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Annual Review of Physical Chemistry

Volume 69, 2018

Exploring Energy Landscapes

Abstract

Recent advances in the potential energy landscapes approach are highlighted, including both theoretical and computational contributions. Treating the high dimensionality of molecular and condensed matter systems of contemporary interest is important for understanding how emergent properties are encoded in the landscape and for calculating these properties while faithfully representing barriers between different morphologies. The pathways characterized in full dimensionality, which are used to construct kinetic transition networks, may prove useful in guiding such calculations. The energy landscape perspective has also produced new procedures for structure prediction and analysis of thermodynamic properties. Basin-hopping global optimization, with alternative acceptance criteria and generalizations to multiple metric spaces, has been used to treat systems ranging from biomolecules to nanoalloy clusters and condensed matter. This review also illustrates how all this methodology, developed in the context of chemical physics, can be transferred to landscapes defined by cost functions associated with machine learning.

Keyword(s): energy landscapes, enhanced sampling, global optimization, machine learning, rare events
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2018-04-20
2024-05-09
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Literature Cited

  1. Murrell JN, Laidler KJ. 1.  1968. Symmetries of activated complexes. Trans. Faraday. Soc. 64:371–77 [Google Scholar]
  2. Trygubenko SA, Wales DJ. 2.  2004. A doubly nudged elastic band method for finding transition states. J. Chem. Phys. 120:2082–94 [Google Scholar]
  3. Henkelman G, Jónsson H. 3.  2000. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113:9978–85 [Google Scholar]
  4. Henkelman G, Uberuaga BP, Jónsson H. 4.  2000. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113:9901–4 [Google Scholar]
  5. Munro LJ, Wales DJ. 5.  1999. Defect migration in crystalline silicon. Phys. Rev. B 59:3969–80 [Google Scholar]
  6. Henkelman G, Jónsson H. 6.  1999. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111:7010–22 [Google Scholar]
  7. Kumeda Y, Munro LJ, Wales DJ. 7.  2001. Transition states and rearrangement mechanisms from hybrid eigenvector-following and density functional theory. Application to C10H10 and defect migration in crystalline silicon. Chem. Phys. Lett. 341:185–94 [Google Scholar]
  8. Zeng Y, Xiao P, Henkelman G. 8.  2014. Unification of algorithms for minimum mode optimization. J. Chem. Phys. 140:044115 [Google Scholar]
  9. Rao F, Caflisch A. 9.  2004. The protein folding network. J. Mol. Biol. 342:299–306 [Google Scholar]
  10. Noé F, Fischer S. 10.  2008. Transition networks for modeling the kinetics of conformational change in macromolecules. Curr. Op. Struct. Biol. 18:154–62 [Google Scholar]
  11. Prada-Gracia D, Gómez-Gardeñes J, Echenique P, Fernando F. 11.  2009. Exploring the free energy landscape: from dynamics to networks and back. PLOS Comput. Biol. 5:e1000415 [Google Scholar]
  12. Wales DJ. 12.  2010. Energy landscapes: some new horizons. Curr. Op. Struct. Biol. 20:3–10 [Google Scholar]
  13. Forst W. 13.  1973. Theory of Unimolecular Reactions New York: Academic Press
  14. Wales DJ. 14.  2002. Discrete path sampling. Mol. Phys. 100:3285–305 [Google Scholar]
  15. Wales DJ. 15.  2004. Some further applications of discrete path sampling to cluster isomerization. Mol. Phys. 102:891–908 [Google Scholar]
  16. Joseph JA, Röder K, Chakraborty D, Mantell RG, Wales DJ. 16.  2017. Exploring biomolecular energy landscapes. Chem. Commun. 53:6974–88 [Google Scholar]
  17. Stillinger FH, Weber TA. 17.  1984. Packing structures and transitions in liquids and solids. Science 225:983–89 [Google Scholar]
  18. Wales DJ. 18.  1993. Coexistence in small inert-gas clusters. Mol. Phys. 78:151–71 [Google Scholar]
  19. Wales DJ. 19.  2003. Energy Landscapes Cambridge, UK: Cambridge Univ. Press
  20. Stillinger FH. 20.  1995. A topographic view of supercooled liquids and glass formation. Science 267:1935–39 [Google Scholar]
  21. Strodel B, Wales DJ. 21.  2008. Free energy surfaces from an extended harmonic superposition approach and kinetics for alanine dipeptide. Chem. Phys. Lett. 466:105–15 [Google Scholar]
  22. Sharapov VA, Meluzzi D, Mandelshtam VA. 22.  2007. Low-temperature structural transitions: circumventing the broken-ergodicity problem. Phys. Rev. Lett. 98:105701 [Google Scholar]
  23. Swendsen RH, Wang JS. 23.  1986. Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57:2607–9 [Google Scholar]
  24. Geyer G. 24.  1991. Markov chain Monte Carlo maximum likelihood. Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface EK Keramidas 156–63 Fairfax Station, VA: Interface Found. [Google Scholar]
  25. Hukushima K, Nemoto K. 25.  1996. Exchange Monte Carlo method and application to spin glass simulations. J. Phys. Soc. Jpn. 65:1604–8 [Google Scholar]
  26. Stillinger FH, Weber TA. 26.  1982. Hidden structure in liquids. Phys. Rev. A 25:978–89 [Google Scholar]
  27. Doye JPK, Wales DJ. 27.  2002. Saddle points and dynamics of Lennard-Jones clusters, solids, and supercooled liquids. J. Chem. Phys. 116:3777–88 [Google Scholar]
  28. Becker OM, Karplus M. 28.  1997. The topology of multidimensional potential energy surfaces: theory and application to peptide structure and kinetics. J. Chem. Phys. 106:1495–517 [Google Scholar]
  29. Wales DJ, Miller MA, Walsh TR. 29.  1998. Archetypal energy landscapes. Nature 394:758–60 [Google Scholar]
  30. Krivov SV, Karplus M. 30.  2002. Free energy disconnectivity graphs: application to peptide models. J. Chem. Phys. 117:10894–903 [Google Scholar]
  31. Evans DA, Wales DJ. 31.  2003. Free energy landscapes of model peptides and proteins. J. Chem. Phys. 118:3891–97 [Google Scholar]
  32. Wales DJ, Doye JPK. 32.  1997. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101:5111–16 [Google Scholar]
  33. Doye JPK, Wales DJ, Miller MA. 33.  1998. Thermodynamics and the global optimization of Lennard-Jones clusters. J. Chem. Phys. 109:8143–53 [Google Scholar]
  34. Doye JPK, Miller MA, Wales DJ. 34.  1999. The double-funnel energy landscape of the 38-atom Lennard-Jones cluster. J. Chem. Phys. 110:6896–906 [Google Scholar]
  35. Neirotti JP, Calvo F, Freeman DL, Doll JD. 35.  2000. Phase changes in 38 atom Lennard-Jones clusters. I: A parallel tempering study in the canonical ensemble. J. Chem. Phys. 112:10340–49 [Google Scholar]
  36. Calvo F, Neirotti JP, Freeman DL, Doll JD. 36.  2000. Phase changes in 38 atom Lennard-Jones clusters. II: A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles. J. Chem. Phys. 112:10350–57 [Google Scholar]
  37. Frantsuzov PA, Mandelshtam VA. 37.  2005. Size-temperature phase diagram for small Lennard-Jones clusters. Phys. Rev. E 72:037102 [Google Scholar]
  38. Predescu C, Frantsuzov PA, Mandelshtam VA. 38.  2005. Thermodynamics and equilibrium structure of Ne38 cluster: quantum mechanics versus classical. J. Chem. Phys. 122:154305 [Google Scholar]
  39. Liu HB, Jordan KD. 39.  2005. On the convergence of parallel tempering Monte Carlo simulations of LJ38. J. Phys. Chem. B 109:5203–7 [Google Scholar]
  40. Sharapov VA, Mandelshtam VA. 40.  2007. Solid-solid structural transformations in Lennard-Jones clusters: accurate simulations versus the harmonic superposition approximation. J. Phys. Chem. A 111:10284–91 [Google Scholar]
  41. Jones JE, Ingham AE. 41.  1925. On the calculation of certain crystal potential constants, and on the cubic crystal of least potential energy. Proc. R. Soc. A 107:636–53 [Google Scholar]
  42. Doye JPK, Miller MA, Wales DJ. 42.  1999. Evolution of the potential energy surface with size for Lennard-Jones clusters. J. Chem. Phys. 111:8417–28 [Google Scholar]
  43. Mackay AL. 43.  1962. A dense non-crystallographic packing of equal spheres. Acta Cryst 15:916–18 [Google Scholar]
  44. Oakley MT, Johnston RL, Wales DJ. 44.  2013. Symmetrisation schemes for global optimisation of atomic clusters. Phys. Chem. Chem. Phys. 15:3965–76 [Google Scholar]
  45. Mandelshtam VA, Frantsuzov PA, Calvo F. 45.  2006. Structural transitions and melting in LJ74–78 Lennard-Jones clusters from adaptive exchange Monte Carlo simulations. J. Phys. Chem. A 110:5326–32 [Google Scholar]
  46. Calvo F. 46.  2010. Free-energy landscapes from adaptively biased methods: application to quantum systems. Phys. Rev. E 82:046703 [Google Scholar]
  47. Wales DJ. 47.  2013. Surveying a complex potential energy landscape: overcoming broken ergodicity using basin-sampling. Chem. Phys. Lett. 584:1–9 [Google Scholar]
  48. Sehgal RM, Maroudas D, Ford DM. 48.  2014. Phase behavior of the 38-atom Lennard-Jones cluster. J. Chem. Phys. 140:104312 [Google Scholar]
  49. Picciani M, Athenes M, Kurchan J, Tailleur J. 49.  2011. Simulating structural transitions by direct transition current sampling: the example of LJ38. J. Chem. Phys. 135:034108 [Google Scholar]
  50. de Souza VK, Wales DJ. 50.  2008. Energy landscapes for diffusion: analysis of cage-breaking processes. J. Chem. Phys. 129:164507 [Google Scholar]
  51. de Souza VK, Wales DJ. 51.  2009. Connectivity in the potential energy landscape for binary Lennard-Jones systems. J. Chem. Phys. 130:194508 [Google Scholar]
  52. Niblett SP, de Souza VK, Stevenson JD, Wales DJ. 52.  2016. Dynamics of a molecular glass former: energy landscapes for diffusion in ortho-terphenyl. J. Chem. Phys. 145:024505 [Google Scholar]
  53. de Souza VK, Stevenson JD, Niblett SP, Farrell JD, Wales DJ. 53.  2017. Defining and quantifying frustration in the energy landscape: applications to atomic and molecular clusters, biomolecules, jammed and glassy systems. J. Chem. Phys. 146:124103 [Google Scholar]
  54. Chebaro Y, Ballard AJ, Chakraborty D, Wales DJ. 54.  2015. Intrinsically disordered energy landscapes. Sci. Rep. 5:10386 [Google Scholar]
  55. Chakrabarti D, Wales DJ. 55.  2011. Coupled linear and rotary motion in supramolecular helix handedness inversion. Soft Matter 7:2325–28 [Google Scholar]
  56. Röder K, Wales DJ. 56.  2017. Transforming the energy landscape of a coiled-coil peptide via point mutations. J. Chem. Theory Comput. 13:1468–77 [Google Scholar]
  57. Doye JPK, Wales DJ. 57.  1999. The dynamics of structural transitions in sodium chloride clusters. J. Chem. Phys. 111:11070–79 [Google Scholar]
  58. Krivov SV, Karplus M. 58.  2004. Hidden complexity of free energy surfaces for peptide (protein) folding. PNAS 101:14766–70 [Google Scholar]
  59. Krivov SV, Karplus M. 59.  2006. One-dimensional free-energy profiles of complex systems: progress variables that preserve the barriers. J. Phys. Chem. B 110:12689–98 [Google Scholar]
  60. Muff S, Caflisch A. 60.  2008. Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single-point mutation of a β-sheet miniprotein. Proteins Struct. Funct. Bioinf. 70:1185–95 [Google Scholar]
  61. Krivov SV, Karplus M. 61.  2008. Diffusive reaction dynamics on invariant free energy profiles. PNAS 105:13841–46 [Google Scholar]
  62. Wales DJ. 62.  2015. Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape. J. Chem. Phys. 142:130901 [Google Scholar]
  63. Steinhardt PJ, Nelson DR, Ronchetti M. 63.  1983. Bond-orientational order in liquids and glasses. Phys. Rev. B 28:784–805 [Google Scholar]
  64. van Duijneveldt JS Frenkel D. 64.  1992. Computer simulation study of free energy barriers in crystal nucleation. J. Chem. Phys. 96:4655–68 [Google Scholar]
  65. Frenkel D, Smit B. 65.  2002. Understanding Molecular Simulation London: Academic Press, 2nd ed..
  66. Ferrenberg AM, Swendsen RH. 66.  1988. New Monte Carlo technique for studying phase transitions. Phys. Rev. Lett. 61:2635–38 [Google Scholar]
  67. Ferrenberg AM, Swendsen RH. 67.  1989. Optimized Monte Carlo data analysis. Phys. Rev. Lett. 63:1195–98 [Google Scholar]
  68. Weerasinghe S, Amar FG. 68.  1993. Absolute classical densities of states for very anharmonic systems and applications to the evaporation of rare gas clusters. J. Chem. Phys. 98:4967–83 [Google Scholar]
  69. Chill ST, Stevenson J, Ruehle V, Shang C, Xiao P. 69.  et al. 2014. Benchmarks for characterization of minima, transition states, and pathways in atomic, molecular, and condensed matter systems. J. Chem. Theory Comput. 10:5476–82 [Google Scholar]
  70. Mantell RG, Pitt CE, Wales DJ. 70.  2016. GPU-accelerated exploration of biomolecular energy landscapes. J. Chem. Theory Comput. 12:6182–91 [Google Scholar]
  71. Kusumaatmaja H, Whittleston CS, Wales DJ. 71.  2012. A local rigid body framework for global optimization of biomolecules. J. Chem. Theory Comput. 8:5159–65 [Google Scholar]
  72. Doye JPK, Wales DJ. 72.  1995. Calculation of thermodynamic properties of small Lennard-Jones clusters incorporating anharmonicity. J. Chem. Phys. 102:9659–72 [Google Scholar]
  73. Doye JPK, Wales DJ. 73.  1995. An order-parameter approach to coexistence in atomic clusters. J. Chem. Phys. 102:9673–88 [Google Scholar]
  74. Calvo F, Doye JPK, Wales DJ. 74.  2001. Characterization of anharmonicities on complex potential energy surfaces: perturbation theory and simulation. J. Chem. Phys. 115:9627–36 [Google Scholar]
  75. Georgescu I, Mandelshtam VA. 75.  2012. Self-consistent phonons revisited. I. The role of thermal versus quantum fluctuations on structural transitions in large Lennard-Jones clusters. J. Chem. Phys. 137:144106 [Google Scholar]
  76. Li Z, Scheraga HA. 76.  1987. Monte Carlo-minimization approach to the multiple-minima problem in protein folding. PNAS 84:6611–15 [Google Scholar]
  77. Wales DJ, Scheraga HA. 77.  1999. Global optimization of clusters, crystals and biomolecules. Science 285:1368–72 [Google Scholar]
  78. Leary RH, Doye JPK. 78.  1999. New tetrahedral global minimum for the 98-atom Lennard-Jones cluster. Phys. Rev. E 60:R6320–22 [Google Scholar]
  79. Shang C, Wales DJ. 79.  2014. Communication: Optimal parameters for basin-hopping global optimization based on Tsallis statistics. J. Chem. Phys. 141:071101 [Google Scholar]
  80. Sutherland-Cash K, Wales D, Chakrabarti D. 80.  2015. Free energy basin-hopping. Chem. Phys. Lett. 625:1–4 [Google Scholar]
  81. Calvo F, Schebarchov D, Wales DJ. 81.  2016. Grand and semigrand canonical basin-hopping. J. Chem. Theory Comput. 12:902–9 [Google Scholar]
  82. Jellinek J, Krissinel E. 82.  1996. NinAlm alloy clusters: analysis of structural forms and their energy ordering. Chem. Phys. Lett. 258:283–92 [Google Scholar]
  83. Schebarchov D, Wales DJ. 83.  2013. Communication: A new paradigm for structure prediction in multicomponent systems. J. Chem. Phys. 139:221101 [Google Scholar]
  84. Schebarchov D, Wales DJ. 84.  2014. Structure prediction for multicomponent materials using biminima. Phys. Rev. Lett. 113:156102 [Google Scholar]
  85. Schebarchov D, Wales DJ. 85.  2015. Quasi-combinatorial energy landscapes for nanoalloy structure optimisation. Phys. Chem. Chem. Phys. 17:28331–38 [Google Scholar]
  86. Labastie P, Whetten RL. 86.  1990. Statistical mechanics of the cluster solid-liquid transition. Phys. Rev. Lett. 65:1567–70 [Google Scholar]
  87. Calvo F, Labastie P. 87.  1995. Configurational density of states from molecular dynamics simulations. Chem. Phys. Lett. 247:395–400 [Google Scholar]
  88. Martiniani S, Schrenk KJ, Stevenson JD, Wales DJ, Frenkel D. 88.  2016. Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings. Phys. Rev. E 93:012906 [Google Scholar]
  89. Martiniani S, Schrenk KJ, Stevenson JD, Wales DJ, Frenkel D. 89.  2016. Structural analysis of high-dimensional basins of attraction. Phys. Rev. E 94:031301 [Google Scholar]
  90. Wales DJ. 90.  2017. Decoding heat capacity features from the energy landscape. Phys. Rev. E 95:030105(R) [Google Scholar]
  91. Strodel B, Whittleston CS, Wales DJ. 91.  2007. Thermodynamics and kinetics of aggregation for the GNNQQNY peptide. J. Am. Chem. Soc. 129:16005–14 [Google Scholar]
  92. Ballard AJ, Stevenson JD, Das R, Wales DJ. 92.  2016. Energy landscapes for a machine learning application to series data. J. Chem. Phys. 144:124119 [Google Scholar]
  93. Ballard AJ, Das R, Martiniani S, Mehta D, Sagun L. 93.  et al. 2017. Energy landscapes for machine learning. Phys. Chem. Chem. Phys. 19:12585–603 [Google Scholar]
  94. Pavlovskaia M, Tu K, Zhu SC. 94.  2015. Mapping the energy landscape of non-convex optimization problems. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2015) XC Tai, E Bae, TF Chan, M Lysaker 421–35 Cham, Switz.: Springer
  95. Das R, Wales DJ. 95.  2017. Machine learning prediction for classification of outcomes in local minimisation. Chem. Phys. Lett. 667:158–64 [Google Scholar]
  96. Wales DJ. 96.  1992. Basins of attraction for stationary-points on a potential-energy surface. J. Chem. Soc. Faraday Trans. 88:653–57 [Google Scholar]
  97. Wales DJ. 97.  1993. Locating stationary-points for clusters in Cartesian coordinates. J. Chem. Soc. Faraday Trans. 89:1305–13 [Google Scholar]
  98. Asenjo D, Stevenson JD, Wales DJ, Frenkel D. 98.  2013. Visualizing basins of attraction for different minimization algorithms. J. Phys. Chem. B 117:12717–23 [Google Scholar]
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Exploring Energy Landscapes
Annual Review of Physical Chemistry 69, 401 (2018); https://doi.org/10.1146/annurev-physchem-050317-021219
/content/journals/10.1146/annurev-physchem-050317-021219
/content/journals/10.1146/annurev-physchem-050317-021219
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