We have developed an evolutionary algorithm (EA) for the global minimum search of molecular clusters. The EA is able to discover all the putative global minima of water clusters up to (H(2)O)(20) and benzene clusters up to (C(6)H(6))(30). Then, the EA was applied to search for the global minima structures of (C(6)H(6))(n)(+) with n = 2-20, some of which were theoretically studied for the first time. Our results for n = 2-6 are consistent with previous theoretical work that uses a similar interaction potential. Excluding the very symmetric global minimum structure for n = 9, the growth pattern of (C(6)H(6))(n)(+) with n ≥ 7 involves the (C(6)H(6))(2)(+) dimer motif, which is placed off-center in the cluster. Such observation indicates that potentials commonly used in the literature for (C(6)H(6))(n)(+) cannot reproduce the icosahedral-type packing suggested by the available experimental data.

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.

We extend the scope of a recent method for superimposing two molecules ( J. Chem. Phys. 2009, 131, 124126-1-124126-10 ) to include the identification of chiral structures. This methodology is tested by applying it to several organic molecules and water clusters that were subjected to geometry optimization. The accuracy of four simpler, non-superimposing approaches is then analyzed by comparing pairs of structures for argon and water clusters. The structures considered in this work were obtained by a Markovian walk in the coordinate space. First, a random geometry is generated, and then, the iterative application of a mutation operator ensures the creation of increasingly dissimilar structures. The discriminating power of the non-superimposing approaches is tested by comparing the corresponding dissimilarity measures with the root-mean-square distance obtained from the superimposing method. Finally, we showcase the application of those methods to characterize the diversity of solutions in global geometry optimization by evolutionary algorithms.

This investigation uses a recent methodology, essentially based on our evolutionary algorithm (EA) to get new insights about the energetics and structure of the first solvation shells of lithium ion in polar solvents that form important hydrogen bonds. We employed the EA to search for the low-energy structures of the Li + (H 2 O) n and Li + (CH 3 OH) n clusters (with n 6 20) as modeled by commonly used rigid nonpolarizable force-field potentials. Particular emphasis is given to the characterization of the putative global minima; for Li + (H 2 O) 17 , the EA discovered a new global minimum with five water molecules directly coordinating the ion. Smaller-size clusters were, then, re-optimized by employing electronicstructure methods, namely, DFT (with the B3LYP functional and both the 6-31+G ⁄ and 6-311+G ⁄⁄ basis sets) and MP2 (with the aug-cc-pVDZ basis set). In the case of Li + (H 2 O) n , the ab initio global minimum structures are similar to those obtained with the EA up to n = 10. However, for n = 17, the structure of the global minimum discovered by the EA is different from the lowest-energy cluster obtained after re-optimization at the MP2/augcc-pVDZ level of theory. Such energy reorder may be attributed to the water-water interaction. As for the Li + (CH 3 OH) n clusters, the re-optimization process leads more often to a reorder in the energy of the minimum structures. Thus, forfluxional clusters like the Li + (CH 3 OH) n ones that show a huge number of stationary configurations within a small energy window, it is mandatory to carefully choose various structures, besides the global minimum, to be re-optimized at the ab initio or DFT levels. Due to the difficulty on choosing adequate departing structures by the usually employed chemical intuition, we noticed that some low-energy minima (including the global one) of even small Li + (CH 3 OH) n clusters were missed in literature. We showcase this problem in the Li + (CH 3 OH) 6 cluster, whose vibrational frequencies in the CO stretching region and corresponding infrared intensities were calculated at the DFT level of theory and compared with previously reported results.

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 Ca 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'.