Basin Paving Research Articles

Atlas of putative minima and low-lying energy networks of water clusters n = 3-25.

We report a database consisting of the putative minima and ∼3.2 × 106 local minima lying within 5 kcal/mol from the putative minima for water clusters of sizes n = 3-25 using an improved version of the Monte Carlo temperature basin paving (MCTBP) global optimization procedure in conjunction with the ab initio based, flexible, polarizable Thole-Type Model (TTM2.1-F, version 2.1) interaction potential for water. Several of the low-lying structures, as well as low-lying penta-coordinated water networks obtained with the TTM2.1-F potential, were further refined at the Møller-Plesset second order perturbation (MP2)/aug-cc-pVTZ level of theory. In total, we have identified 3 138 303 networks corresponding to local minima of the clusters n = 3-25, whose Cartesian coordinates and relative energies can be obtained from the webpage https://sites.uw.edu/wdbase/. Networks containing penta-coordinated water molecules start to appear at n = 11 and, quite surprisingly, are energetically close (within 1-3 kcal/mol) to the putative minima, a fact that has been confirmed from the MP2 calculations. This large database of water cluster minima spanning quite dissimilar hydrogen bonding networks is expected to influence the development and assessment of the accuracy of interaction potentials for water as well as lower scaling electronic structure methods (such as different density functionals). Furthermore, it can also be used in conjunction with data science approaches (including but not limited to neural networks and machine and deep learning) to understand the properties of water, nature's most important substance.

Understanding the structure and hydrogen bonding network of (H2O)32and (H2O)33: an improved Monte Carlo temperature basin paving (MCTBP) method and quantum theory of atoms in molecules (QTAIM) analysis

Large water clusters are of particular interest because of their connection to liquid water and the intricate hydrogen bonding networks they possess.

A combination of Monte Carlo Temperature Basin Paving and Graph theory: Water cluster low energy structures and completeness of search

The knowledge of degree of completeness of energy landscape search by stochastic algorithms is often lacking. A graph theory based method is used to investigate the completeness of search performed by Monte Carlo Temperature Basin Paving (MCTBP) algorithm for (H2O)n, (n =6, 7, and 20). In the second part of the work, a combination of MCTBP and graph theory was used to devise a new algorithm for finding low energy structures of (H2O)n, (n =21-25), where input structures for (H2O)n comes from the graphs of (H2O)n−1. The new algorithm can be a complementary tool to the MCTBP method. The completeness of search of the energy landscape of water clusters has been investigated by a combination of graph theory and Monte Carlo approach. It was found that the combined technique gives more insight to the low energy structures than Monte Carlo based method.

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations.

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the cluster's Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

A theoretical study of hydrated molecular clusters of amines and dicarboxylic acids

Amines and carboxylic acids have been recognized as important precursor species in atmospheric new particle formation. In this study, the interaction between dimethylamine and succinic acid is investigated using Basin Paving Monte Carlo (BPMC) sampling with the classical force field to obtain low energy conformers of dimethylamine and succinic acid hydrated molecular clusters. Geometry optimization and frequency calculations are further performed on the basis of the BPMC results using density functional theory. At standard temperature and pressure, dimethylamine binds to succinic acid with a bonding energy of 14.2 kcal mol(-1), smaller than that of dimethylamine with sulfuric acid (21.1 kcal mol(-1)). Hydration promotes proton transfer from succinic acid to dimethylamine and consequently increases the interaction strength, while proton transfer from sulfuric acid to dimethylamine occurs without hydration. On the other hand, the reactivity of sulfuric acid with dimethylamine decreases with the degree of hydration of sulfuric acid. The free energies of formation for hydrated clusters consisting of dimethylamine and succinic acid reveal that the interaction between amines and dicarboxylic acids likely exerts a synergetic effect on atmospheric aerosol nucleation by formation of aminium carboxylate ion pairs.

Finding low energy minima of (H2O)25 and (H2O)30 with temperature basin paving Monte Carlo method with effective fragment potential: New ‘global minimum’ and graph theoretical characterization of low energy structures

Determination of low energy structures for large water clusters requires fast and efficient geometry optimization algorithm. A new implementation of the Monte Carlo temperature basin paving (MCTBP) method (J. Phys. Chem. A 2011, 115 (42), 11866) has been used to find low energy structures of (H2O)25 and (H2O)30. MCTBP algorithm uses local minimization in combination with Monte Carlo sampling similar to the basin hopping algorithm. The difference between basin hopping and MCTBP is that in the MCTBP method, Boltzmann factor used in sampling is modified based on the history of sampling favoring lesser sampled structures in subsequent steps. In the new implementation of MCTBP, visit of similar structures during the course of optimization is reduced. With this new implementation, we have found several structures for both the clusters (6 for (H2O)25 and 13 for (H2O)30) lower in energy than previously reported lowest energy structure when the energy is calculated with effective fragment potential. Detailed explanations of the low energy structures are given both in terms of their three dimensional and graph theoretical description. A statistical analysis of the optimization runs show that the low energy structures are visited repeatedly in different trajectories indicating the robustness of the algorithm.

Facilitating Minima Search for Large Water Clusters at the MP2 Level via Molecular Tailoring.

Water clusters (H2O)20 and (H2O)25 are explored at the Møller-Plesset second-order perturbation (MP2) level of theory. Geometry optimization is carried out on favorable structures, initially generated by the temperature basin paving (TBP) method, utilizing the fragment-based molecular tailoring approach (MTA). MTA-based stabilization energies at the complete basis set limit are accurately estimated by grafting the energy correction using a smaller basis set. For prototypical cases, the minima are established via MTA-based vibrational frequency calculations at the MP2/aug-cc-pVDZ level. The potential of MTA in tackling large clusters is further demonstrated by performing geometry optimization at MP2/aug-cc-pVDZ starting with the global minimum of (H2O)30 reported by Monte Carlo (MC) and molecular dynamics (MD) investigations. The present study brings out the efficacy of MTA in performing computationally expensive ab initio calculations with minimal off-the-shelf hardware without significant loss of accuracy.

Determination of low-energy structures of a small RNA hairpin using Monte Carlo–based techniques

The energy landscape of RNA is known to be extremely rugged, and hence finding low-energy structures starting from a random structure is a challenging task for any optimization algorithm. In the current work, we have investigated the ability of one Monte Carlo-based optimization algorithm, Temperature Basin Paving, to explore the energy landscape of a small RNA T-loop hairpin. In this method, the history of the simulation is used to increase the probability of states less visited in the simulation. It has been found that using both energy and end-to-end distance as the biasing parameters in the simulation, the partially folded structure of the hairpin starting from random structures could be obtained.

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.

Monte Carlo Energy Landscape Paving and Basin Paving simulation of RNA T-loop hairpin

Conformational landscape of RNA T-loop hairpin has been investigated by Energy Landscape Paving (ELP) and Basin Paving (BP) Monte Carlo simulations. Both ELP and BP simulations use memory of the simulation to increase the probability of the states less visited. The unfolded structures of the RNA were obtained from the folded one by ELP method. Structures were folded from extended structures by BP method. Choice of different parameters, including the use of the end-to-end distance of RNA as a memory term, in the simulations to accelerate sampling is discussed. It has been found that both ELP and BP are highly efficient techniques for unfolding and folding RNA T-loop hairpin.

Efficient conformational sampling by Monte Carlo Basin Paving method: Distribution of minima on the energy surface of (H 2O) 20 and (H 2O) 50

The efficiency of Basin Paving method [Phys. Rev. E 73 (2006) 015701(R)], a Monte Carlo based optimization algorithm, is investigated by applying it to (H 2O) 20 and (H 2O) 50. It is found that Basin Paving does a better sampling of low energy minima compared to the well known Basin Hopping method. The large number of minima obtained from this work is used to form a network of water cluster minima. From the properties of the network, it is found that (H 2O) 50 minima are more uniformly distributed in the conformational space than that of (H 2O) 20.

Computational study of the Trp‐cage miniprotein based on the ECEPP/3 force field

Using a newly developed Monte Carlo global optimization method called basin paving, we have performed an ab initio computation for the structure of Trp-cage based on the ECEPP/3 force field in vacuo. The lowest energy minimum has been located. Its corresponding configuration is comparable to the native structure of Trp-cage (PDB code 1L2Y) with a backbone root mean square deviation of 2.24 A.

Conformational Study of Met-Enkephalin Based on the ECEPP Force Fields

We report a computational study of the small peptide Met-enkephalin based on the ECEPP/2 and ECEPP/3 force fields using the basin paving method. We have located a new global minimum when using the ECEPP/3 force field with peptide angles ω fixed at 180°. With this new result, we can conclude that the lowest energy configurations of Met-enkephalin predicted based on all four versions of ECEPP have a classic γ-turn centered at residue Gly 3 and a β-turn at residues Gly 3-Phe 4. However, minor differences between the structures also exist.

Monte Carlo basin paving: An improved global optimization method

We propose a global optimization procedure, basin paving, which is based on the combination of the optimization strategies behind basin hopping and energy landscape paving. As an example, we describe its application in the protein structure prediction by examining two well-studied peptides, where we have found lower potential energy minima than previously located. We also compare the statistics of the searching trajectories produced by basin paving, basin hopping, and energy landscape paving.