The Limited Predictive Power of the Pauling Rules

The Pauling rules have been used for decades to rationalise the crystal structures of ionic compounds. Despite their importance, there has been no statistical assessment of the performances of these five empirical rules so far. Here, we rigorously and automatically test all five Pauling rules for a large data set of around 5000 known oxides. We discuss each Pauling rule separately, stressing their limits and range of application in terms of chemistries and structures. We conclude that only 13 % of the oxides simultaneously satisfy the last four rules, indicating a much lower predictive power than expected.     

Generalized bond orders

We introduce generalized bond orders defined in terms of weighted Kekule valence structures. The weights were determined by the contributions of linearly independent and minimal conjugated circuits in individual Kekule valence structure. When special values for the contributions of conjugated circuits of different size are assumed, one obtains quantities that show considerable similarity to the Pauling and the Clar's bond orders. Pauling bond orders are obtained when one assumes that all conjugated circuits make equal contribution to bond orders. © 1994 John Wiley & Sons, Inc.     

Pauling’s resonating valence bond theory of metals: some studies on lithium clusters

We report for the first time fully ab initio valence bond (VB) calculations with explicit use of the unsynchronized resonance structures introduced by Pauling [1]. We show that resonance involving these structures largely determines the stability and conformation of the Li ₄ cluster and plays a central role in a VB explanation of the 3-center bonds in planar alkali clusters. The theory can make qualitative predictions on the behaviour of general metallic clusters, and can relate stability and conformation to electronic structure, thus indicating the origin of magic numbers. This first ab initio test of Pauling’s resonating VB theory confirms the importance of the metallic orbital and the covalent character of the metal-metal bond.     

一种确定氧化数的新方法

氧化数是元素的重要性质,在无机化学中应用广泛。长期以来,确定元素氧化数主要根据桐山良一和鲍林等建立的规则,这些规则对于氧化数概念在化学中的推广普及起了很大的作用,但在遇到结构复杂或未知化合物时有时仍然会出现问题。本文根据IUPAC的氧化数定义提出,氧化数完全取决于成键两原子之间的电子供需关系,元素的最高正氧化数受到其原子价层电子数的限制,而元素的最低负氧化数受到同周期稀有气体元素外层电子数与其价层电子数差值的限制,据此建立了确定元素氧化数的新方法,该方法既不需要考虑分子结构,也不依赖元素氧化数的习惯规定,符合氧化数概念提出的初衷,简便易行,例外情况少,不仅适合大学化学教学,也适合中学化学教学。     

Resonance energies of large conjugated hydrocarbons by a statistical method

We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekulé valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekulé valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekulé valence structures allow one not only to obtain the expression for molecular resonance energies (RE ) and numerical estimates for RE , but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders.     

Correlation of bond metallicity measures to electronegativity for binary oxides

We have investigated alkali, alkaline‐earth, and rutile binary oxides within density functional theory (DFT) and Bader's atoms‐in‐molecules theory, focusing on properties of bond and ring critical points, and their relations to band gap and Pauling electronegativity. We find linear relations of kinetic energy density, electron density, and the gap divided by kinetic energy density at the bond critical points to the difference of Pauling electronegativities of the cation and oxygen anion. At the ring critical points of rutile compounds, we also find that some bond metallicity measures are linearly related to the difference of electronegativities. This study extends our knowledge about the relations between bond critical points, band gap, and electronegativity, but also shows for the first time a quantitative relation between quantities at the ring critical points and global properties of the compounds.     

Determination of McGowan volumes for ions and correlation with van der Waals volumes

The McGowan volume has been widely used for the analysis of physicochemical and biochemical properties in chemistry and drug industry. Because McGowan volumes are not available for ions, its application is limited to only neutral compounds. Pauling radii of metallic ions have been collected and studied to obtain McGowan volumes for ions. Regression analysis was carried out between Pauling radii (R(p)) and McGowan radii (R(x)) for a wide range of compounds. It was found that Pauling radii and McGowan radii derived from McGowan volumes by using a volume-radius formula are linearly related (R(x) = 1.115R(p) + 0.0623, r(2) = 0.995). This equation is then used to calculate McGowan volumes for various ions and charged groups. McGowan volumes have been calculated for inorganic, organic, and organometallic compounds and correlated with van der Waals volumes. Results show that McGowan volumes (V(x)) are entirely equivalent to computer-calculated van der Waals volumes.     

Roles of radical characters of pristine and nitrogen-substituted hydrographene in dioxygen bindings

We investigate by means of density functional theory (DFT) calculations how hydrogen-terminated graphenes (hydrographenes) with and without nitrogen impurities interact with dioxygen. The current study aims at searching whether hydrographenes can be utilized as cathode catalysts in fuel cell with a focus on dioxygen binding, the first step in oxygen reduction reaction (ORR). If hydrographenes have a nanometer-size rhombic structure with zigzag edges, unpaired electrons are localized at their edges with or without the nitrogen impurities. Spin localization comes from frontier orbitals of the nanometer-size hydrographenes whose amplitudes appear only at their edges. Due to their radical characters, dioxygen can bind to an edge carbon atom of the hydrographenes under the condition where fuel cell is usually operated. There are two types of dioxygen binding into a hydrographene: one is a Pauling fashion where one C-O bond is formed and the other is a bridging fashion with two formed C-O bonds. In the bridging fashion, the formation of the two C-O bonds activates dioxygen, and then radical characters of the oxygen atoms completely disappear. In contrast, the Pauling fashions retain an unpaired electron on the oxygen atom that does not participate to the C-O bond formation. The existence of radical oxygen atoms would facilitate the next step in ORR (the initial proton transfer to an adsorbed dioxygen), whereas such facilitative effects cannot be seen in its absence. According to DFT calculations, the Pauling-type bindings are always energetically preferred over the bridging-type bindings. In particular, the C→N substitution enhances the preferences of the Pauling-type binding over the bridging-type binding compared with the pristine case. Accordingly DFT calculations demonstrate that radical characters of edge carbons of a nanometer-sized rhombic hydrographene play a crucial role in dioxygen bindings in a Pauling fashion that would be responsible for enhancing the catalytic activity in fuel cell.     

Pursuing High-Resolution Structures of Nicotinic Acetylcholine Receptors: Lessons Learned from Five Decades

Since their discovery, nicotinic acetylcholine receptors (nAChRs) have been extensively studied to understand their function, as well as the consequence of alterations leading to disease states. Importantly, these receptors represent pharmacological targets to treat a number of neurological and neurodegenerative disorders. Nevertheless, their therapeutic value has been limited by the absence of high-resolution structures that allow for the design of more specific and effective drugs. This article offers a comprehensive review of five decades of research pursuing high-resolution structures of nAChRs. We provide a historical perspective, from initial structural studies to the most recent X-ray and cryogenic electron microscopy (Cryo-EM) nAChR structures. We also discuss the most relevant structural features that emerged from these studies, as well as perspectives in the field.     

Azulene – Thiophene – Cyanoacrylic acid dyes with donor-π-acceptor structures. Synthesis,characterisation and evaluation in dye-sensitized solar cells

We report the synthesis of five new azulene containing dyes, having D-π-A type structures. These dyes are synthesised using a sulfonium salt cross-coupling reaction. The dyes have been evaluated spectroscopically, electrochemically, crystallographically, and as sensitizers in dye-sensitized solar cells. We propose a rationale for the dyes' spectroscopic properties and performance in cells, based on conformational data derived from their crystal structures.     

Energetic determinants of oligomeric state specificity in coiled coils

The coiled coil is one of the simplest and best-studied protein structural motifs, consisting of two to five helices wound around each other. Empirical rules have been established on the tendency of different core sequences to form a certain oligomeric state but the physical forces behind this specificity are unclear. In this work, we model four sequences onto the structures of dimeric, trimeric, tetrameric, and pentameric coiled coils. We first examine the ability of an effective energy function (EEF1.1) to discriminate the correct oligomeric state for a given sequence. We find that inclusion of the translational, rotational, and side-chain conformational entropy is necessary for discriminating the native structures from their misassembled counterparts. The decomposition of the effective energy into residue contributions yields theoretical values for the oligomeric propensity of different residue types at different heptad positions. We find that certain calculated residue propensities are general and consistent with existing rules. For example, leucine at d favors dimers, leucine at a favors tetramers or pentamers, and isoleucine at a favors trimers. Other residue propensities are sequence context dependent. For example, glutamine at d favors trimers in one context and pentamers in another. Charged residues at e and g positions usually destabilize higher oligomers due to higher desolvation. Nonpolar residues at these positions confer pentamer specificity when combined with certain residues at positions a and d. Specifically, the pair Leua-Alag' or the inverse was found to stabilize the pentamer. The small energy gap between the native and misfolded counterparts explains why a few mutations at the core sites are sufficient to induce a change in the oligomeric state of these peptides. A large number of possible experiments are suggested by these results.     

Bond length features of linear carbon chains of finite to infinite size: Visual interpretation from Pauling bond orders

Schemes for Kekulé structure counting of linear carbon chains are suggested. Mathematical formulas, which calculate the Pauling bond order P(k, N) of a chemical bond numbered by k, are given for the carbon chain with N carbon atoms. By use of the least‐squares fitting of a linearity, relationships between Pauling bond orders and bond lengths are obtained, and such correlation of the Pauling bond order–bond length can be qualitatively extended to the excited states. The relative magnitudes of Pauling bond orders in unsaturated carbon chains dominate C–C bond lengths a well as the bond length feature with the chain size increasing. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 144–149, 2003     

Nature of the chemical bond and prediction of radiation tolerance in pyrochlore and defect fluorite compounds

The radiation tolerance of synthetic pyrochlore and defect fluorite compounds has been studied using ion irradiation. We show that the results can be quantified in terms of the critical temperature for amorphization, structural parameters, classical Pauling electronegativity difference, and disorder energies. Our results demonstrate that radiation tolerance is correlated with a change in the structure from pyrochlore to defect fluorite, a smaller unit cell dimension, and lower cation-anion disorder energy. Radiation tolerance is promoted by an increase in the Pauling cation-anion electronegativity difference or, in other words, an increase in the ionicity of the chemical bonds. A further analysis of the data indicates that, of the two possible cation sites in ideal pyrochlore, the smaller B-site cation appears to play the major role in bonding. This result is supported by ab initio calculations of the structure and bonding, showing a correlation between the Mulliken overlap populations of the B-site cation and the critical temperature.     

Quantum mechanical studies on model α‐pleated sheets

Pauling and Corey proposed a pleated‐sheet configuration, now called α‐sheet, as one of the protein secondary structures in addition to α‐helix and β‐sheet. Recently, it has been suggested that α‐sheet is a common feature of amyloidogenic intermediates. We have investigated the stability of antiparallel β‐sheet and two conformations of α‐sheet in solution phase using the density functional theoretical method. The peptides are modeled as two‐strand acetyl‐(Ala)₂‐N‐methylamine. Using stages of geometry optimization and single point energy calculation at B3LYP/cc‐pVTZ//B3LYP/6‐31G* level and including zero‐point energies, thermal, and entropic contribution, we have found that β‐sheet is the most stable conformation, while the α‐sheet proposed by Pauling and Corey has 13.6 kcal/mol higher free energy than the β‐sheet. The α‐sheet that resembles the structure observed in molecular dynamics simulations of amyloidogenic proteins at low pH becomes distorted after stages of geometry optimization in solution. Whether the α‐sheets with longer chains would be increasingly favorable in water relative to the increase in internal energy of the chain needs further investigation. Different from the quantum mechanics results, AMBER parm94 force field gives small difference in solution phase energy between α‐sheet and β‐sheet. The predicted amide I IR spectra of α‐sheet shows the main band at higher frequency than β‐sheet. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Bond orders and electron delocalization indices for S–N,S–C and S–S bonds in 1,2,3-dithiazole systems

A parametric QTAIM-based (topological) model of bond orders and a modification of the Pauling bond order model are proposed for N,S-containing heterocycles, in particular, for 1,2,3-dithiazoles and 1,2,3-dithiazolium systems, which are prone to the formation of stable radicals and therefore are promising compounds in photovoltaics. These models have been parameterized for covalent S–N, S–C and S–S bonds using the electron delocalization indices. A modified Pauling’s bond order model uses turning radii, that is, the distances within which the potential acting on an electron in a system still tends to return that electron to the atomic basin, and avoids the need to choose the hybridization state of bound atoms arbitrarily.     

First-Principles Study of La Doping Effects on the Electronic Structures and Photocatalytic Properties of Anatase TiO2

The effects of doping concentration, position and oxygen vacancy defect on the stability, electronic and optical properties of La-doped anatase TiO₂ have been investigated based on DFT+U method. The calculations indicated that the doping concentration and sites of La affected the stability and band gap of La-doped TiO₂ significantly due to the lattice distortion, which obey the ionic Pauling’s rules and crystal field theories; moreover, the simulated adsorption spectrum shows an obviously increase in the photocatalysis properties, which are in good agreement with recently experimental measurements. The oxygen vacancy defect will enhance the structural stability and the adsorption of visible light in La-doped TiO₂ system, which is important in photocatalytic application.     

STRUCTURAL RULES OF TRANSITIONMETAL CARBONYL COMPOUNDS

In this article we have proposed two topological rules to account for the electronic structures of transition-metal carbonyl compounds. The second rule is applied to those which have polyhedral metalhc skeletons with triangular faces and their derivates, while the first rule is applied to all the others We have used these two rules to analyze 261 structure-known compounds with the number of metal atoms from 2 to 12, and the results show that the two rules are in good agreement with the experimental facts. Furthermore, we have also derived from the second rule a formula which can be used to account for the electronic structures of closedpacking carbonyl compounds and which is the same as that given by Ciani and his coworkers.     

Three‐electron two‐center bonding in cycloimmonium ylides

We explore the possibility that a 3‐electron‐2‐center bonding exists in cycloimmonium ylides. To detect this bonding in a polyatomic system, 3‐electron‐1‐hole density operators, characterizing a Pauling 3‐electron bond, are used in the framework of second quantization formalism. The weights of 3‐electron resonance structures are calculated and compared with the weights of 2‐electron structures for the ylide bond of pyridinium dicyanomethylide; the correlations of (↑↓) and (↑) electronic events, involved in the 3‐electron resonance structures, are also investigated. The calculations are performed in various approximation levels, and both orthogonal and nonorthogonal natural atomic orbitals are adopted. All calculations show that a 3‐electron bond exists between N and C atoms of ylide bond, but this bonding is not extended in C atoms of the pyridinium group. The interactions of α,β electrons (at the configuration interaction [CI] level) increase the localization of electrons, the weights of 3‐electron resonance structures, and thus the probability for 3‐electron bonding. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004