Reversal of Orbital Symmetry Control in Electrocyclic Ring Closures through Craig‐Möbius Aromaticity

Experimentalists are challenged to find the organometallic thermal electrocyclizations that are computationally predicted to proceed with opposite stereoselectivity compared to their metal‐free parent 4n and 4n+2 π‐electron systems. While ring closure of, for example, s‐cis‐butadiene proceeds conrotatory, an iron alkyl complex formed by replacement of a (CH) unit by an [FeH] metal fragment results in a disrotatory electrocyclization.     

Continuous symmetry measures for complex symmetry group

Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB₄ complexes, and the symmetry of several Lennard‐Jones clusters. © 2014 Wiley Periodicals, Inc.     

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     

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non‐Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z‐component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half‐filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non‐Abelian point group. The C₆₀ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Symmetry operation measures

We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.     

Ring‐Opening of Benzocyclobutenol with Mild Bases and Trapping with Dieneophiles

The treatment of benzocyclobutenol with a mild base has been investigated. This reaction results in an electrocyclic opening of the cyclobutene to the corresponding o‐quinodimethane, which has been successfully treated with aldehydes and electron‐deficient alkenes to form benzolactols and benzocyclohexenes respectively.     

群链R3i-D4d-C2v及dN体系在C2v对称性场中的能量矩阵

R_(3i)—D_(4d)—C_(2v)是一条群链。本文讨论如何应用D_(4d)群的标准基函作为C_(2v)群的基函来写出d~N体系在C_(2v)对称性场中各配场谱项的能量矩阵H_1。H_1中的H_(el)。部分完全可以应用D_(4d)的H_1中的H_(el)。,因而简化了计算。所得能量矩阵H_1与前文列出的H_1等价。     

Continuous Symmetry Measures. VI. The Relations Between Polyhedral Point-Group/Subgroup Symmetries

We extend our analysis of the symmetry content of the classical polyhedra [1] to the analysis of the degree of polyhedral subgroup symmetries. The quantitative levels of the hierarchical polyhedral symmetries series of O_h, D_4h and D_2h of hexacoordinated structures, as well as the relations between them, serve as an example. A distinction is made between two types of measures: quantitative evaluation of the degree of symmetry, and quantitative evaluation of the degree of content of a reference shape.     

Convenient ‘one-pot’ synthesis of 3,4-substituted tetrahydrothiophenes through tandem Michael-Henry and Michael-Michael reactions

In situ generated nitro alkenes underwent tandem Michael-Henry and Michael-Michael sequences leading to the ‘one-pot’ formation of 3,4-substituted tetrahydrothiophenes using the commercially available 1,4-dithiane-2,5-diol (the dimer of mercaptoacetaldehyde) or its 4-mercapto-2-butenoates derivatives as suitable bifunctional partners, respectively.     

Catalytic Isofunctional Reactions—Expanding the Repertoire of Shuttle and Metathesis Reactions

Transfer hydrogenation, alkene metathesis, and alkyne metathesis possess great value to the synthetic chemistry community. One of the key features of these processes is their reversibility, which can be attributed to the presence of the same number and type of functional groups in both the reactants and products, making these reactions isofunctional. These classic reactions have recently inspired the development of novel shuttle and metathesis reactions that offer great promise for synthetic chemistry. This Review describes and systematically categorizes both recent and older examples of shuttle and metathesis reactions other than transfer hydrogenation and alkene/alkyne metathesis.     

Radical and Radical–Ionic Multicomponent Processes

All in one pot! Radical, radical–ionic, and radical–organometallic MCR are highly convergent processes, representing a useful pathway to molecular and structural diversity (see scheme). This concept article highlights recent developments in the field and shows the potential of the strategy for the economical elaboration of various kinds of organic substrates.

     

Tetrahedral Fulleroids

Fulleroids are cubic convex polyhedra with faces of size 5 or greater. They are suitable models of carbon molecules. In this paper sufficient and necessary conditions for existence of fulleroids of tetrahedral symmetry types and with pentagonal and n-gonal faces only depending on number n are presented. Either infinite series of examples are found to prove existence or nonexistence is proved using symmetry invariants.     

Fuzzy space periodic symmetries for polyynes and their cyano-compounds

In our previous papers on the molecular fuzzy symmetry, we analyzed the basic characterization in connection with the fuzzy point group symmetry. In this paper, polyynes and their cyano-derivatives are chosen as a prototype of linear molecules to probe the one-dimensional fuzzy space group of parallel translation. It is notable that the space group is an infinite group whereas the point group is a finite group. For the fuzzy point group, we focus on considering the fuzzy characterization introduced due to the difference of atomic types in the monomer through point symmetry transformation in the beginning; and then we consider the difference between the infinity of space group and the finite size of real molecules. The difference between the point group and the space group lies in the translation symmetry transformation. This is the theme of this work. Starting with a simple case, we will only analyze the one-dimensional translation transformation and space fuzzy inversion symmetry transformation in this paper. The theory of the space group is often used in solid state physics; and some of its conclusions will be referred to. More complicated fuzzy space groups will be discussed in our future papers.     

A new ‘one-pot’ synthesis of 2-substituted 3-nitro pyrrolidines through a multicomponent domino reaction

An efficient ‘one-pot’ synthesis of the title compounds based on a multicomponent domino reaction between imines and 3-nitro-1-propanol methanesulfonate has been developed.     

Symmetrizer: Algorithmic determination of point groups in nearly symmetric molecules

Symmetry is an extremely useful and powerful tool in computational chemistry, both for predicting the properties of molecules and for simplifying calculations. Although methods for determining the point groups of perfectly symmetric molecules are well‐known, finding the closest point group for a “nearly” symmetric molecule is far less studied, although it presents many useful applications. For this reason, we introduce Symmetrizer, an algorithm designed to determine a molecule's symmetry elements and closest matching point groups based on a user‐adjustable tolerance, and then to symmetrize that molecule to a given point group geometry. In contrast to conventional methods, Symmetrizer takes a bottom‐up approach to symmetry detection by locating all possible symmetry elements and uses this set to deduce the most probable point groups. We explain this approach in detail, and assess the flexibility, robustness, and efficiency of the algorithm with respect to various input parameters on several test molecules. We also demonstrate an application of Symmetrizer by interfacing it with the WebMO web‐based interface to computational chemistry packages as a showcase of its ease of integration. © 2012 Wiley Periodicals, Inc.     

Synthesis of Highly Substituted Cyclobutane Fused‐Ring Systems from N‐Vinyl β‐Lactams through a One‐Pot Domino Process

In this contribution, aminocyclobutanes, as well as eight‐membered enamide rings, have been made from N‐vinyl β‐lactams. The eight‐membered products have been formed by a [3,3]‐sigmatropic rearrangement, whereas the aminocyclobutanes have been derived from a domino [3,3]‐rearrangement/6π‐electrocyclisation process. The aminocyclobutanes have been obtained in a highly diastereoselective fashion. The cyclobutane ring system tolerates fusion even if adjacent quaternary centres are present. Systems containing up to four fused rings are readily accessible. The reaction profile has been investigated by using Gaussian 03. This study suggests that two reaction pathways for aminocyclobutane formation are possible. In one pathway the [3,3]‐sigmatropic rearrangement is the rate‐limiting step and in the second pathway the electrocyclisation is rate limiting. Taken together, these reactions should facilitate the construction of fused heterocycles.     

Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.