Symmetry measures of the electron density

In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C₆ symmetry along the B_2u distortion mode of benzene and an analysis of rotational symmetry for different six‐member ring heterocycles. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Shape and symmetry of heptacoordinate transition-metal complexes: structural trends

The stereochemistries of heptacoordinate transition-metal complexes are analyzed by using continuous symmetry and shape measures of their coordination spheres. The distribution of heptacoordination through the transition-metal series is presented based on structural database searches including organometallic and Werner-type molecular complexes, metalloproteins, and extended solids. The most common polyhedron seems to be the pentagonal bipyramid, while different preferences are found for specific families of compounds, as in the complexes with three or four carbonyl or phosphine ligands, which prefer the capped octahedron or the capped trigonal prism rather than the pentagonal bipyramid. The symmetry maps for heptacoordination are presented and shown to be helpful for detecting stereochemical trends. The maximal symmetry interconversion pathways between the three most common polyhedra are defined in terms of symmetry constants and a large number of experimental structures are seen to fall along those paths.     

Shape and spin state in four-coordinate transition-metal complexes: the case of the d(6) configuration

Generalized polyhedral interconversion coordinates are defined within the framework of Avnir's continuous shape measures. The application of such interconversion coordinates to the study of the potential energy surfaces that define the stereochemical choice in four-coordinate transition metal complexes with different spin states is presented, and the correlation between potential energy curves and distribution of experimental structures along the tetrahedron to square interconversion path is shown for the case of the d(6) transition-metal complexes.     

Pseudosymmetry analysis of molecular orbitals

We introduce a pseudosymmetry analysis of molecular orbitals by means of the newly proposed irreducible representation measures. To do that we define first what we consider as molecular pseudosymmetry and the relationships of this concept with those of approximate symmetry and quasisymmetry. We develop a general algorithm to quantify the pseudosymmetry content of a given object within the framework of the finite group algebra. The obtained mathematical expressions are able to decompose molecular orbitals by means of the irreducible representations of any reference symmetry point group. The implementation and usefulness of the pseudosymmetry analysis of molecular orbitals is demonstrated in the study of σ and π orbitals in planar and nonplanar polycyclic aromatic hydrocarbons and the t_2g and e_g character of the d‐orbitals in the [FeH₆]^3? anion in its high spin state along the Bailar twist pathway. © 2013 Wiley Periodicals, Inc.     

Molecular Rotors of Coronene in Charge‐Transfer Solids

Ten types of neutral charge transfer (CT) complexes of coronene (electron donor; D) were obtained with various electron acceptors (A). In addition to the reported 7,7,8,8‐tetracyanoquinodimethane (TCNQ) complex of 1:1 stoichiometry with a DA‐type alternating π column, TCNQ also afforded a 3:1 complex, in which a face‐to‐face dimer of parallel coronenes ( Cor‐A s) is sandwiched between TCNQs to construct a DDA‐type alternating π column flanked by another coronene ( Cor‐B ). Whereas solid‐state ²H NMR spectra of the 1:1 TCNQ complex formed with deuterated coronene confirmed the single in‐plane 6‐fold flipping motion of the coronenes, two unsynchronized motions were confirmed for the 3:1 TCNQ complex, which is consistent with a crystallographic study. Neutral [Ni(mnt)₂] (mnt: maleonitriledithiolate) as an electron acceptor afforded a 5:2 complex with a DDA‐type alternating π column flanked by another coronene, similar to the 3:1 TCNQ complex. The fact that the Cor‐A s in the [Ni(mnt)₂] complex arrange in a non‐parallel fashion must cause the fast in‐plane rotation of Cor‐A relative to that of Cor‐B . This is in sharp contrast to the 3:1 TCNQ complex, in which the dimer of parallel Cor‐A s shows inter‐column interactions with neighboring Cor‐A s. The solid‐state ¹H NMR signal of the [Ni(mnt)₂] complex suddenly broadens at temperatures below approximately 60 K, indicating that the in‐plane rotation of the coronenes undergoes down to approximately 60 K; the rotational rate reaches the gigahertz regime at room temperature. Rotational barriers of these CT complexes, as estimated from variable‐temperature spin–lattice relaxation time (T₁) experiments, are significantly lower than that of pristine coronene. The investigated structure–property relationships indicate that the complexation not only facilitates the molecular rotation of coronenes but also provides a new solid‐state rotor system that involves unsynchronized plural rotators.     

Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure

We provide analytical solutions of the Continuous Symmetry Measure (CSM) equation for several symmetry point-groups, and for the associated Continuous Chirality Measure (CCM), which are quantitative estimates of the degree of a symmetry-point group or chirality in a structure, respectively. We do it by solving analytically the problem of finding the minimal distance between the original structure and the result obtained by operating on it all of the operations of a specific G symmetry point group. Specifically, we provide solutions for the symmetry measures of all of the improper rotations point group symmetries, S(n), including the mirror (S(1), C(S)), inversion (S(2), C(i)) as well as the higher S(n)s (n > 2 is even) point group symmetries, for the rotational C(2) point group symmetry, for the higher rotational C(n) symmetries (n > 2), and finally for the C(nh) symmetry point group. The chirality measure is the minimal of all S(n) measures.     

Association and Shape of Molecules Using Free Length Theory

Abstract

Traditionally workers engaged in calculation of the ultrasonic velocity in liquid mixtures using Jacobson's Free Length Theory (FLT) arrive at the conclusion that the predictions of FLT produce large deviations when compared with experimental velocities. Such workers seemed to have ignored the necessity of incorporating two parameters in FLT as originally suggested by Jacobson himself: one, to account for the association, and the other, for the shape of the component molecules in the mixture. By introducing the association factor and deriving explicit expressions for different shapes of the molecules, the present work has demonstrated that FLT might be made to predict ultrasonic velocities in the mixtures better. Also this approach can very well be used to account for molecular associations and shapes.     

聚炔、累积多烯与全碳环分子的模糊对称性

近年来我们关于分子模糊对称性的工作多属于模糊点对称性的研究, 关于模糊空间对称性探讨较少. 聚炔作为线状一维模糊周期分子, 我们曾对其进行了初步分析. 虽然对于聚炔分子骨架的分析比较全面, 但由于繁冗的计算使我们对分子轨道(MO)模糊对称性的分析只限于少数典型分子. 本文将对不同的聚炔分子MO模糊对称性特征进行较为系统的分析. 结果表明包含不同碳原子数目的分子轨道模糊对称性参数值之间有一定相关性. 此外我们还对一些相关体系分子的MO进行分析, 累积多烯分子虽然并非线型分子, 但其π-MO相关的碳原子处于线性位置, 可依模糊一维周期的G11体系处理. 按Born-Karman近似, 即n个单元的一维周期对称群与Cn点群同构, 本文还分析了相关的全碳环分子的MO的对称性和模糊对称性. 努力寻求与一维周期性相关的模糊对称性规律性特征.     

Induction of the Columnar Phase of Unconventional Dendrimers by Breaking the C2 Symmetry of Molecules

Two triazine‐based unconventional dendrimers were prepared and characterized by ¹H and ¹³C NMR spectroscopy, mass spectrometry, and elemental analysis. Differential scanning calorimetry, polarizing microscopy, and powder XRD studies showed that these dendrimers display columnar liquid‐crystalline phases during thermal treatment. This is ascribable to breaking of their C₂ symmetry. The molecular conformations of prepared dendrimers were obtained by computer simulation with the MM3 model of the CaChe program in the gas phase. The simulation showed that the conformations of the prepared dendrimers are rather flat and disfavor formation of the LC phase. However, due to C₂‐symmetry breaking, the prepared dendrimers have structural isomers in the solid state and thus show the desired columnar phases. This new strategy should be applicable to other types of unconventional dendrimers with rigid frameworks.     

Effects of a lysophosphatidylcholine and a phosphatidylcholine on the morphology of taurocholic acid-based mixed micelles as determined by small-angle X-ray scattering

We previously showed that Caco-2 cell absorption of β-carotene from taurocholic acid (TA)-based mixed micelles differed depending on the composition of the micelles. In this study, the shapes and sizes of TA-based mixed micelles, that is, mixed micelles of TA, 1-oleoyl-rac-glycerol (MG), oleic acid (OLA), and either 1-palmitoyl-sn-glycero-3-phosphocholine (MPPC; i.e., a lysophospholipid) or 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC; i.e., a phospholipid) (60:3:1:0.75–12) were determined by using small-angle X-ray scattering (SAXS). We found that increasing the ratio of MPPC in mixed micelles of TA, MG, OLA, and MPPC was responsible for the previously observed enhanced β-carotene absorption by Caco-2 cells and changed the micelle shape from core–shell spherical to core–shell ellipsoidal. In contrast, increasing the ratio of POPC in mixed micelles of TA, MG, OLA, and POPC was responsible for the suppressed β-carotene absorption by the cells, changed the micelle shape from core–shell spherical to core–shell ellipsoidal to core–shell cylindrical, and caused a rapid increase in micelle volume. These results will be useful for understanding the mechanisms that mediate β-carotene absorption by cells and for developing technologies to improve the intestinal absorption of lipophilic components of drugs and nutrients.     

Mirror Symmetry Breaking by Chirality Synchronisation in Liquids and Liquid Crystals of Achiral Molecules

Spontaneous mirror symmetry breaking is an efficient way to obtain homogeneously chiral agents, pharmaceutical ingredients and materials. It is also in the focus of the discussion around the emergence of uniform chirality in biological systems. Tremendous progress has been made by symmetry breaking during crystallisation from supercooled melts or supersaturates solutions and by self‐assembly on solid surfaces and in other highly ordered structures. However, recent observations of spontaneous mirror symmetry breaking in liquids and liquid crystals indicate that it is not limited to the well‐ordered solid state. Herein, progress in the understanding of a new dynamic mode of symmetry breaking, based on chirality synchronisation of transiently chiral molecules in isotropic liquids and in bicontinuous cubic, columnar, smectic and nematic liquid crystalline phases is discussed. This process leads to spontaneous deracemisation in the liquid state under thermodynamic control, giving rise to long‐term stable symmetry‐broken fluids, even at high temperatures. These fluids form conglomerates that are capable of extraordinary strong chirality amplification, eventually leading to homochirality and providing a new view on the discussion of emergence of uniform chirality in prebiotic systems.     

A Symmetry adapted tessellation of the GEPOL surface: applications to molecular properties in solution

A procedure to partition the GEPOL molecular surface into tesserae that respects the molecular symmetry constraints is presented. Using this method it is possible to build a solvent reaction field for the Polarizable Continuum Model with the same symmetry of the nuclear potential. Several applications are reported and discussed to evaluate the performance of this new procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1262–1272, 2001     

Rhombicuboctahedral Ag100: Four-Layered Octahedral Silver Nanocluster Adopting the Russian Nesting Doll Model

Precise atomic structure of metal nanoclusters (NCs) is fundamental for elucidating the structure–property relationships and the inherent size-evolution principles. Reported here is the largest known FCC-based (FCC=face centered cubic) silver nanocluster, [Ag₁₀₀(SC₆H₃^3,4F₂)₄₈(PPh₃)₈]⁻: the first all-octahedral symmetric nesting Ag nanocluster with a four-layered Ag₆@Ag₃₈@Ag₄₈S₂₄@Ag₈S₂₄P₈ structure, consistent symmetry elements, and a unique rhombicuboctahedral morphology distinct from theoretical predictions and previously reported FCC-based Ag clusters. DFT studies revealed extensive interlayer interactions and degenerate frontier orbitals. The FCC-based Russian nesting doll model constitutes a new platform for the study of the size-evolution principles of Ag NCs.     

Charge Neutralization Drives the Shape Reconfiguration of DNA Nanotubes

Reconfiguration of membrane protein channels for gated transport is highly regulated under physiological conditions. However, a mechanistic understanding of such channels remains challenging owing to the difficulty in probing subtle gating‐associated structural changes. Herein, we show that charge neutralization can drive the shape reconfiguration of a biomimetic 6‐helix bundle DNA nanotube (6HB). Specifically, 6HB adopts a compact state when its charge is neutralized by Mg²⁺; whereas Na⁺ switches it to the expanded state, as revealed by MD simulations, small‐angle X‐ray scattering (SAXS), and FRET characterization. Furthermore, partial neutralization of the DNA backbone charges by chemical modification renders 6HB compact and insensitive to ions, suggesting an interplay between electrostatic and hydrophobic forces in the channels. This system provides a platform for understanding the structure–function relationship of biological channels and designing rules for the shape control of DNA nanostructures in biomedical applications.     

复合稀土对Fe-Mn-Si-Ni-C合金形状记忆效应的影响

通过弯曲法测量、热循环训练、扫描电镜、X射线衍射等方法，研究了复合稀土对Fe-Mn-Si-Ni-C合金形状记忆效应的影响。研究结果表明，Fe-Mn-Si-Ni-C合金中加入复合稀土，能够明显细化合金的金相组织，显著提高合金的形状记忆效应，并使合金表现出微弱的双程记忆效应。试验结果还表明，第一种训练途径以及加入微量复合稀土是降低应力诱发ε马氏体稳定化行之有效的方法，X射线衍射结果表明，该训练方法有助于提高合金中ε→γ转变的ε逆转变率，对提高合金的记忆性能起积极的作用。     

Liquid crystalline properties and photochromism of 4-alkyl-N-(4-alkloxysalicylidene)anilines

Eight new homologous series of 4-alkyl-N-(4-alkloxysalicylidene)anilines were synthesized. The phase transitions of these homologues were determined using differential scanning calorimetry and polarizing optical microscopy. The homologues began to exhibit liquid crystalline phases as the terminal alkyl or alkoxyl chains were lengthened. In addition, some members of these homologues series exhibited photochromism in the solid state.     

Isomers of Dithienocyclopentapyrene-Based Non-Fullerene Electron Acceptors: Configuration Effect on Photoelectronic Properties

One pair of isomers, centrosymmetric anti- Py - 1 and axisymmetric syn- Py - 2 , was designed and synthesized with an acceptor–donor–acceptor (A–D–A) structure by choosing dithienocyclopentapyrene with four 4-hexylphenyl side chains as the D unit, and 2-(5,6-difluoro-3-oxo-2,3-dihydro-1H-inden-1-ylidene) malononitrile as the A unit. In-depth structure–property relationship studies revealed that the isomers have similar UV/Vis absorption, fluorescence emission, and energy levels but significant differences in molecular shape, polarity, and charge mobility. Solution-processed bulk-heterojunction (BHJ) small-molecule organic solar cells with Py - 1 as the electron-acceptor material and PTB7-Th as the electron-donor material exhibit a power conversion efficiency (PCE) of 6.07 %, or 60 % higher than that of Py - 2 (3.7 %), which could be mainly attributed to the higher and more balanced hole/electron mobilities and better phase separation of the Py - 1 -based active layer.     

苯并菲盘状液晶的合成、亲氟效应及分子对称性对介晶性的影响

New symmetrical and asymmetrical triphenylene-containing discotic liquid crystals with two different peripheral alkyl chains, known as sym-TP(OC6H13)3(OR)3 and asym-TP(OC6H13)3(OR)3, were synthesized. Their thermotropic liquid crystal properties were investigated through polarizing optical microscopy (POM), differential scanning calorimetry (DSC) and X-ray diffraction (XRD) analyses. The asyrranetdcal discogens are 2,6,11-rialkoxy-3,7,10-trihexyloxytriphenylenes, with the alkyl chain carbon numbers varying from 3-10, 12, and 14, while the symmetrical compounds are 2,6,10-trialkyloxy-3,7,11-trihexyloxytriphenylene. Two fluoroalkoxy substituted triphenylene discogens, 2,6,10-td(4,4,4-trifluorobutoxy)-3,7,11-trihexyloxytriphenylene and its asymmetrical isomer 2,6,11-tri(4,4,4-trifluorobutoxy)-3,7,10-trihexyloxytdphenylene were prepared. These two compounds show higher melting and clearing points than their alkoxy analogs, which implies that fluorophilic effect exists in the formation and stabilization of discotic columnar mesophase. The triphenylene derivatives TP(OC6H13)3(OR)3 with two different peripheral chains, symmetrically or asymmetrically attached on triphenylene cores, have lower melting points and clearing points than those of the higher symmetrical compounds TP(OR)6 with the same total chain carbon numbers. The mixed-chain-triphenylenes with longer alkoxy chains (n=9,10,12,14) show columnarmesophase at room temperature.