A global optimization perspective on molecular clusters

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.

Toward an Ideal Particle Swarm Optimizer for Multidimensional Functions

The Particle Swarm Optimization (PSO) method is a global optimization technique based on the gradual evolution of a population of solutions called particles. The method evolves the particles based on both the best position of each of them in the past and the best position of the whole. Due to its simplicity, the method has found application in many scientific areas, and for this reason, during the last few years, many modifications have been presented. This paper introduces three modifications to the method that aim to reduce the required number of function calls while maintaining the accuracy of the method in locating the global minimum. These modifications affect important components of the method, such as how fast the particles change or even how the method is terminated. The above modifications were tested on a number of known universal optimization problems from the relevant literature, and the results were compared with similar techniques.

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.

Leading Interaction Components in the Structure and Reactivity of Noble Gases Compounds

The nature, strength, range and role of the bonds in adducts of noble gas atoms with both neutral and ionic partners have been investigated by exploiting a fine-tuned integrated phenomenological–theoretical approach. The identification of the leading interaction components in the noble gases adducts and their modeling allows the encompassing of the transitions from pure noncovalent to covalent bound aggregates and to rationalize the anomalous behavior (deviations from noncovalent type interaction) pointed out in peculiar cases. Selected adducts affected by a weak chemical bond, as those promoting the formation of the intermolecular halogen bond, are also properly rationalized. The behavior of noble gas atoms excited in their long-life metastable states, showing a strongly enhanced reactivity, has been also enclosed in the present investigation.

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

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.

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.

An assessment of the random-phase approximation functional and characteristics analysis for noncovalent cation-π interactions

The binding energy is of great importance in understanding the formation and stability of noncovalent interactions. However, the determination of the binding energy with high precision and efficiency in medium- and long-range noncovalent interactions is still challenging for quantum chemistry. Here, we assess the performance of random-phase approximation (RPA), a fully non-local fifth-rung of the Jacob ladder functional, in determining the binding energy of cation-π systems (cation = Li⁺, Na⁺, Be²⁺, Mg²⁺, Al⁺, and NH₄⁺; π = C₆H₆), which, to the best of our knowledge, has not been investigated. Using experimental results as the benchmark, we systematically compared the RPA method to the other ab initio methods (DFT/B3LYP, MP2, CCSD(T), and QCISD(T)) both in calculation accuracy and efficiency. From the perspective of accuracy, RPA is the best among these approaches, followed by the CCSD(T) and QCISD(T) methods. DFT/B3LYP and MP2 provide the worst accuracy. In addition, the computational efficiency of RPA is much faster than that of CCSD(T) and QCISD(T). We believe that RPA is a robust method for the precise description of medium- and long-range noncovalent interactions and is capable of providing benchmarking data. The interaction strength and interaction nature of cation-π systems are further analyzed by atoms in molecules (AIM) and the color-mapped reduced density gradient (RDG) isosurface, which are consistent with the characteristics of a typical cation-π interaction.

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'.