Unveiling Möbius/Hückel Topology and Aromaticity in A Core-Expanded [10]Annulene at Different Oxidation States.

The exploration of annulene's conformation, electronic properties and aromaticity has generated enduring interest over the years, yet it continues to present formidable challenges for annulenes with more than ten carbon atoms. In this study, we present the synthesis of a stable [10]cyclo-para-phenylmethine derivative (1), which bears a resemblance to [10]annulene. 1 can be readily oxidized into its respective cations, wherein electrons are effectively delocalized along the backbone, resulting in different conformations and aromaticity. Both 1 and its tetracation (14+ ⋅ 4SbF6 - ) exhibit a nearly planar conformation with a rectangular shape, akin to the E,Z,E,Z,Z-[10]annulene. In contrast, the radical cation (1⋅+ ⋅ SbCl6 - ) possesses a doubly twisted Hückel topology. Furthermore, the dication (12+ ⋅ 2SbCl6 - ) displays conformational flexibility in solution and crystalizes with the simultaneous presence of Möbius-twisted (1a2+ ⋅ 2SbCl6 - ) and Hückel-planar (1b2+ ⋅ 2SbCl6 - ) isomers in its unit cell. Detailed experimental measurements and theoretical calculations reveal that: (1) 1 demonstrates localized aromaticity with an alternating benzenoid/quinoid structure; (2) 1a2+ ⋅ 2SbCl6 - and 1b2+ ⋅ 2SbCl6 - with 48π electrons are weakly Möbius aromatic and Hückel antiaromatic, respectively; (3) 14+ ⋅ 4SbF6 - exhibits Hückel aromaticity (46π) and open-shell diradical character.

Quantum chemical "Aufbau" principles: how to estimate the shape of highly flexible (bio-)polymers? A recursively extendable "chemion picture" of Euler-Hückel-type.

An outline is given of how to split the n-dimensional space of torsion angles occurring in flexible (bio-)polymers (like alkanes, nucleic acids, or proteins, for instance) into n one-dimensional potential curves. Forthcoming applications will focus on the "protein folding problem," beginning with polyglycine. CONTEXT: In accordance with Euler's topology rules, molecules are considered to be composed of "vertices" (atoms, ligands, bonding sites, functional groups, and bigger fragments). Following Hückel, each vertex is represented by only one basis function. Starting from the "monofocal" hydrids CH[Formula: see text], NH[Formula: see text], OH[Formula: see text], FH, and SiH[Formula: see text], PH[Formula: see text], SH[Formula: see text], ClH as anchor units, "chemionic" Hamiltonians (of individual "chemion ensembles" and proportional nuclear charges) are constructed recursively, together with an appropriate basis set for the first five (normal) alkanes and some related oligomers like primary alcohols, alkyl amines, and alkyl chlorides. METHODS: Standard methods ("Restricted Hartree-Fock RHF" and "Full Configuration Interaction FCI") are used to solve the various stationary Schrödinger equations. Two software packages are indispensable: "SMILES" for integral evaluations over Slater-type orbitals (STO), and "Numerical Recipes" for matrix diagonalizations and inversions. While managing with only two-center repulsion integrals, "implicit multi-center integrations" lead us to the non-empirical fundament of Hoffmann's "Extended-Hückel Theory."

Thermoelectric Properties of Porphyrin Nano Rings: A Theoretical and Modelling Investigation.

Propagation of De Broglie waves through nanomolecular junctions is greatly affected by molecular topology changes, which in turn plays a key role in determining the electronic and thermoelectric properties of source|molecule|drain junctions. The probing and realization of the constructive quantum interference (CQI) and a destructive quantum interference (DQI) are well established in this work. The critical role of quantum interference (QI) in governing and enhancing the transmission coefficient T(E), thermopower (S), power factor (P) and electronic figure of merit (ZelT) of porphyrin nanorings has been investigated using a combination of density functional theory (DFT) methods, a tight binding (Hückel) modelling (TBHM) and quantum transport theory (QTT). Remarkably, DQI not only dominates the asymmetric molecular pathways and lowering T(E), but also improves the thermoelectric properties.

Impact of pH on Gas-Particle Partitioning of Semi-Volatile Organics in Multicomponent Aerosol.

The partitioning of semivolatile organic compounds (SVOCs) between the condensed and gas phases can have significant implications for the properties of aerosol particles. In addition to affecting size and composition, this partitioning can alter radiative properties and impact cloud activation processes. We present measurements and model predictions on how activity and pH influence the evaporation of SVOCs from particles to the gas phase, specifically investigating aqueous inorganic particles containing dicarboxylic acids (DCAs). The aerosols are studied at the single-particle level by using optical trapping and cavity-enhanced Raman spectroscopy. Optical resonances in the spectra enable precise size tracking, while vibrational bands allow real-time monitoring of pH. Results are compared to a Maxwell-type model that accounts for volatile and nonvolatile solutes in aqueous droplets that are held at a constant relative humidity. The aerosol inorganic-organic mixture functional group activity coefficients thermodynamic model and Debye-Hückel theory are both used to calculate the activities of the species present in the droplet. For DCAs, we find that the evaporation rate is highly sensitive to the particle pH. For acidity changes of approximately 1.5 pH units, we observe a shift from a volatile system to one that is completely nonvolatile. We also observe that the pH itself is not constant during evaporation; it increases as DCAs evaporate, slowing the rate of evaporation until it eventually ceases. Whether a DCA evaporates or remains a stable component of the droplet is determined by the difference between the lowest pKa of the DCA and the pH of the droplet.

Mono-valent salt corrections for RNA secondary structures in the ViennaRNA package.

BACKGROUND: RNA features a highly negatively charged phosphate backbone that attracts a cloud of counter-ions that reduce the electrostatic repulsion in a concentration dependent manner. Ion concentrations thus have a large influence on folding and stability of RNA structures. Despite their well-documented effects, salt effects are not handled consistently by currently available secondary structure prediction algorithms. Combining Debye-Hückel potentials for line charges and Manning's counter-ion condensation theory, Einert et al. (Biophys J 100: 2745-2753, 2011) modeled the energetic contributions of monovalent cations on loops and helices. RESULTS: The model of Einert et al. is adapted to match the structure of the dynamic programming recursion of RNA secondary structure prediction algorithms. An empirical term describing the salt dependence of the duplex initiation energy is added to improve co-folding predictions for two or more RNA strands. The slightly modified model is implemented in the ViennaRNA package in such way that only the energy parameters but not the algorithmic structure is affected. A comparison with data from the literature show that predicted free energies and melting temperatures are in reasonable agreement with experiments. CONCLUSION: The new feature in the ViennaRNA package makes it possible to study effects of salt concentrations on RNA folding in a systematic manner. Strictly speaking, the model pertains only to mono-valent cations, and thus covers the most important parameter, i.e., the NaCl concentration. It remains a question for future research to what extent unspecific effects of bi- and tri-valent cations can be approximated in a similar manner. AVAILABILITY: Corrections for the concentration of monovalent cations are available in the ViennaRNA package starting from version 2.6.0.

Diffusiophoresis of a Weakly Charged Liquid Metal Droplet.

Diffusiophoresis of a weakly charged liquid metal droplet (LMD) is investigated theoretically, motivated by its potential application in drug delivery. A general analytical formula valid for weakly charged condition is adopted to explore the droplet phoretic behavior. We determined that a liquid metal droplet, which is a special category of the conducting droplet in general, always moves up along the chemical gradient in sole chemiphoresis, contrary to a dielectric droplet where the droplet tends to move down the chemical gradient most of the time. This suggests a therapeutic nanomedicine such as a gallium LMD is inherently superior to a corresponding dielectric liposome droplet in drug delivery in terms of self-guiding to its desired destination. The droplet moving direction can still be manipulated via the polarity dependence; however, there should be an induced diffusion potential present in the electrolyte solution under consideration, which spontaneously generates an extra electrophoresis component. Moreover, the smaller the conducting liquid metal droplet is, the faster it moves in general, which means a smaller LMD nanomedicine is preferred. These findings demonstrate the superior features of an LMD nanomedicine in drug delivery.

Site Identification by Ligand Competitive Saturation-Biologics Approach for Structure-Based Protein Charge Prediction.

Protein-based therapeutics typically require high concentrations of the active protein, which can lead to protein aggregation and high solution viscosity. Such solution behaviors can limit the stability, bioavailability, and manufacturability of protein-based therapeutics and are directly influenced by the charge of a protein. Protein charge is a system property affected by its environment, including the buffer composition, pH, and temperature. Thus, the charge calculated by summing the charges of each residue in a protein, as is commonly done in computational methods, may significantly differ from the effective charge of the protein as these calculations do not account for contributions from bound ions. Here, we present an extension of the structure-based approach termed site identification by ligand competitive saturation-biologics (SILCS-Biologics) to predict the effective charge of proteins. The SILCS-Biologics approach was applied on a range of protein targets in different salt environments for which membrane-confined electrophoresis-determined charges were previously reported. SILCS-Biologics maps the 3D distribution and predicted occupancy of ions, buffer molecules, and excipient molecules bound to the protein surface in a given salt environment. Using this information, the effective charge of the protein is predicted such that the concentrations of the ions and the presence of excipients or buffers are accounted for. Additionally, SILCS-Biologics also produces 3D structures of the binding sites of ions on the proteins, which enable further analyses such as the characterization of protein surface charge distribution and dipole moments in different environments. Notable is the capability of the method to account for competition between salts, excipients, and buffers on the calculated electrostatic properties in different protein formulations. Our study demonstrates the ability of the SILCS-Biologics approach to predict the effective charge of proteins and its applicability in uncovering protein-ion interactions and their contributions to protein solubility and function.

How a highly acidic SH3 domain folds in the absence of its charged peptide target.

Charged residues on the surface of proteins are critical for both protein stability and interactions. However, many proteins contain binding regions with a high net charge that may destabilize the protein but are useful for binding to oppositely charged targets. We hypothesized that these domains would be marginally stable, as electrostatic repulsion would compete with favorable hydrophobic collapse during folding. Furthermore, by increasing the salt concentration, we predict that these protein folds would be stabilized by mimicking some of the favorable electrostatic interactions that take place during target binding. We varied the salt and urea concentrations to probe the contributions of electrostatic and hydrophobic interactions for the folding of the yeast SH3 domain found in Abp1p. The SH3 domain was significantly stabilized with increased salt concentrations due to Debye-Huckel screening and a nonspecific territorial ion-binding effect. Molecular dynamics and NMR show that sodium ions interact with all 15 acidic residues but do little to change backbone dynamics or overall structure. Folding kinetics experiments show that the addition of urea or salt primarily affects the folding rate, indicating that almost all the hydrophobic collapse and electrostatic repulsion occur in the transition state. After the transition state formation, modest yet favorable short-range salt bridges are formed along with hydrogen bonds, as the native state fully folds. Thus, hydrophobic collapse offsets electrostatic repulsion to ensure this highly charged binding domain can still fold and be ready to bind to its charged peptide targets, a property that is likely evolutionarily conserved over 1 billion years.

Why Hoffmann? His Chemistry.

Why was it that Roald Hoffmann was the perfect collaborator for R. B. Woodward for proposing the Principle of Conservation of Orbital Symmetry as the solution to the no-mechanism puzzle? This publication presents 17 "tools" that Hoffmann used extensively and effectively prior to the Woodward-Hoffmann collaboration that would he call upon reveal the mechanism of pericyclic reactions. In a sense, this is a biography of Hoffmann with a focus on his personal and professional skills as of May 5, 1964.

Why Hoffmann? The Person and the Young Chemical Physicist.

In 1965, R. B. Woodward and Roald Hoffmann published five communications that formed the basis of the Principle of Conservation of Orbital Symmetry which explained mechanisms of all pericyclic reactions and predicted the allowedness and forbiddeness of such reactions, whether thermal or photochemical. A brief biographical discussion of Hoffmann up to May 1964 is explains why Hoffmann was the ideal individual to participate in the collaboration with Woodward. Why May 1964? Because it was then that the Woodward-Hoffmann collaboration began.

Retaining Hückel Aromaticity in the Triplet Excited State of Azobenzene.

The implication of the potential concept of aromaticity in the relaxed lowest triplet state of azobenzene, an efficient molecular switch, using elementary aromaticity indices based on magnetic, electronic, and geometric criteria has been discussed. Azobenzene exhibits a major Hückel aromatic character retained in the diradical lowest relaxed triplet state (T1 ) by virtue of a twisted geometry with partial delocalization of unpaired electrons in the perpendicular p-orbitals of two nitrogen atoms to the corresponding phenyl rings. The computational analysis has been expanded further to stilbene and N-diphenylmethanimine for an extensive understanding of the effect of closed-shell Hückel aromaticity in double-bond-linked phenyl rings. Our analysis concluded that stilbene has Hückel aromatic character in the relaxed T1 state and N-diphenylmethanimine has a considerable Hückel aromaticity in the phenyl ring near the carbon atom while a paramount Baird aromaticity in the phenyl ring near the nitrogen atom of the C=N double bond. The results reveal the application of excited-state aromaticity as a general tool for the design of molecular switches.

Hückel- and Baird-Type Global Aromaticity in a 3D Fully Conjugated Molecular Cage.

Global aromaticity in 3D π-conjugated molecular cages remains largely unexplored. Herein, we report the facile synthesis of a fully conjugated molecular cage (1) containing two bridged triphenylamine units and three quinoidal bithiophene arms. X-ray crystallographic analysis, NMR/ESR measurements and theoretical calculations reveal that: 1) its dication (12+ ) has an open-shell singlet ground state and is 3D globally aromatic, with individual macrocycles being 2D Hückel aromatic; 2) its tetracation (14+ ) has a triplet ground state and is also 3D globally aromatic, with individual macrocycles being 2D Baird aromatic; and 3) its hexacation (16+ ) has a closed-shell nature and shows local aromaticity. The study demonstrated a close relationship between 2D Hückel/Baird aromaticity and 3D global π-aromaticity.

Analytical solution to dielectric droplet diffusiophoresis under Debye-Hückel approximation.

A simple analytical formula is obtained for the diffusiophoresis of a dielectric fluid droplet in symmetric binary electrolyte solutions under Debye-Hückel approximation valid for weakly charged droplets. The chemiphoresis is found to yield negative mobilities most of the time for droplets of constant surface charge density, which implies that the droplets tend to move away from the source releasing ionic chemicals. This is undesirable in some practical applications like drug delivery with liposomes in terms of conveying the drug-carrying liposomes to the desired area in the human body releasing specific ionic chemicals utilizing the self-guiding nature of diffusiophoresis. The further involvement of the electrophoresis component, however, may change the scenario via the oriented electric field generated by the induced diffusion potential. The lesson here is that while the impact of the chemiphoresis component is determined by nature and uncontrollable, the electrophoresis component serves as an artificially adjustable factor via choosing droplets with the surface charge of appropriate sign in practical applications. The results here have potential use in practical applications such as drug delivery. The portable simple analytical formula is a powerful asset to experimental researchers and design engineers in colloid science and technology to facilitate their works.

Occurrence of Double Bond in π-Aromatic Rings: An Easy Way to Design Doubly Aromatic Carbon-Metal Structures.

A chemical bonding of several metallabenzenes and metallabenzynes was studied via an adaptive natural density partitioning (AdNDP) algorithm and the induced magnetic field analysis. A unique chemical bonding pattern was discovered where the M=C (M: Os, Re) double bond coexists with the delocalized 6c-2e π-bonding elements responsible for aromatic properties of the investigated complexes. In opposition to the previous description where 8 delocalized π-electrons were reported in metallabenzenes and metallabenzynes, we showed that only six delocalized π-electrons are present in those molecules. Thus, there is no deviation from Hückel's aromaticity rule for metallabenzynes/metallabenzenes complexes. Based on the discovered bonding pattern, we propose two thermodynamically stable novel molecules that possess not only π-delocalization but also retain six σ-delocalized electrons, rendering them as doubly aromatic species. As a result, our investigation gives a new direction for the search for carbon-metal doubly aromatic molecules.

Heat transfer analysis for EMHD peristalsis of ionic-nanofluids via curved channel with Joule dissipation and Hall effects.

The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell's model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid's velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of [Formula: see text].

Valence Bond Theory-Its Birth, Struggles with Molecular Orbital Theory, Its Present State and Future Prospects.

This essay describes the successive births of valence bond (VB) theory during 1916-1931. The alternative molecular orbital (MO) theory was born in the late 1920s. The presence of two seemingly different descriptions of molecules by the two theories led to struggles between the main proponents, Linus Pauling and Robert Mulliken, and their supporters. Until the 1950s, VB theory was dominant, and then it was eclipsed by MO theory. The struggles will be discussed, as well as the new dawn of VB theory, and its future.

Extended Hückel Semi-Empirical Approach as an Efficient Method for Structural Defects Analysis in 4H-SiC.

This paper presents an efficient method to calculate the influence of structural defects on the energy levels and energy band-gap for the 4H-SiC semiconductor. The semi-empirical extended Hückel method was applied to both ideal 4H-SiC crystal and different structures with defects like vacancies, stacking faults, and threading edge dislocations. The Synopsys QuatumATK package was used to perform the simulations. The results are in good agreement with standard density functional theory (DFT) methods and the computing time is much lower. This means that a structure with ca. 1000 atoms could be easily modeled on typical computing servers within a few hours of computing time, enabling fast and accurate simulation of non-ideal atomic structures.

Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface.

Poisson-Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson-Boltzmann theory, we calculate the surface potential inside a Wigner-Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

Guidelines for Tuning the Excited State Hückel-Baird Hybrid Aromatic Character of Pro-Aromatic Quinoidal Compounds*.

Pro-aromatic molecules have higher-energy diradicaloid states that are significantly influenced by resonance structures in which conjugated rings take on Hückel-aromatic character. Recently, it has been argued that there are also pro-aromatic molecules that adopt central units with 4nπ-electron Baird-aromatic character in the T1 state, although detailed analysis suggests that these compounds are better labelled as T1 Hückel-Baird hybrid molecules where Hückel-aromaticity dominates. Herein, we consider a series of symmetrically substituted conjugated rings with potential Baird aromaticity in the lowest excited triplet and singlet states. Our computational results allow us to establish general guidelines for the rational design of molecules with excited state Hückel/Baird aromaticity in pro-aromatic quinoidal compounds. We found two main strategies to promote high Baird aromatic character: 1) anionic and small conjugated rings with electron donating groups as substituents and small exocyclic groups with electron withdrawing substituents, or 2) electron deficient conjugated rings with exocyclic electron-donor substitution.

To inquire the effects of different geometric electrodes on current characteristics of C24 fullerene molecular junction.

Two different types of geometric electrode configurations were utilized to form C24 fullerene based molecular junction. The C24 molecule was intercalated in-between gold electrodes with two different shapes viz. knife edge and flat edge and the resultant molecular junctions (MJs) were simulated using nonequilibrium Green's function combined with semiempirical extended Huckel theory (EHT). Different transport parameters, namely projected device density of states, current-voltage curve, differential conductance curve, molecular orbitals, and transmission spectra were investigated at discrete bias voltages to gain insight about the various transport phenomena occurring in these molecular junctions. The results show that when the C24 fullerene is placed in between the flat-edged electrodes, current and conductance are higher in magnitude in comparison to the knife-edged configuration. These deductions give us a new perspective to design advanced molecular devices for electronics applications in the future.