Monte Carlo temperature basin paving with effective fragment potential: an efficient and fast method for finding low-energy structures of water clusters (H2O)20 and (H2O)25.

Determining low-energy structures of large water clusters is a challenge for any optimization algorithm. In this work, we have developed a new Monte Carlo (MC)-based method, temperature basin paving (TBP), which is related to the well-known basin hopping method. In the TBP method, the Boltzmann weight factor used in MC methods is dynamically modified based on the history of the simulation. The states that are visited more are given a lower probability by increasing their temperatures and vice versa. This allows faster escapes from the states frequently visited in the simulation. We have used the TBP method to find a large number of low-energy minima of water clusters of size 20 and 25. We have found structures energetically same to the global minimum structures known for these two clusters. We have compared the efficiency of this method to the basin-hopping method and found that it can locate the minima faster. Statistical efficiency of the new method has been investigated by running a large number of trajectories. The new method can locate low-energy structures of both the clusters faster than some of the reported algorithms for water clusters and can switch between high energy and low-energy structures multiple times in a simulation illustrating its efficiency. The large number of minima obtained from the simulations is used to get both general and specific features of the minima. The distribution of minima for these two clusters based on the similarity of their oxygen frames shows that the (H(2)O)(20) can have different variety of structures, but for (H(2)O)(25), low-energy structures are mostly cagelike. Several (H(2)O)(25) structures are found with similar energy but with different cage architectures. Noncage structures of (H(2)O)(25) are also found but they are 6-7 kcal/mol higher in energy from the global minimum. The TBP method is likely to play an important role for exploring the complex energy landscape of large molecules.

[1]  Mark S. Gordon,et al.  The Effective Fragment Potential Method: A QM-Based MM Approach to Modeling Environmental Effects in Chemistry , 2001 .

[2]  Mark S. Gordon,et al.  An interpretation of the enhancement of the water dipole moment due to the presence of other water molecules. , 2008, The journal of physical chemistry. A.

[3]  W. Kabsch.  A solution for the best rotation to relate two sets of vectors , 1976 .

[4]  Kenneth D. Jordan,et al.  Theoretical study of small water clusters : low-energy fused cubic structures for (H2O)n, n = 8, 12, 16, and 20 , 1993 .

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

[6]  P. N. Day,et al.  A study of water clusters using the effective fragment potential and Monte Carlo simulated annealing , 2000 .

[7]  A. Fujii,et al.  Spectral signatures of four-coordinated sites in water clusters: infrared spectroscopy of phenol-(H2O)n (∼20 ≤ n ≤ ∼50). , 2011, The journal of physical chemistry. A.

[8]  Nobuyuki Akai,et al.  The effect of cooperative hydrogen bonding on the OH stretching-band shift for water clusters studied by matrix-isolation infrared spectroscopy and density functional theory. , 2005, Physical chemistry chemical physics : PCCP.

[9]  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.

[10]  H. Kabrede,et al.  Using vibrational modes in the search for global minima of atomic and molecular clusters , 2006 .

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

[12]  Teresa Head-Gordon,et al.  The structure of ambient water , 2010 .

[13]  P. Bandyopadhyay,et al.  Monte Carlo Energy Landscape Paving and Basin Paving simulation of RNA T-loop hairpin , 2011 .

[14]  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.

[15]  W. Goddard,et al.  Accurate Energies and Structures for Large Water Clusters Using the X3LYP Hybrid Density Functional , 2004 .

[16]  P. Bandyopadhyay.  Efficient conformational sampling by Monte Carlo Basin Paving method: Distribution of minima on the energy surface of (H2O)20 and (H2O)50 , 2010 .

[17]  U. Buck,et al.  Solid water clusters in the size range of tens–thousands of H2O: a combined computational/spectroscopic outlook , 2004 .

[18]  Wencai Lu,et al.  Energetic and fragmentation stability of water clusters (H2O)n, n = 2–30 , 2011 .

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

[20]  Ajit J. Thakkar,et al.  Improved minima-hopping. TIP4P water clusters, (H2O)n with n⩽37 , 2009 .

[21]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

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

[23]  V. Buch,et al.  Search for Low Energy Structures of Water Clusters (H2O)n, n = 20−22, 48, 123, and 293 , 2003 .

[24]  A. Fujii,et al.  Infrared spectra and hydrogen-bonded network structures of large protonated water clusters H+(H2O)n (n=20-200). , 2010, Angewandte Chemie.

[25]  Ulrich H E Hansmann,et al.  Global optimization by energy landscape paving. , 2002, Physical review letters.

[26]  R. Unger,et al.  Finding the lowest free energy conformation of a protein is an NP-hard problem: proof and implications. , 1993, Bulletin of mathematical biology.

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

[28]  S. Goedecker.  Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. , 2004, The Journal of chemical physics.

[29]  Edoardo Aprà,et al.  High-level ab initio calculations for the four low-lying families of minima of (H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks. , 2005, The Journal of chemical physics.