Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster Stabilized by Boron Ligands.

The design of boron-based molecular rotors stems from boron-carbon binary clusters containing multiple planar hypercoordinate carbons (phCs, such as C2B8). However, the design of boron-coordinated phCs is challenging due to boron's tendency to occupy hypercoordinate centers more than carbon. Although this challenge has been addressed, the designed clusters of interest have not exhibited dynamic fluxionality similar to that of the initial C2B8. To address this issue, we report a σ/π doubly aromatic CB2H5+ cluster, the first global minimum containing a boron-coordinated planar tetracoordinate carbon atom with dynamic fluxionality. Dynamics simulations show that two ligand H atoms exhibit alternate rotation, resulting in an intriguing dynamic fluxionality in this cluster. Electronic structure analysis reveals the flexible bonding positions of the ligand H atoms because they do not participate in π delocalized bonding nor bond to any other non-carbon atom, highlighting this rotational fluxionality. Unprecedentedly, the fluxional process involves not only the usual conversion of the number of bonding atoms, but also the type of bonding (3c π bonds ↔ 4c σ bonds), which is an uncommon fluxional mechanism. The cluster represents an effort to apply phC species to molecular machines.

CBe2 H5 - : Unprecedented 2σ/2π Double Aromaticity and Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster.

A 14-electron ternary anionic CBe2 H5 - cluster containing a planar tetracoordinate carbon (ptC) atom is designed herein. Remarkably, it can be stabilized by only two beryllium atoms with both π-acceptor/σ-donor properties and two hydrogen atoms, which means that the conversion from planar methane (transition state) to ptC species (global minimum) requires the substitution of only two hydrogen atoms. Moreover, two ligand H atoms exhibit alternate rotation, giving rise to interesting dynamic fluxionality in this cluster. The electronic structure analysis reveals the flexible bonding positions of ligand H atoms due to C-H localized bonds, highlighting the rotational fluxionality in the cluster, and two CBe2 3c-2e delocalized bonds endow its rare 2σ/2π double aromaticity. Unprecedentedly, the fluxional process exhibits a conversion in the type of bonding (σ bond↔π bond), which is an uncommon fluxional mechanism. The cluster can be seen as an attempt to apply planar hypercoordinate carbon species to molecular motors.

MB16 - (M=Sc, Y, La): Perfect Bowl-Like Boron Clusters.

The introduction of transition-metal doping has engendered a remarkable array of unprecedented boron motifs characterized by distinctive geometries and bonding, particularly those heretofore unobserved in pure boron clusters. In this study, we present a perfect (no defects) boron framework manifesting an inherently high-symmetry, bowl-like architecture, denoted as MB16 - (M=Sc, Y, La). In MB16 -, the B16 is coordinated to M atoms along the C5v-symmetry axis. The bowl-shaped MB16 - structure is predicted to be the lowest-energy structure with superior stability, owing to its concentric (2 π+10 π) dual π aromaticity. Notably, the C5v-symmetry bowl-like B16 - is profoundly stabilized through the doping of an M atom, facilitated by strong d-pπ interactions between M and boron motifs, in conjunction with additional electrostatic stabilization by an electron transfer from M to the boron motifs. This concerted interplay of covalent and electrostatic interactions between M and bowl-like B16 renders MB16 - a species of exceptional thermodynamic stability, thus making it a viable candidate for gas-phase experimental detection.

Exploration of Free Energy Surface of the Au10 Nanocluster at Finite Temperature.

The first step in comprehending the properties of Au10 clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au10 nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme's dispersion with Becke-Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50-800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.

Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding.

Among the list of planar tetracoordinate atoms, the smallest element hydrogen is missing. No experimental and theoretical evidence have ever been put forwarded. Herein, we introduce the first planar tetracoordinate hydrogen atom (ptH) in the global minimum geometry of In4 H+ cluster. Bonding analysis indicates that the central hydrogen atom is acting like a proton and significant charge transfer from the surrounding In4 framework results in a negative charge of the central hydrogen atom. The proposed global minimum geometry possesses σ-aromaticity and the central hydrogen atom forms unusual multicentre bond with more than three centres.

Pushing The Extreme of Multicentre Bonding: Planar Pentacoordinate Hydride.

Planar hypercoordination has sparkled interest among the researchers from last few decades. Most of the elements in the Periodic Table have shown this remarkable structural feature. However, the smallest element, hydrogen, is missing in the list. No evidence is there in the literature. Herein, we introduce the first planar pentacoordinate hydrogen atom (ppH) in the global minimum geometry of Li5 H6 - cluster. Bonding analysis indicates that the central hydrogen atom is stabilized by multicentre bonding with five surrounding Li atoms. Natural charge analysis reveals that the central hydrogen is acting like a hydride which is strongly attracted by the positively charged surrounding lithium centres. The ppH structure is stabilized by strong electrostatic attraction as well as extensive multicentre bonding. Aromaticity has no role to play here. The cluster is dynamically stable and is expected to be detected in gas phase.

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.

Comments on "Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding".

In a recent communication (Angew. Chem. Int. Ed. 2024, 63, e202317312), Kalita et al. studied In4H+ system within the frame of single-reference approximation (SRA) and found that the global energy minimum (1 a) adopted the singlet state and a planar tetracoordinate hydrogen (ptH), while the second lowest isomer (1 b) located 3.0 kcal/mol above 1 a and adopted the triplet state as well as non-planar structure with a quasi-ptH. They assessed the reliability of SRA by checking the T1-diagnostic values of coupled cluster calculations. However, according to our multi-configurational second-order perturbation theory calculations at the CASPT2(12,13)/aug-cc-pVQZ (aug-cc-pVQZ-PP for In) level, both 1 a and 1 b exhibit obvious multi-referential characters, as reflected by their largest reference coefficients of 0.928 (86.1 %) and 0.938 (88.0 %), respectively. Moreover, 1 b is 5.05 kcal/mol lower than 1 a at this level, that is, what can be observed in In4H+ system is the quasi-ptH.

Reply to the Comments on Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding.

Recently, Huo et al. has commented on our communication (Angew. Chem. Int. Ed. 2024, 63, e202317312, DOI: 10.1002/anie.202317312), regarding the multireference character (MRC) of our proposed cluster. Their argument is based on small HOMO-LUMO gap, fractional occupation density (FOD) and CASPT2(12,13) calculations. They also proposed that the singlet planar In4H+ cluster cannot be observed. We present our calculations which reveals that some of their arguments are based on wrong interpretation of data and inadequate use of methodology. While we certainly agree with the strong physical ground of FOD, CASSF and CASPT2 methodology, we believe that such analysis for clusters is not adequate.

Planar Hexacoordinate Beryllium: Covalent Bonding Between s-block Metals.

Achieving a planar hypercoordinate arrangement of s-block metals through covalent bonding with ligands is challenging due to the strong ionicity involved. Herein, we report the first case of a neutral binary global minimum containing a planar hexacoordinate beryllium atom. The central Be atom is coordinated by six active Be atoms, the latter in turn are enclosed by an equal number of more electronegative chlorine atoms in the periphery, forming a star-like phBe cluster (Be©Be6 Cl6 ). Importantly, the cluster exhibits dynamically stabilized stemming geometrically from the appropriate matching of metal-ligand size and electronically from adherence to the octet rule as well as possessing a 6σ/2π double aromaticity. Remarkably, energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) analysis reveals a significant covalent interaction between the ligand and the central metal beryllium atoms, a fact further supported by a large Wiberg bond index. This cluster is a promising synthetic as its excellent electronic, dynamic and thermodynamic stability.

Global Planar Tetra-, Penta- and Hexa-coordinate Silicon Clusters Constructed by Decorating SiO3 with Alkali Metals.

The achievement of the rule-breaking planar hypercoordinate motifs (carbon and other elements) is mainly attributed to a practical electronic stabilization mechanism, where the bonding of the central atom pz π electrons is a crucial issue. We have demonstrated that strong multiple bonds between the central atom and partial ligands can be an effective approach to explore stable planar hypercoordinate species. A set of planar tetra-, penta- and hexa-coordinate silicon clusters were herein found to be the lowest-energy structure, which can be viewed as decorating SiO3 by alkali metals in the MSiO3 - , M2 SiO3 and M3 SiO3 + (M=Li, Na) clusters. The strong charge transfer from M atoms to SiO3 effectively results in [M]+ SiO3 2- , [M2 ]2+ SiO3 2- and [M3 ]3+ SiO3 2- salt complexes, where the Si-O multiple bonding and structural integrity of the Benz-like SiO3 framework is maintained better than the corresponding SiO3 2- motifs. The bonding between M atoms and SiO3 motif is best described as M+ forming a few dative interactions by employing its vacant s, p, and high-lying d orbitals. These considerable M←SiO3 interactions and Si-O multiple bonding give rise to the highly stable planar hypercoordinate silicon clusters.

CAl4X4 (X = Te, Po): Double Aromatic Molecular Stars Containing Planar Tetracoordinate Carbon Atoms.

Planar tetracoordinate carbon (ptC) species are scarce and exotic. Introducing four peripheral Te/Po auxiliary atoms is an effective strategy to flatten the tetrahedral structure of CAl4 (Td, 1A1). Neutral CAl4X4 (X = Te, Po) clusters possess quadrangular star structures containing perfect ptC centers. Unbiased density functional theory (DFT) searches and high-level CCSD(T) calculations suggest that these ptC species are the global minima on the potential energy surfaces. Bonding analyses indicate that 40 valence-electron (VE) is ideal for the ptC CAl4X4 (X = Te, Po): one delocalized π and three σ bonds for the CAl4 core; four lone pairs (LPs) of four X atoms, eight localized Al-X σ bonds, and four delocalized Al-X-Al π bonds for the periphery. Thus, the ptC CAl4X4 (X = Te, Po) clusters possess the stable eight electron structures and 2π + 6σ double aromaticity. Born-Oppenheimer molecular dynamics (BOMD) simulations indicate that neutral ptC CAl4X4 (X = Te, Po) clusters are robust.

σ-Aromatic MAl6S6 (M = Ni, Pd, Pt) Stars Containing Planar Hexacoordinate Transition Metals.

Hypercoordinate transition-metal species are mainly dominated by the 18-valence-electron (18ve) counting. Herein, we report ternary MAl6S6 (M = Ni, Pd, Pt) clusters with the planar hexacoordinate metal (phM) centers, which feature 16ve counting instead of the classic 18ve rule. These global-minimum clusters are established via unbiased global searches, followed by PBE0 and single-point CCSD(T) calculations. The phM MAl6 units are stabilized by six peripheral bridging S atoms in these star-like species. Chemical bonding analyses reveal that there are 10 delocalized electrons around the phM center, which can render the aromaticity according to the (4n + 2) Hückel rule. It is worth noting that adding an (or two) electron(s) to its π-type lowest unoccupied molecular orbital (LUMO) will make the system unstable.

B7 Be6 B7 : A Boron-Beryllium Sandwich Complex.

Planar boron clusters have often been regarded as "π-analogous" to aromatic arenes because of their similar delocalized π-bonding. However, unlike arenes such as C5 H5 - and C6 H6 , boron clusters have not previously shown the ability to form sandwich complexes. In this study, we present the first sandwich complex involving beryllium and boron, B7 Be6 B7 . The global minimum of this combination adopts a unique architecture having a D6h geometry, featuring an unprecedented monocyclic Be6 ring sandwiched between two quasi-planar B7 motifs. The thermochemical and kinetic stability of B7 Be6 B7 can be attributed to strong electrostatic and covalent interactions between the fragments. Chemical bonding analysis shows that B7 Be6 B7 can be considered as a [B7 ]3- [Be6 ]6+ [B7 ]3- complex. Moreover, there is a significant electron delocalization within this cluster, supported by the local diatropic contributions of the B7 and Be6 fragments.

Automated Search For The Low-Lying Energy Isomers of Rhamnolipids and Related Organometallic Complexes.

Rhamnolipids (RMLs) are a widely studied biosurfactant due to their high biodegradability and environmentally friendly production. However, the knowledge of the structure-property relationship of RMLs is imperative for the design of highly efficient applications. Aiming to a better understanding of it at a molecular level, we performed an automated search for low energy structures of the most abundant RMLs, namely, Rha-C10 , Rha-C10 -C10 , Rha-Rha-C10 and Rha-Rha-C10 -C10 and their respective C2 -congeners. Besides that, selected neutral metal complexes were also considered. We found that several low-energy congeners have internal hydrogen bonds. Moreover, geometries in "closed" conformation were always more stable than "open" ones. Finally, the energy diferences between open and closed conformations of K+ , Ni2+ , Cu2+ and Zn2+ complexes were found to be 23.5 kcal mol-1 , 62.8 kcal mol-1 , 24.3 kcal mol-1 and 41.6 kcal mol-1 , respectively, indicating a huge structural reorganization after the complex formation.

Linear Group 13 E≡E Triple Bonds in E2 Li6 2.

The triply bonded heavier main-group compounds have a textbook trans-bent geometry, in contrast to a familiar linear form found for the lightest analogues. Strikingly, the unexpected linear group 13 E≡E triple bonds were herein found in the D4h -symmetry E2 Li6 2+ clusters, and they possess a large barrier (>18.0 kcal/mol) towards the dissociation of Li+ . The perfectly surrounded Li4 motifs and two linear coordinated Li atoms strongly suppress the increasing nonbonded electron density of heavier E atoms, making two degenerate π bonds and one multi-center σ bond in linear heavier main-group triple bonds. The surrounding Li6 motifs not only creates an effective electronic structure to form a linear E≡E triple bond, but the resulting electrostatic interactions account for the highly stable global E2 Li6 2+ clusters.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures.

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer's probability of occurrence in a Boltzmann-weighted superposition of each isomer's spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

Electronic Transmutation (ET): Chemically Turning One Element into Another.

The concept of electronic transmutation (ET) depicts the processes that by acquiring an extra electron, an element with the atomic number Z begins to have properties that were known to only belong to its neighboring element with the atomic number Z+1. Based on ET, signature compounds and chemical bonds that are composed of certain elements can now be designed and formed by other electronically transmutated elements. This Minireview summarizes the recent developments and applications of ET on both the theoretical and experimental fronts. Examples on the ET of Group 13 elements into Group 14 elements, Group 14 elements into Group 15 elements, and Group 15 elements into Group 16 elements are discussed. Compounds and chemical bonding composed of carbon, silicon, germanium, phosphorous, oxygen and sulfur now have analogues using transmutated boron, aluminum, gallium, silicon, nitrogen, and phosphorous.

Experimental conformational energy maps of proteins and peptides.

We have presented an extensive analysis of the peptide backbone dihedral angles in the PDB structures and computed experimental Ramachandran plots for their distributions seen under a various constraints on X-ray resolution, representativeness at different sequence identity percentages, and hydrogen bonding distances. These experimental distributions have been converted into isoenergy contour plots using the approach employed previously by F. M. Pohl. This has led to the identification of energetically favored minima in the Ramachandran (ϕ, ψ) plots in which global minima are predominantly observed either in the right-handed α-helical or the polyproline II regions. Further, we have identified low energy pathways for transitions between various minima in the (ϕ,ψ) plots. We have compared and presented the experimental plots with published theoretical plots obtained from both molecular mechanics and quantum mechanical approaches. In addition, we have developed and employed a root mean square deviation (RMSD) metric for isoenergy contours in various ranges, as a measure (in kcal.mol-1 ) to compare any two plots and determine the extent of correlation and similarity between their isoenergy contours. In general, we observe a greater degree of compatibility with experimental plots for energy maps obtained from molecular mechanics methods compared to most quantum mechanical methods. The experimental energy plots we have investigated could be helpful in refining protein structures obtained from X-ray, NMR, and electron microscopy and in refining force field parameters to enable simulations of peptide and protein structures that have higher degree of consistency with experiments. Proteins 2017; 85:979-1001. © 2017 Wiley Periodicals, Inc.

Fast search algorithms for computational protein design.

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state-of-the-art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well-established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of A* to produce conformations in increasing order of energy, we defined new A* strategies combining CFN lower bounds, with new side-chain positioning-based branching scheme. Beyond the speedups obtained in the new A*-CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ A* combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms.