A tabu-search based strategy for modeling molecular aggregates and binary reactions

Nonlinearity and anthocyanin colour expression: A mathematical analysis of anthocyanin association kinetics and equilibria

Anthocyanins are polyphenolic compounds that provide pigmentation in plants as reflected by pH-dependent structural transformations between the red flavylium cation, purple quinonoidal base, blue quinonoidal anion, colourless hemiketal, and pale yellow chalcone species. Thermodynamically stable conditions of hydrated plant cell vacuoles in vivo correspond to the colourless hemiketal, yet anthocyanin colour expression appears in an important variety of hues within plant organs such as flowers and fruit. Moreover, anthocyanin colour from grape berries is significant in red winemaking processes as it plays a crucial role in determining red wine quality. Here, nonlinear ordinary differential equations were developed to represent the evolution in concentration of various anthocyanin species in both monomeric (chemically reactive) and self-associated (temporally stable) forms for the first time, and simulations were verified experimentally. Results indicated that under hydrating conditions, anthocyanin pigmentation is preserved by self-association interactions, based on pigmented monomeric anthocyanins experiencing colour loss whereas colour-stable self-associated anthocyanins increase in concentration nonlinearly over time. In particular, self-association of the flavylium cation and the quinonoidal base was shown to influence colour expression and stability within Geranium sylvaticum flower petals and Vitis vinifera grape skins. This study ultimately characterises fundamental mechanisms of anthocyanin stabilisation and generates a quantitative framework for anthocyanin-containing systems.

Nanoclusters and nanoalloys of group 13 elements (B, Al, and Ga): benchmarking of methods and analysis of their structures and energies

We investigated the structural and energetic properties of nanoclusters and nanoalloys composed of group 13 elements (B, Al, and Ga) up to a cluster size of 12. We conducted a comprehensive benchmark analysis of density functional and post-Hartree-Fock methods to identify efficient and accurate approaches for studying these systems using our benchmark dataset (BAlGa16) consisting of sixteen dimers and trimers. We compared different density functionals and post-Hartree-Fock methods using bond length and binding energy as parameters. B2PLYP closely follows CCSD(T) for geometry optimization, while REVPBE, BPBE, and PBE show cost-accuracy balanced performances. MRACPF was used as the reference for benchmarking energies, with NEVPT2 being the most accurate method, followed by CCSD(T) and DLPNO-CCSD(T). M06 and range-separated hybrid functionals perform well. Based on a cost-accuracy analysis, we recommend M06/def2-SVP as the preferred method. Additionally, we explored the structural evolution of pure, binary, and ternary clusters of group 13 elements up to 12 atoms, uncovering global and local minima. Ga clusters exhibited more rectangular faces compared to the predominantly trigonal faces of B and Al clusters. Binary clusters showed B in center positions, while Ga preferred outer positions, confirming the higher cohesion of B. The most favorable size of binary clusters (12) exhibited similar compositions of Al and Ga atoms. Compositions with 16.67-40% B, 16.67-60% Al, and 20-50% Ga were estimated to have negative mixing energies, indicating their relative stability.

ReNeGate: A Reaction Network Graph-Theoretical Tool for Automated Mechanistic Studies in Computational Homogeneous Catalysis

Exploration of the chemical reaction space of chemical transformations in multicomponent mixtures is one of the main challenges in contemporary computational chemistry. To remove expert bias from mechanistic studies and to discover new chemistries, an automated graph-theoretical methodology is proposed, which puts forward a network formalism of homogeneous catalysis reactions and utilizes a network analysis tool for mechanistic studies. The method can be used for analyzing trajectories with single and multiple catalytic species and can provide unique conformers of catalysts including multinuclear catalyst clusters along with other catalytic mixture components. The presented three-step approach has the integrated ability to handle multicomponent catalytic systems of arbitrary complexity (mixtures of reactants, catalyst precursors, ligands, additives, and solvents). It is not limited to predefined chemical rules, does not require prealignment of reaction mixture components consistent with a reaction coordinate, and is not agnostic to the chemical nature of transformations. Conformer exploration, reactive event identification, and reaction network analysis are the main steps taken for identifying the pathways in catalytic systems given the starting precatalytic reaction mixture as the input. Such a methodology allows us to efficiently explore catalytic systems in realistic conditions for either previously observed or completely unknown reactive events in the context of a network representing different intermediates. Our workflow for the catalytic reaction space exploration exclusively focuses on the identification of thermodynamically feasible conversion channels, representative of the (secondary) catalyst deactivation or inhibition paths, which are usually most difficult to anticipate based solely on expert chemical knowledge. Thus, the expert bias is sought to be removed at all steps, and the chemical intuition is limited to the choice of the thermodynamic constraint imposed by the applicable experimental conditions in terms of threshold energy values for allowed transformations. The capabilities of the proposed methodology have been tested by exploring the reactivity of Mn complexes relevant for catalytic hydrogenation chemistry to verify previously postulated activation mechanisms and unravel unexpected reaction channels relevant to rare deactivation events.

CSinGe4-n2+ (n = 1-3): prospective systems containing planar tetracoordinate carbon (ptC)

Density functional theory (DFT) based calculations have been carried out to explore the potential energy surface (PES) of CSi_nGe_4-n^2+/+/0 (n = 1-3) systems. The global minimum structures in the di-cationic states (1a, 1b, and 1c) contain a planar tetracoordinate carbon (ptC). For the CSi₂Ge₂²⁺ system, the second stable isomer (2b) also contains a ptC with 0.67 kcal mol^-1 higher energy than that of the 1b ptC isomer. The global minima of the neutral and mono-cationic states of the designed systems are not planar. The 1a, 1b, and 1c structures follow the 18 valence electron rule. The relative energies of the low-lying isomers of CSiGe₃²⁺, CSi₂Ge₂²⁺, and CSi₃Ge²⁺ systems with respect to the global minima were calculated using the CCSD(T)/aug-cc-pVTZ method. Ab initio molecular dynamics simulations for 50 ps time indicate that all the global minimum structures (1a, 1b, and 1c) are kinetically stable at 300 K and 500 K temperatures. The natural bond orbital (NBO) analysis suggests strong σ-acceptance of the ptC from the four surrounding atoms and simultaneously π-donation occurs from the ptC center. The nucleus independent chemical shift (NICS) showed σ/π-dual aromaticity. We hope that the designed di-cationic systems may be viable in the gas phase.

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.

Relativistic Effects in Platinum Nanocluster Catalysis: A Statistical Ensemble-Based Analysis

Nanoclusters are materials of paramount catalytic importance. Among various unique properties featured by nanoclusters, a pronounced relativistic effect can be a decisive parameter in governing their catalytic activity. A concise study delineating the role of relativistic effects in nanocluster catalysis is carried by investigating the oxygen reduction reaction (ORR) activity of a Pt₇ subnanometer cluster. Global optimization analysis shows the critical role of spin-orbit coupling (SOC) in regulating the relative stability between structural isomers of the cluster. An overall improved ORR adsorption energetics and differently scaled adsorption-induced structural changes are identified with SOC compared to a non-SOC scenario. Ab initio atomistic thermodynamics analysis predicted nearly identical phase diagrams with significant structural differences for high coverage oxygenated clusters under realistic conditions. Though inclusion of SOC does not bring about drastic changes in the overall catalytic activity of the cluster, it is having a crucial role in governing the rate-determining step, transition-state configuration, and energetics of elementary reaction pathways. Furthermore, a statistical ensemble-based approach illustrates the strong contribution of low-energy local minimum structural isomers to the total ORR activity, which is significantly scaled up along the activity improving direction within the SOC framework. The study provides critical insights toward the importance of relativistic effects in determining various catalytic activity relevant features of nanoclusters.

Molecular size and molecular structure: Discriminating their changes upon chemical reactions in terms of information entropy

Structural descriptors take the central place in the digitalization of chemical reactions. Information entropy is one of such descriptors that has been a seminal for numerous derivative indices. Previously, we have studied the rules of calculating information entropies of molecular ensembles based on the corresponding values of constituting molecules and found that the complexity of the ensemble has the contributions from the molecular structure and the size of the molecules. Considering chemical reaction as the conversion of one molecular ensemble to another allows calculating the change in information entropy as well as its components associated with molecular-structure and molecular-size changes. We demonstrate that both total information entropy change and its contributions are characteristic for the selected classes of chemical reactions and exemplify this approach with the cycloaddition and exchange reactions widespread in organic chemistry.

BAl4Mg−/0/+: Global Minima with a Planar Tetracoordinate or Hypercoordinate Boron Atom

We have explored the chemical space of BAl4Mg−/0/+ for the first time and theoretically characterized several isomers with interesting bonding patterns. We have used chemical intuition and a cluster building method based on the tabu-search algorithm implemented in the Python program for aggregation and reaction (PyAR) to obtain the maximum number of possible stationary points. The global minimum geometries for the anion (1a) and cation (1c) contain a planar tetracoordinate boron (ptB) atom, whereas the global minimum geometry for the neutral (1n) exhibits a planar pentacoordinate boron (ppB) atom. The low-lying isomers of the anion (2a) and cation (3c) also contain a ppB atom. The low-lying isomer of the neutral (2n) exhibits a ptB atom. Ab initio molecular dynamics simulations carried out at 298 K for 2000 fs suggest that all isomers are kinetically stable, except the cation 3c. Simulations carried out at low temperatures (100 and 200 K) for 2000 fs predict that even 3c is kinetically stable, which contains a ppB atom. Various bonding analyses (NBO, AdNDP, AIM, etc.) are carried out for these six different geometries of BAl4Mg−/0/+ to understand the bonding patterns. Based on these results, we conclude that ptB/ppB scenarios are prevalent in these systems. Compared to the carbon counter-part, CAl4Mg−, here the anion (BAl4Mg−) obeys the 18 valence electron rule, as B has one electron fewer than C. However, the neutral and cation species break the rule with 17 and 16 valence electrons, respectively. The electron affinity (EA) of BAl4Mg is slightly higher (2.15 eV) than the electron affinity of CAl4Mg (2.05 eV). Based on the EA value, it is believed that these molecules can be identified in the gas phase. All the ptB/ppB isomers exhibit π/σ double aromaticity. Energy decomposition analysis predicts that the interaction between BAl4−/0/+ and Mg is ionic in all these six systems.

Role of atomicity in the oxygen reduction reaction activity of platinum sub nanometer clusters: A global optimization study

Metal nanoclusters are an important class of materials for catalytic applications. Sub nanometer clusters are relatively less explored for their catalytic activity on account of undercoordinated surface structure. Taking this into account, we studied platinum-based sub nanometer clusters for their catalytic activity for oxygen reduction reaction (ORR). A comprehensive analysis with global optimization is carried out for structural prediction of the platinum clusters. The energetic and electronic properties of interactions of clusters with reaction intermediates are investigated. The role of structural sensitivity in the dynamics of clusters is unraveled, and unique intermediate specific interactions are identified. ORR energetics is examined, and exceptional activity for sub nanometer clusters are observed. An inverse size versus activity relationship is identified, challenging the conventional trends followed by larger nanoclusters. The principal role of atomicity in governing the catalytic activity of nanoclusters is illustrated. The structural norms governing the sub nanometer cluster activity are shown to be markedly different from larger nanoclusters.

Six Low-Lying Isomers of C11H8 Are Unidentified in the Laboratory-A Theoretical Study

Isomers of C₁₁H₈ have been theoretically examined using density functional theory and coupled-cluster methods. The current investigation reveals that 2aH-cyclopenta[cd]indene (2), 7-ethynyl-1H-indene (6), 4-ethynyl-1H-indene (7), 6-ethynyl-1H-indene (8), 5-ethynyl-1H-indene (9), and 7bH-cyclopenta[cd]indene (10) remain elusive till date in the laboratory. The puckered low-lying isomer 2 lies at 9 kJ mol^-1 below the experimentally known molecule, cyclobuta[de]naphthalene (3), at the fc-CCSD(T)/cc-pVTZ//fc-CCSD(T)/cc-pVDZ level of theory. 2 lies at 36 kJ mol^-1 above the thermodynamically most stable and experimentally known isomer, 1H-cyclopenta[cd]indene (1), at the same level. It is identified that 1,2-H transfer from 1 yields 2H-cyclopenta[cd]indene (14) and subsequent 1,2-H shift from 14 yields 2. Appropriate transition states have been identified, and intrinsic reaction coordinate calculations have been carried out at the B3LYP/6-311+G(d,p) level of theory. Recently, 1-ethynyl-1H-indene (11) has been detected using synchrotron-based vacuum ultraviolet ionization mass spectrometry. 2-Ethynyl-1H-indene (4) and 3-ethynyl-1H-indene (5) have been synthetically characterized in the past. While the derivatives of 7bH-cyclopenta[cd]indene (10) have been isolated elsewhere, the parent compound remains unidentified till date in the laboratory. Although C₁₁H₈ is a key elemental composition of astronomical interest for the formation of polycyclic aromatic hydrocarbons in the interstellar medium, none of its low-lying isomers have been characterized by rotational spectroscopy though they are having a permanent dipole moment (μ ≠ 0). Therefore, energetic and spectroscopic properties have been computed, and the present investigation necessitates new synthetic studies on C₁₁H₈, in particular 2, 6-10, and also rotational spectroscopic studies on all low-lying isomers.

CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom

Isomers of CAl4Mg and CAl4Mg− have been theoretically characterized for the first time. The most stable isomer for both the neutral and anion contain a planar tetracoordinate carbon (ptC) atom. Unlike the isovalent CAl4Be case, which contains a planar pentacoordinate carbon atom as the global minimum geometry, replacing beryllium with magnesium makes the ptC isomer the global minimum due to increased ionic radii of magnesium. However, it is relatively easier to conduct experimental studies for CAl4Mg0/− as beryllium is toxic. While the neutral molecule containing the ptC atom follows the 18 valence electron rule, the anion breaks the rule with 19 valence electrons. The electron affinity of CAl4Mg is in the range of 1.96–2.05 eV. Both the global minima exhibit π/σ double aromaticity. Ab initio molecular dynamics simulations were carried out for both the global minima at 298 K for 10 ps to confirm their kinetic stability.

Si2C5H2 isomers - search algorithms versus chemical intuition

The pros and cons of using search algorithms alone in identifying new geometries have been discussed by using the Si₂C₅H₂ elemental composition as an example. Within 30 kcal mol^-1 at the CCSD(T)/def2-TZVP//PBE0/def2-TZVP level of theory, the coalescence kick and cuckoo methods postulate merely four isomers (1, 3, 6, and 7) for Si₂C₅H₂ (O. Yañez et. al., Chem. Commun., 2017, 53, 12112). On the contrary, chemical intuition yields fourteen (2, 4, 5, and 8-18) new isomers within the same energy range at the B3LYP/6-311++G(2d,2p) level of theory. Based on the relative energies of the first eleven isomers of Si₂C₅H₂ (1, C_2v, 0.00; 2, C_s, 21.39; 3, C_s, 21.95; 4, C_s, 22.76; 5, C_s, 24.74; 6, C_s, 25.34; 7, C_s, 25.64; 8, C_s, 25.79; 9, C_s, 27.20; 10, C_2v, 28.59; and 11, C_2v, 29.16 kcal mol^-1) calculated at the CCSD(T)/cc-pVTZ level of theory, it is evident that the search algorithms had missed at least seven isomers in the same energy range. The relative energy gaps of isomers 12-18 fall in the range of 30-40 kcal mol^-1 at the latter level of theory. Consequentially, this scenario triggers a speculation going forward with search algorithms alone in the search of all new isomers. While one cannot underestimate the power of these algorithms, the role of chemical intuition may not be completely neglected. Retrospectively, the fourteen new isomers found by chemical intuition may help in writing better search algorithms. All eighteen isomers - including the most stable isomer with a planar tetracoordinate carbon atom 1- remain elusive in the laboratory to date. Thus, structural and spectroscopic parameters have been presented here, which may possibly aid the future experimental studies.

A Global Optimizer for Nanoclusters

We have developed an algorithm to automatically build the global minimum and other low-energy minima of nanoclusters. This method is implemented in PyAR (https://github.com/anooplab/pyar) program. The global optimization in PyAR involves two parts, generation of several trial geometries and gradient-based local optimization of the trial geometries. While generating the trial geometries, a Tabu list is used for storing the information of the already used trial geometries to avoid using the similar trial geometries. In this recursive algorithm, an n-sized cluster is built from the geometries of n−1 clusters. The overall procedure automatically generates many unique minimum energy geometries of clusters with size from 2 up to n using this evolutionary growth strategy. We have used our strategy on some of the well-studied clusters such as Pd, Pt, Au, and Al homometallic clusters, Ru-Pt and Au-Pt binary clusters, and Ag-Au-Pt ternary cluster. We have analyzed some of the popular parameters to characterize the clusters, such as relative energy, singlet-triplet energy difference, binding energy, second-order energy difference, and mixing energy, and compared with the reported properties.