aRMSD: A Comprehensive Tool for Structural Analysis

Position of substituents directs the electron transfer properties of entatic state complexes: new insights from guanidine-quinoline copper complexes

In a previous study, we showed that the properties and the ability as an entatic state model of copper guanidine quinoline complexes are significantly influenced by a methyl or methyl ester substituent in the 2-position. To prove the importance of the 2-position of the substituent, two novel guanidine quinoline ligands with a methyl or methyl ester substituent in the 4-position and the corresponding copper complexes were synthesized and characterized in this study. The influence of the substituent position on the copper complexes was investigated with various experimental and theoretical methods. The molecular structures of the copper complexes were examined in the solid state by single-crystal X-ray diffraction (SCXRD) and by density functional theory (DFT) calculations indicating a strong dependency on the substituent position compared to the systems substituted in the 2-position from the previous study. Further, the significantly different influence on the donor properties in dependency on the substituent position was analyzed with natural bond orbital (NBO) calculations. By the determination of the redox potentials, the impact on the electrochemical stabilization was examined. With regard to further previously analyzed guanidine quinoline copper complexes, the electrochemical stabilization was correlated with the charge-transfer energies calculated by NBO analysis and ground state energies, revealing the substituent influence and enabling a comparatively easy and accurate possibility for the theoretical calculation of the relative redox potential. Finally, the electron transfer properties were quantified by determining the electron self-exchange rates via the Marcus theory and by theoretical calculation of the reorganization energies via Nelsen's four-point method. The results gave important insights into the dependency between the ability of the copper complexes as entatic state model and the type and position of the substituent.

Geometrical benchmarking and analysis of redox potentials of copper(I/II) guanidine-quinoline complexes: Comparison of semi-empirical tight-binding and DFT methods and the challenge of describing the entatic state (part III)

Copper guanidine-quinoline complexes are an important class of bioinorganic complexes that find utilization in electron and atom transfer processes. By substitution of functional groups on the quinoline moiety the electron transfer abilities of these complexes can be tuned. In order to explore the full substitution space by simulations, the accurate theoretical description of the effect of functional groups is essential. In this study, we compare three different methods for the theoretical description of the structures. We use the semi-empirical tight-binding method GFN2-xTB, the density functional TPSSh and the double-hybrid functional B2PLYP. We evaluate the methods on five different complex pairs (Cu(I) and Cu(II) complexes), and compare how well calculated energies can predict the redox potentials. We find even though B2PLYP and TPSSh yield better accordance with the experimental structures. GFN2-xTB performs surprisingly well in the geometry optimization at a fraction of the computational cost. TPSSh offers a good compromise between computational cost and accuracy of the redox potential for real-life complexes.

Identifying molecular structural features by pattern recognition methods

Identification of molecular structural features is a central part of computational chemistry. It would be beneficial if pattern recognition techniques could be incorporated to facilitate the identification. Currently, the quantification of the structural dissimilarity is mainly carried out by root-mean-square-deviation (RMSD) calculations such as in molecular dynamics simulations. However, the RMSD calculation underperforms for large molecules, showing the so-called “curse of dimensionality” problem. Also, it requires consistent ordering of atoms in two comparing structures, which needs nontrivial effort to fulfill. In this work, we propose to take advantage of the point cloud recognition using convex hulls as the basis to recognize molecular structural features. Two advantages of the method can be highlighted. First, the dimension of the input data structure is largely reduced from the number of atoms of molecules to the number of atoms of convex hulls. Therefore, the dimensionality curse problem is avoided, and the atom ordering process is saved. Second, the construction of convex hulls can be used to define new molecular descriptors, such as the contact area of molecular interactions. These new molecular descriptors have different properties from existing ones, therefore they are expected to exhibit different behaviors for certain machine learning studies. Several illustrative applications have been carried out, which provide promising results for structure–activity studies.

Identification of molecular structural features by point clouds and convex hulls.

IRA: A Shape Matching Approach for Recognition and Comparison of Generic Atomic Patterns

We propose a versatile, parameter-less approach for solving the shape matching problem, specifically in the context of atomic structures when atomic assignments are not known a priori. The algorithm Iteratively suggests Rotated atom-centered reference frames and Assignments (iterative rotations and assignments (IRA)). The frame for which a permutationally invariant set-set distance, namely, the Hausdorff distance, returns a minimal value is chosen as the solution of the matching problem. IRA is able to find rigid rotations, reflections, translations, and permutations between structures with different numbers of atoms, for any atomic arrangement and pattern, periodic or not. When distortions are present between the structures, optimal rotation and translation are found by further applying a standard singular value decomposition-based method. To compute the atomic assignments under the one-to-one assignment constraint, we develop our own algorithm, constrained shortest distance assignments (CShDA). The overall approach is extensively tested on several structures, including distorted structural fragments. The efficiency of the proposed algorithm is shown as a benchmark comparison against two other shape matching algorithms. We discuss the use of our approach for the identification and comparison of structures and structural fragments through two examples: a replica-exchange trajectory of a cyanine molecule, in which we show how our approach could aid the exploration of relevant collective coordinates for clustering the data, and a SiO₂ amorphous model, in which we compute distortion scores, and compare them with a classical strain-based potential. The source code and benchmark data are available at https://github.com/mammasmias/IterativeRotationsAssignments.

Molecular structure recognition by blob detection

Molecular structure recognition is fundamental in computational chemistry. The most common approach is to calculate the root mean square deviation (RMSD) between two sets of molecular coordinates. However, this method does not perform well for large molecules. In this work, a new method is proposed for structure comparison. Blob detection is used for recognizing structural features. Fragmentation of molecules is proposed as the pre-treatment. Mapping between blobs and atoms is developed as the post-treatment. A set of key parameters important for blob detections are determined. The dissimilarity is quantified by calculating the Euclidean metric of the blob vectors. The overall algorithm is found to be accurate to distinguish structural dissimilarity. The method has potential to be combined with other pattern recognition techniques for new chemistry discoveries.

Molecular structure recognition is fundamental in computational chemistry.

On the metal-ligand bonding in dinuclear complexes with redox-active guanidine ligands

Coordination compounds with redox-active ligands are currently intensively studied. Within this research theme, redox-active guanidines have been established as a new, eminent class of redox-active ligands. In this work the variation of metal-guanidine bonding in dinuclear transition metal complexes with bridging redox-active tetrakisguanidine ligands is analysed. A series of dinuclear complexes with different metals (Mn, Fe, Co, Ni, Cu and Zn) is synthesized, using either newly prepared redox-active tetrakisguanidino-dioxine or previously reported tetrakisguanidino-benzene ligands. The discussion of the bond properties in this work is predominantly based on the trends of structural parameters, derived from determination of single-crystal structures by X-ray diffraction and quantum chemical calculations. In addition, the trends in the redox potentials and magnetometric (SQUID) measurements on some of the complexes are included. Due to their combined σ- and π-electron donor capability, redox-active guanidine ligands are weak-field ligands; the σ- and π-bonding contributions vary with the metal. The results highlight the peculiarity of copper-guanidine bonding with a high π-bond contribution to metal-guanidine bonding, enabled by structural distortion of the coordination mode from tetrahedral in the direction of square-planar, short copper-guanidine bonds and minor displacement of the copper atoms from the ligand aromatic plane.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

Local Fluxionality of Surface-Deposited Cluster Catalysts: The Case of Pt7 on Al2O3

Subnano surface-supported catalytic clusters can be generally characterized by many low-energy isomers accessible at elevated temperatures of catalysis. The most stable isomer may not be the most catalytically active. Additionally, isomers may interconvert across barriers, i.e., exhibit fluxionality, during catalysis. To study the big picture of the cluster fluxional behavior, we model such a process as isomerization graph using bipartite matching algorithm, harmonic transition state theory, and paralleled nudged elastic band method. All the minimal energy paths form a minimum spanning tree (MST) of the original graph. Detailed inspection shows that, at temperatures typical for catalysis, the cluster geometry changes frequently within several regions in the MST, while transition across regions is less likely. As a further confirmation, the structural similarity analysis was additionally performed based on molecular dynamics trajectories. This local fluxionality picture provides a new perspective on understanding finite-temperate catalytic processes.

Tuning the nucleophilicity of electron-rich diborane(4) compounds with bridging guanidinate substituents by substitution

The proton affinity, HOMO energy and ionization energy of electron-rich sp³–sp³-hybridized diborane(4) compounds with bridging guanidinate substituents can be varied by substitution.

What is the best or most relevant global minimum for nanoclusters? Predicting, comparing and recycling cluster structures with WASP@N

Our WASP@N project is an open-access database of cluster structures with a web-assisted interface and toolkit for structure prediction.

ArbAlign: A Tool for Optimal Alignment of Arbitrarily Ordered Isomers Using the Kuhn-Munkres Algorithm

When assessing the similarity between two isomers whose atoms are ordered identically, one typically translates and rotates their Cartesian coordinates for best alignment and computes the pairwise root-mean-square distance (RMSD). However, if the atoms are ordered differently or the molecular axes are switched, it is necessary to find the best ordering of the atoms and check for optimal axes before calculating a meaningful pairwise RMSD. The factorial scaling of finding the best ordering by looking at all permutations is too expensive for any system with more than ten atoms. We report use of the Kuhn-Munkres matching algorithm to reduce the cost of finding the best ordering from factorial to polynomial scaling. That allows the application of this scheme to any arbitrary system efficiently. Its performance is demonstrated for a range of molecular clusters as well as rigid systems. The largely standalone tool is freely available for download and distribution under the GNU General Public License v3.0 (GNU_GPL_v3) agreement. An online implementation is also provided via a web server ( http://www.arbalign.org ) for convenient use.