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.     

Structural and pathway complexity of beta-strand reorganization within aggregates of human transthyretin(105-115) peptide

Interstrand conformational rearrangements of human transthyretin peptide (TTR(105-115)) within dimeric aggregates were simulated by means of molecular dynamics (MD) with implicit solvation model for a total length of 48 micros. The conformations sampled in the MD simulations were clustered to identify free energy minima without any projections of free energy surface. A connected graph was constructed with nodes (=clusters) and edges corresponding to free energy minima and transitions between nodes, respectively. This connected graph which reflects the complexity of the free energy surface was used to extract the transition disconnectivity graph, which reflects the overall free energy barriers between pairs of free energy minima but does not contain information on transition paths. The routes of transitions between important free energy minima were obtained by further processing the original graph and the MD data. We have found that both parallel and antiparallel aggregates are populated. The parallel aggregates with different alignment patterns are separated by nonnegligible free energy barriers. Multiroutes exist in the interstrand conformational reorganization. Most visited routes do not dominant the kinetics, while less visited routes contribute a little each but they are numerous and their total contributions are actually dominant. There are various kinds of reptation motions, including those through a beta-bulge, side-chain aided reptation, and flipping or rotation of a hairpin formed by one strand.     

Entropic effects on hydrated alkali-metal cations: infrared spectroscopy and ab initio calculations of M+(H2O)(x=2-5) cluster ions for M = Li, Na, K, and Cs

A delicate balance between competing and cooperating noncovalent interactions determines the three-dimensional structure of hydrated alkali-metal ion clusters. A critical factor influencing the balance reached is the internal energy content (or effective temperature) of the ion cluster. Cold cluster ions (approximately 50-150 K) have little internal energy, and enthalpic contributions have a greater influence on the relative population of low-lying minima. In clusters whose internal energy distributions correspond to temperatures approximately 250-500 K, entropic effects are expected to influence which structural isomers are present, favoring those where free energy has been minimized. Infrared photodissociation spectra of M(+)(H2O)(x=2-5) (approximately 250-500 K) are reported for M = Li, Na, K, and Cs to explore ion dependencies and entropic effects on the observed three-dimensional structure.     

Characterizing molecular motion in H2O and H3O+ with dynamical instability statistics

Sets of finite-time Lyapunov exponents characterize the stability and instability of classically chaotic dynamical trajectories. Here we show that their sample distributions can contain subpopulations identifying different types of dynamics. In small isolated molecules these dynamics correspond to distinct elementary motions, such as isomerizations. Exponents are calculated from constant total energy molecular dynamics simulations of H(2)O and H(3)O(+), modelled with a classical, reactive, all-atom potential. Over a range of total energy, exponent distributions for these systems reveal that phase space exploration is more chaotic near saddles corresponding to isomerization and less chaotic near potential energy minima. This finding contrasts with previous results for Lennard-Jones clusters, and is explained in terms of the potential energy landscape.     

Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver

An alternative strategy to find the minimal energy structure of nanoclusters is presented and implemented. We use it to determine the structure of metallic clusters. It consists in an unbiased search, with a global minimum algorithm: conformational space annealing. First, we find the minima of a many-body phenomenological potential to create a data bank of putative minima. This procedure assures us the generation of a set of cluster configurations of large diversity. Next, the clusters in this data bank are relaxed by ab initio techniques to obtain their energies and geometrical structures. The scheme is successfully applied to magic number 13 atom clusters of rhodium, palladium, and silver. We obtained minimal energy cluster structures not previously reported, which are different from the phenomenological minima. Moreover, they are not always highly symmetric, thus casting some doubt on the customary biased search scheme, which consists in relaxing with density functional theory global minima chosen among high symmetry structures obtained by means of phenomenological potentials.     

Chemical identification of icosahedral structure for cobalt and nickel clusters

Reactions of bare and hydrogenated cobalt and nickel clusters with ammonia and with water are used to determine cluster geometrical structure. Saturation measurements determine the total number of ammonia binding sites on cluster surfaces. A pattern of minima in the number of such sites is found to correlate with the sequence of closed shells and subshells expected for icosahedral packing in the 50- to 120-atom size range (50- to 200-atom range for hydrogenated clusters). In many cases there are 12 sites at the minima, the number that would be expected for preferred ammonia binding sites on closed (sub)shells of icosahedral clusters. The equilibrium adsorption of a single water molecule provides a sensitive measure of changes in cluster-water binding energy. A pattern of binding energy maxima is found, once again correlating with icosahedral structure, but for clusters having one metal atom more than the closed (sub)shells. In general, hydrogenation enhances the patterns of minima and maxima. These observations are explained in terms of the expected nature of ammonia and water binding to icosahedral clusters.     

Surveying a potential energy surface by eigenvector-following

We have developed a method to search potential energy surfaces which avoids some of the difficulties associated with trapping in local minima. Steps are directly taken between minima using eigenvector-following. Exploration of this space by low temperature Metropolis Monte Carlo is a useful global optimisation tool. This method successfully finds the lowest energy icosahedral minima of Lennard- Jones clusters from random starting configurations, but cannot find the global minimum in a reasonable time for difficult cases such as the 38-atom Lennard-Jones cluster where the face-centred-cubic truncated octahedron is lowest in energy. However, by performing searches at higher temperatures, we have found a pathway between the truncated octahedron and the lowest energy icosahedral minima. Such a pathway may be illustrative of some of the structural transformations that are observed for supported metal clusters by electron microscopy.     

Ar n HF van der Waals clusters revisited. I. New low-energy isomeric structures for n=6-13

New low-lying isomeric structures of Ar(n)HF clusters are reported for n=6-13. They were determined using simulated annealing and evolutionary programming, for pairwise additive intermolecular potential energy surfaces. New global minima were found for the clusters with n=7, 10, 11. The new lowest-energy structure of Ar(7)HF and several new local minima for n=6, 7 clusters have the HF bound on a threefold surface site, consistent with the recent spectroscopic data for Ar(n)HF clusters in helium nanodroplets. A new type of low-energy local minima were determined for n=9-13 clusters.     

Electron delocalization in trinuclear mixed-valence clusters

Possible trapped valence states in trimeric mixed-valence clusters are considered. The adiabatic potential in the space of a doubly-degenerate e vibration is calculated. Conditions under which minima with different electron distributions exist are determined. The coexistence of localized and delocalized distributions is possible.     

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.     

Global potential energy minima of C60(H2O)n clusters

Likely candidates for the global potential energy minima of C60(H2O)n clusters with n < or = 21 are found using basin-hopping global optimization. The potential energy surfaces are constructed using the TIP4P intermolecular potential for the water molecules, a Lennard-Jones water-fullerene potential, and a water-fullerene polarization potential, which depends on the first few nonvanishing C60 multipole polarizabilities. This combination produces a rather hydrophobic water-fullerene interaction. As a consequence, the water component of the lowest C60(H2O)n minima is quite closely related to low-lying minima of the corresponding TIP4P (H2O)n clusters. In most cases, the geometrical substructure of the water molecules in the C60(H2O)n global minimum coincides with that of the corresponding free water cluster. Exceptions occur when the interaction with C60 induces a change in geometry. This qualitative picture does not change significantly if we use the TIP3P model for the water-water interaction. Structures such as C60@(H2O)60, in which the water molecules surround the C60 fullerene, correspond to local minima with much higher potential energies. For such a structure to become the global minimum, the magnitude of the water-fullerene interaction must be increased to an unphysical value.     

H·(H2O)n clusters: microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm (GEGA)

A new version of the ab initio gradient embedded genetic algorithm (GEGA) program for finding the global minima on the potential energy surface (PES) of mixed clusters formed by molecules and atoms is reported. The performance of the algorithm is demonstrated on the neutral H·(H(2)O)(n) (n = 1-4) clusters, that is, a radical H atom solvated in 1-4 water molecules. These clusters are of a fundamental interest. The solvated hydrogen atom forms during photochemical events in water, or during scavenging of solvated electrons by acids, and transiently exists in biological systems and possibly in inclusion complexes in the deep ocean and in the ice shield of earth. The processes associated with its existence are intriguingly complex, however, and have been the subject of decades-long debates. Using GEGA, we explicate the apparently extreme structural diversity in the H·(H(2)O)(n) (n = 1-4) clusters. All considered clusters have four basic structural types: type I, where the H radical is weakly coordinated to the oxygen atom of one of the water molecules; type II, where H is weakly coordinated to a H atom of one of the water molecules; type III, consisting of H(2), the OH radical, and n - 1 H(2)O molecules; and type IV, consisting of H(3)O and n - 1 H(2)O. There are myriads of isomers of all four types. The lowest energy species of types I and II are the isoenergetic global minima. H·(H(2)O)(n) clusters appear to be a challenging case for GEGA because they have many shallow minima close in energy some of which are significantly less stable than the global minimum. Additionally, the global minima themselves have high structural degeneracy, they are only weakly bound, and they are prone to dissociation. GEGA performed exceptionally well in finding both the global and the low-energy local minima that were subsequently confirmed at higher levels of theory.     

Energy landscapes of ion clusters in isotropic quadrupolar and octupolar traps

The energy landscapes of ion clouds confined in isotropic quadrupolar and octupolar traps are characterized for several representative cluster sizes. All clusters exhibit stable multishell structures that belong to separate funnels. Quadrupolar confinement leads to more homogeneous clusters and denser distributions of isomers than octupolar confinement. Statistical analysis of the transition states indicates that the barriers associated with intrashell motion are lower but more asymmetric and more cooperative compared to intershell motion. The relaxation between low-energy funnels with different arrangements of shells mostly exhibits Arrhenius kinetics, with a weak variation of the activation energy at higher temperatures.     

Novel method for geometry optimization of molecular clusters: application to benzene clusters

A heuristic and unbiased method for searching optimal geometries of clusters of nonspherical molecules was constructed from the algorithm recently proposed for Lennard-Jones atomic clusters. In the method, global minima are searched by using three operators, interior, surface, and orientation operators. The first operator gives a perturbation on a cluster configuration by moving molecules near the center of mass of a cluster, and the second one modifies a cluster configuration by moving molecules to the most stable positions on the surface of a cluster. The moved molecules are selected by employing a contribution of the molecules to the potential energy of a cluster. The third operator randomly changes the orientations of all molecules. The proposed method was applied to benzene clusters. It was possible to find new global minima for (C6H6)11, (C6H6)14, and (C6H6)15. Global minima for (C6H6)16 to (C6H6)30 are first reported in this article.     

Density functional calculations of Ni5 and Ni6 clusters

Density functional calculations on the electronic structure and magnetic properties of Ni₅ and Ni₆ clusters are presented in this work. The geometry and spin state of clusters are optimized for several starting symmetries. Moreover, those calculations are followed by a vibrational analysis to discriminate between real minima and saddle-points on the potential energy surface of clusters. Equilibrium geometries, electronic configurations, binding energies, magnetic moments, and harmonic frequencies of stable Ni₅ and Ni₆ clusters are reported.     

A theoretical investigation on optimal structures of ethane clusters (C2H6)n with n ≤ 25 and their building-up principle

Geometry optimization of ethane clusters (C(2)H(6))(n) in the range of n ≤ 25 is carried out with a Morse potential. A heuristic method based on perturbations of geometries is used to locate global minima of the clusters. The following perturbations are carried out: (1) the molecule or group with the highest energy is moved to the interior of a cluster, (2) it is moved to stable positions on the surface of a cluster, and (3) orientations of one and two molecules are randomly modified. The geometry obtained after each perturbation is optimized by a quasi-Newton method. The global minimum of the dimer is consistent with that previously reported. The putative global minima of the clusters with 3 ≤ n ≤ 25 are first proposed and their building-up principle is discussed.     

Global optimization of binary Lennard-Jones clusters using three perturbation operators

Global optimization of binary Lennard-Jones clusters is a challenging problem in computational chemistry. The difficulty lies in not only that there are enormous local minima on the potential energy surface but also that we must determine both the coordinate position and the atom type for each atom and thus have to deal with both continuous and combinatorial optimization. This paper presents a heuristic algorithm (denoted by 3OP) which makes extensive use of three perturbation operators. With these operators, the proposed 3OP algorithm can efficiently move from a poor local minimum to another better local minimum and detect the global minimum through a sequence of local minima with decreasing energy. The proposed 3OP algorithm has been evaluated on a set of 96 × 6 instances with up to 100 atoms. We have found most putative global minima listed in the Cambridge Cluster Database as well as discovering 12 new global minima missed in previous research.     

Clever and efficient method for searching optimal geometries of lennard-jones clusters

An unbiased algorithm for determining global minima of Lennard-Jones (LJ) clusters is proposed in the present study. In the algorithm, a global minimum is searched by using two operators: one modifies a cluster configuration by moving atoms to the most stable positions on the surface of a cluster and the other gives a perturbation on a cluster configuration by moving atoms near the center of mass of a cluster. The moved atoms are selected by employing contribution of the atoms to the potential energy of a cluster. It was possible to find new global minima for LJ506, LJ521, LJ536, LJ537, LJ538, and LJ541 together with putative global minima of LJ clusters of 10-561 atoms reported in the literature. This indicates that the present method is clever and efficient for cluster geometry optimization.     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Efficiency of random search procedures along the silicon cluster series: Si(n) (n=5-10, 15, and 20)

The efficiency of the simplest isomeric search procedure consisting in random generation of sets of atomic coordinates followed by density functional theory geometry optimization is tested on the silicon cluster series (Si(5-10, 15, 20)). Criteria such as yield, isomer distributions and recurrences are used to clearly establish the performance of the approach with respect to increasing cluster size. The elimination of unphysical candidate structures and the use of distinct box shapes and theoretical levels are also investigated. For the smaller Si(n) (n=5-10) clusters, the generation of random coordinates within a spherical box is found to offer a reasonable alternative to more complex algorithms by allowing straightforward identification of every known low-lying local minima. The simple stochastic search of larger clusters (i.e. Si(15) and Si(20)) is however complicated by the exponentially increasing number of both low- and high-lying minima leading to rather arbitrary and non-comprehensive results.