007.09.017
20. P. J. Knowles and J. M. Murrell, Mol. Phys. MOPHAM 0026-8976 87, 827 (1996). 10.1080/00268979650027180
21. S. D. Bosanac and J. M. Murrell, Chem. Phys. Lett. CHPLBC 0009-2614 254, 69 (1996). 10.1016/0009-2614(96)00229-1
22. S. D. Bosanac and J. M. Murrell, Chem. Phys. Lett. CHPLBC 0009-2614 291, 64 (1998). 10.1016/S0009-2614(98)00560-0
23. D. J. Wales and H. A. Scheraga, Science SCIEAS 0036-8075 285, 1368 (1999). 10.1126/science.285.5432.1368 (Pubitemid 29411661)
24. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. JCPSA6 0021-9606 21, 1087 (1953). 10.1063/1.1699114
25. J. H. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan Press, Ann Arbor, 1975).
26. Applications of Evolutionary Computation in Chemistry, Springer Series in Structure and Bonding, edited by, R. L. Johnston, (Springer, Berlin, Heidelberg, New York, 2004).
27. To preserve a direct comparability of our data with the previously reported equilibrium structures and binding energies of He N+ by Knowles and Murrell (Ref.), we used the parametrization of the interaction model exactly as reported in Refs.
28. Note that there is a typographic error in Table 4 of Ref. consisting in interchanging β′ and β″. Consequently, β′ must be written instead of β″ and vice versa therein so that a correct expressions, compatible with those of Eq., are obtained.
29. H. M. Cartwright, in Applications of Evolutionary Computation in Chemistry, Springer Series in Structure and Bonding, edited by, R. L. Johnston, (Springer, Berlin, Heidelberg, New York, 2004), pp. 1-32.
30. F. Gray, Pulse code communication, U.S. Patent 2,632,058, 1953.
31. R. Hamming, Coding and Information Theory (Prentice-Hall, Englewood Cliffs, New York, 1980).
32. B. Hartke, in Applications of Evolutionary Computation in Chemistry, Springer Series in Structure and Bonding, edited by, R. L. Johnston, (Springer, Berlin, Heidelberg, New York, 2004), pp. 33-53.
33. The energy needed for a full separation of the atoms of a cluster, He N+ → He+ + (N-1) He, without the inclusion of the zero-point energy.
34. D. M. Deaven and K. M. Ho, Phys. Rev. Lett. PRLTAO 0031-9007 75, 288 (1995). 10.1103/PhysRevLett.75.288
35. B. Hartke, J. Comput. Chem. JCCHDD 0192-8651 20, 1752 (1999). 10.1002/(SICI)1096-987X(199912)20:16<1752::AID-JCC7>3.0.CO;2-0
36. Computer times required for obtaining the global minimum of LJ38 (Refs.) vary between 120 and 850 s on a computer with two 2.5 GHz Intel Xeon Quad CPUs. Our algorithm is thus less efficient for this cluster and cluster size than a more genotype-based algorithm of Ref., where ≈1,000 s of computer time have been reported for a single 400-MHz Intel Pentium II processor, but still capable of providing realistic data at acceptable computer effort.
37. F. Marinetti, E. Bodo, F. A. Gianturco, and E. Yurtsever, ChemPhysChem CPCHFT 1439-4235 9, 2618 (2008). 10.1002/cphc.200800457
38. F. A. Gianturco and M. P. de Lara-Castels, Int. J. Quantum Chem. IJQCB2 0020-7608 60, 593 (1996). 10.1002/(SICI)1097-461X(1996)60:1<593::AID- QUA57>3.0.CO;2-8
39. The monomer evaporation energies as well as the differences of the binding energies from their local means calculated at the harmonic approximation level are not shown in Fig. as they seem completely incorrect, at least for N6. For example, the monomer evaporation energies are negative for many cluster sizes above this size limit.
40. P. W. Stephens and J. G. King, Phys. Rev. Lett. PRLTAO 0031-9007 51, 1538 (1983). 10.1103/PhysRevLett.51.1538
41. N. Kobayashi, T. Kojima, and Y. Kaneko, J. Phys. Soc. Jpn. JUPSAU 0031-9015 57, 1528 (1988). 10.1143/JPSJ.57.1528
42. S. Denifl, M. Stano, A. Stamatovic, P. Scheier, and T. D. Märk, J. Chem. Phys. JCPSA6 0021-9606 124, 054320 (2006). 10.1063/1.2163346 (Pubitemid 43202698)
43. B. E. Callicoatt, K. Förde, L. F. Jung, T. Ruchti, and K. C. Janda, J. Chem. Phys. JCPSA6 0021-9606 109, 10195 (1998). 10.1063/1.477713 (Pubitemid 128678454)
44. H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies, and C. Winkler, J. Chem. Phys. JCPSA6 0021-9606 92, 6875 (1990). 10.1063/1.458275
45. I. Paidarová and R. Polák (unpublished).
46. R. A. Aziz, A. R. Janzen, and M. R. Moldover, Phys. Rev. Lett. PRLTAO 0031-9007 74, 1586 (1995). 10.1103/PhysRevLett.74.1586
47. A. R. Janzen and R. A. Aziz, J. Chem. Phys. JCPSA6 0021-9606 107, 914 (1997). 10.1063/1.474444
48. R. Hellmann, E. Bich, and E. Vogel, Mol. Phys. MOPHAM 0026-8976 105, 3013 (2007). 10.1080/00268970701730096
49. J. J. Hurly and J. B. Mehl, J. Res. Natl. Inst. Stand. Technol. JRITEF 1044-677X 112, 75 (2007).
50. Our nonsystematic global structure optimizations performed for model (c) show that the geometric structure of the most stable isomers are also independent on the diatomic inputs used, at least for the smaller cluster sizes. For larger cluster sizes one can, however, expect that for alternate neutral diatomic potentials changes may occur in the structure and occupation of neutral shells.
51. Note that, in contrast with our results obtained for helium and the data reported for the heavier rare gases, tetramer ionic cores were found in the most stable isomers of neon cations for cluster sizes N=4-14 (Refs.). However, these four-atom cores consist of a dimer subunit carrying usually more than 90% of the positive charge and are, thus, effectively dimerlike.
52. T. Ikegami, T. Kondow, and S. Iwata, J. Chem. Phys. JCPSA6 0021-9606 98, 3038 (1993). 10.1063/1.464130
53. R. Kalus, I. Paidarová, D. Hrivák, P. Paška, and F. X. Gad́a, Chem. Phys. CMPHC2 0301-0104 294, 141 (2003). 10.1016/j.chemphys.2003.07.004
54. P. Paška, D. Hrivák, and R. Kalus, Chem. Phys. CMPHC2 0301-0104 286, 237 (2003). 10.1016/S0301-0104(02)00934-5
55. E. Buonomo, F. A. Gianturco, F. Schneider, P. D. Lara-Castells, G. Delgado-Barrio, S. Miret-Artes, and P. Villarreal, Chem. Phys. Lett. CHPLBC 0009-2614 259, 641 (1996). 10.1016/0009-2614(96)00750-6
56. H. Haberland, B. V. Issendorff, R. Frötenicht, and J. P. Toennies, J. Chem. Phys. JCPSA6 0021-9606 102, 8773 (1995). 10.1063/1.468980
57. D. J. Wales and J. P. K. Doye, J. Phys. Chem. JPCHAX 0022-3654 101, 5111 (1997).
58. F. Y. Naumkin and D. J. Wales, Mol. Phys. MOPHAM 0026-8976 93, 633 (1998). 10.1080/00268979809482250
59. D. Bonhommeau, A. Viel, and N. Halberstadt, J. Chem. Phys. JCPSA6 0021-9606 123, 054316 (2005). 10.1063/1.1953530 (Pubitemid 41203894)
60. F. Karlick, B. Lepetit, R. Kalus, I. Paidarová, and F. X. Gad́a, J. Chem. Phys. JCPSA6 0021-9606 128, 124303 (2008). 10.1063/1.2841019 (Pubitemid 351474071)