Graphs to chemical structures 5. Combinatorial enumeration of centroidal and bicentroidal three-dimensional trees as stereochemical models of alkanes

Three-dimensional trees (3D-trees), which are defined as a 3D version of trees, are enumerated by Fujita’s proligand method formulated in Part 1 to Part 3 of this series (Fujita in Theor Chem Acc 113:73–79, 113:80–86, 2005; 115:37–53, 2006). Such 3D-trees are classified into centroidal and bicentroidal 3D-trees, which correspond to respective promolecules having proligands as substituents. In order to enumerate such centroidal and bicentroidal 3D-trees, cycle indices with chirality fittingness (CI-CFs) are formulated as being composed of three kinds of sphericity indices, i.e., a _d for homospheric cycles, c _d for enantiospheric cycles, and b _d for hemispheric cycles. The CI–CFs are capable of giving itemized results with respect to chiral and achiral 3D-trees so that they are applied to derive functional equations (a(x), c(x ²), and b(x)). The generating functions of planted 3D-trees, which are formulated and calculated elsewhere, are introduced into such functional equations. Thereby, the numbers of 3D-trees or equivalently those of alkanes as stereoisomers are calculated and collected up to a carbon content of 20 in a tabular form. Now, the enumeration problem initiated by a mathematician Cayley (Philos Mag 47(4):444–446, 1874) has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.     

Combinatorial enumeration of three-dimensional trees as stereochemical models of alkanes: an approach based on Fujita’s proligand method and dual recognition as uninuclear and binuclear promolecules

Three-dimensional (3D) trees, which are defined as a 3D extension of trees, are enumerated by Fujita’s proligand method (Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86; 115 (2006) 37–53). Such 3D-trees are dually recognized as uninuclear promolecules and as binuclear ones. The 3D-trees regarded as uninuclear promolecules are enumerated to give the gross number of 3D-trees, which suffers from redundancy due to contaminants. To evaluate the number of such contaminants, the 3D-trees are alternatively enumerated as binuclear promolecules. Cycle indices with chirality fittingness (CI-CFs) composed of three kinds of sphericity indices (SIs), i.e., a _d for homospheric cycles, c _d for enantiospheric cycles, and b _d for hemispheric cycles are obtained for evaluating promolecules of the two kinds. The CI-CFs for the uninuclear promolecules and those for the related binuclear promolecules are compared in terms of the dichotomy between balanced 3D-trees and unbalanced 3D-trees. Thereby, the redundancy due to such contaminants is deleted effectively so as to give the net number of 3D-trees. The validity of this procedure is proved in three ways, all of which are based on the respective modes of the correspondence between uninuclear promolecules and binuclear ones. In order to enumerate 3D-trees by following this procedure, the CI-CFs are converted into functional equations by substituting the SIs for a(x ^d ), c(x ^d ), and b(x ^d ). Thereby, the numbers of 3D-trees or equivalently those of alkanes as stereoisomers are calculated under various conditions and collected up to 20 carbon content in a tabular form. Now, the stereochemical problems (on the number of stereoisomers) by van’t Hoff (van’t~Hoff, Arch. Néerlandaises des Sci. Exactes et Nat, 9 (1874) 445–454”) and by LeBel (LeBel, Bull. Soc. Chim. Fr. (2), 22 (1874) 337–347) and the enumeration problems (on the number of trees) by Cayley (Cayley, Philos. Mag. 47 (1874) 444–446), both initiated in the 1870s, have been solved in a common theoretical framework, which satisfies both chemical and mathematical requirements.     

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.     

Combinatorial approach to group hierarchy for stereoskeletons of ligancy 4

Fujita’s proligand method developed originally for combinatorial enumeration under point groups (Fujita in Theor Chem Acc 113:73–79, 2005) is extended to meet the group hierarchy, which stems from the stereoisogram approach for integrating geometric aspects and stereoisomerism in stereochemistry (Fujita in J Org Chem 69:3158–3165, 2004). Thereby, it becomes applicable to enumeration under respective levels of the group hierarchy. Combinatorial enumerations are conducted to count inequivalent pairs of (self-)enantiomers under a point group, inequivalent quadruplets of RS-stereoisomers under an RS-stereoisomeric group, inequivalent sets of stereoisomers under a stereoisomeric group, and inequivalent sets of isoskeletomers under an isoskeletal group. In these enumerations, stereoskeletons of ligancy 4 are used as examples, i.e., a tetrahedral skeleton, an allene skeleton, an ethylene skeleton, an oxirane skeleton, a square planar skeleton, and a square pyramidal skeleton. Two kinds of compositions are used for the purpose of representing molecular formulas in an abstract fashion, that is to say, the compositions for differentiating proligands having opposite chirality senses and the compositions for equalizing proligands having opposite chirality senses. Thereby, the classifications of isomers are accomplished in a systematic fashion.     

Graphs to chemical structures 3. General theorems with the use of different sets of sphericity indices for combinatorial enumeration of nonrigid stereoisomers

The extended sphericity indices of k-cycles, which were defined in Part 2 of this series (S. Fujita, Theor Chem Acc, Online: http://www.springerlink.com/index/10.1007/s00214-004-0606-z) according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle, are further extended to prove more general theorems for enumerating nonrigid stereoisomers with rotatable ligands. One of the extended points is the use of different sets of sphericity indices to treat one or more orbits contained in skeletons and ligands. Another is to take account of chirality in proligands and sub-proligands, the latter of which are introduced to consider further inner structures of ligands. Two theorems for enumerating nonrigid stereoisomers are proved by adopting two schemes of their derivation, i.e., the scheme ``positions of a skeleton ⇐ proligands ⇐ ligands (positions of a ligand ⇐ sub-proligands)' and the scheme ``(positions of a skeleton ⇐ proligands ⇐ ligands (positions of a ligand)) ⇐ sub-proligands'. The theorems are applied to the stereoisomerism of trihydroxyglutaric acids. Thereby, it is demonstrated where Pólya's theorem and other previous methods are deficient, when applied to the enumeration of stereoisomers.     

Differential kinetic thermal lens determination of aniline and 4-nitroaniline

Thermal lens spectrometry was used for the differential kinetic determination of aniline (over the concentration range of 8 × 10⁻⁴–3.2 × 10⁻³ M) and 4-nitroaniline (2 × 10⁻⁴–1.6 × 10⁻³ M) present in combination in a single sample based on the oxidation reaction with periodate ions in an acidic medium (this determination is not possible with the spectrophotometric monitoring of the rate of reaction). The thermal lens procedure (λ_e = 488.0 nm; 80 mW) was characterized by good performance characteristics in the determination of aniline (c _min = 3 × 10⁻⁴ M; c _d = 8 × 10⁻⁴ M) and 4-nitroaniline (c _min = 7 × 10⁻⁵ M; c _d = 2 × 10⁻⁴ M), simplicity, and rapidity.     

Crystal Structure and Characterisation of Mercury(II) Dichromate(VI)

Dark-red single crystals of HgCr₂O₇ were grown by reacting HgO and CrO₃ in excess at 200°C for four days. The crystal structure (space group P3₂, Z = 3, a = 7.2389(10), c = 9.461(2) ?, 1363 structure factors, 57 parameters, R[F ²>2σ(F ²)] = 0.0369, wR(F ² all) = 0.0693) was determined from a crystal twinned by merohedry according to (110). It consists of nearly linear HgO₂ units ( [`(d)]{\bar {d}} (Hg–O) = 2.02 ?) and dichromate units that are linked into infinite chains ‘O₃Cr–O–CrO₃–Hg–O₃Cr–O–CrO₃’ running parallel to the c-axis. Six additional Hg–O contacts between 2.73 and 2.96 ? stabilise the structural arrangement. The dichromate anion exhibits a staggered conformation with a bent Cr–O–Cr bridging angle of 140.7(6)°. Upon heating above 300°C, HgCr₂O₇ decomposes in a two-step mechanism to Cr₂O₃. The title compound was additionally characterised by vibrational spectroscopy.     

Kinetic Analysis of Thermal Decomposition of Ca(OH)2 Formed During Hydration of Commercial Portland Cement by DSC

In this paper, evaluation of kinetic parameters (the activation energy – E,the pre-exponential factor – A and the reaction order – n) with simultaneous determination of the possible reaction mechanism of thermal decomposition of calcium hydroxide (portlandite), Ca(OH)₂ formed during hydration of commercial Portland-slag cement, by means of differential scanning calorimetry (DSC) in non-isothermal conditions with a single heating–rate plot has been studied and discussed. The kinetic parameters and a mechanism function were calculated by fitting the experimental data to the integral, differential and rate equation methods. To determine the most probable mechanism, 30 forms of the solid-state mechanism functions, f(α_c) have been tried. Having used the procedure developed and the appropriate program support, it has been established that the non-isothermal thermal decomposition of calcium hydroxide in the acceleratory period (0.004<α_c<0.554) can be described by the rate equation: d α_c/dT=A/βexp(−E/RT)f(α_c), which is based on the concept of the mechanism reaction:f(α_c)=2(α_c)^1/2. The mechanism functions as well as the values of the kinetic parameters are in good agreement with those given in literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Water Structure in Concentrated Salt Solutions

In concentrated salt solutions the average distances between the ions, d ^av=1.1844⋅(∑ν _i c _i )^−1/3 nm, are commensurate with the sizes of the solvated ions, so that no ‘bulk solvent’ remains. This is illustrated with two saturated aqueous solutions, where 16.67 mol⋅dm⁻³ CsF at 75 °C has d ^av(Cs–F)=0.368 nm and 14.54 mol⋅dm⁻³ LiI at 80 °C has d ^av(Li–I)=0.385 nm. The minimal distance required for the bare ions (sum of their radii) are 0.303 nm for CsF and 0.289 nm for LiI. Hence no water molecule, diameter 0.276 nm, can be fitted between the ions to form linear or slightly bent hydrogen bonds. Some recent work ignoring such constraints, even in 3–6 mol⋅dm⁻³ solutions, is criticized on this account.     

Spectral and electrochemical study of coordination molecules Cu4OX6L4: 3-Pyridylmethanol and 4-pyridylmethanol Cu4OBrnCl(6−n)(pm)4 complexes

The tetranuclear Cu₄OBr_nCl_(6−n)(pm)₄ complexes, where pm = 3-pyridylmethanol (3-pm), 4-pyridylmethanol (4-pm) and n = 0−6 with trigonal bipyramidal coordination of copper(II) were prepared and their infrared and electronic absorption spectra as well as cyclic voltammograms in nitromethane solutions were measured. The molecules exhibit strong single infrared Cu₄O stretching absorptions between 580 and 530 cm⁻¹ which are in linear correlations with the number of halides, n. Far infrared absorptions assigned to Cu-Br, Cu-Cl, and Cu-N stretching vibrations appear at higher wavenumbers for 3-pm complexes compared with those for 4-pm complex molecules. Two strongly overlapped d–d bands in the region 11300–13100 cm⁻¹ assigned to and e(d _xz, d _yz) → a ₁(d _z ²) transitions in the trigonal bipyramidal coordination of the copper(II) atoms were resolved by Gaussian analysis. Both, 3-pm and 4-pm ligands produce in the complex molecules almost the same ligand field. The maxima of the Gaussian d–d components vary with the parameter n and are for both series of the complexes deviated from linearity, more for the low-energy d–d bands than for high-energy analogues. The electrochemical reduction in nitromethane is significantly less reversible for 4-pm complex molecules compared with that of 3-pm analogues. Formal reduction potentials E′ _c for 3-pm complexes were observed in the range 478 (n = 0)−599 (n = 6) mV. The plot E′ _c vs. n is significantly deviated from linearity. It is suggested that the reducing electrons enter the half-filled d _z ² orbital of the copper(II) atom. The different spectral and electrochemical results obtained for 3-and 4-pm complexes are explained by different structural distortions, bond lengths, and charge distributions produced by halide ligand variations. The results are also discussed with previously reported data on analogous pyridine, 3-methylpyridine and 4-methylpyridine complexes.     

Reaction of thiosemicarbazide with n-cyanoguanidine: synthesis of 3,5-diamino-1-thiocarbamoyl-and 3,5-diamino-1-thiazol-2-yl-1,2,4-triazoles

The reaction of thiosemicarbazide with N-cyanoguanidine in an acidic medium afforded 3,5-diamino-1-thiocarbamoyl-1,2,4-triazole, whose condensation with α-halo ketones gave 3,5-diamino-1-thiazol-2-yl-1,2,4-triazoles 7a–d. The latter were also prepared by the independent synthesis from 2-hydrazinothiazoles and N-cyanoguanidine. Acylation of compounds 7a,d under mild conditions and their condensation with aldehydes occur at the C(3′)NH₂group. The structure of aroyl derivative 11c was established by X-ray diffraction. Acylation of diaminothiazolyltriazole 7a in boiling Ac₂O afforded 3,5-diacetylamino-1-(4-phenylthiazol-2-yl)-1,2,4-triazole. Hydrogenation of arylidene derivatives 14b,c and aroyl derivative 11c gave the corresponding benzylaminotriazoles 15a,b. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 329–334, February, 2006.     

Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267]

We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113: 267] yields very reliable estimates of the Hartree–Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form yields HF limits E _HF,∞ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets.     

Sodium and silver phosphate glasses doped with chlorides of Fe,Mn and Zn

A number of samples of sodium and silver phosphate glasses doped with various compositions of some transition metals viz. iron, manganese and zinc chlorides alongwith undoped samples of sodium and silver phosphate glasses were synthesized and characterized by X-ray diffraction, IR spectral, electrical conductivity and differential scanning calorimetry (DSC). The glass transition temperature (T _g) and crystallization temperature (T _c) values obtained from DSC curves were found to increase with increasing concentration of the dopant Fe/Mn/Zn chlorides in both sodium and silver phosphate glasses and the following sequence is observed: T _g(–FeCl₃)>T _g(–MnCl₂)>T _g(–ZnCl₂) T _c(–FeCl₃)>T _c(–MnCl₂)>T _c(–ZnCl₂) The increase in T _g and T _c values indicate enhanced chemical durability of the doped glasses. The electrical conductivity values and the results of FTIR spectral studies have been correlated with the structural changes in the glass matrix by the addition of different transition metal cations as dopants.     

Speciation of BCxNy films grown by PECVD with trimethylborazine precursor

Films of BC _x N _y were produced in a plasma-enhanced chemical vapor deposition process using trimethylborazine as precursor and with H₂, He, N₂, and NH₃, respectively, as auxiliary gas. These films deposited on Si(100) wafers or fused quartz glass substrates were characterized chemically by X-ray photoelectron spectroscopy and by synchrotron radiation-based total-reflection X-ray fluorescence combined with near-edge X-ray absorption fine structure. Independent of the auxiliary gas, the B–N bonds are dominating. Furthermore, B–C and N–C bonds were identified. Oxygen, present in the bulk (in contrast to the surface layer of some nanometers, where molecular oxygen and/or water are absorbed) as an impurity, is bonded to boron or to carbon, respectively. The relation of boron and nitrogen changes with the character of the auxiliary gas: c _B/c _N ≈ 4:3 (for H₂ and He) and c _B/c _N ≈ 1 (for N₂ or NH₃). Furthermore, physical properties such as the refractive index and the optical band-gap energy were determined.     

Crystal Structure and Characterisation of Mercury(II) Dichromate(VI)

Summary. Dark-red single crystals of HgCr₂O₇ were grown by reacting HgO and CrO₃ in excess at 200°C for four days. The crystal structure (space group P3₂, Z = 3, a = 7.2389(10), c = 9.461(2) ?, 1363 structure factors, 57 parameters, R[F ²>2σ(F ²)] = 0.0369, wR(F ² all) = 0.0693) was determined from a crystal twinned by merohedry according to (110). It consists of nearly linear HgO₂ units ( (Hg–O) = 2.02 ?) and dichromate units that are linked into infinite chains ‘O₃Cr–O–CrO₃–Hg–O₃Cr–O–CrO₃’ running parallel to the c-axis. Six additional Hg–O contacts between 2.73 and 2.96 ? stabilise the structural arrangement. The dichromate anion exhibits a staggered conformation with a bent Cr–O–Cr bridging angle of 140.7(6)°. Upon heating above 300°C, HgCr₂O₇ decomposes in a two-step mechanism to Cr₂O₃. The title compound was additionally characterised by vibrational spectroscopy.     

Electronic absorption spectra of charge-transfer complexes and effects of substituents in radical cations

The effects of X substituents on the energies of charge-transfer bandshv _CT in electronic absorption spectra of charge-transfer complexes of π-, n-, or σ-donors (DX) with π- or σ-acceptors (A) as well as on the ionization potentialsI _D of individual DX molecules are described by the equationhv _CT(l _D)=a +bσ₁ +cσ _R ⁺ +dσ_α. When DX and A are fixed, the inductive (bσ₁), resonance (cσ _R ⁺ ), and polarization (dσ_α) contributions tohv _CT andI _D are virtually identical. The electronic structure of the D^.+X donor component of the compact [A^.−, D^.+X] radical-ionic pair in a solution is similar to that of the radical cation generated upon photoionization of the individual DX molecule in the gaseous phase. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1002–1006, June, 2000.     

The immobilization of Cytochrome c on MWNT–PAMAM–Chit nanocomposite incorporated with DNA biocomposite film modified glassy carbon electrode for the determination of nitrite

A novel and sensitive biosensor was developed for the determination of nitrite. Firstly, multi-walled carbon nanotubes–poly(amidoamine)–chitosan (MWNT–PAMAM–Chit) nanocomposite along with the incorporation of DNA was used to modify the glassy carbon electrode. Then the immobilization of Cyt c was accomplished using electrochemical deposition method by consecutive cyclic voltammetry (CV) scanning in a neutral Cyt c solution. CV behaviors of the modified electrodes showed that the MWNT–PAMAM–Chit nanocomposite is a good platform for the immobilization of DNA and Cyt c in order, at the same time, an excellent promoter for the electron transfer between Cyt c and the electrode. At high potential, the immobilized Cyt c could be further oxidized into highly reactive Cyt c π-cation by two-step electrochemical oxidation, which could oxidize NO₂ ⁻ into NO₃ ⁻ in the solution. Therefore, a nitrite biosensor based on the biocatalytic oxidation of the immobilized Cyt c was fabricated, which showed a fast response to nitrite (less than 5 s). The linear range of 0.2–80 μM and a detection limit of 0.03 μM was obtained. Finally, the application in food analysis using sausage as testing samples was also investigated.     

Influence of containing moisture on hydrothermal stability of modified collagen thermal characteristics analysis by DSC

The thermal stability of sheepskin collagen cross-linked with chrome sulfate and mimosa (MI)–oxazolidine (OZ), respectively, had been researched in this experiment. All samples’ shrinkage temperatures (T _s) are determined by a special T _s-testing-apparatus and denaturation temperatures (T _d) are determined by the differential scanning calorimetry. The relations between the modified collagens containing moisture and their hydrothermal stability, T _s or T _d, were studied. The results show that the cross linking agents can enhance the thermal stability of modified collagen whose T _s are 109.8 and 110.6 °C for collagen treated with chrome and MI–OZ, respectively. When the samples contain 25–71.9% moisture for chrome leather and 20–71.1% for leather treated with MI–OZ, the hydrothermal stability will decrease with the increase of moisture. It was found that the difference between T _s and T _d of collagen modified by chrome is more obvious than that of collagen modified with MI–OZ. And when the moisture of chrome leather exceeds 55%, T _d cannot express thermal stability of modified collagen as a substitute for T _s, and the moisture is 40% for leather tanned with MI–OZ.     

Thermal stability and crystallization kinetics in superionic glasses using electrical conductivity–temperature cycles

The present work demonstrates application of electrical conductivity (σ)–temperature (T) cycles to investigate thermal properties viz., crystallization and glass transition kinetics in AgI–Ag₂O–V₂O₅–MoO₃ superionic glasses. The σ–T cycles are carefully performed at various heating rates, viz., 0.5, 1, 3, 5, and 7 K/min. The conductivity in Ag⁺ ion conducting glasses exhibit anomalous deviation from Arrhenius behavior near glass transition temperature (T _g) followed by a drastic fall at crystallization (T _c). The temperature corresponding to maximum rate of crystallization (T _p) is obtained from the derivative of σ–1/T plots. With increasing heating rates, the characteristic temperatures (T _g, T _p) are found to be shifting monotonically toward higher temperatures. Thus, activation energy of structural relaxation E _s, crystallization E _c and other thermal stability parameters have been obtained from σ–T cycles using Kissinger equation and Moynihan formulation. For a comparative study, these kinetics parameters have also been calculated from differential scanning calorimetry plots. The parameters obtained from both the methods are found to be comparable within experimental error.