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.     

Enumeration of digraphs with a given automorphism group

Four methods are described for enumerating digraphs with a given automorphism group: (1) a generating-function method based on subduced cycle indices, (2) a generating-function method based on partial cycle indices, (3) a method based on the elementary superposition theorem, and (4) a method based on the partial superposition theorem. All of these methods are based on the concept of unit subduced cycle indices and construct a set of versatile tools for combinatorial enumeration. They are applied to the enumeration of five-vertex digraphs with a given automorphism group. The table of marks and its inverse for the symmetric group of degree 5 are recalled. The table of USCIs of this roup is obtained.Dedicated to Professor Frank Harary.     

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.     

Combinatorial enumeration of ethane derivatives as three-dimensional chemical structures,not as graphs. A systematic approach for enumerating and characterizing stereoisomers of tartaric acids and related compounds

Fujita’s proligand method is applied to the enumeration of ethane derivatives, where the counting of stereoisomers of tartaric acids is examined in detail as a probe for testing the versatility of the method. The cycle index with chirality fittingness (CI-CF) for enumerating ethane derivatives is obtained by Fujita’s proligand method and compared with the CI-CF derived alternatively by the direct calculation of permutations of substitution positions. The two CI-CFs are identical with each other so that the methodology underlying in Fujita’s method is demonstrated in a concrete fashion. The enumeration results are compared with those derived by Pólya’s corona. Fujita’s proligand method is shown to be capable of enumerating stereoisomers, whereas Pólya’s corona is concluded to enumerate graphs, but not stereoisomers. The conceptually change from graphs to three-dimensional (3D) chemical structures is discussed, where the superiority of Fujita’s proligand method is demonstrated.     

Subduction of dominant representations for combinatorial enumeration

Summary A new method for giving cycle indices is presented for combinatorial enumeration. Thus, cyclic groups are characterized by markaracter tables, the elements of which are determined by the orders of their subgroups. A set of such cyclic groups (defined as dominant subgroups) is used to characterize a group G of finite order, where the markaracter table for the group G is constructed with respect to dominant representations (DRs), which are defined as coset representations corresponding to the dominant subgroups. By starting from the markaracter table, we propose an essential set of subdominant markaracter tables and a magnification set for the group G; the latter concept clarifies the relationship between each subdominant markaracter table and the markaracter table of a dominant subgroup. The subduction of DRs is obtained by the markaracter table to produce a dominant subduction table and a dominant USCI (unit-subduced cycle index) table. The latter is used to evaluate a cycle index to be applied to combinatorial enumeration. The cycle index is shown to be equivalent to the couterpart of our previous approach concerning both cyclic and non-cyclic subgroups. The latter, in turn, has been proved to be equivaltent to the cycle index obtained by the Redfield-Pólya theorem.     

Investigation of the role of the C-PCM solvent effect in reactivity indices

It has been shown recently, how the coupling between electronic degrees of freedom and vibrational modes is reflected in the properties of molecules. The necessary derivatives have been analyzed and their thermodynamic relations were demonstrated. This present work is focused on the analysis of a molecular system, under the influence of C-PCM induced solvent effect. The analysis is based on reactivity indices derived from DFT. The shift of frequency for diatomic molecules has been obtained. It has been identified as chemical force effect. The role of nuclear reactivity indices has been emphasized. This concept has been extended to obtain regional chemical potential values within C-PCM model for polyatomic molecules.     

Oxime-based salen-type tetradentate ligands with high stability against imine metathesis reaction

Although salen and its analogues are versatile chelate ligands in inorganic and organometallic chemistry, synthesis of unsymmetrical salen derivatives consisting of two different salicylideneimine moieties is difficult because of the C=N bond recombination. To develop stable analogues of salen-type ligands, we synthesized a series of new ligands salamo (=1,2-bis(salicylideneaminooxy)ethane) on the basis of O-alkyl oxime instead of the imine moiety. Eight salamo ligands 1a-h were prepared in 64-88% yields as colorless crystals from the corresponding salicylaldehydes 2a-h. The crystal structure of 1a-c suggests that the oxime-OH form is more predominant than the keto-NH form. The reaction of 2a-e with excess 1,2-bis(aminooxy)ethane gave monooximes 3a-e in 59-86%, which further reacted with a different salicylaldehyde to afford unsymmetrical salamo ligands 4-8 as stable crystals in 51-70%. No reaction took place when a mixture of salamo derivatives 1a and 1b was treated at 40 degrees C in H2O/MeCN (5:95). However, the metathesis reaction of salen derivatives 9a and 9b completed in 2 h to give a statistical mixture. Monooxime 3b was much more stable than monoimine 11 which is difficult to be isolated. These results indicate the extremely high stability of the salamo derivatives 1 and precursors 3.     

Sc3N@C80: computations on the two-isomer equilibrium at high temperatures.

Reported herein are computations on the relative concentrations of the two experimentally known isomers of Sc3N@C80 , that is, those produced by encapsulation of Sc3N in two particular C80 cages that obey the isolated-pentagon rule, namely, with I(h) and D(5h) symmetries. The calculations are based on density functional methods and have been carried out using the Gibbs energy over a broad temperature interval. It has been computed that, if a relatively free motion of the encapsulate inside the cages is allowed, the observed populations of 10 and 17 % for the D(5h) Sc3N@C80 species are reached at temperatures of 2100 and 2450 K, respectively. The inclusion of the entropy term is essential as, if it is neglected, the D(5h) Sc3N@C80 population at a temperature of 2100 K would be a mere 1 %, owing to the relatively large interisomeric separation potential energy of 19 kcal mol(-1).     

Reduced cycle indices and their applications in enumeration of NMR signals and equivalence classes

An efficient technique is formulated based on a polynomial structure which we call the reduced cycle index for the enumeration of equivalence classes and NMR signals under group action. The reduced cycle indices are shown to be the cycle index polynomials of a subset of significantly smaller order of the point group of the molecule. Thus, the reduced cycle indices are much simpler and their use leads to a considerable reduction in tile computation of the generating functions from the cycle indices and irreducible representations contained in a set.Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar.     

Synthesis, structure, and magnetism of three azido-bridged Co2+ compounds with a flexible coligand 1,2-(tetrazole-1-yl)ethane

By utilizing suitable coligand endi (1,2-(tetrazole-1-yl)ethane)) with variable conformations, we synthesized three new azido-bridged Co(2+) compounds with molecular formulas Co(endi)(N3)2 (1, 3) and Co(endi)2(N3)2 (2) by tuning the stoichiometric ratio of ligand/metal and the concentration of the solution. All of the compounds have been characterized structurally and magnetically. In all three structures, the azide ions use the end-to-end mode to link the Co(2+) centers to the 1D chain (1) and 2D (4,4) layers (2 and 3). The endi coligands adopt a trans conformation in compound 1 and a gauche conformation in compounds 2 and 3. Linked by bridging endi, the 1D chains in compound 1 and 2D layers in compound 3 are extended, resulting in the final 2D layer for compound 1 and the 3D network for compound 3, whereas in compound 2, the endi acts as only a terminal ligand to separate the 2D layers. Compound 1 consists of dual end-to-end azido-bridged 1D Co(2+) chains that are linked by trans endi into a 2D layer and are further extended to a 3D framework through H bonds. Compound 2 is a 2D (4,4) layer that is connected by end-to-end azido ions. The gauche endi ligands act as terminal ligands to separate the neighboring layers thoroughly. Compound 3 has a (4,4) 2D layer that is similar to that of compound 2, and these layers are further extended to a 3D network through gauche endi. The magnetic investigation shows that compound 3 is antiferromagnetically coupled and compound 2 is a weak ferromagnet with a critical temperature of 22 K, which is quite high compared with that of the previously reported 2D azido-bridged Co(2+) compounds.     

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.     

1,4-Di(1,2,3-triazol-1-yl)butane as building block for the preparation of the iron(II) spin-crossover 2D coordination polymer

The novel bidentate ligand 1,4-di(1,2,3-triazol-1-yl)butane (bbtr) reacts with Fe(ClO4)2 x 6H2O to form the 2D coordination polymer with (3,6) network topology. The {[Fe(bbtr)3](ClO4)2}infinity represents an example of spin-crossover material based on 1,2,3-triazole as donor group, and displays an abrupt spin transition accompanied by a thermal hysteresis loop (T(1/2)decrease = 101 K and T(1/2)increase = 109 K).     

Crystal structure and dynamic properties of a bimetallic cyano complex Cd(C4H8O2)Cu(CN)3 with an interpenetrating 3D framework containing a 1,4-dioxane bridging ligand as a rotor

The title complex Cd(C(4)H(8)O(2))Cu(CN)(3) has a 3D twofold interpenetrating framework structure. The structural base of the framework is a planar hexagonal network complex of [Cu(CN)(3)Cd](infinity) ,which is formed with cyanides connecting the coordination sites of Cu(i) ions with a triangle planar form and the equatorial coordination sites of Cd(ii) ions with a trigonal bipyramid form. The networks are stacked and a 1,4-dioxane molecule coordinates to two Cd(ii) ions in alternate networks as a bridging ligand. The 1,4-dioxane ligand penetrates a hexagonal window of the network sandwiched between the bridged networks. This 1,4-dioxane bridge completes the 3D twofold interpenetrating framework structure. (2)H-NMR powder patterns of the deuterated complex Cd(C(4)D(8)O(2))Cu(CN)(3) revealed the dynamics of the 1,4-dioxane bridge as a rotor. Above 253 K, the 1,4-dioxane ligand undergoes rotational motion combined with a ring inversion between two chair conformations. The free energy of activation DeltaG(double dagger) for the ring inversion was calculated to be 41.4(7) kJ mol(-1) at 298 K.     

Rhodium complex with ethylene ligands supported on highly dehydroxylated MgO: synthesis, characterization, and reactivity

Mononuclear rhodium complexes with reactive olefin ligands, supported on MgO powder, were synthesized by chemisorption of Rh(C(2)H(4))(2)(C(5)H(7)O(2)) and characterized by infrared (IR), (13)C MAS NMR, and extended X-ray absorption fine structure (EXAFS) spectroscopies. IR spectra show that the precursor adsorbed on MgO with dissociation of acetylacetonate ligand from rhodium, with the ethylene ligands remaining bound to the rhodium, as confirmed by the NMR spectra. EXAFS spectra give no evidence of Rh-Rh contributions, indicating that site-isolated mononuclear rhodium species formed on the support. The EXAFS data also show that the mononuclear complex was bonded to the support by two Rh-O bonds, at a distance of 2.18 A, which is typical of group 8 metals bonded to oxide supports. This is the first simple and nearly uniform supported mononuclear rhodium-olefin complex, and it appears to be a close analogue of molecular catalysts for olefin hydrogenation in solution. Correspondingly, the ethylene ligands bonded to rhodium in the supported complex were observed to react with H(2) to form ethane, and the supported complex was catalytically active for the ethylene hydrogenation at 298 K. The ethylene ligands also underwent facile exchange with C(2)D(4), and exposure of the sample to carbon monoxide led to the formation of rhodium gem dicarbonyls.     

Liquid-phase force field and dipole moment derivatives with respect to internal coordinates of benzene

This paper presents an analysis of the infrared vibrational intensities found for C(6)H(6), C(6)D(6) and C(6)H(5)D in the liquid phase, motivated in part by the quite marked intensity differences between the fundamentals of C(6)H(6) and C(6)D(6) in the liquid, and between corresponding vibrations in the liquid and gas phases. The analysis is carried out under the harmonic approximation and results from a determination of the force field for liquid C(6)H(6), C(6)D(6) and C(6)H(5)D. The force constants for the liquid-phase are presented and compared to those in the literature for the gas-phase. Previously reported experimental intensities are used along with the eigenvectors of the force field analysis to determine the dipole moment derivatives with respect to symmetry and internal coordinates. The dipole moment derivatives with respect to internal coordinates obtained are partial differentialmicro/ partial differentials=0.38+/-0.02DebyeA(-1), partial differentialmicro/ partial differentialt=0.24+/-0.01, partial differentialmicro/ partial differentialbeta=0.26+/-0.01, and partial differentialmicro/ partial differentialgamma=0.64+/-0.03DebyeA(-1). There is very little difference between the dipole moment derivatives with respect to internal coordinates obtained from non-linear least squares fitting of the two D(6h) isotopomers and those obtained from non-linear least squares fitting of the three isotopomers. The results show that there is significant intensity sharing in the CH stretch region of C(6)H(5)D between the fundamental and combination bands.     

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D _3h ) and adamantane (T _d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D _3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T _d point symmetry group. This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling (Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which is widely used by chemists. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008.     

Structures and kinetic stabilities of the possible complexes of mononuclear Ni and (N2)x (x = 1-4)

Ab initio and density functional theory (DFT) methods have been applied to study the structures and kinetic stabilities of the possible products of the reactions of mononuclear nickel with (N(2))(x) (x = 1-4). Energy analyses show that end-on bound Ni(N(2))(x) (x = 1-4) complexes are preferred to side-on and N(4) bound ones. Several decomposition and isomerization pathways for Ni(N(2))(x) (x = 2-4) were investigated at the B3LYP/6-31G level of theory. The present study suggests that besides the four experimentally assigned complexes (NiN(2) (C(infinity)(v)), Ni(N(2))(2) (D(infinity)(h)), Ni(N(3))(2) (D(3)(h)), and Ni(N(2))(4) (T(d))), another two complexes (Ni(N(2))(4) (C(2)(v)) and Ni(N(2))(4) (D(4)(d))) are likely to be kinetically stable, while other complexes may be kinetically unstable with barrier heights of less than 30 kcal/mol. The present study also suggests that side-on bound N(2) ligand is ready to transform into the end-on bound one, while N(4) ligand is hard to transform into side-on or end-on bound N(2) ligand.     

Highly efficient cyclization of o-iodobenzoates with aldehydes catalyzed by cobalt bidentate phosphine complexes: a novel entry to chiral phthalides

Methyl 2-iodobenzoates 1 a-c undergo cyclization reactions with various aromatic aldehydes 2 a-m (RC6H4CHO: R=H 2 a, 4-CH3 2 b, 4-tBu 2 c, 4-OMe 2 d, 3-OMe 2 e, 4-Cl 2 f, 4-CF3 2 g, 4-CN 2 h, 4-Ph 2 i; benzo[d][1,3]dioxole-5-carbaldehyde (2 j), 1-napthaldehyde (2 k), benzofuran-2-carbaldehyde (2 l), and isonicotinaldehyde (2 m)) in the presence of [CoI2(dppe)] (dppe=1,2-bis(diphenylphosphino)ethane) and Zn powder in dry THF at 75 degrees C for 24 h to give the corresponding phthalide derivatives 3 a-m and 3 q-t in good to excellent yields. Under similar reaction conditions, less reactive aliphatic aldehydes, heptanal (2 n), butyraldehyde (2 o), and 2-phenylacetaldehyde (2 p) also underwent cyclization reactions with 1 a to provide 3 n-p, respectively, in fair to good yields. The catalytic reaction can be further extended to cinnamyl aldehyde (2 q) with 1 a to give the corresponding phthalide derivative 3 u. This synthetic method is compatible with a variety of functional groups on the aryl ring of 2. The high efficiency of the cobalt catalyst containing a dppe (dppe=1,2-bis(diphenylphosphino)ethane) ligand encouraged us to investigate the asymmetric version of the present catalytic reaction by employing bidentate chiral ligands. Thus, aromatic aldehydes 2 a-c, 2 f, and 2 g undergo cyclization with 2-iodobenzoate (1 a) smoothly in the presence of [CoI2{(S,S)-dipamp}] ((S,S)-dipamp=(1S,2S)-(+)-bis[2-methoxyphenyl]phenylphosphino)ethane) and zinc powder in THF at 75 degrees C for 24 h, giving the corresponding (S)-phthalides 4 a-e in 81-89% yields with 70-98% ee. A possible mechanism for the present catalytic reaction is proposed.