Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule

4N Baird's rule represented the extension of Hückel's 4N + 2 rule to triplet state systems. In this work we extend the 2(N + 1)(2) Hirsch rule for spherical aromatic species to open-shell spherical compounds and we provide evidence that those spherical species having a same-spin half-filled last energy level with the rest of the levels being fully-filled, i.e., those having 2N(2) + 2N + 1 electrons and S = N + ?, are aromatic.     

How substrate solvation contributes to the enantioselectivity of subtilisin toward secondary alcohols

The current rule to predict the enantiopreference of subtilisin toward secondary alcohols is based on the size of the substituents at the stereocenter and implies that the active site contains two differently sized pockets for these substituents. Several experiments are inconsistent with the current rule. First, the X-ray structures of subtilisin show there is only one pocket (the S1' pocket) approximately the size of a phenyl group to bind secondary alcohols. Second, the rule often predicts the incorrect enantiomer for reactions in water. To resolve these contradictions, we refine the current rule to show that subtilisin binds only one substituent of a secondary alcohol and leaves the other in solvent. To test this refined empirical rule, we show that the enantioselectivity of a series of secondary alcohols in water varied linearly with the difference in hydrophobicity (log P/P0) of the substituents. This hydrophobicity difference accounts for the solvation of one substituent in water.     

Application of Badger's rule to heme and non-heme iron-oxygen bonds: an examination of ferryl protonation states

To gain insight into the protonation state of enzymatic ferryl species we have examined the applicability of Badger's rule to heme and non-heme iron-oxygen bonds. Using density functional theory we have calculated r(e) and nu(e) for the Fe-O bonds of complexes with different axial ligands, iron-oxidation, oxygen-protonation, and spin states. Our results indicate that Badger's rule holds for heme and non-heme oxo and hydroxo complexes. We find that the long Fe-O bonds that have been reported in the crystal structures of the ferryl forms of myoglobin, horseradish peroxidase, cytochrome c peroxidase, and catalase deviate substantially from the values predicted by Badger's rule, while the short Fe-O bonds obtained from X-ray absorption measurements are in good agreement with Badger's rule. In light of our analysis we conclude that the ferryl forms of myoglobin, horseradish peroxidase, and cytochrome c peroxidase are authentic iron(IV)oxos with Fe-O bonds on the order of 1.66 A and pKa's < 4.     

A general,most basic rule for ion dissociation: Protonated molecules

Contrary to the common but potentially misleading belief that when a protonated molecule is excited, it is its most stable protomer that will mandatorily dissociate, we demonstrate herein that, when rationalizing or predicting the chemistry of such ions, we should always search for the most labile protomer. This “most labile protomer” rule, based on the mobile proton model, states therefore that when a protonated molecule is heated, during ionization or by collisions for instance, the loosely bonded proton (H⁺) can acquire enough energy to detach itself from the most basic site of the molecule and then freely “walk through” the molecular framework to eventually find, if available, another protonation site, forming other less stable but more labile protomers, that is, protomers that may display lower dissociation thresholds. To demonstrate the validity of the “most labile protomer” rule as well as the misleading nature of the “most stable protomer” rule, we have selected several illustrative molecules and have collected their ESI(+)-MS/MS. To compare energies of precursors and products, we have also performed PM7 calculations and elaborated potential energy surface diagrams for their possible protomers and dissociation thresholds. We have also applied the “most labile protomer” rule to reinterpret—exclusively via classical charge-induced dissociation cleavages—several dissociation processes proposed for protonated molecules. In an accompanying letter, we have also applied a similar “most labile electromer” rule to ionized molecules.     

分子筛中TO4四面体的电荷效应

以AlCl₃和PCl₅与APO-5分子筛气固相反应结果为出发点,应用Pauling静电规则和量子化学计算考察了硅铝分子筛和磷铝分子筛同晶置换反应中的电性因素和能量因素。比较Loewenstein规则和静电规则在分子筛中的应用,得出结论:Loewensteio规则的本质是静电规则,这一规则的内容具有较大的局限性,应扩展为带同种电荷的TO₄四面体不相连规则。量子化学的计算证明了上述结论的正确性。     

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.     

Guidelines proposed for designing organic ferromagnets by using a quantum chemical approach

For predicting the characteristics of organic ferromagnetic substances, we have previously proposed a simple rule for conjugated organic molecules based on molecular orbital coefficients by the simple Hückel??s nonbonding molecular orbital (NBMO) method. In this work, we extended the rule to systems including heteroatoms to become more widely applicable to various magnetic polymers. It was proven that the linkage between molecules having an NBMO conserves the original NBMO levels even for the supermolecule after the linkage. In addition, we have also proposed an index to estimate the amount of possessing ferromagnetic property. The reliability of the rule and index is examined by applying both the density functional theory (DFT) with functional methods, i.e., B3LYP, B3PW91, BLYP, PBEPBE, and PBEP86, and the complete active space SCF (CASSCF) calculations to several model molecules.     

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G) and nonlinear (N ₁) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively.This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse.For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.     

硼烷簇合物的结构规则

从超额电子数出发，提出了1种稠合型硼烷的结构规则，讨论了各种规则间的关系。     

The Nowotny chimney ladder phases: whence the 14 electron rule?

The late transition metal Nowotny chimney ladder phases (NCLs, T(t)E(m); T, groups 7-9; E, groups 13 and 14) follow a 14 electron rule: the total number of valence electrons per T atom is 14. In this paper, we extract a chemical explanation for this rule from extended Hückel calculations; we focus on RuGa(2), the parent NCL structure. A gap between filled and unfilled bands arises from the occupation of two Ga-Ga bonding/Ru-Ga nonbonding orbitals per RuGa(2), independent of k-point. In addition, the five Ru d levels are filled. Together this makes for 7 filled bands at each k-point, or 14 electrons per Ru. We discuss the connections between this 14 electron rule and the 18 electron rule of organometallic complexes.     

Fourier analysis,correlation functions and nonadiabatic electron transfer: Wavepackets and exact representations

Summary We investigate the validity of several common approximations in the analysis of nonadiabatic intramolecular electron transfer rate constants. Utilizing the Fourier representation of the golden rule form, we study the evolution of the vibrational correlation function that represents the density-of-states-weighted Franck-Condon factor. In particular, we test the validity of the perturbation theoretic golden rule form and of the Gaussian wavepacket representation for the vibrational wavefunctions against numerically exact quantum mechanical propagations. Although specific cases are found in which both of these break down, for a wide range of conditions (including anharmonic behavior and frequency changes), both the Gaussian wavepacket representation and the golden rule are excellent approximations.     

Jointly handling potency and toxicity of antimicrobial peptidomimetics by simple rules from desirability theory and chemoinformatics

Today, emerging and increasing resistance to antibiotics has become a threat to public health worldwide. Antimicrobial peptides have unique action mechanisms making them an attractive therapeutic prospect to be applied against resistant bacteria. However, the major drawback is related with their high hemolytic activity which cancels out the safety requirements for a human antibiotic. Therefore, additional efforts are needed to develop new antimicrobial peptides that possess a greater potency for bacterial cells and less or no toxicity over erythrocytes. In this paper, we introduce a practical approach to simultaneously deal with these two conflicting properties. The convergence of machine learning techniques and desirability theory allowed us to derive a simple, predictive, and interpretable multicriteria classification rule for simultaneously handling the antibacterial and hemolytic properties of a set of cyclic β-hairpin cationic peptidomimetics (Cβ-HCPs). The multicriteria classification rule exhibited a prediction accuracy of about 80% on training and external validation sets. Results from an additional concordance test have shown an excellent agreement between the multicriteria classification rule predictions and the predictions from independent classifiers for complementary antibacterial and hemolytic activities, respectively, evidencing the reliability of the multicriteria classification rule. The rule was also consistent with the general mode of action of cationic peptides pointing out its biophysical relevance. We also propose a multicriteria virtual screening strategy based on the joint use of the multicriteria classification rule, desirability, similarity, and chemometrics concepts. The ability of such a virtual screening strategy to prioritize selective (nonhemolytic) antibacterial Cβ-HCPs was assessed and challenged for their predictivity regarding the training, validation, and overall data. In doing so, we were able to rank a selective antibacterial Cβ-HCP earlier than a biologically inactive or nonselective antibacterial Cβ-HCP with a probability of ca. 0.9. Our results thus indicate that promising chemoinformatics tools were obtained by considering both the multicriteria classification rule and the virtual screening strategy, which could, for instance, be used to aid the discovery and development of potent and nontoxic antimicrobial peptides.     

Elasticity‐Dependent Fast Underwater Adhesion Demonstrated by Macroscopic Supramolecular Assembly

Macroscopic supramolecular assembly (MSA) is a recent development in supramolecular chemistry to associate visible building blocks through non‐covalent interactions in a multivalent manner. Although various substrates (e.g. hydrogels, rigid materials) have been used, a general design rule of building blocks in MSA systems and interpretation of the assembly mechanism are lacking and are required. Herein we design three model systems with varied elastic modulus and correlated the MSA probability with the elasticity. Based on the effects of substrate deformability on multivalency, we have proposed an elastic‐modulus‐dependent rule that building blocks below a critical modulus of 2.5 MPa can achieve MSA for the used host/guest system. Moreover, this MSA rule applies well to the design of materials for fast underwater adhesion: Soft substrates (0.5 MPa) can achieve underwater adhesion within 10 s with one order of magnitude higher strength than that of rigid substrates (2.5 MPa).     

New combining rules for rare gas van der waals parameters

New combining rules are proposed for the well depth, ?, and interaction distance, σ, describing nonbonded interatomic forces for rare gas pair interactions. Concepts underlying current combining rules applied in simulations of macromolecular and polymer systems are shown to be incompatible with experimental data on the rare gases. The current combining rules are compared with the new results using the experimental data. Mathematical properties of combining rules are considered, and it is shown how to reduce combining rule formulas from a two-parameter to a single-parameter problem. It is also shown how to graphically analyze combining rules against experimental data. We demonstrate using this analysis technique that the rare gas potentials do not obey a single combining rule for the ? parameter but do follow a single combining rule for the σ parameter. Finally, we demonstrate that a combining rule using both ? and ω can be used to predict the ? parameters for the mixed rare gas pairs. © John Wiley & Sons, Inc.     

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpson's rule, Gauss-Legendre, Gauss-Kronrod-Patterson, and Clenshaw-Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpson's rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ-states. We demonstrate that Simpson's rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss-Legendre, Gauss-Kronrod-Patterson, or Clenshaw-Curtis integration, are used; no more than seven λ-states, which in the case of Clenshaw-Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennett's acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft-core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennett's acceptance ratio method. Therefore, we recommend Bennett's acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.     

Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization

We have only rules of thumb with which to predict how a material will crystallize, chief among which is Ostwald's rule of stages. It states that the first phase to appear upon transformation of a parent phase is the one closest to it in free energy. Although sometimes upheld, the rule is without theoretical foundation and is not universally obeyed, highlighting the need for microscopic understanding of crystallization controls. Here we study in detail the crystallization pathways of a prototypical model of patchy particles. The range of crystallization pathways it exhibits is richer than can be predicted by Ostwald's rule, but a combination of simulation and analytic theory reveals clearly how these pathways are selected by microscopic parameters. Our results suggest strategies for controlling self-assembly pathways in simulation and experiment.     

A general,most basic rule for ion dissociation: Ionized molecules

Herein we revisit a basic rule for the interpretation of ion chemistry of ionized molecules, first proposed by the pioneers of MS spectra interpretation, but somewhat overlooked over the years. This rule states that, when rationalizing or predicting the dissociation chemistry of an ionized molecule (M^+.), a model analog to the “mobile proton model,” that is, a “mobile electron model” via “e^--jumping” should be considered. Ground-state M^+. is indeed the first species to be considered, but “e^--jumping” may eventually lead to other more energetic electromers—ionized molecules that differ only in the location of the missing electron—and each one of these electromers may dissociate via distinctive routes. In such a scenario, the route involving not necessarily the ground-state M^+., but the most labile electromer could become predominant or even exclusive. We argue that this “most labile electromer” rule, as well as an analogous “most labile protomer” rule that we have proposed for protonated molecules in an accompanying article, with the application of our conventional toolbox of a few cleavages and rearrangements, greatly simplifies the interpretation and prediction of ion chemistry.     

Development of a read-across workflow for skin irritation and corrosion predictions

We developed a read-across workflow using the OECD QSAR Toolbox for the prediction of skin irritation and corrosion. In the workflow, we gathered analogues using an improved profiler for skin irritation and corrosion to define valid categories. In addition, we refined categories by removing chemicals based on melting points and structural features. Finally, prediction results were obtained using our self-determined rule for read-across. In this rule, we decided the number of analogues from which the read-across is performed, analogue selection criteria (i.e. high similarity vs. near log P_ow) and prediction rule (i.e. majority vs. unanimity). We created a program for the optimization of read-across workflows. We applied this program to 313 chemicals in the training set and sought the optimized workflows among >1000 possible choices of profilers and ways of subcategorization and data gap filling. Use of the optimized workflows provided highly accurate, unbiased, user-independent and reproducible read-across predictions. The prediction results obtained from read-across workflows can be used for the selection of in vitro test methods or as part of the weight-of-evidence approaches in the Integrated Approach on Testing and Assessment for skin irritation and corrosion. Moreover, these results can be used for screening purposes and/or preliminary hazard assessment.     

New quinoxaline-piperazine-oxazole conjugates: Synthesis,in vitro anticancer,in silico ADMET,and molecular docking studies

In this paper, we describe the synthesis of some new quinoxaline-piperazine-oxazole amide conjugates 6a-n from 3-chloroquinoxaline-2-carbonitrile using well-known reaction sequences. The synthesized compounds were characterized by ¹H NMR,¹³C NMR, and mass spectral analysis. The compounds were tested for their in vitro antiproliferative activity toward four different cancer cell lines such as PC-3, MCF-7, DU-145, and A-549 by MTT method. The compounds, 6c, 6h, 6i , and 6n were found to be more potent than the standard Erlotinib. In vitro tyrosine kinase EGFR inhibition studies using four potent compounds revealed that 6n has double inhibiting tendency with value IC₅₀ of 0.22 μM and 6h with value of IC₅₀ 0.27 μM compared to reference compound. Molecular docking studies of active compounds, 6c , 6h , 6i , and 6n on EGFR receptor suggested that all the compounds have more binding energies than that of Erlotinib. Furthermore, the in silico pharmacokinetic profile was accomplished for the active compounds, 6c , 6h , 6i , and 6n using SWISS/ADME and pk CSM, whereas compounds, 6h , 6i , and 6c followed Lipinski rule, Veber rule, Egan rule and Muegge rule. The remaining compound 6n did not follow Lipinski rule, Ghose rule because one common violation, that is, because of high molecular weight (MW > 350).