Li6 E5 Li6 : Tetrel Sandwich Complexes with 10-π-Electrons.

When (4n +2) π-electrons are located in single planar ring, it conventionally qualifies as aromatic. According Hückel's rule, systems possessing ten π-electrons should be aromatic. Herein we report a series of D5h  Li6 E5 Li6 sandwich structures, representing the first global minima featuring ten π-electrons E5 10- ring (E=Si-Pb). However, these π-electrons localize as five π-lone-pairs rather than delocalized orbitals. The high symmetry structure achieved is a direct consequence of σ-aromaticity, particularly favored in elements from Si to Pb, resulting in a pronounced diatropic ring current flow that contributes to the enhanced stability of these systems.

Aromaticity and Magnetic Behavior in Benzenoids: Unraveling Ring Current Combinations.

Nowadays, an active research topic is the connection between Clar's rule, aromaticity, and magnetic properties of polycyclic benzenoid hydrocarbons. In the present work, we employ a meticulous magnetically induced current density analysis to define the net current flowing through any cyclic circuit, connecting it to aromaticity based on the ring current concept. Our investigation reveals that the analyzed polycyclic systems display a prominent global ring current, contrasting with subdued semi-local and local ring currents. These patterns align with Clar's aromatic π-sextets only in cases where migrating π-sextet structures are invoked. The results of this study will enrich our comprehension of aromaticity and magnetic behavior in such systems, offering significant insights into coexisting ring current circuits in these systems.

Exploration of the potential energy surface in mixed Zintl clusters applying an automatic Johnson polyhedra generator: the case of arachno E6M24- (E = Si, Ge, Sn; M = Sb, Bi).

A new algorithm called Automatic Johnson Cluster Generator (AJCG) is presented, which, as its name indicates, allows the definition of the desired Johnson polyhedron to subsequently carry out all the possible permutations between the atoms that form this polyhedron. This new algorithm allows the exhaustive study of the structures' potential energy surface (PES). In addition, the AJCG algorithm is helpful for the study of three-dimensional compounds such as boranes or Zintl clusters and their structural derivatives with two or more different atoms. The automatic filling of vertices is particularly useful in mixed compounds because of the possibility of taking into account all possible configurations in the structure. As a test system, we investigated the arachno-type E6M24- (E = Si, Ge, Sn; M = Sb, Bi) structure which has eight vertices and complies with Wade-Mingos rules. Initially, we defined a bipyramidal structure (10 vertices), and filled the vertices with the atoms in all possible configurations. Since the selected system has eight atoms, the two remaining vertices were filled with pseudo atoms to complete the structure. After re-optimizing the initial population generated with AJCG, a large number of isomers with energy below 10 kcal mol-1 are identified. These results show that the most stable isomers possess homonuclear M-M bonds, except Sn6Bi24-. Although the overall putative minima differ at the PBE0-D3 and DLPNO-CCSD(T) levels, they are always competitive minima. In addition to using high-precision methodologies to correctly study relative energies, applying solvent effects in highly charged systems becomes mandatory. The aromatic character of these studied systems was demonstrated qualitatively with two- and three-dimensional mapping and quantitatively by calculating the value of the z-component of the induced magnetic field at the cage center, including scalar and spin-orbit correction for relativistic effects. The compounds studied have a high degree of aromaticity, which allows us to establish that despite structural modifications (i.e., from closo to arachno), the aromaticity is preserved.

Revisiting the potential-energy surface of CnBe3n+2H2n+22+ (n = 2-4) clusters: are planar pentacoordinate carbon structures the global minima?

Using various exploration strategies, in this study, we investigated the potential energy surfaces (PES) of CBe5H5+ and CnBe3n+2H2n+22+ (n = 2-4) clusters. Previous studies proposed that the planar pentacoordinate carbons (ppCs) were the global minima of these clusters. However, our study identified new putative global minima and competitive isomers, refuting some previous assignments. We employed several methods, including evolutive-inspired stochastic approaches guided by "chemical criteria", and ab initio molecular dynamics simulations at elevated temperatures. Our results showed that the size of the scanned population significantly affected the evolutive method and that constrained or guided procedures showed an advantage in identifying better minima for larger systems. This study demonstrated that using multiple complementary strategies can result in a wider variety of minima in a given energy range. Our findings provide valuable insights into exploring the potential energy surfaces of clusters, mainly medium-sized clusters, which could be the connections between small clusters and nanomaterials.

E6C15 (E = Si-Pb): polycyclic aromatic compounds with three planar tetracoordinate carbons.

A systematic exploration of the potential energy surface reveals two global minima with three planar tetra coordinate carbons (ptCs) and two global minima with three quasi-ptCs for E6C15 (E = Si-Pb) combinations. These consist of aromatic polycyclic templates suitable for further design of different materials without hindering the ptC texture.

Bowl-shaped Cluster CuB12 - : A Viable Global Minimum with Twofold Aromaticity.

A low-lying structure is revealed for the CuB12 - cluster, which is bowl-shaped. It consists of a triangular CuB2 base and a B10 rim. Molecular dynamics simulations indicates its structural robustness; at an elevated temperature (600 K), the base rotates reversibly within the B10 perimeter. Chemical bonding analysis detects 2σ- and 3π-delocalized bonds, suggesting double aromaticity. This is also confirmed by two diatropic and concentric ring currents under an external magnetic field.

Why an integrated approach between search algorithms and chemical intuition is necessary?

Though search algorithms are appropriate tools for identifying low-energy isomers, fixing several constraints seems to be a fundamental prerequisite to successfully running any structural search program. This causes some potential setbacks as far as identifying all possible isomers, close to the lowest-energy isomer, for any elemental composition. The number of explored candidates, the choice of method, basis set, and availability of CPU time needed to analyze the various initial test structures become necessary restrictions in resolving the issues of structural isomerism reasonably. While one could arrive at new structures through chemical intuition, reproducing or achieving those exact same structures requires increasing the number of variables in any given program, which causes further constraints in exploring the potential energy surface in a reasonable amount of time. Thus, it is emphasized here that an integrated approach between search algorithms and chemical intuition is necessary by taking the C12O2Mg2 system as an example. Our initial search through the AUTOMATON program yielded 1450 different geometries. However, through chemical intuition, we found eighteen new geometries within 40.0 kcal mol-1 at the PBE0-D3/def2-TZVP level. These results indirectly emphasize that an integrated approach between search algorithms and chemical intuition is necessary to further our knowledge in chemical space for any given elemental composition.

Planar Elongated B12 Structure in M3B12 Clusters (M = Cu-Au).

Here, it is shown that the M3B12 (M = Cu-Au) clusters' global minima consist of an elongated planar B12 fragment connected by an in-plane linear M3 fragment. This result is striking since this B12 planar structure is not favored in the bare cluster, nor when one or two metals are added. The minimum energy structures were revealed by screening the potential energy surface using genetic algorithms and density functional theory calculations. Chemical bonding analysis shows that the strong electrostatic interactions with the metal compensate for the high energy spent in the M3 and B12 fragment distortion. Furthermore, metals participate in the delocalized π-bonds, which infers an aromatic character to these species.

Planar Hypercoordinate Carbons in Alkali Metal Decorated CE3 2- and CE2 2- Dianions.

After exploring the potential energy surfaces of Mm CE2 p (E=S-Te, M=Li-Cs, m=2, 3 and p=m-2) and Mn CE3 q (E=S-Te, M=Li-Cs, n=1, 2, q=n-2) combinations, we introduce 38 new global minima containing a planar hypercoordinate carbon atom (24 with a planar tetracoordinate carbon and 14 with a planar pentacoordinate carbon). These exotic clusters result from the decoration of V-shaped CE2 2- and Y-shaped CE3 2- dianions, respectively, with alkali counterions. All these 38 systems fulfill the geometrical and electronic criteria to be considered as true planar hypercoordinate carbon systems. Chemical bonding analyses indicate that carbon is covalently bonded to chalcogens and ionically connected to alkali metals.

Kick-Fukui: A Fukui Function-Guided Method for Molecular Structure Prediction.

Here, we introduce a hybrid method, named Kick-Fukui, to explore the potential energy surface (PES) of clusters and molecules using the Coulombic integral between the Fukui functions in the first screening of the best individuals. In the process, small stable molecules or clusters whose combination has the stoichiometry of the explored species are used as assembly units. First, a small set of candidates has been selected from a large and stochastically generated (Kick) population according to the maximum value of the Coulombic integral between the Fukui functions of both fragments. Subsequently, these few candidates are optimized using a gradient method and density functional theory (DFT) calculations. The performance of the program has been evaluated to explore the PES of various systems, including atomic and molecular clusters. In most cases studied, the global minimum (GM) has been identified with a low computational cost. The strategy does not allow to identify the GM of some silicon clusters; however, it predicts local minima very close in energy to the GM that could be used as the initial population of evolutionary algorithms.

Neither too Classic nor too Exotic: One-Electron Na⋠B Bond in NaBH3 - Cluster.

It is here reported that the NaBH3 - cluster exhibits a Na⋅B one-electron bond, a well-established type of electron-deficient bonding in the literature. The topological analysis of the electron localization function, at the correlated level, reveals that Na- , when approaching the bonding distance, fairly distributes its valence electron pair between two lobes. One of these electrons is used to bond with BH3 , which participates through its boron empty p-orbital. Furthermore, the bonding situation of LiBH3 - , KBH3 - , MgBH3 , and CaBH3 global minima structures are similar to that of NaBH3 - , extending the family of these new one-electron bond systems with biradicaloid character.

Li8 Si8 , Li10 Si9 , and Li12 Si10 : Assemblies of Lithium-Silicon Aromatic Units.

We report the global minima structures of Li8 Si8 , Li10 Si9 , and Li12 Si10 systems, in which silicon moieties maintain structural and chemical bonding characteristics similar to those of their building blocks: the aromatic clusters Td -Li4 Si4 and C2v -Li6 Si5 . Electron counting rules, chemical bonding analysis, and magnetic response properties verify the silicon unit's aromaticity persistence. This study demonstrates the feasibility of assembling silicon-based nanostructures from aromatics clusters as building blocks.

Planar Hexacoordinate Carbons: Half Covalent, Half Ionic.

Herein, the first global minima containing a planar hexacoordinate carbon (phC) atom are reported. The fifteen structures belong to the CE3 M3 + (E=S-Te and M=Li-Cs) series and satisfy both geometric and electronic criteria to be considered as a true phC. The design strategy consisted of replacing oxygen in the D3h  CO3 Li3 + structure with heavy and less electronegative chalcogens, inducing a negative charge on the C atom and an attractive electrostatic interaction between C and the alkali-metal cations. The chemical bonding analyses indicate that carbon is covalently bonded to three chalcogens and ionically connected to the three alkali metals.

Analysis of the electronic delocalization in some isoelectronic analogues of B12 doped with beryllium and/or carbon.

In the current work, a new family of isoelectronic analogues to B12 is reported. The construction of this family was performed through the isoelectronic substitution principle to generate species such as B11C+, B11Be-, B10BeC, B10C22+, B10Be22- B9Be2C-, and B9BeC2+. The search for the global minimum was realized by utilizing genetic algorithms, while the induced magnetic field, electronic localization function, magnetic current densities, and multicenter aromaticity criteria were calculated to understand their electronic delocalization. Our results show that, in general, C atoms avoid hypercoordination, whereas we have found species with Be atoms located in hypercoordinated positions that are relatively stable. Our analysis of aromaticity indicates that B12 has double σ and π disk aromaticity. Mono, double or triple substitution of B by C+ or Be- reduces somewhat the aromaticity of the clusters, but less in the case of Be- substitution.

Aromatic ouroboroi: heterocycles involving a σ-donor-acceptor bond and 4n + 2 π-electrons.

The aromaticity and dynamics of a set of recently proposed neutral 5- and 6-membered heterocycles that are closed by dative (donor-acceptor) or multi-center σ bonds, and have resonance forms with a Hückel number of π-electrons, are examined. The donors and acceptors in the rings include N, O, and F, and B, Be, and Mg, respectively. The planar geometry of the rings, coupled with evidence from different measures of aromaticity, namely the NICSzz, and NICSπzz components of the conventional nucleus independent chemical shifts (NICS), and ring current strengths (RCS), indicate non-trivial degrees of aromaticity in certain cases, including the cyclic C3B2OH6 and C3BOH5 isomers, both with three bonds to the O site in the ring. The former is lower in energy by at least 17.6 kcal mol-1 relative to linear alternatives obtained from molecular dynamics simulations in this work. Some of the other systems examined are best described as non-aromatic. Ring opening, closing, and isomerization are observed in molecular dynamics simulations for some of the systems studied. In a few cases, the ring indeed persists.

Orbital-Weighted Dual Descriptor for the Study of Local Reactivity of Systems with (Quasi-) Degenerate States.

An alternative response function, based on the dual descriptor in terms of Koopmans' approximation, is hereby proposed for the description of chemical reactivity in systems with (quasi-) degenerate frontier molecular orbitals. This descriptor is constructed from Fukui functions that include contributions from different orbitals, i.e., orbital-weighted Fukui functions. The methodology is applied to three case studies: the first case consists of a series of benchmark organic and inorganic molecules from which the dual descriptor, based only on frontier orbitals, is not appropriate to describe their reactivity. The second case deals with the proper description of chemical reactivity in Diels-Alder reactions between fullerene C60 and cyclopentadiene (CP), revealing the importance of considering secondary orbital interactions for an adequate regioselectivity description. The third, and last case, consists of a series of polycyclic aromatic hydrocarbons (PAHs) possessing molecular orbital degeneracy. By means of analyzing of this descriptor, an alternative approach to the description of aromaticity is proposed. In all cases, the proposed index called "orbital-weighted dual descriptor" has proven to accurately describe the chemical reactivity and aromaticity of the studied systems.

AUTOMATON: A Program That Combines a Probabilistic Cellular Automata and a Genetic Algorithm for Global Minimum Search of Clusters and Molecules.

A novel program for the search of global minimum structures of atomic clusters and molecules in the gas phase, AUTOMATON, is introduced in this work. This program involves the following: first, the generation of an initial population, using a simplified probabilistic cellular automaton method, which allows easy control of the adequate distribution of atoms in space; second, the fittest individuals are selected to evolve, through genetic operations (mating and mutations), until the best candidate for a global minimum surfaces. In addition, we propose a simple way to build the descendant structures by establishing a ranking of genes to be inherited. Thus, by means of a chemical formula checker procedure, genes are transferred to the offspring, ensuring that they always have the appropriate type and number of atoms. It is worth noting that a fraction of the fittest group is subject to mutation operations. This program also includes algorithms to identify duplicate structures: one based on geometric similarity and another on the similar distribution of atomic charges. The effectiveness of the program was evaluated in a group of 45 molecules, considering organic and organometallic compounds (benzene, cyclopentadienyl anion, and ferrocene), Zintl ion clusters [Sn9- m- nGe mBi n](4- n)- ( n = 1-4 and m = 0-(9- n)), star-shaped clusters (Li7E5+, E = BH, C, Si, Ge) and a variety of boron-based clusters. The global minimum and the lowest-energy isomers reported in the literature were found for all the cases considered in this article. These results successfully prove AUTOMATON's effectiveness on the identification of energetically preferred structures of a wide variety of chemical species.

A Fukui function-guided genetic algorithm. Assessment on structural prediction of Sin (n = 12-20) clusters.

Theoretical studies are essential for the structural characterization of clusters, when it comes to rationalize their unique size-dependent properties and composition. However, the rapid growth of local minima on the potential energy surface (PES), with respect to cluster size, makes the candidate identification a challenging undertaking. In this article, we introduce a hybrid strategy to explore the PES of clusters. This proposal involves the use of a biased initial population of a genetic algorithm procedure. Each individual in this population is built by assembling small fragments, according to the best matching of the Fukui function. The performance of a genetic algorithm procedure. The performance of the method is assessed on the PES exploration of medium-sized Sin clusters (n = 12-20). The most relevant results are: (a) the method converges at almost half of the time used by the canonical version of the GA and, (b) in all the studied cases, with the exception of Si13 and Si16 , the method allowed to identify the global minimum (GM) and other important low-lying structures. Additionally, the apparent deficiency of the proposal to identify the GM was corrected when a Si atom, or other low-lying isomers, were considered to build the clusters. © 2017 Wiley Periodicals, Inc.

Proposal of a simple and effective local reactivity descriptor through a topological analysis of an orbital-weighted fukui function.

The prediction of reactivity is one of the long-standing objectives of chemistry, contributing to enforce the link between theory and experiment. In particular, the regioselectivity of aromatic molecules has motivated the proposal of different reactivity descriptors based on foundational theories, like Frontier Molecular Orbital (FMO) theory and density functional theory, to predict and rationalize such regioselectivity. This article examines cases where reactivity descriptors, based on FMO theories, are known to have failed, specifically on electrophilic aromatic substitution reactions, through a simple but effective new reactivity model: the Orbital-weighted Fukui function ( fw-(r)) and its topological analysis. Interestingly, this descriptor proves to be effective in adequately predicting regioselectivities where other approximations failed. © 2017 Wiley Periodicals, Inc.