Subduction of coset representations. An application to enumeration of chemical structures with achiral and chiral ligands

Molecules derived from a parent skeleton are enumerated where both achiral ligands as well as chiral ligands are allowed. Chirality fittingness of an orbit is proposed in order to permit chiral ligands. The enumeration is conducted with and without consideration of obligatory minimum valency (OMV). The effect of the OMV is formulated by assigning different weights to the respective orbits of the parent skeleton. The importance of coset representations and their subduction by subgroups is discussed. The subduced representations are classified into three classes through their chirality fittingness, which determines the mode of substitution with chiral and achiral ligands. Several novel concepts such as a unit subduced cycle index and a subduced cycle index are given in general forms.     

Efficient algorithms to enumerate isomers and diamutamers with more than one type of substituent

In this paper we describe numeric as well as symbolic algorithms for the enumeration of substitutional isomers with an unlimited number of different achiral substituents. We consider three different scenarios: first, the enumeration of diamutamers with a given set of ligand types and ligand multiplicity, second, the enumeration of diamutamer libraries with a given ligand assortment pattern, and, third, the enumerations of libraries with diamutamers exhibiting a limited number of ligands.     

Importance of the proligand-promolecule model in stereochemistry. I. The unit-subduced-cycle-index (USCI) approach to geometric features of prismane derivatives

Among the four methods of the unit-subduced-cycle-index (USCI) approach (Fujita in Symmetry and Combinatorial Enumeration in Chemistry. Springer, Berlin, Heidelberg, 1991), the fixed-point-matrix (FPM) method and the partial-cycle-index (PCI) method have been applied to the combinatorial enumeration of prismane derivatives. These enumeration processes are based on the proligand-promolecule model, which enables us to take account of achiral and chiral proligands. Prochirality in a geometric meaning has been discussed in general by emphasizing the presence of enantiospheric orbits in enumerated prismane derivatives. An enantiospheric orbit accommodating chiral proligands (along with achiral ones) has been shown to exhibit prochirality by using various prismane derivatives as examples. On the other hand, the scope of pseudoasymmetry has been extended to cover such a rigid skeleton as prismane in addition to a usual pseudoasymmetric center as a single atom, where the proligand-promolecule model plays an essential role.     

Systematic enumeration of nonrigid isomers with given ligand symmetries

A new method for enumerating nonrigid isomers with rotatable ligands has been developed so as to take the symmetries of the ligands into consideration. The method has been based on extended partial cycle indices and has been applied to the enumeration of methyl ether derivatives, tetramethylallene derivatives, and 2,2-dimethylpropane derivatives. These results have been compared with the enumeration results of the corresponding promolecules. The factorization of terms in generating functions has been discussed so that the new method is capable of examining the relationship between promolecules and molecules quantitatively.     

Sphericities of Double Cosets,Double Coset Representations,and Fujita’s Proligand Method for Combinatorial Enumeration of Stereoisomers

The concepts of double coset representations and sphericities of double cosets are proposed to characterize stereoisomerism, where double cosets are classified into three types, i.e., homospheric double cosets, enantiospheric double cosets, or hemispheric double cosets. They determine modes of substitutions (i.e., chirality fittingness), where homospheric double cosets permit achiral ligands only; enantiospheric ones permit achiral ligands or enantiomeric pairs; and hemispheric ones permit achiral and chiral ligands. The sphericities of double cosets are linked to the sphericities of cycles which are ascribed to right coset representations. Thus, each cycle is assigned to the corresponding sphericity index (a _d , c _d , or b _d ) so as to construct a cycle indices with chirality fittingness (CI-CFs). The resulting CI-CFs are proved to be identical with CI-CFs introduced in Fujita’s proligand method (S. Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86). The versatility of the CI-CFs in combinatorial enumeration of stereoisomers is demonstrated by using methane derivatives as examples, where the numbers of achiral plus chiral stereoisomers, those of achiral stereoisomers, and those of chiral stereoisomers are calculated separately by means of respective generating functions.     

Chiral relay: a novel strategy for the control and amplification of enantioselectivity in chiral Lewis acid promoted reactions

Chiral Lewis acid catalysis has emerged as one of the premiere method to control stereochemistry. Much effort has gone into the design of superior ligands with increasing steric extension to shield distant reactive sites. We report here an alternative and complementary approach based on a "chiral relay". This strategy focuses on the improved design of achiral templates which may relay and amplify the stereochemistry from ligands. The essence of this strategy is that the chiral Lewis acid would effectively convert an achiral template into a chiral non-racemic template. This approach combines the advantages of enantioselective catalysis (substoichiometric amount of the chiral inducer) with the ones of chiral auxiliary control (efficient and predictable stereocontrol).     

Cooperative Catalysis: Combining an Achiral Metal Catalyst with a Chiral Brønsted Acid Enables Highly Enantioselective Hydrogenation of Imines

Asymmetric hydrogenation of imines leads directly to chiral amines, one of the most important structural units in chemical products, from pharmaceuticals to materials. However, highly effective catalysts are rare. This article reveals that combining an achiral pentamethylcyclopentadienyl (Cp*)–iridium complex with a chiral phosphoric acid affords a catalyst that allows for highly enantioselective hydrogenation of imines derived from aryl ketones, as well as those derived from aliphatic ones, with ee values varying from 81 to 98 %. A range of achiral iridium complexes containing diamine ligands were examined, for which the ligands were shown to have a profound effect on the reaction rate, enantioselectivity and catalyst deactivation. The chiral phosphoric acid is no less important, inducing enantioselection in the hydrogenation. The induction occurs, however, at the expense of the reaction rate.     

Nanoscale metal coordination macrocycles fabricated by using "dimeric" dipyrrins

Covalently linked dipyrrin (dipyrromethene) dimers have afforded nanoscale [2+2]-type neutral coordination macrocycles with a diagonal of about 1.6 nm. Two moieties of the achiral dipyrrin-Zn(II) complex yield the chiral coordination macrocycles as minor species, as well as major meso stereoisomers by the covalent linkages. Tetrahedral Zn(II) coordination by using acyclic ligands enables the dipyrrin-metal complex units to readily rotate and pass through the cavity of the nanorings in order to reveal the transitions between the chiral and achiral isomers.     

The numbers of chiral and achiral alkanes and monosubstituted alkanes

Whereas the theory for the enumeration of the optical isomers of the lakyl radicals and the alkanes has long been understood, this is not the case for the corresponding archiral isomers. We present for the first time recurrence formulae for counting the number of archiral isomers of the alkyl radicals and the alkanes. For chiral and archiral alkanes and monosubstituted alkanes, numerical results up to C₁₄ are tabulated.After presenting the history of the problem and the necessary definitions, we proceed to derive functional equations on the various generating functions, which readily yield the more explicit recurrence formulae usefule for numerical calculations. In the process, we first re-derive Pólya's expression for planted steric trees using his classical enumeration theorem. This result is then extended to the enumeration of free steric trees using the now standard tree-counting method due to Otter and known as a dissimilarity characteristic equation.By definition, a steric tree is a quartic tree (all points having degree 1 or 4) in which the four neighbors of every carbon point are given a tetrahedral configuration. Building on the methods of the first two authors for counting chiral and archiral trees in the plane, we obtain the formula for counting achiral steric trees, thus setting a problem first enunciated by van't Hoff and Le Bel in 1874.     

Graphs to chemical structures 1. Sphericity indices of cycles for stereochemical extension of Pólya’s theorem

Pólyas theorem has been concluded to be concerned with graphs, but not with chemical structures, where it is incapable of treating chiral ligands properly. In order to take account of chiral ligands along with achiral ones, coset representations (CRs) for cyclic subgroups have been examined to classify permutations of the CRs into proper and improper elements. As a result, a k-cycle contained in each permutation has been classified into an enantiospheric, homospheric, or hemispheric one. Thereby, sphericity indices of k-cycles have been defined according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle. On the basis of the sphericity indices, cycle indices with chirality fittingness (CIs-CF) have been defined in place of Pólyas cycle indices. The CIs-CF have been proved to be capable of enumerating of stereoisomers with chiral and achiral ligands. Their capabilities have been confirmed by using allene derivatives as examples.     

Optimization of catalyst enantioselectivity and activity using achiral and meso ligands

The optimization of asymmetric catalysts for enantioselective synthesis has conventionally revolved around the synthesis and screening of enantiopure ligands. In contrast, we have optimized an asymmetric reaction by modification of a series of achiral ligands. Thus, employing (S)-3,3'-diphenyl BINOL [(S)-Ph(2)-BINOL] and a series of achiral diimine and diamine activators in the asymmetric addition of alkyl groups to benzaldehyde, we have observed enantiomeric excesses between 96% (R) and 75% (S) of 1-phenyl-1-propanol. Some of the ligands examined have low-energy chiral conformations that can contribute to the chiral environment of the catalyst. These include achiral diimine ligands with meso backbones that adopt chiral conformations, achiral diimine ligands with backbones that become axially chiral on coordination to metal centers, achiral diamine ligands that form stereocenters on coordination to metal centers, and achiral diamine ligands with pendant groups that have axially chiral conformations. Additionally, we have structurally characterized (Ph(2)-BINOLate)Zn(diimine) and (Ph(2)-BINOLate)Zn(diamine) complexes and studied their solution behavior.     

双官能度手性和消旋苯并噁嗪的合成及热性能研究

采用无溶剂法合成了新型双酚A和双酚AF(六氟双酚A)基手性和消旋苯并噁嗪单体,利用红外光谱(FTIR)、核磁共振氢谱(1H-NMR)、旋光仪和高效液相色谱(HPLC)对单体结构和性质进行了表征,通过差式扫描量热仪(DSC)和热重分析仪(TGA)对苯并噁嗪的固化行为及聚合物的热性能进行了研究.结果表明,无溶剂法合成苯并噁嗪单体具有反应速度快、产率高、对环境友好等特点;双官能度消旋苯并噁嗪单体由内消旋和外消旋异构体组成,且内消旋苯并噁嗪单体含量高于外消旋;手性和消旋苯并噁嗪单体具有相同的开环聚合行为;由于消旋苯并噁嗪分子的立体构型不同,使得聚苯并噁嗪的自由体积减小,分子链的堆积更加致密,因而消旋聚苯并噁嗪的玻璃化转变温度(Tg)和热稳定性均高于手性聚苯并噁嗪和传统的双酚A-苯胺型聚苯并噁嗪;此外,C—F键具有高的解离能,因而双酚AF基聚苯并噁嗪的热性能显著提高.     

手性异构体的片断染色计数

将配体取代看作对骨架点的染色, 通过染色片断的对称性分类, 直接计数取代手性和非手性异构体. 列表示出典型结果. 将Polya定理推广于陪集, 与片断染色计数进行比较。     

Möbius function and characteristic monomials for combinatorial enumeration

After the definitions of amplified representations and number-theoretical vectors, the markaracter table of a cyclic subgroup is converted into the corresponding Q-conjugacy character table. The conversion is shown to necessitate an interconversion matrix that contains M?bius functions as elements. Since the interconversion matrix gives characteristic monomials for cyclic groups, all the powers appearing in each of the characteristic monomials are shown to be integers. Characteristic monomials for finite groups are then built up by starting from those of cyclic groups. This procedure clarifies the fact that all the powers appearing in each characteristic monomial for finite groups are integers. The relationship between characteristic monomial tables and unit-subduced-cycle-index tables is discussed with respect to their application to isomer enumeration. Received: 15 July 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

Subduction of Q-conjugacy representations and characteristic monomials for combinatorial enumeration

A new method of combinatorial enumeration is presented. The subduction of Q-conjugacy representations gives a characteristic subduction table and a characteristic monomial table. A cycle index is defined on the basis of such monomials and used for combinatorial enumeration of isomers. Received: 10 October 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Synthesis and application of chiral bisphosphines through lithiation-conjugate addition tandem cyclization of chiral alpha,beta,psi,omega-unsaturated bisphosphine oxide

Upon treatment with lithium diisopropylamide achiral and chiral alpha,beta,psi,omega-unsaturated bisphosphine oxides underwent lithiation-conjugate addition tandem cyclization to afford the corresponding endo-alpha,beta-unsaturated cyclic bisphosphine oxides; sequential stereoselective reduction of the cyclized bisphosphine oxide gave the corresponding trans- and cis-bisphosphines that were successfully applicable in a catalytic asymmetric hydrogenation as chiral bisphosphine ligands.     

A novel example of chiral counteranion induced enantioselective metal catalysis: the importance of ion-pairing in copper-catalyzed olefin aziridination and cyclopropanation

A new ion-pairing route to achieve asymmetric catalysis has been observed in the copper-catalyzed aziridination of styrene with a chiral counteranion. Structural studies suggest that enantioinduction occurs via ion-pairing of the cationic copper catalyst in the chiral pocket created by the anion. The degree of asymmetric induction can be tuned with features that affect ion-pairing, such as achiral and chiral ligands, temperature, and solvent polarity.     

The USCI approach and elementary superposition for combinatorial enumeration

Summary The elementary superposition theorems are presented for enumerating chemical compounds that contain achiral and chiral ligands. Subduced cycle indices (SCI-CF), partial cycle indices (PCI-CF), and cycle indices (CI-CF) with chirality fittingness are defined by starting from unit subduced cycle indices with chirality fittingness (USCI-CF). All of these indices afford generating functions that are proved to be applicable to combinatorial enumeration. In addition, the concept of elementary superposition with and without chirality fittingness is proposed to provide the elementary superposition theorems. These theorems provide us with a new methodology of enumerating compounds, in which the numbers of isomers are obtained without relying on generating functions and are itemized with respect to molecular formulas (weights) and symmetries. The operation is defined on the basis of the elementary superposition. Thereby, we derive superposition theorems concerning the PCI-CFs and the CI-CFs. These are applicable to combinatorial enumeration.     

Iridium‐Catalyzed H/D Exchange: Ligand Complexes with Improved Efficiency and Scope

Hydrogen isotope exchange (HIE) is one of the most attractive tools for the introduction of deuterium or tritium to an organic compound. Herein, iridium complexes with N,P‐ligands, highly active catalysts for asymmetric double bond reductions, have been tested for their HIE capabilities. Electron‐rich ligands, containing dicyclohexylphosphines or phosphinites, have been identified as excellent ligands for efficient deuterium incorporation. Substrates with strong directing groups, that is, pyridines, ketones, and amides, as well as weak ligating units, such as, nitro, sulfones, and sulfonamides, could be labeled efficiently. With the addition of tris(pentafluorophenyl) borane to the reaction mixture, also highly deactivating nitrile substituents were well tolerated in the reaction. Based on the excellent results obtained with the chiral ThrePhox ligand, a structurally simpler, achiral ligand was developed. The iridium complex containing this ligand, proved to be a powerful catalyst for HIE reactions.     

A study on the stability,chirality, and theoretical spectra of the heterofullerenes C69X (X = N,P, As,B, Si,Ge)

There are two chiral and three achiral C₆₉X isomers possible. The achiral structures belong to the C_S group of symmetry while the chiral ones possess no symmetry elements. The stability of all five C₆₉X heterofullerenes for each of the X heteroatoms (X = N, P, As, B, Si, Ge) was determined at the (U)B3LYP/6-31G¹ level. The isomer population in an equilibrium mixture varies with the heteroatom type: the highest content of the chiral isomers was predicted for boron (92%) and nitrogen (47% plus 48%), while for the other heteroatoms studied the achiral isomers significantly dominate. For the chiral structures, four different sinister-rectus chirality measures, ^SRCM: pure geometrical, labeled, mass, and charge, were calculated by our CHIMEA program. We found that the labeled and mass chirality measures calculated for the two types of chiral isomers did correlate with each other. For each chiral C₆₉X molecule, spectroscopic VCD, IR, Raman, and NMR characteristics are discussed and demonstrated for their possible use for future identification and distinction of the isomers.