A global optimization perspective on molecular clusters

Although there is a long history behind the idea of chemical structure, this is a key concept that continues to challenge chemists. Chemical structure is fundamental to understanding most of the properties of matter and its knowledge for complex systems requires the use of state-of-the-art techniques, either experimental or theoretical. From the theoretical view point, one needs to establish the interaction potential among the atoms or molecules of the system, which contains all the information regarding the energy landscape, and employ optimization algorithms to discover the relevant stationary points. In particular, global optimization methods are of major importance to search for the low-energy structures of molecular aggregates. We review the application of global optimization techniques to several molecular clusters; some new results are also reported. Emphasis is given to evolutionary algorithms and their application in the study of the microsolvation of alkali-metal and Ca2+ ions with various types of solvents. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’.

[1]  Robert J. Harrison,et al.  Development of transferable interaction models for water. II. Accurate energetics of the first few water clusters from first principles , 2002 .

[2]  Martin T. Dove,et al.  DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism , 2006 .

[3]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[4]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[5]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[6]  M. Albertí,et al.  Potassium ion surrounded by aromatic rings: molecular dynamics of the first solvation shell , 2014 .

[7]  B. Pan,et al.  Structures, stability, vibration entropy and IR spectra of hydrated calcium ion clusters [Ca(H(2)O)(n)](2+) (n = 1-20, 27): a systematic investigation by density functional theory. , 2010, The journal of physical chemistry. A.

[8]  David Feller,et al.  The role of databases in support of computational chemistry calculations , 1996, J. Comput. Chem..

[9]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[10]  P. Jeffrey Hay,et al.  Gaussian Basis Sets for Molecular Calculations , 1977 .

[11]  B. Hartke,et al.  Dodecahedral clathrate structures and magic numbers in alkali cation microhydration clusters. , 2002, Chemphyschem : a European journal of chemical physics and physical chemistry.

[12]  J. L. Llanio-Trujillo,et al.  New insights on lithium-cation microsolvation by solvents forming hydrogen-bonds: Water versus methanol , 2013 .

[13]  B. Hartke,et al.  A new proposal for the reason of magic numbers in alkali cation microhydration clusters , 2005 .

[14]  Ho,et al.  Molecular geometry optimization with a genetic algorithm. , 1995, Physical review letters.

[15]  B. Hartke Global geometry optimization of clusters using genetic algorithms , 1993 .

[16]  Fernando Pirani,et al.  Beyond the Lennard-Jones model: a simple and accurate potential function probed by high resolution scattering data useful for molecular dynamics simulations. , 2008, Physical chemistry chemical physics : PCCP.

[17]  S. Xantheas,et al.  The binding energies of the D2d and S4 water octamer isomers: high-level electronic structure and empirical potential results. , 2004, Journal of Chemical Physics.

[18]  Francisco B. Pereira,et al.  A study on diversity for cluster geometry optimization , 2009, Evol. Intell..

[19]  Jorge M. C. Marques,et al.  Analysis of Locality in Hybrid Evolutionary Cluster Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[20]  C. Chaudhuri,et al.  Microsolvation of the lithium ion by methanol in the gas phase , 2004 .

[21]  F. Wöhler Analytische Versuche über die Cyansäure , 1824 .

[22]  Hiroshi Takeuchi Development of an Efficient Geometry Optimization Method for Water Clusters , 2008, J. Chem. Inf. Model..

[23]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[24]  Albeiro Restrepo,et al.  Structural characterization of the (methanol)4 potential energy surface. , 2009, The journal of physical chemistry. A.

[25]  R. J. Boyd,et al.  A Density Functional Study of Methanol Clusters. , 2007, Journal of chemical theory and computation.

[26]  Edoardo Aprà,et al.  High-level ab initio calculations for the four low-lying families of minima of (H2O)20. I. Estimates of MP2/CBS binding energies and comparison with empirical potentials. , 2004, The Journal of chemical physics.

[27]  H. Takeuchi Structures, stability, and growth sequence patterns of small homoclusters of naphthalene, anthracene, phenanthrene, phenalene, naphthacene, and pyrene , 2013 .

[28]  Corey J. Weinheimer,et al.  Size selectivity by cation–π interactions: Solvation of K+ and Na+ by benzene and water , 1999 .

[29]  D. Quiñonero,et al.  Cation-π versus anion-π interactions: Energetic, charge transfer, and aromatic aspects , 2004 .

[30]  Fernando Pirani,et al.  Low‐energy structures of benzene clusters with a novel accurate potential surface , 2015, J. Comput. Chem..

[31]  Hiroshi Takeuchi,et al.  Novel Method for Geometry Optimization of Molecular Clusters: Application to Benzene Clusters , 2007, J. Chem. Inf. Model..

[32]  Jan Andzelm,et al.  Gaussian Basis Sets for Molecular Calculations , 2012 .

[33]  William L. Jorgensen,et al.  Energy component analysis for dilute aqueous solutions of lithium(1+), sodium(1+), fluoride(1-), and chloride(1-) ions , 1984 .

[34]  David J. Wales,et al.  Global minima of water clusters (H2O)n, n≤21, described by an empirical potential , 1998 .

[35]  B. Hartke,et al.  Experimental and theoretical investigation of microsolvation of Na+-ions in the gas phase by high resolution mass spectrometry and global cluster geometry optimization , 2002 .

[36]  T. H. Dunning Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .

[37]  Jun Li,et al.  Basis Set Exchange: A Community Database for Computational Sciences , 2007, J. Chem. Inf. Model..

[38]  A. Wachters,et al.  Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms , 1970 .

[39]  J. L. Llanio-Trujillo,et al.  Alkali-ion microsolvation with benzene molecules. , 2012, The journal of physical chemistry. A.

[40]  Xin Yang,et al.  Structure of the Na(x)Cl(x+1) (-) (x=1-4) clusters via ab initio genetic algorithm and photoelectron spectroscopy. , 2004, The Journal of chemical physics.

[41]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[42]  Jeffrey H. Williams,et al.  The molecular electric quadrupole moment and solid-state architecture , 1993 .

[43]  E. Williams,et al.  Hydrated alkali metal ions: spectroscopic evidence for clathrates. , 2013, The journal of physical chemistry. A.

[44]  M. M. Pires,et al.  Structural, Energetic, and Infrared Spectra Insights into Methanol Clusters (CH3OH)n, for n = 2-12, 16, 20. ONIOM as an Efficient Method of Modeling Large Methanol Clusters. , 2007, Journal of chemical theory and computation.

[45]  Sergey Kazachenko,et al.  Methanol clusters (CH3OH)n: putative global minimum-energy structures from model potentials and dispersion-corrected density functional theory. , 2013, The Journal of chemical physics.

[46]  W. L. Jorgensen Revised TIPS for simulations of liquid water and aqueous solutions , 1982 .

[47]  J. L. Llanio-Trujillo,et al.  Microsolvation of the potassium ion with aromatic rings: comparison between hexafluorobenzene and benzene. , 2013, The journal of physical chemistry. A.

[48]  Julius Jellinek,et al.  Energy Landscapes: With Applications to Clusters, Biomolecules and Glasses , 2005 .

[49]  David J. Wales,et al.  Global minima for water clusters (H2O)n, n ⩽ 21, described by a five-site empirical potential , 2005 .

[50]  John Arthur Niesse,et al.  Global optimization of atomic and molecular clusters using the space-fixed modified genetic algorithm method , 1997, J. Comput. Chem..

[51]  A Shayeghi,et al.  Pool-BCGA: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters. , 2015, Physical chemistry chemical physics : PCCP.

[52]  Francisco B. Pereira,et al.  An evolutionary algorithm for the global optimization of molecular clusters: application to water, benzene, and benzene cation. , 2011, The journal of physical chemistry. A.

[53]  G. Rossi,et al.  Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[54]  Jorge M. C. Marques,et al.  How Different Are Two Chemical Structures? , 2010, J. Chem. Inf. Model..

[55]  F. Huisken,et al.  Infrared spectroscopy of size-selected water and methanol clusters. , 2000, Chemical reviews.

[56]  William L. Jorgensen,et al.  Aromatic-aromatic interactions: free energy profiles for the benzene dimer in water, chloroform, and liquid benzene , 1990 .

[57]  D. Wales,et al.  Global minima and energetics of Li+(H2O)n and Ca2+(H2O)n clusters for n ⩽ 20 , 2005 .

[58]  Jun Zhang,et al.  Global optimization of clusters of rigid molecules using the artificial bee colony algorithm. , 2016, Physical chemistry chemical physics : PCCP.

[59]  Anastassia N Alexandrova,et al.  Search for the Lin(0/+1/-1) (n = 5-7) Lowest-Energy Structures Using the ab Initio Gradient Embedded Genetic Algorithm (GEGA). Elucidation of the Chemical Bonding in the Lithium Clusters. , 2005, Journal of chemical theory and computation.

[60]  Hiroshi Takeuchi,et al.  Structural features of small benzene clusters (C6H6)n (n ≤ 30) as investigated with the all-atom OPLS potential. , 2012, The journal of physical chemistry. A.

[61]  Bernd Hartke,et al.  Global Geometry Optimization of Molecular Clusters: TIP4P Water , 2000 .

[62]  Johannes M. Dieterich,et al.  A size resolved investigation of large water clusters. , 2014, Physical chemistry chemical physics : PCCP.

[63]  K. Lonsdale The Structure of the Benzene Ring , 1928, Nature.

[64]  Andreas Heßelmann,et al.  Accurate Intermolecular Interaction Energies from a Combination of MP2 and TDDFT Response Theory. , 2010, Journal of chemical theory and computation.

[65]  R. Johnston,et al.  A genetic algorithm for the structural optimization of Morse clusters , 2000 .

[66]  R. Hentschke,et al.  Global Minima of Water Clusters (H2O)N, N ≤ 25, Described by Three Empirical Potentials , 2003 .

[67]  Yong L. Xiao,et al.  Genetic algorithm: a new approach to the prediction of the structure of molecular clusters , 1993 .

[68]  Hiroshi Takeuchi,et al.  Geometry optimization of carbon dioxide clusters (CO2)n for 4 < or = n < or = 40. , 2008, The journal of physical chemistry. A.

[69]  Kalyanmoy Deb,et al.  Self-Adaptive Genetic Algorithms with Simulated Binary Crossover , 2001, Evolutionary Computation.

[70]  Bernd Hartke,et al.  Global cluster geometry optimization by a phenotype algorithm with Niches: Location of elusive minima, and low-order scaling with cluster size , 1999, J. Comput. Chem..

[71]  Thomas L. Starr,et al.  Calculation of the crystal structures of hydrocarbons by molecular packing analysis , 1977, Comput. Chem..

[72]  Johannes M. Dieterich,et al.  OGOLEM: Global cluster structure optimisation for arbitrary mixtures of flexible molecules. A multiscaling, object-oriented approach , 2010 .

[73]  Gregory S. Tschumper,et al.  Assignment of the infrared spectra of the methanol trimer , 1999 .

[74]  A. Laaksonen,et al.  The effect of ions on solid–liquid phase transition in small water clusters. A molecular dynamics simulation study , 2003 .

[75]  Corey J. Weinheimer,et al.  Competitive solvation of K+ by benzene and water: Cation-π interactions and π-hydrogen bonds , 1998 .

[76]  R. Johnston Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries , 2003 .