Volume 39, Issue 9

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d -2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN) 2- 5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

The integrability of Hamiltonians of the type H(P 1 , P 2 , Q 1 , Q 2 ) = P i ·G i (Q 1, Q 2 ), G i 2 π-periodic in Q 1 , Q 2 , is investigated numerically and analytically. With G i = ω i + F i (Q 1 , Q 2 ) and = H 0 = ω i + P i , the unperturbed frequencies ω i = ∂H 0 /∂P i , are independent of the momenta, and KAM theory cannot be applied. Surface of section plots and Fourier analysis of orbits reveal that "most" Hamiltonians are integrable. Possibly non-integrable Hamiltonians do not show "island plus ergodic region" structure but sequences which tend towards infinity. No theory is available to distinguish completely the classes of integrable and non-integrable functions G i (Q 1 ,Q 2 ). In such a theory the problem of "small denominators" would play an essential role just as in KAM theory.

The Conformal Solution and Flory's expressions for the free energy of mixing ΔG M of a binary liquid alloy have been modified by using a form for the enthalpy of mixing ΔH M which incorporates the concentration dependence given by Miedema's semiempirical model. This model emphasizes the importance of the atomic cell-surface area concentration in evaluating ΔH M . The modified forms of ΔG M have been used to construct the liquidus curves of NaCs and NaK.

The rate constant of the reaction NH 2 +CH 4 →NH 3 +CH 3 was measured at temperatures of about 1800 K by time-resolved UV-spectroscopy of the products behind incident shock waves. NH 2 was produced by the presence and thermal decomposition of hydrazine. The data were evaluated by fitting simulated concentration-time-profiles to the measured ones. A mean rate constant k = (4±2) 10 11 cm 3 mol -1 s -1 1730 <T/K < 1950 was obtained. The temperature dependence of the reaction is discussed.

The millimeterwave spectrum of fluoroacetonitrile (CH 2 FCN) in the ground state has been investigated in the region between 50 and 150 GHz. The transitions have been fitted to a Hamiltonian using three rotational constants, five quartic and seven sextic centrifugal distortion constants in the symmetric top reduction by van Eijck and Typke and in the s-reduction of Watson. Further Watson's "determinable constants" have been calculated.

We performed a pulse sequence experiment utilizing a technique, which is comparable with two-dimensional NMR-spectroscopy. Some theoretical considerations based on the three-level Bloch equations are given. This double resonance technique may be useful for the assignment of complicated spectra.

The rotational spectra of vibrationally excited CF 3 NC states (ν 4 , ν 6 , ν 7 , ν 8 , 2ν 8 and 3ν 8 ) have been recorded and analyzed for the transitions J: 1→2, 2→3 and 3→4 using (for the degenerate states) a simplified frequency expression based on perturbation theory. The following vibration/rotation interaction parameters were derived (in MHz): α 4 : 0.145, α 6 : - 5.585, q + 6 4.241, α 7 : 2.350, q + 7 : 1.438, α 8 : - 10.610, and q + 8 : 5.101. The Coriolis constant ζ À 88 was determined to be 0.672 in good agreement with the value calculated from the force field.

Fourier transform infrared spectra of the monoisotopic species H 3 74 Ge 79 Br and H 3 74 Ge 81 Br have been recorded in the ν 1 /ν 4 region near 2100 cm -1 with a resolution of 0.015 cm -1 and in the ν 6 and 2 ν 6 regions near 580 and 1150 cm -1 with a resolution of 0.04 cm -1 . Rotational analyses based on ~ 1500, ~1100 and ~ 300 data of ν 1 /ν 4 , ν 6 and 2 ν 6 respectively for each isotopomer have been performed, and ground state and excited state vibrational, rotational and rovibrational parameters have been determined, ν 1 , 2115.815 0(2)/2115.813 4(2) cm -1 , and ν 4 , 2126.016 5(1) 2126.016 7(1) cm -1 (H 3 74 Ge 79 Br/H 3 74 Ge 81 Br), are weakly coupled by Coriolis x, y resonance, ζ 1,4 ≃ - 0.021. ν 6 , 577.601 2(4)/577.541 7(4) cm -1 , and ν 4 are affected by / (±2, ±2) resonance. Furthermore, the hot bands (ν 1 +ν 3 )-ν 3 , (ν 3 +ν 4 )-ν 3 , (ν 3 +ν 6 )-ν 3 , 2ν 6 ±2 - ν 6 ±2 and 2ν 0 6 - ν 6 ±1 have been detected and analyzed.

The experimental findings by Klemm et al. that in molten LiCl the isotope effect on the lithium mobilities increases with temperature and that the isotope effect between the two isotopically pure melts, i.e. 6 LiCl and 7 LiCl is greater than that in natural LiCl are reflected by the self-exchange velocities of the Li-isotopes near the Cl - -ions obtained by MD.

The frequency shift of methanolic OH stretching bands by different nonpolar solvents at different temperatures can be described quantitatively by an equation proposed recently relating it to the temperature dependence of van der Waals interactions. The method shows that methanolic OH groups are surrounded by about 40% more solvent molecules than t-butanol OH groups. Frequency shifts of CH 3 OH by binary solvent mixtures demonstrate an averaged potential with small preference of the solvent with higher interaction.

A Cannizzaro disproportionation reaction of 4-nitrosobenzaldehyde (I) and sodium hydroxide in dioxane-water media is kinetically studies by UV-Vis. absorption spectroscopy. The reaction did not give the expected products, namely 4-nitrosobenzyl alcohol and 4-nitrosobenzoic acid, but gave equimolecular quantities of 4,4′-diformylazoxybenzene (II) and 4,4′-dicarboxyazoxybenzene (III) and was found to exhibit third-order kinetics, second-order in aldehyde and firstorder in base. The rate constants as well as the activation thermodynamic parameters were calculated for different temperatures and different dioxane-water compositions, and discussed on the bases of dielectric constant, viscosity and heat of mixing of the medium components. The rate determining step is a hydride ion transfer from the adduct (formed from the attack of one hydroxide ion on molecule of I) to another molecule of I. A mechanism is given to explain the formation of the end reaction products.

A detailed stability analysis of the one dimensional steady state solutions for the Brusselator model under the conditions of diffusion of initial (non-autocatalytic) components has been performed both for zero flux as well as fixed boundary conditions. In addition to subcritical as well as supercritical bifurcations, situations have been observed where all solution branches at a bifurcation point are unstable. A case of degenerate steady state bifurcation (2 solutions emanating from the same bifurcation point) has also been noticed. A transient simulation of the system in growth reveals the importance of growth rate on the pattern selection process and suggests that the selection of branches at a bifurcation point may be influenced by perturbations/ fluctuations. It also indicates that a stability analysis of the bifurcation diagram alone cannot decide the state of the system in a transient process, and under certain situations complex behavior may be observed at limit points. Numerical calculations on coupled cells indicate that a heterogenity in the system can introduce multiple (two) time scales in the system. As the ratio of time scales increases, aperiodic or irregular oscillations are observed for the 'fast' variable. A combination of cells with one cell in a steady-state mode and the other in a periodic motion results in a combined motion of the entire system. For a distributed parameter system, a heterogenity can cause development of sharp local concentration gradients, alter the stability properties of steady state as well as periodic solutions and can cause partitioning of the system.

It is demonstrated that the sinh-Gordon equation can be written as covariant exterior derivatives of Lie algebra valued differential forms and, moreover, that these nonlinear differential equations represent a completely integrable system.