On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.     

Ambient synthesis of spiro[4H-pyran-oxindole] derivatives under [BMIm]BF4 catalysis

A simple and efficient one-pot approach for assembling some fused spiro[4H-pyran-oxindole] heterocycles by means of three-component reactions between isatins, malononitrile or ethyl cyano-acetate, and 1,3-dicarbonyl compounds is reported. The combinatorial syntheses were achieved for the first time without applying extra activation energy at ambient temperature while making use of [BMIm]BF₄ as an ionic liquid catalyst. Good functional group tolerance and broad scope of usable substrates are other prominent features of the present methodology.     

Water increases rates of epoxidation by Mn(III)porphyrins/imidazole/IO4(-) in CH2Cl2. Analogy with peroxidase and chlorite dismutase

Manganese(III)-meso-tetraphenylporphyrin [Mn(TPP)] and manganese(III)-meso-tetrakis(pentafluorophenyl)porphyrin [Mn(TPFPP)] catalyse the epoxidation of cyclooctene by IO(4)(-) in the presence of excess imidazoles, in both dry CH(2)Cl(2) and CH(2)Cl(2) saturated with H(2)O. The reaction rates of the electron deficient Mn(TPFPP) are a factor 24 less than those of Mn(TPP); however, the former increases 15-30 times in the presence of water, while those of Mn(TPP) do so by a factor of 2-3. The most striking catalytic enhancement caused by the addition of water was observed with 2-methylimidazole and Mn(TPFPP). As deprotonation of imidazoles may play a significant role in the presence of water, we found that manganese(III)-meso-tetrakis(phenyl-4-sulfonato)porphyrin [Mn(TPPS)] decreases the NH proton pK(a) of axially coordinated imidazole from 14.2 to 9.5. We conclude that the imidazole ligand is partially deprotonated in the presence of water. The latter enables the solvation of imidazolium ions that are formed simultaneously. The imidazolate form of the co-catalyst is a much stronger donor than the imidazole itself, providing electron density to Mn(III) and thus promoting oxygen transfer. The failure of N-methylimidazole to increase the reaction rates upon addition of water supports this hypothesis. A functionally related deprotonation has been shown to occur in horseradish peroxidase (J. S. de Ropp, V. Thanabal, G. N. La Mar, J. Am. Chem. Soc. 1985, 107, 8270-8272) and in chlorite dismutase (B. R. Goblirsch, B. R. Streit, J. L. Dubois, C. M. Wilmot, J. Biol. Inorg. Chem. 2010, 15, 879-888). Mn(III)porphyrins in combination with imidazoles and water constitute a functional biomimetic model of peroxidases.     

The extent of molecular orientation at liquid/vapor interface of pyridine and its alkyl derivatives by molecular dynamics simulation

In this paper, molecular dynamics simulation was performed to investigate the liquid∕vapor interfacial structure of neat polar liquids. Large-scale ensembles of liquid pyridine and its alkyl derivatives, 4-methylpyridine and 4-ethylpyridine, were simulated by classical molecular dynamics at 298 K. For the liquid system of low polarity, the surface density profile of the atoms meet exactly at the middle of interfacial region, and atoms of hydrophobic nature can be hardly discriminated from hydrophilic ones in either vapor or liquid sides. For a liquid system of high polarity, the density profile of atoms with different nature is highly discriminated all over the interfacial region, and as the polarity increases, a dense region of atomic density is clearly developed in the subsurface region. The recognized bivariate method was also used to study the molecular orientational distribution quantitatively. Orientational analysis of the three liquid systems indicates that the pyridine ring plane in the outmost surface tends to be vertical. Its tendency in the innermost interfacial region is parallel. The orientational states available to 4-ethylpyridine and pyridine are discriminated by predicting the possibility of a bisector-wise tumbling for the ring plane in pyridine and a side-wise tumbling in 4-ethylpyridine. The orientational distribution maps explain the trend of experimental surface tension and surface entropy. As the dipole moment of these liquids increases with the alkyl chain length, the surface structural profile changes from a regular definite one to a surface of complex atomic structure involving a dense phase near the interface. The development of dense region in alkyl derivatives is the result of segregation of molecules due to the alkyl group, which is captured and discriminated by molecular dynamics simulation even when the length of a short alkyl chain is increased by one carbon atom.     

Faltings’ local–global principle for finiteness dimension of cofinite modules

Archiv der Mathematik - Let R denote a commutative Noetherian ring, $$\mathfrak {a}$$ an ideal of R, and M an $$\mathfrak {a}$$ -cofinite R-module. The purpose of this article is to show that for a...     

Variational transition state theory with multidimensional tunnelling and kinetic isotope effects in the reactions of C2H6, C2H5D and C2D6 with .CCl3 to produce CHCl3 and CDCl3

ABSTRACT

Rate constants for the reactions of C₂H₆, C₂H₅D and C₂D₆ with .CCl₃. for the production of CHCl₃ and CDCl₃ (k₁, k₂, k₃ and k₄) were computed using variational transition state theory coupled with hybrid-meta density functional theory (MPWB1K) over the temperature range of 200–2900 K. The ground-state vibrational adiabatic potential was plotted for all channels. Small- and large-curvature tunnelling were determined to include quantum effects in the calculation of rate constants. Harmonic vibrational frequencies along the reaction path were calculated in curvilinear coordinates with scaled frequencies. Anharmonicity was included in the lowest-frequency torsion. The position of formation and dissociation of bonds was specified using the variation in harmonic vibrational frequencies along the reaction path. Representative tunnelling energy and the thermally averaged transmission probability at 298 K (P(E)exp?( ? ΔE/RT)) were determined for the reactions in which tunnelling is important. The kinetic isotope effect was used to calculate the considerable contributions of tunnelling and vibration. The expressions for rate constants were determined using nonlinear least-square fitting over the temperature range of 200–2900 K.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.