An Evolutionary Algorithm for the Global Optimization of Molecular Clusters: Application to Water, Benzene, and Benzene Cation

On assessing the carbon capture performance of graphynes with particle swarm optimization

Tackling climate change is one of the greatest challenges of current times and therefore the development of efficient technologies to limit anthropogenic emissions is of utmost urgency. Recent research towards this goal has alluded to the use of carbon-based solid sorbents for carbon capture. Graphynes (GYs), an interesting class of porous carbon membranes, have recently proven their potential as excellent membranes for gas adsorption and separation. Herein, we explored the CO2 and N2 adsorption characteristics and CO2/N2 selectivities of a class of GYs, namely γ-GY-1, γ-GY-2 and γ-GY-4. We investigated the putative global minimum geometries of adsorbed unary (n = 2-10) and binary (n : m; n, m ∈ [1, 8]) clusters of CO2 and N2 by employing a stochastic global optimization method called particle swarm optimization in conjunction with empirical intermolecular force field formulations. The intervening interactions are modeled using various pairwise potentials, including Lennard-Jones potential, improved Lennard-Jones potential, Buckingham potential and Coulombic potential. The binding energies for both unary and binary clusters are highest for adsorption on γ-GY-1, followed by γ-GY-2. The putative global minimum geometries suggested that N2 molecules preferred binding over the pore centres while CO2 molecules showed higher clustering propensity than any binding site preference. The predicted interaction energies suggested higher selectivity for CO2 over N2 for all the three γ-GYs.

Energetics and spectroscopic studies of CNO (-) (H 2 O) n $$ {\mathbf{CNO}}^{\left(\hbox{-} \right)}{\left({\mathbf{H}}_{\mathbf{2}}\mathbf{O}\right)}_{\mathbf{n}} $$ clusters and the temperature dependencies of the isomers: An approach based on a combined recipe of parallel tempering and quantum chemical methods

A system associated with several number of weak interactions supports numerous number of stable structures within a narrow range of energy. Often, a deterministic search method fails to locate the global minimum geometry as well as important local minimum isomers for such systems. Therefore, in this work, the stochastic search technique, namely parallel tempering, has been executed on the quantum chemical surface of theCNO (-) (H 2 O) n $$ {\mathrm{CNO}}^{\left(\hbox{-} \right)}{\left({\mathrm{H}}_2\mathrm{O}\right)}_n $$ system forn = 1 $$ n=1 $$ -8 to generate global minimum as well as several number of local minimum isomers. IR spectrum can act as the fingerprint property for such system to be identified. Thus, IR spectroscopic features have also been included in this work. Vertical detachment energy has also been calculated to obtain clear information about number of water molecules in several spheres around the central anion. In addition, in a real experimental scenario, not only the global but also the local minimum isomers play an important role in determining the average value of a particular physically observable property. Therefore, the relative conformational populations have been determined for all the evaluated structures for the temperature range between 20K and 400K. Further to understand the phase change behavior, the configurational heat capacities have also been calculated for different sizes.

Mechanism of ionic dissociation of HCl in the smallest water clusters

The dissociation of strong acids into water is a fundamental process in chemistry and biology. Determining the minimum number of water molecules that can result in an ionic dissociation of hydrochloric acid (HCl → H+ + Cl-) remains a challenging subject. In this study, the reactions of H2O with HCl(H2O)n-1 (HCl-H2O cluster), i.e., HCl(H2O)n-1 + H2O (n = 3-7), were investigated by using the direct ab initio molecular dynamics (AIMD) method. Direct AIMD calculations were performed to set the collision energy of H2O to zero for all trajectories. For n = 3, no reaction occurred. In contrast, HCl dissociated to H+ + Cl- at n = 4, forming a contact ion pair (cIP) and solvent-separated ion pair (ssIP) as products. The reactions were expressed as HCl(H2O)3 + H2O → H3O+(H2O)2Cl- (ssIP), and HCl(H2O)3 + H2O → H3O+(Cl-)(H2O)2 (cIP). The ion pair (IP) products were dependent on the collision site of H2O relative to HCl(H2O)3. For n = 5-7, both IPs were formed through the reaction between H2O and HCl(H2O)n-1 (n = 5-7). The reaction between HCl and (H2O)4 (HCl + (H2O)4 → HCl(H2O)4) was non-reactive in IP formation. The reaction mechanism was discussed based on the theoretical results.

Monte Carlo-Simulated Annealing and Machine Learning-Based Funneled Approach for Finding the Global Minimum Structure of Molecular Clusters

Understanding the physical underpinnings and geometry of molecular clusters is of great importance in many fields, ranging from studying the beginning of the universe to the formation of atmospheric particles. To this end, several approaches have been suggested, yet identifying the most stable cluster geometry (i.e., global potential energy minimum) remains a challenge, especially for highly symmetric clusters. Here, we suggest a new funneled Monte Carlo-based simulated annealing (SA) approach, which includes two key steps: generation of symmetrical clusters and classification of the clusters according to their geometry using machine learning (MCSA-ML). We demonstrate the merits of the MCSA-ML method in comparison to other approaches on several Lennard-Jones (LJ) clusters and four molecular clusters-Ser8(Cl-)2, H+(H2O)6, Ag+(CO2)8, and Bet4Cl-. For the latter of these clusters, the correct structure is unknown, and hence, we compare the experimental and simulated fragmentation patterns, and the fragmentation of the proposed global minimum matches experiments closely. Additionally, based on the fragmentation of the predicted betaine cluster, we were able to identify hitherto unknown neutral fragmentation channels. In comparison to results obtained with other methods, we demonstrated a superior ability of MCSA-ML to predict clusters with high symmetry and similar abilities to predict clusters with asymmetrical structures.

Combined molecular dynamics and coordinate driving method for automatically searching complicated reaction pathways

The combined molecular dynamics and coordinate driving (MD/CD) method is updated and generalized in this work to broaden its applications in automatically searching reaction pathways for complicated reactions. In this updated version, MD simulations are performed with the GFN's family of methods to systematically sample conformers for almost any systems with atomic numbers Z ≤ 86. The improved CD procedure is greatly accelerated by applying a pre-screening stage at the semiempirical GFN2-xTB level. An automatic module based on the Marcus theory and its improved version (the Wolynes theory) is designed to include single electron transfer (SET) processes into reaction pathways. The capabilities of this method are demonstrated by exploring the most possible reaction pathways of three experimentally reported reactions: the organophosphine-catalyzed trans phosphinoboration, the Fe(II) complex-mediated C(sp2)-H borylation reaction, and the SET-triggered deaminative radical cross-coupling reaction. Comprehensive reaction networks are obtained for all three reactions with reasonable computational costs. Detailed mechanisms for these reactions can account for the reported experimental facts.

GAMaterial-A genetic-algorithm software for material design and discovery

Genetic algorithms (GAs) are stochastic global search methods inspired by biological evolution. They have been used extensively in chemistry and materials science coupled with theoretical methods, ranging from force-fields to high-throughput first-principles methods. The methodology allows an accurate and automated structural determination for molecules, atomic clusters, nanoparticles, and solid surfaces, fundamental to understanding chemical processes in catalysis and environmental sciences, for instance. In this work, we propose a new genetic algorithm software, GAMaterial, implemented in Python3.x, that performs global searches to elucidate the structures of atomic clusters, doped clusters or materials and atomic clusters on surfaces. For all these applications, it is possible to accelerate the GA search by using machine learning (ML), the ML@GA method, to build subsequent populations. Results for ML@GA applied for the dopant distributions in atomic clusters are presented. The GAMaterial software was applied for the automatic structural search for the Ti₆ O₁₂ cluster, doping Al in Si₁₁ (4Al@Si₁₁ ) and Na₁₀ supported on graphene (Na₁₀ @graphene), where DFTB calculations were used to sample the complex search surfaces with reasonably low computational cost. Finally, the global search by GA of the Mo₈ C₄ cluster was considered, where DFT calculations were made with the deMon2k code, which is interfaced with GAMaterial.

How solvent determines the molecular reactive conformation and the selectivity: Solvation spheres and energy

In solution, the solvent determines the molecular conformation and the chemical reaction viability and selectivity. When solvent-solute and solvent-solvent interactions present similar strengths, explicit salvation is the best way to describe a system. The problem to solve is how big the explicit shell should be. In this paper, we want to answer one of the fundamental questions in the implementation of explicit solvation, exactly how many solvent molecules should be added and where they should be placed. Here we determine the first solvent sphere around a molecule and describe how it controls the conformation and selectivity of a selected reaction. NMR experiments were carried out to identify the number of solvent molecules around the solute that constitutes the first solvent sphere, and the interaction between this solvent sphere and the solute was detected using DFT and QTAIM calculations. A new approach to the solvation energy is presented. Finally, we established the role of solvent molecules in the conformation of the solute and in the transition states that produce the two possible products of the reaction.

A new active learning approach for adsorbate-substrate structural elucidation in silico

Adsorbate interactions with substrates (e.g. surfaces and nanoparticles) are fundamental for several technologies, such as functional materials, supramolecular chemistry, and solvent interactions. However, modeling these kinds of systems in silico, such as finding the optimum adsorption geometry and energy, is challenging, due to the huge number of possibilities of assembling the adsorbate on the surface. In the current work, we have developed an artificial intelligence (AI) approach based on an active learning (AL) method for adsorption optimization on the surface of materials. AL uses machine learning (ML) regression algorithms and their uncertainties to make a decision (based on a policy) for the next unexplored structures to be computed, increasing, though, the probability of finding the global minimum with a small number of calculations. The methodology allows an accurate and automated structural elucidation of the adsorbate on the surface, based on the minimization of the total electronic energy. The new AL method for adsorption optimization was developed and implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial) program and was applied for C₆₀@TiO₂ anatase (101). It marks another software extension with a new feature in addition to the automatic structural elucidation of defects in materials and of nanoparticles as well. SCC-DFTB calculations were used to build the complex search surfaces with a reasonably low computational cost. An artificial neural network (NN) was employed in the AL framework evaluated together with two uncertainty quantification methods: K-fold cross-validation and non-parametric bootstrap (BS) resampling. Also, two different acquisition functions for decision-making were used: expected improvement (EI) and the lower confidence bound (LCB).

Integration of theory, simulation, artificial intelligence and virtual reality: a four-pillar approach for reconciling accuracy and interpretability in computational spectroscopy

The established pillars of computational spectroscopy are theory and computer based simulations. Recently, artificial intelligence and virtual reality are becoming the third and fourth pillars of an integrated strategy for the investigation of complex phenomena. The main goal of the present contribution is the description of some new perspectives for computational spectroscopy, in the framework of a strategy in which computational methodologies at the state of the art, high-performance computing, artificial intelligence and virtual reality tools are integrated with the aim of improving research throughput and achieving goals otherwise not possible. Some of the key tools (e.g., continuous molecular perception model and virtual multifrequency spectrometer) and theoretical developments (e.g., non-periodic boundaries, joint variational-perturbative models) are shortly sketched and their application illustrated by means of representative case studies taken from recent work by the authors. Some of the results presented are already well beyond the state of the art in the field of computational spectroscopy, thereby also providing a proof of concept for other research fields.

Application of Optimization Algorithms in Clusters

The structural characterization of clusters or nanoparticles is essential to rationalize their size and composition-dependent properties. As experiments alone could not provide complete picture of cluster structures, so independent theoretical investigations are needed to find out a detail description of the geometric arrangement and corresponding properties of the clusters. The potential energy surfaces (PES) are explored to find several minima with an ultimate goal of locating the global minima (GM) for the clusters. Optimization algorithms, such as genetic algorithm (GA), basin hopping method and its variants, self-consistent basin-to-deformed-basin mapping, heuristic algorithm combined with the surface and interior operators (HA-SIO), fast annealing evolutionary algorithm (FAEA), random tunneling algorithm (RTA), and dynamic lattice searching (DLS) have been developed to solve the geometrical isomers in pure elemental clusters. Various model or empirical potentials (EPs) as Lennard-Jones (LJ), Born-Mayer, Gupta, Sutton-Chen, and Murrell-Mottram potentials are used to describe the bonding in different type of clusters. Due to existence of a large number of homotops in nanoalloys, genetic algorithm, basin-hopping algorithm, modified adaptive immune optimization algorithm (AIOA), evolutionary algorithm (EA), kick method and Knowledge Led Master Code (KLMC) are also used. In this review the optimization algorithms, computational techniques and accuracy of results obtained by using these mechanisms for different types of clusters will be discussed.

Aggregation of coronene: the effect of carboxyl and amine functional groups

The aggregation of coronene is relevant to understand the formation of carbon nanomaterials, including graphene quantum dots (GQDs) that show exceptional photophysical properties. This article evaluates the influence of carboxyl and amine substituting groups on the aggregation of coronene by performing a global optimization study based on a new potential energy surface. The structures of clusters with substituted coronene are similar to those formed by un-substituted monomers, that is, stacked (non-stacked) motifs are favoured for small-size (large-size) clusters. Nonetheless, the presence of carboxyl and amine groups leads to an increase of the number of local minima of comparable energy. The clusters with substituted monomers have also shown to enhance the attractive component interaction, which can be attributed to weak induction and charge transfer effects and to stronger electrostatic contributions. Moreover, the calculated height of magic-number structures of the clusters in this work is compatible with the morphology of the GQDs reported in the literature.

Modeling microsolvation clusters with electronic-structure calculations guided by analytical potentials and predictive machine learning techniques

We propose a new methodology to study, at the density functional theory (DFT) level, the clusters resulting from the microsolvation of alkali-metal ions with rare-gas atoms. The workflow begins with a global optimization search to generate a pool of low-energy minimum structures for different cluster sizes. This is achieved by employing an analytical potential energy surface (PES) and an evolutionary algorithm (EA). The next main stage of the methodology is devoted to establish an adequate DFT approach to treat the microsolvation system, through a systematic benchmark study involving several combinations of functionals and basis sets, in order to characterize the global minimum structures of the smaller clusters. In the next stage, we apply machine learning (ML) classification algorithms to predict how the low-energy minima of the analytical PES map to the DFT ones. An early and accurate detection of likely DFT local minima is extremely important to guide the choice of the most promising low-energy minima of large clusters to be re-optimized at the DFT level of theory. In this work, the methodology was applied to the Li+Krn (n = 2-14 and 16) microsolvation clusters for which the most competitive DFT approach was found to be the B3LYP-D3/aug-pcseg-1. Additionally, the ML classifier was able to accurately predict most of the solutions to be re-optimized at the DFT level of theory, thereby greatly enhancing the efficiency of the process and allowing its applicability to larger clusters.

Sphere Encapsulated Monte Carlo: Obtaining Minimum Energy Configurations of Large Aromatic Systems

We introduce a simple global optimization approach that is able to find minimum energy configurations of clusters containing aromatic molecules. The translational and rotational perturbations required in Monte Carlo-based methods often lead to unrealistic configurations within which two or more molecular rings intersect, causing many of the computational steps to be rejected and the optimization process to be inefficient. Here we develop a modification of the basin-hopping global optimization procedure tailored to tackle problems with intersecting molecular rings. Termed the Sphere Encapsulated Monte Carlo (SEMC) method, this method introduces sphere-based rearrangement and minimization steps at each iteration, and its performance is shown through the exploration of potential energy landscapes of polycyclic aromatic hydrocarbon (PAH) clusters, systems of interest in combustion and astrophysics research. The SEMC method provides clusters that are accurate to 5% mean difference of the minimum energy at a 10-fold speed up compared to previous work using advanced molecular dynamics simulations. Importantly, the SEMC method captures key structural characteristics and molecular size partitioning trends as measured by the molecular radial distances and coordination numbers. The advantages of the SEMC method are further highlighted in its application to previously unstudied heterogeneous PAH clusters.

Aggregation enhancement of coronene molecules by seeding with alkali-metal ions

Microsolvation constitutes the first step in the formation of cluster structures of molecules that surround a solute in the bulk and it allows for a deep insight into the relationship between the structure of the solvation shells and other physical properties. We propose semiempirical potential energy functions that are able to describe the interaction between K+ or Cs+ with coronene. Such functions were calibrated through the comparison with accurate estimations of the interaction between the cation and the planar hydrocarbon, obtained by means of ab initio electronic-structure calculations. By employing the potential energy functions and an evolutionary algorithm (EA), we have investigated the structure and energetics of the clusters resulting from the microsolvation of either K+ or Cs+ with coronene molecules. The reliability of the results for smaller clusters was checked by performing geometry re-optimization exploiting a suitable DFT level of theory. This has allowed for the characterization of the first solvation shells of planar molecules of coronene around an alkali-metal ion. It has also been found that the presence of metal ion impurities considerably enhances the formation of small coronene clusters leading to much stronger binding energies for heterogeneous with respect to homogeneous aggregates. These clusters could represent relevant species involved in the early stages of soot nucleation.

Two-level stochastic search of low-energy conformers for molecular spectroscopy: implementation and validation of MM and QM models

The search for stationary points in the molecular potential energy surfaces (PES) is a problem of increasing relevance in molecular sciences especially for large, flexible systems featuring several large-amplitude internal motions.

Role of the vibrational contribution in Coulomb explosion of dicationic neon gas clusters: a parallel tempering based study

The problem of Coulomb explosion in dicationic neon gas clusters has been investigated with special emphasis on the role of the vibrational contribution. The problem has been handled by describing the dicationic neon gas system with an adequate potential energy surface comprising dispersive interaction, Coulombic and polarizability containing terms. This potential energy surface, if explored for various sizes of the clusters, shows Coulombic explosion features below a certain threshold size. However this classical treatment fails to account for the correct threshold predicted from other studies including experiments. This signifies that quantum effects play an important role. With the incorporation of the vibrational contribution as the quantum effect, it is seen that reduction in the threshold value indeed occurs and the amount of decrease significantly varies with temperature. The whole study has been done using the stochastic search strategy or parallel tempering to explore the potential energy surface of the system. The stochastic strategy guarantees the achievement of a low energy solution as it is not stuck in local energy basins.

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.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.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'.

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'.

An adaptive mutation simulated annealing based investigation of Coulombic explosion and identification of dissociation patterns in (CO2)n2+ clusters

In this communication, we would like to discuss the advantages of adaptive mutation simulated annealing (AMSA) over standard simulated annealing (SA) in studying the Coulombic explosion of (CO₂)_n²⁺ clusters for n = 20–68, where ‘n’ is the size of the cluster.

An investigation on the structure, spectroscopy and thermodynamic aspects of Br2((-))(H2O)n clusters using a conjunction of stochastic and quantum chemical methods

In this work we obtained global as well as local structures of Br2((-))(H2O)n clusters for n = 2 to 6 followed by the study of IR-spectral features and thermochemistry for the structures. The way adopted by us to obtain structures is not the conventional one used in most cases. Here we at first generated excellent quality pre-optimized structures by exploring the suitable empirical potential energy surface using stochastic optimizer simulated annealing. These structures are then further refined using quantum chemical calculations to obtain the final structures, and spectral and thermodynamic features. We clearly showed that our approach results in very quick and better convergence which reduces the computational cost and obviously using the strategy we are able to get one [i.e. global] or more than one [i.e. global and local(s)] energetically lower structures than those which are already reported for a given cluster size. Moreover, IR-spectral results and the evolutionary trends in interaction energy, solvation energy and vertical detachment energy for global structures of each size have also been presented to establish the utility of the procedure employed.

Low-energy structures of benzene clusters with a novel accurate potential surface

The benzene-benzene (Bz-Bz) interaction is present in several chemical systems and it is known to be crucial in understanding the specificity of important biological phenomena. In this work, we propose a novel Bz-Bz analytical potential energy surface which is fine-tuned on accurate ab initio calculations in order to improve its reliability. Once the Bz-Bz interaction is modeled, an analytical function for the energy of the Bzn clusters may be obtained by summing up over all pair potentials. We apply an evolutionary algorithm (EA) to discover the lowest-energy structures of Bzn clusters (for n=2-25), and the results are compared with previous global optimization studies where different potential functions were employed. Besides the global minimum, the EA also gives the structures of other low-lying isomers ranked by the corresponding energy. Additional ab initio calculations are carried out for the low-lying isomers of Bz3 and Bz4 clusters, and the global minimum is confirmed as the most stable structure for both sizes. Finally, a detailed analysis of the low-energy isomers of the n = 13 and 19 magic-number clusters is performed. The two lowest-energy Bz13 isomers show S6 and C3 symmetry, respectively, which is compatible with the experimental results available in the literature. The Bz19 structures reported here are all non-symmetric, showing two central Bz molecules surrounded by 12 nearest-neighbor monomers in the case of the five lowest-energy structures.

Phase changes of the water hexamer and octamer in the gas phase and adsorbed on polycyclic aromatic hydrocarbons

We investigate thermodynamic properties of small water clusters adsorbed on polycyclic aromatic hydrocarbons (PAHs), which are relevant systems in the context of astrophysical and atmospheric chemistry. We present heat capacity curves computed from parallel-tempering molecular dynamics and Monte Carlo simulations that were performed using the self-consistent-charge density-functional based tight-binding method. These curves are characteristic of the phase changes occurring in the aggregates and provide useful information on the evolution of the interaction between the water molecules and the PAHs as a function of temperature. After benchmarking our approach on the water hexamer and octamer in the gas phase, we present some results for these same clusters adsorbed on coronene and circumcoronene. When compared to the curves obtained for the isolated water clusters, the phase change temperature significantly decreases for the (H2O)8-PAH clusters whereas it depends on the nature of the PAH in the case of the hexamer. We analyse these differences as connected to the relative energies of the optimized characteristic isomers and to their dynamical behavior. We also evidence the population changes of the various cluster isomers as a function of temperature.

Exploring energy landscapes: from molecular to mesoscopic systems

We review a comprehensive computational framework to survey the potential energy landscape for systems composed of rigid or partially rigid molecules. Illustrative case studies relevant to a wide range of molecular clusters and soft and condensed matter systems are discussed.

Microsolvation of the potassium ion with aromatic rings: comparison between hexafluorobenzene and benzene

We employ a recently developed methodology to study structural and energetic properties of the first solvation shells of the potassium ion in nonpolar environments due to aromatic rings, which is important to understand the selectivity of several biochemical phenomena. Our evolutionary algorithm is used in the global optimization study of clusters formed of K(+) solvated with hexafluorobenzene (HFBz) molecules. The global intermolecular interaction for these clusters has been decomposed in HFBz-HFBz and in K(+)-HFBz contributions, using a potential model based on different decompositions of the molecular polarizability of hexafluorobenzene. Putative global minimum structures of microsolvation clusters up to 21 hexafluorobenzene molecules were obtained and compared with the analogous K(+)-benzene clusters reported in our previous work (J. Phys. Chem. A 2012, 116, 4947-4956). We have found that both K(+)-(Bz)n and K(+)-(HFBz)n clusters show a strong magic number around the closure of the first solvation shell. Nonetheless, all K(+)-benzene clusters have essentially the same first solvation shell geometry with four solvent molecules around the ion, whereas the corresponding one for K(+)-(HFBz)n is completed with nine HFBz species, and its structural motif varies as n increases. This is attributed to the ion-solvent interaction that has a larger magnitude for K(+)-Bz than in the case of K(+)-HFBz. In addition, the ability of having more HFBz than Bz molecules around K(+) in the first solvation shell is intimately related to the inversion in the sign of the quadrupole moment of the two solvent species, which leads to a distinct ion-solvent geometry of approach.

Competitive role of CH4-CH4 and CH-π interactions in C6H6-(CH4)n aggregates: the transition from dimer to cluster features

The intermolecular methane-methane and benzene (Bz)-methane interactions formulated in this paper are suitable to investigate systems of increasing complexity. The proposed CH(4)-CH(4) and Bz-CH(4) potential energy functions are indeed applied to study some macroscopic properties of methane and important features of both small Bz-(CH(4))(n) (n > 1-10) clusters and Bz surrounded by several CH(4) molecules. Relevant parameters of the interaction, derived from molecular polarizability components, have been proved to be useful to describe in a consistent way both size repulsion and dispersion attraction forces. The proposed potential model also allows one to isolate the role of the different intermolecular energy contributions. The spatial distribution of the CH(4) molecules in the clusters is investigated by means of molecular dynamics simulations under various conditions, even when methane phase transition from liquid to gas is likely to occur. In addition, several properties, such as radial distribution functions, density values, and mean diffusion coefficients, are analyzed in detail.

Alkali-ion microsolvation with benzene molecules

The target of this investigation is to characterize by a recently developed methodology, the main features of the first solvation shells of alkaline ions in nonpolar environments due to aromatic rings, which is of crucial relevance to understand the selectivity of several biochemical phenomena. We employ an evolutionary algorithm to obtain putative global minima of clusters formed with alkali-ions (M(+)) solvated with n benzene (Bz) molecules, i.e., M(+)-(Bz)(n). The global intermolecular interaction has been decomposed in Bz-Bz and in M(+)-Bz contributions, using a potential model based on different decompositions of the molecular polarizability of benzene. Specifically, we have studied the microsolvation of Na(+), K(+), and Cs(+) with benzene molecules. Microsolvation clusters up to n = 21 benzene molecules are involved in this work and the achieved global minimum structures are reported and discussed in detail. We observe that the number of benzene molecules allocated in the first solvation shell increases with the size of the cation, showing three molecules for Na(+) and four for both K(+) and Cs(+). The structure of this solvation shell keeps approximately unchanged as more benzene molecules are added to the cluster, which is independent of the ion. Particularly stable structures, so-called "magic numbers", arise for various nuclearities of the three alkali-ions. Strong "magic numbers" appear at n = 2, 3, and 4 for Na(+), K(+), and Cs(+), respectively. In addition, another set of weaker "magic numbers" (three per alkali-ion) are reported for larger nuclearities.