144 6 Global Optimization with the Minima Hopping Method
method [26] minima hopping can be used to find global minima structures within
the highly accurate density functional scheme. Minima hopping has up to now
mainly been applied to the structure determination of nonperiodic systems, but it
should be equally well applicable to periodic systems.
References
1. Wales, D. (2003) Energy Landscapes Cam-
bridge University Press, Cambridge.
2. Wooten, F., Winer, K., and Weaire, D.
(1985) Computer generation of struc-
tural models of amorphous Si and Ge.
Phys. Rev. Lett, 54, 1392.
3. Goedecker, S., Deutsch, T., and Billard,
L. (2002) A fourfold coordinated point
defect in silicon, Phys. Rev. Lett, 88,
235501.
4. Li, Z. and Sheraga, H.A. (1987) Monte
Carlo minimization approach to the
multiple minima problem in protein
folding. Proc. Natl. Acad. Sci. USA, 84,
6611.
5. Goedecker, S. (2004) J. Chem. Phys , 120,
9911; Goedecker, S., Hellmann, W.,
and Lenosky, T. (2005) Phys. Rev. Lett,
95, 055501.
6. Jensen, F. (1999) Computational Chem-
istry, Wiley, New York.
7. Roy, S. (2008) Goedecker, S., and
Hellmann, V. A Bell–Evans–Polanyi
principle for molecular dynamics tra-
jectories and its implications for global
optimization, Phys. Rev. E, 77, 056707.
8. Henkelman, G., and Jonsson, H. (1999)
A dimer method for finding saddle
points on high dimensional potential
surfaces using only first derivatives. J.
Chem. Phys, 111, 7010.
9. Roy, S. (2009) PhD thesis, University of
Basel.
10. The condition given in the original pub-
lication [5] is only valid for values of
β
2
, β
3
, α
1
, α
2
which are close to one in
which case the equations agree to first
order.
11. Amsler, M. (2009) Master thesis, Univer-
sity of Basel.
12. Amsler, M., Ghasemi, S. A., Goedecker,
S., Neelov, A., and Genovese, L. (2009)
Adsorption of small NaCl clusters on
surfaces of silicon nanostructures.
Nanotechnology, 20, 445301.
13. Rose, J. P., and Berry, R. S. (1993)
(KCl)
32
and the possibilities for glassy
clusters, J. Chem. Phys, 98, 3262.
14. Martin, T. P. (1980) The structure of
ionic clusters: Thermodynamic func-
tions, energy surfaces, and SIMS. J.
Chem. Phys, 72, 3506.
15. Schoenborn, S., Goedecker, S., Roy, S.,
and Oganov, A. R. (2009) Evolutionary
algorithms and minima hopping for
cluster structure prediction. J. Chem.
Phys, 130, 144108.
16. Hartke, B. J. (1999) J. Comput. Chem,
20, 1752 .
17. Yang, X., Cai, W., and Shao, X. (2007) J.
Comp. Chem, 28, 1427.
18. Goedecker, S., Hellmann, W., and
Lenosky, T. (2005) Global minimum de-
termination of the Born–Oppenheimer
surface within density functional theory.
Phys. Rev. Lett, 95, 055501.
19. Hellmann, W., Hennig, R. G.,
Goedecker, S., Umrigar, C. J., Delley,
B., and Lenosky, T. (2007) Questioning
the existence of a well defined ground
state for silicon clusters, Phys. Rev. B,
75, 085411.
20. Ghasemi,S.A.,Amsler,M.,Hennig,
R. G., Roy, S., Goedecker, S., Umrigar,
C. J., Genovese, L., Lenosky, T. J.,
Morishita, T., and Nishio, K. The energy
landscape of silicon systems and its
description by force fields, tight binding
schemes, density functional methods
and quantum Monte Carlo methods.
arXiv:0910.4050.
21. Bao, K., Goedecker, S., Koga, K.,
Lancon, F., and Neelov, A. (2009) Struc-
ture of large gold clusters obtained
by global optimization using the min-
ima hopping method. Phys. Rev. B, 79,
041405.
22. (2005) Structural properties of nanoclus-
ters: Energetic, thermodynamic, and
kinetic effects. Francesca Baletto and