Energy Landscapes and Structure Prediction Using Basin-Hopping

Modern Methods of Crystal Structure Prediction

Volumn , Issue , 2010, Pages 29-54

  Wales, David J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Basin hopping global optimisation; Clusters; Disconnectivity graphs; Energy landscapes; Glass formers

Indexed keywords

EID: 84886063402     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527632831.ch2     Document Type: Chapter

References (196)

1. Wales, D. J. (2003) Energy Landscapes. Cambridge University Press, Cambridge.
2. Born, M. and Oppenheimer, J. R. (1927) Zur quantentheorie der molekeln. Ann. Physik, 84, 457-484.
3. Robb, M. A., Bernardi, F., and Olivucci, M. (1995) Conical intersections as a mechanistic feature of organic photochemistry. Pure Appl. Chem, 67, 783-789.
4. Yarkony, D. R. (1998) Conical intersections: diabolical and often misunderstood. Acc. Chem. Res., 31, 511.
5. Allen, M. P. and Tildesley, D. J. (1987) Computer Simulation of Liquids. Clarendon Press, Oxford.
6. Frenkel, D. and Smit, B. (2002) Understanding Molecular Simulation, second edition. Academic Press, London.
7. Murrell, J. N. and Laidler, K. J. (1968) Symmetries of activated complexes. Trans. Faraday. Soc., 64, 371.
8. Wales, D. J. and Doye, J. P. K. (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.
9. Doye, J. P. K. and Wales, D. J. (1998) Thermodynamics of global optimization. Phys. Rev. Lett., 80, 1357-1360.
10. Wales, D. J. and Scheraga, H. A. (1999) Global optimization of clusters, crystals and biomolecules. Science, 285, 1368-1372.
11. McGinty, D. J. (1971) Vapor phase homogenous nucleation and the thermodynamic properties of small clusters of argon atoms. J. Chem. Phys., 55, 580.
12. Burton, J. J. (1972) Vibrational frequencies and entropies of small clusters of atoms. J. Chem. Phys., 56, 3133.
13. Hoare, M. R. (1979) Structure and dynamics of simple microclusters. Adv. Chem. Phys., 40, 49.
14. Stillinger, F. H. and Weber, T. A. (1984) Packing structures and transitions in liquids and solids. Science, 225, 983.
15. Franke, G., Hilf, E. R., and Borrmann, P. (1993) The structure of small clusters: multiple normal-modes model. J. Chem. Phys., 98, 3496.
16. Wales, D. J. (1993) Coexistence in small inert-gas clusters. Mol. Phys., 78, 151.
17. Wales, D. J., Doye, J. P. K, Miller, M. A., Mortenson, P. N., and Walsh, T. R. (2000) Energy landscapes: from clusters to biomolecules. Adv. Chem. Phys., 115, 1-111.
18. Strodel, B. and Wales, D. J. (2008) Free energy surfaces from an extended harmonic superposition approach and kinetics for alanine dipeptide. Chem. Phys. Lett., 466, 105-115.
19. Krivov, S. V. and Karplus, M. (2002) Free energy disconnectivity graphs: application to peptide models. J. Chem. Phys., 117, 10894-10903.
20. Wales, D. J. (2002) Discrete path sampling. Mol. Phys., 100, 3285-3305.
21. Chekmarev, S. F., Krivov, S. V., and Karplus, M. (2005) Folding time distributions as an approach to protein folding kinetics. J. Phys. Chem. B, 109, 5312-5330.
22. Noé, F., Krachtus, D., Smith, J. C., and Fischer, S. (2006) Transition networks for the comprehensive characterisation of complex conformational change in proteins. J. Chem. Theory Comput., 2, 840-857.
23. Noe, F., Oswald, M., Reinelt, G., Fischer, S., and Smith, J. C. (2006) Computing best transition pathways in high-dimensional systems: application to the αl&rlhar2; ß &rlhar2; αr transitions in octaalanine. Multiscale Model Sim., 5, 393-419.
24. Wales, D. J. (2006) Energy landscapes: calculating pathways and rates. Int. Rev. Phys. Chem., 25, 237-282.
25. Boulougouis, G. C. and Theodorou, D. N. (2007) Dynamical integration of a Markovian web: a first passage time approach. J. Chem. Phys., 127, 084903.
26. Noe, F. and Fischer, S. (2008) Transition networks for modeling the kinetics of conformational change in macromolecules. Curr. Op. Struct. Biol., 18, 154-162.
27. Trygubenko, S. A. and Wales, D. J. (2004) A doubly-nudged elastic band method for finding transition states. J. Chem. Phys., 120, 2082.
28. Henkelman, G. and Jónsson, H. (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys., 111, 7010-7022.
29. Henkelman, G., Uberuaga, B. P., and Jónsson, H. (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys., 113, 9901-9904.
30. Henkelman, G. and Jónsson, H. (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys., 113, 9978-9985.
31. Munro, L. J. and Wales, D. J. (1999) Defect migration in crystalline silicon. Phys. Rev. B, 59, 3969-3980.
32. Kumeda, Y., Munro, L. J., and Wales, D. J. (2001) Transition states and rearrangement mechanisms from hybrid eigenvector-following and density functional theory. Application to C10 H10 and defect migration in crystalline silicon. Chem. Phys. Lett., 341, 185-194.
33. Pelzer, H. and Wigner, E. (1932) Z. Phys. Chem., B15, 445.
34. Forst, W. (1973) Theory of Unimolecular Reactions. Academic Press, New York.
35. Miller, W. H. (1976) Importance of nonseparability in quantum mechanical transition-state theory. Acc. Chem. Res., 9, 306-312.
36. Wales, D. J. (2004) Some further applications of discrete path sampling to cluster isomerization. Mol. Phys., 102, 891-908.
37. Carr, J. M. and Wales, D. J. (2005) Global optimization and folding pathways of selected alpha-helical proteins. J. Chem. Phys., 123, 234901.
38. Strodel, B., Whittleston, C. S., and Wales, D. J. (2007) Thermodynamics and kinetics of aggregation for the GN-NQQNY peptide. J. Amer. Chem. Soc., 129, 16005-16014.
39. Carr, J. M. and Wales, D. J. (2008) Folding pathways and rates for the three-stranded beta-sheet peptide beta3s using discrete path sampling. J. Phys. Chem. B, 112, 8760-8769.
40. Li, Z. and Scheraga, H. A. (1987) Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proc. Natl. Acad. Sci. USA, 84, 6611-6615.
41. Wales, D. J. (2005) The energy landscape as a unifying theme in molecular science. Phil. Trans. Roy. Soc. A, 363, 357-377.
42. Wales, D. J. and Bogdan, T. V. (2006) Potential energy and free energy landscapes. J. Phys. Chem. B, 110, 20765-20776.
43. Sibani, P., Schön, J. C., Salamon, P., and Andersson, J. (1993) Emergent hierarchical structures in complex-system dynamics. Europhys. Lett., 22, 479.
44. Schön, J. C. (1996) Studying the energy hypersurface of multi-minima systems - the threshold and the lid algorithm. Ber. Bunsenges. Phys. Chem., 100, 1388.
45. Schön, J. C., Putz, H., and Jansen, M. (1996) Studying the energy hypersurface of continuous systems - the threshold algorithm. J. Phys. Cond. Matt., 8, 143.
46. Schön, J. C. (2002) Energy landscape of two-dimensional lattice polymers. J. Phys. Chem. A, 106, 10886-10892.
47. Czerminski, R. and Elber, R. (1990) Reaction path study of conformational transitions in flexible systems: applications to peptides. J. Chem. Phys., 92, 5580-5601.
48. Becker, O. M. and Karplus, M. (1997) The topology of multidimensional potential energy surfaces: theory and application to peptide structure and kinetics. J. Chem. Phys., 106, 1495-1517.
49. Wales, D. J., Miller, M. A., and Walsh, T. R (1998) Archetypal energy landscapes. Nature, 394, 758.
50. Miller, M. A. and Wales, D. J. (1999) Energy landscape of a model protein. J. Chem. Phys., 111, 6610-6616.
51. Altis, A., Otten, M., Nguyen, P. H., Hegger, R., and Stock, G. (2008) Construction of the free energy landscape of biomolecules via dihedral angle principal component analysis. J. Chem. Phys., 128, 245102.
52. Krivov, S. V. and Karplus, M. (2004) Hidden complexity of free energy surfaces for peptide (protein) folding. Proc. Nat. Acad. Sci. USA, 101, 14766-14770.
53. Krivov, S. V. and Karplus, M. (2006) One-dimensional free-energy profiles of complex systems: progress variables that preserve the barriers. J. Phys. Chem. B, 110, 12689-12698.
54. Muff, S. and Caflisch, A. (2008) Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single-point mutation of a ß-sheet miniprotein. Proteins: Struct, Func. Bioinf., 70, 1185-1195.
55. Komatsuzaki, T., Hoshino, K., Matsunaga, Y., Rylance, G. J., Johnston, R. L., and Wales, D. J. (2005) How many dimensions are required to approximate the potential energy landscape of a model protein? J. Chem. Phys., 122, 084714.
56. Evans, D. A. and Wales, D. J. (2003) Free energy landscapes of model peptides and proteins. J. Chem. Phys., 118, 3891-3897.
57. Shaffer, J. S. and Chakraborty, A. K. (1993) Dynamics of poly(methyl methacrylate) chains adsorbed on aluminum surfaces. Macromolecules, 26, 1120-1136.
58. Doye, J. P. K. and Wales, D. J. (1995) Calculation of thermodynamic properties of small Lennard-Jones clusters incorporating anharmonicity. J. Chem. Phys., 102, 9659-9672.
59. Calvo, F., Doye, J. P. K., and Wales, D. J. (2001) Characterization of an-harmonicities on complex potential energy surfaces: perturbation theory and simulation. J. Chem. Phys., 115, 9627-9636.
60. Calvo, F., Doye, J. P. K., and Wales, D. J. (2001) Quantum partition functions from classical distributions. Application to rare gas clusters. J. Chem. Phys., 114, 7312-7329.
61. Jones, J. E. and Ingham, A. E. (1925) On the calculation of certain crystal potential constants, and on the cubic crystal of least potential energy. Proc. R. Soc. A, 107, 636-653.
62. Doye, J. P. K., Miller, M. A., and Wales, D. J. (1999) Evolution of the potential energy surface with size for Lennard-Jones clusters. J. Chem. Phys., 111, 8417-8428.
63. Stillinger, F. H. and Weber, T. A. (1985) Computer simulation of local order in condensed phases of silicon. Phys. Rev. B, 31, 5262-5271.
64. Middleton, T. F. and Wales, D. J. (2001) Energy landscapes of model glass formers. Phys. Rev. B, 64, 024205.
65. Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., and Kollman, P. A. (1995) A second generation force field for the simulation of proteins, nucleic acids and organic molecules. J. Am. Chem. Soc., 117, 5179-5197.
66. Mortenson, P. N., Evans, D. A., and Wales, D. J. (2002) Energy landscapes of model polyalanines. J. Chem. Phys., 117, 1363-1376.
67. Kumeda, Y. and Wales, D. J. (2003) Ab initio study of rearrangements between C60 fullerenes. Chem. Phys. Lett., 374, 125-131.
68. Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W., and Klein, M. L. (1983) Comparison of simple potential functions for simulating liquid water. J. Chem. Phys., 79, 926-935.
69. Chartrand, G. (1985) Introductory Graph Theory. Dover, New York.
70. Bryngelson, J. D. and Wolynes, P. G. (1987) Spin glasses and the statistical mechanics of protein folding. Proc. Natl. Acad. Sci. USA, 84, 7524-6915.
71. Goldstein, R. A., Luthey-Schulten, Z. A., and Wolynes, P. G. (1992) Optimal protein-folding codes from spin-glass theory. Proc. Natl. Acad. Sci. USA, 89(11): 4918-4922.
72. Mackay, A. L. (1962) A dense non-crystallographic packing of equal spheres. Acta Cryst., 15, 916-918.
73. Walsh, T. R. and Wales, D. J. (1998) Relaxation dynamics of C60. J. Chem. Phys., 109, 6691-6700.
74. Leopold, P. E., Montal, M., and Onuchic, J. N. (1992) Protein folding funnels: a kinetic approach to the sequence-structure relationship. Proc. Natl. Acad. Sci. USA, 89, 8721-8725.
75. Bryngelson, J. D., Onuchic, J. N., Socci, N. D., and Wolynes, P. G. (1995) Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins: Struct., Func. Gen., 21, 167-195.
76. Miller, M. A., Doye, J. P. K., and Wales, D. J. (1999) Structural relaxation in Morse clusters: energy landscapes. J. Chem. Phys., 110, 328-334.
77. Doye, J. P. K., Miller, M. A., and Wales, D. J. (1999) The double-funnel energy landscape of the 38-atom Lennard-Jones cluster. J. Chem. Phys., 110, 6896-6906.
78. Neirotti, J. P., Calvo, F., Freeman, D. L., and Doll, J. D. (2000) Phase changes in 38-atom Lennard-Jones clusters. I. a parallel tempering study in the canonical ensemble. J. Chem. Phys., 112, 10340.
79. Calvo, F., Neirotti, J. P., Freeman, D. L., and Doll, J. D. (2000) Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and micro-canonical ensembles. J. Chem. Phys., 112, 10350.
80. Steinhardt, P. J., Nelson, D. R., and Ronchetti, M. (1983) Bond-orientational order in liquids and glasses. Phys. Rev. B, 28, 784-805.
81. van Duijneveldt, J. S. and Frenkel, D. (1992) Computer simulation study of free energy barriers in crystal nucle-ation. J. Chem. Phys., 96, 4655-4668.
82. Doye, J. P. K. and Wales, D. J. (1999) The dynamics of structural transitions in sodium chloride clusters. J. Chem. Phys., 111, 11070-11079.
83. Doye, J. P. K. (2000) Effect of compression on the global optimization of atomic clusters. Phys. Rev. E, 62, 8753-8761.
84. White, R. P. and Mayne, H. R. (1998) An investigation of two approaches to basin hopping minimization for atomic and molecular clusters. Chem. Phys. Lett., 289, 463-468.
85. Xue, G. L. (1991) Molecular conformation on the CM-5 by parallel two-level simulated annealing. J. Global Opt., 4, 187-208.
86. Barron, C., Gomez, S., and Romero, D. (1996) Archimedean polyhedron structure yields a lower energy atomic cluster. Appl. Math. Lett., 9, 75-78.
87. Deaven, D. M., Tit, N., Morris, J. R., and Ho, K. M. (1996) Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chem. Phys. Lett., 256, 195-200.
88. Barron, C., Gomez, S., and Romero, D. (1997) Lower energy icosahedral atomic clusters with incomplete core. Appl. Math. Lett., 10, 25-28.
89. Holland, J. (1975) Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.
90. Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA.
91. Hartke, B. (2001) Global geometry optimization of atomic and molecular clusters by genetic algorithms. In Spector, E. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. Garzon, and E. Burke, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO-2001, page 1284. Morgan Kaufmann, San Francisco.
92. Hartke, B. L. (2002) Efficient global geometry optimization of atomic and molecular clusters. In Pinter, editor, Nonconvex Optimization and its Applications. Kluwer, Dordrecht.
93. Johnston, R. L. and Roberts, C. (2003) Genetic algorithms for the geometry optimization of clusters and nanoparticles. In H. Cartwright, and L. Sztandera, editors, Soft Computing Approaches in Chemistry, pp. 25-61. Physica-Verlag, Heidelberg.
94. Deaven, D. M. and Ho, K. M. (1995) Molecular geometry optimization with a genetic algorithm. Phys. Rev. Lett., 75, 288-291.
95. Turner, G. W., Tedesco, E., Harris, K. D. M., Johnston, R. L., and Kariuki, B. M. (2000) Implementation of Lamarckian concepts in a genetic algorithm for structure solution from powder diffraction data. Chem. Phys. Lett., 321, 183-190.
96. Liu, D. and Nocedal, J. (1989) On the limited memory BFGS method for large scale optimization. Math. Prog., 45, 503-528.
97. Wales, D. J. GMIN: A program for basin-hopping global optimisation. http://www-wales.ch.cam.ac.uk/sofware.html.
98. Wales, D. J. OPTIM: A program for geometry optimisation and pathway calculations. http://www-wales.ch.cam.ac.uk/software.html.
99. Wales, D. J. (1992) Basins of attraction for stationary-points on a potential-energy surface. J. Chem. Soc. Faraday Trans., 88, 653-657.
100. Wales, D. J. (1993) Locating stationary-points for clusters in Cartesian coordinates. J. Chem. Soc. Faraday Trans., 89, 1305-1313.
101. Hoffmann, K. H., Franz, A., and Salamon, P. (2002) Structure of best possible strategies for finding ground states. Phys. Rev. E, 66, 046706.
102. Hansmann, U. H. E. and Wille, L. T. (2002) Global optimization by energy landscape paving. Phys. Rev. Lett., 88, 068105.
103. Goedecker, S. (2004) Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J. Chem. Phys., 120, 9911-9917.
104. Xiang, Y., Jiang, H., Cai, W., and Shao, X. (2004) An efficient method based on lattice construction and the genetic algorithm for optimization of large Lennard-Jones clusters. J. Phys. Chem. A, 108, 3586-3592.
105. Shao, X., Xiang, Y., and Cai, W. (2005) Structural transition from icosahedra to decahedra of large Lennard-Jones clusters. J. Phys. Chem. A, 109, 5193-5197.
106. Zhan, L., Chen, J. Z. Y., Liu, W.-K., and Lai, S. K. (2005) Asynchronous multicanonical basin-hopping method and its application to cobalt nanoclusters. J. Chem. Phys., 122, 244707.
107. Verma, A., Schug, A., Lee, K. H., and Wenzel, W. (2006) Basin-hopping simulations for all-atom protein folding. J. Chem. Phys., 124, 044515.
108. Zhan, L., Chen, J. Z. Y., and Liu, W. K. (2006) Monte Carlo basin paving: an improved global optimization method. Phys. Rev. E, 73, 015701R.
109. Cheng, L. and Yang, J. (2007) Novel lattice-searching method for modeling the optimal strain-free close-packed isomers of clusters. J. Phys. Chem. A, 111, 2336-2342.
110. Cheng, L. and Yang, J. (2007) Global minimum structures of Morse clusters as a function of the range of the potential: 81 ≤ n ≤160. J. Phys. Chem. A, 111, 5287-5293.
111. Kim, H. G., Choi, S. K., and Lee, H. M. (2008) New algorithm in the basin hopping Monte Carlo to find the global minimum structure of unary and binary metallic nanoclusters. J. Chem. Phys., 128, 144702.
112. Cheng, L., Feng, Y., Yang, J., and Yang, J. (2009) Funnel hopping: searching the cluster potential energy surface over the funnels. J. Chem. Phys., 130, 214112.
113. Schonborn, S. E., Goedecker, S., Roy, S., and Oganov, A. R. (2009) The performance of minima hopping and evolutionary algorithms for cluster structure prediction. J. Chem. Phys., 130, 144108.
114. Gehrke, R. and Reuter, K. (2009) Assessing the efficiency of first-principles basin-hopping sampling. Phys. Rev., 79, 085412.
115. Rossi, G. and Ferrando, R. (2009) Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms. J. Phys. Cond. Matt., 21, 084208.
116. Froltsov, V. A. and Reuter, K. (2009) Robustness of 'cut and splice' genetic algorithms in the structural optimization of atomic clusters. Chem. Phys. Lett., 473, 363-366.
117. Cvijovic, D. and Klinowski, J. (1995) Taboo search: an approach to the multiple minima problem. Science, 267, 664-666.
118. Ji, M. and Klinowski, J. (2006) Taboo evolutionary programming: a new method of global optimisation. Proc. Roy. Soc. A, 462, 3613-3627.
119. Zabrodsky, H., Peleg, S., and Avnir, D. (1992) Continuous symmetry measures. J. Am. Chem. Soc., 114, 7843-7851.
120. Katzenelson, O., Hel-Or, H. Z., and Avnir, D. (1996) chirality of large random supramolecular structures. Chem. Eur. J., 2, 174-181.
121. Wales, D. J. (1998) Symmetry, near-symmetry and energetics. Chem. Phys. Lett., 285, 330-336.
122. Wales, D. J. (1998) Erratum: Symmetry, near-symmetry and energetics (vol. 285, p 330). Chem. Phys. Lett., 294, 262.
123. Wales, D. J. and Hodges, M. P. (1998) Global minima of water clusters (H2O)N, N ≤ 21, described by an empirical potential. Chem. Phys. Lett., 286, 65-72.
124. Hartke, B. (2003) Size-dependent transition from all-surface to interior-molecule structures in pure neutral water clusters. Phys. Chem. Chem. Phys., 5, 275-284.
125. Hartke, B. (2008) Morphing Lennard-Jones clusters to TIP4P water clusters: why do water clusters look like they do? Chem. Phys., 346, 286-294.
126. Day, G. M., Chisholm, J., Shan, N., Motherwell, S., and Jones, W. (2004) An assessment of lattice energy minimization for the prediction of crystal structures. Cryst. Growth Des., 4, 1327-1340.
127. Hodges, M. P. and Wales, D. J. (2000) Global minima of protonated water clusters. Chem. Phys. Lett., 324, 279-288.
128. James, T. and Wales, D. J. (2005) Pro-tonated water clusters described by an empirical valence bond potential. J. Chem. Phys., 122, 134306.
129. James, T., Wales, D. J., and Hernández-Rojas, J. (2005) Global minima for water clusters (H2O)N, N < 21, described by a five-site empirical potential. Chem. Phys. Lett., 415, 302-307.
130. Kabrede, H. and Hentschke, R. (2003) Global minima of water clusters (H2O)N, N ≤ 25, described by three empirical potentials. J. Phys. Chem. B, 107, 3914-3920.
131. Kazachenko, S. and Thakkar, A. J. (2009) Improved minima-hopping. TIP4P water clusters, (H2O)N with N ≤ 37. Chem. Phys. Lett., 476, 120-124.
132. Doye, J. P. K. and Wales, D. J. (1999) Structural transitions and global minima of sodium chloride clusters. Phys. Rev. B, 59, 2292-2300.
133. Leary, R. H. and Doye, J. P. K. (1999) Tetrahedral global minimum for the 98-atom Lennard-Jones cluster. Phys. Rev. E, 60, R6320-R6322.
134. Middleton, T. F., Hernández-Rojas, J., Mortenson, P. N., and Wales, D. J. (2001) Crystals of binary Lennard-Jones solids. Phys. Rev. B, 64, 184201.
135. Rapacioli, M., Calvo, F., Spiegelman, F., Joblin, C., and Wales, D. J. (2005) Stacked clusters of polycyclic aromatic hydrocarbon molecules. J. Phys. Chem. A, 109, 2487-2497.
136. Miller, M. A. and Wales, D. J. (2005) Novel structural motifs in clusters of dipolar spheres: knots, links, and coils. J. Phys. Chem. B, 109, 23109-23112.
137. Wales, D. J. and Ulker, S. (2006) Structure and dynamics of spherical crystals characterized for the Thomson problem. Phys. Rev. B, 74, 212101.
138. Wales, D. J., McKay, H., and Altschuler, E. L. (2009) Defect motifs for spherical topologies. Phys. Rev. B, 79, 224115.
139. Wales, D. J., Doye, J. P. K., Dullweber, A., Hodges, M. P., Naumkin, F. Y., Calvo, F., Hernández-Rojas, J., and Middleton, T. F. The Cambridge cluster database, http://www-wales.ch.cam.ac.uk/ccd.html
140. Doye, J. P. K. and Wales, D. J. (1997) Structural consequences of the range of the interatomic potential - a menagerie of clusters. J. Chem. Soc., Faraday Trans., 93, 4233-4243.
141. Doye, J. P. K. and Wales, D. J. (1998) Global minima for transition metal clusters described by Sutton-Chen potentials. New J. Chem., 22, 733-744.
142. Hernández-Rojas, J., Breton, J., Llorente, J. M. G., and Wales, D. J. (2006) Global potential energy minima of C60(H2O)N clusters. J. Phys. Chem. B, 110, 13357-13362.
143. Naumkin, F. Y. and Wales, D. J. (2002) Diatomics-in-molecules potentials incorporating ab initio data: application to ionic, Rydberg-excited, and molecule-doped rare gas clusters. Comput. Phys. Comm., 145, 141-155.
144. Thomson, J.J. (1904) On the structure of the atom. Philos. Mag., 7, 237-265.
145. Bausch, A. R., Cacciuto, A. Bowick, M. J., Dinsmore, A. D., Hsu, M. F., Nelson, D. R., Nikolaides, M. G., Travesset, A., and Weitz, D. A. (2003) Grain boundary scars and spherical crystallography. Science, 299, 1716-1718.
146. Pérez-Garrido, A. and Moore, M. A. (1999) Symmetric patterns of dislocations in Thomson's problem. Phys. Rev. B, 60, 15628-15631.
147. Bowick, M. J., Nelson, D. R., and Travesset, A. (2000) Interacting topological defects on frozen topologies. Phys. Rev. B, 62, 8738-8751.
148. Kroto, H. W., Heath, J. R., O'Brien, S. C., Curl, R. F., and Smalley, R. E. (1985) C60: buckminsterfullerene. Nature, 318, 162-163.
149. Pérez-Garrido, A. (2000) Giant multilayer fullerene structures with symmetrically arranged defects. Phys. Rev. B, 62, 6979-6981.
150. Caspar, D. L. D. and Klug, A. (1962) Physical principles in the construction of regular viruses. Cold Spring Harbour, Symp. Quant. Biol., 27, 1-24.
151. Marzec, C. J. and Day, L. A. (1993) Pattern formation in icosahedral virus capsids: the papova viruses and nudau-relia capensis beta virus. Biophys. J., 65, 2559-2577.
152. Cho, Y.-S., Yi, G.-R., Lim, J.-M., Kim, S.-H., Manoharan, V. N., Pine, D. J., and Yang, S.-M. (2005) Self-organization of bidisperse colloids in water droplets. J. Am. Chem. Soc., 127, 15968-15975.
153. Dodgson, M. J. W. (1996) Investigation on the ground states of a model thin film superconductor on a sphere. J. Phys. A, 29, 2499-2508.
154. Dodgson, M. J. W. and Moore, M. A. (1997) Vortices in a thin-film superconductor with a spherical geometry. Phys. Rev. B, 55, 3816-3830.
155. Simons, K. and Vaz, W. L. C. (2004) Model systems, lipid rafts, and cell membranes. Annu. Rev. Biophys. Biomol. Struct., 33, 269-295.
156. Masuda, Y., Itoh, T., and Koumoto, K. (2005) Self-assembly and micropattern-ing of spherical-particle assemblies. Adv. Mater., 17, 841-845.
157. Lipowsky, P., Bowick, M. J., Meinke, J. H., Nelson, D. R., and Bausch, A. R. (2005) Direct visualization of dislocation dynamics in grain-boundary scars. Nat. Mater., 4, 407-411.
158. Einert, T., Lipowsky, P., Schilling, J., Bowick, M. J., and Bausch, A. R. (2005) Grain boundary scars on spherical crystals. Langmuir, 21, 12076-12079.
159. Pum, D., Messner, P., and Sleytr, U. B. (1991) Role of the s layer in morphogenesis and cell division of the archaebacterium methanocorpusculum sinense. J. Bacteriol., 173, 6865-6873.
160. Sleytr, U. B., Sara, M., Pum, D., and Schuster, B. (2001) Characterization and use of crystalline bacterial cell. Surface layers. Prog. Surf. Sci., 68, 231-278.
161. Albrecht, U. and Leiderer, P. (1992) On the correlation between properties of multielectron dimples and bubbles. J. Low Temp. Phys., 86, 131-251.
162. Leiderer, P. (1995) Ions at helium interfaces. Z. Phys. B, 98, 303-308.
163. Day, G. M., Motherwell, S., and Jones, W. (2005) Beyond the isotropic atom model in crystal structure prediction of rigid molecules: atomic multipoles versus point charges. Cryst. Growth Des., 5, 1023-1033.
164. Oganov, A. R. and Glass, C. W. (2006) Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J. Chem. Phys., 124, 244704.
165. Abraham, N. L. and Probert, M. I. J. (2006) A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction. Phys. Rev. B, 73, 224104.
166. Day, G. M., Motherwell, S., and Jones, W. (2007) A strategy for predicting the crystal structures of flexible molecules: the polymorphism of phe-nobarbital. Phys. Chem. Chem. Phys., 9, 1693-1704.
167. Woodley, S. M. and Catlow, R. (2007) Crystal structure prediction from first principles. Nature Mater., 7, 937-946.
168. Price, S. (2008) From crystal structure prediction to polymorph prediction: interpreting the crystal energy landscape. Phys. Chem. Chem. Phys., 10, 1996-2009.
169. Price, S. L. (2009) Computed crystal energy landscapes for understanding and predicting organic crystal structures and polymorphism. Accounts Chem. Res., 42, 117-126.
170. Doye, J. P. K., Wales, D. J., and Miller, M. A. (1998) Thermodynamics and the global optimization of Lennard-Jones clusters. J. Chem. Phys., 109, 8143-8153.
171. Calvo, F., Bogdan, T. V., de Souza, V. K., and Wales, D. J. (2007) Equilibrium density of states and thermodynamic properties of a model glass former. J. Chem. Phys., 127, 044508.
172. de Souza, V. K. and Wales, D. J. (2008) Energy landscapes for diffusion: analysis of cage-breaking processes. J. Chem. Phys., 129, 164507.
173. Kob, W. and Andersen, H. C. (1994) Scaling behavior in the beta-relaxation regime of a supercooled Lennard-Jones mixture. Phys. Rev. Lett., 73, 1376-1379.
174. Kob, W. and Andersen, H. C. (1995) Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture: the Van Hove correlation function. Phys. Rev. E, 51, 4626-4641.
175. Kob, W. and Andersen, H. C. (1995) Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture. II. intermediate scattering function and dynamic susceptibility. Phys. Rev. E, 52, 4134-4153.
176. Sastry, S., Debenedetti, P. G., and Stillinger, F. H. (1998) Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid. Nature, 393, 554-557.
177. Buöchner, S. and Heuer, A. (1999) Potential energy landscape of a model glass former: thermodynamics, anhar-monicities, and finite size effects. Phys. Rev. E, 60, 6507-6518.
178. Sciortino, F., Kob, W., and Tartaglia, P. (1999) Inherent structure entropy of supercooled liquids. Phys. Rev. Lett., 83, 3214-3217.
179. Middleton, T. F. and Wales, D. J. (2003) Energy landscapes of model glass formers. II. Results for constant pressure. J. Chem. Phys., 118, 4583-4593.
180. Sciortino, F. and Tartaglia, P. (2001) Extension of the fluctuation-dissipation theorem to the physical aging of a model glass-forming liquid. Phys. Rev. Lett., 86, 107-110.
181. Sastry, S. (2001) The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids. Nature, 409, 164-167.
182. Stoddard, S. D. and Ford, J. (1973) Numerical experiments on the stochastic behavior of a Lennard-Jones system. Phys. Rev. A, 8, 1504-1512.
183. Weber, T. A. and Stillinger, F. H. (1985) Local order and structural transitions in amorphous metal-metalloid alloys. Phys. Rev. B, 31, 1954-1963.
184. Fernandez, J. R. and Harrowell, P. (2003) Crystal phases of a glass-forming Lennard-Jones mixture. Phys. Rev. E, 67, 011403.
185. Swendsen, R. H. and Wang, J.-S. (1986) Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett., 57, 2607-2609.
186. Geyer, G. (1991) Markov chain Monte Carlo maximum likelihood. In Keramidas, editor, Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 156-163. Inferface Foundation, Fairfax Station.
187. Ferrenberg, A. M. and Swendsen, R. H. (1988) New Monte Carlo technique for studying phase transitions. Phys. Rev. Lett., 61, 2635-2638.
188. Ferrenberg, A. M. and Swendsen, R. H. (1989) Optimized Monte Carlo data analysis. Phys. Rev. Lett., 63, 1195-1198.
189. Calvo, F. and Labastie, P. (1995) Configurational density of states from molecular dynamics simulations. Chem. Phys. Lett., 247, 395-400.
190. Anderson, P. W. (1979) In Balian, R. Maynard, and G. Toulouse, editors, Ill-Condensed Matter, pp. 159-261. North-Holland, Amsterdam.
191. Dyre, J. C. (2006) The glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys., 78, 953-967.
192. de Souza, V. K. and Wales, D. J. (2009) Connectivity in the potential energy landscape for binary Lennard-Jones systems. J. Chem. Phys., 130, 194508.
193. de Souza, V. K. and Wales, D. J. (2005) Diagnosing broken ergodicity using an energy fluctuation metric. J. Chem. Phys., 123, 134504.
194. Mountain, R. D. and Thirumalai, D. (1989) Measures of effective ergodic convergence in liquids. J. Phys. Chem., 93, 6975-6979.
195. Stillinger, F. H. (1995) A topographic view of supercooled liquids and glass formation. Science, 267, 1935-1939.
196. Doliwa, B. and Heuer, A. (2003) Hopping in a supercooled Lennard-Jones liquid: metabasins, waiting time distribution, and diffusion. Phys. Rev. E, 67, 030501R.