Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser. ash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3 - 100 Torr with SF6 as bath gas and at five temperatures in the range 300 - 625 K. Only slight pressure dependences were found for SiH2 + MeSiH3 ( 485 and 602 K) and for SiH2 + Me2SiH2 ( 600 K). The high pressure rate constants gave the following Arrhenius parameters: [GRAPHICS] These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences ( and also the lack of them for SiH2 + Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2 + MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2 + SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH + SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect ( as observed in other studies).

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

The gas-phase reaction between silylene and 2-butyne: kinetics, isotope studies, pressure dependence studies and quantum chemical calculations

Time-resolved kinetic studies of the reactions of silylene, SiH2, and dideutero-silylene, SiD2, generated by laser. ash photolysis of phenylsilane and phenylsilane-d(3), respectively, have been carried out to obtain rate coefficients for their bimolecular reactions with 2-butyne, CH3C CCH3. The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 294-612 K. The second-order rate coefficients, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equations where the error limits are single standard deviations: log(k(H)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.67 +/- 0.04) + (1.71 +/- 0.33) kJ mol(-1)/RTln10 log(k(D)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.65 +/- 0.01) + (1.92 +/- 0.13) kJ mol(-1)/RTln10 Additionally, pressure-dependent rate coefficients for the reaction of SiH2 with 2-butyne in the presence of He (1-100 Torr) were obtained at 301, 429 and 613 K. Quantum chemical (ab initio) calculations of the SiC4H8 reaction system at the G3 level support the formation of 2,3-dimethylsilirene [cyclo-SiH2C(CH3)=C(CH3)-] as the sole end product. However, reversible formation of 2,3-dimethylvinylsilylene [CH3CH=C(CH3)SiH] is also an important process. The calculations also indicate the probable involvement of several other intermediates, and possible products. RRKM calculations are in reasonable agreement with the pressure dependences at an enthalpy value for 2,3-dimethylsilirene fairly close to that suggested by the ab initio calculations. The experimental isotope effects deviate significantly from those predicted by RRKM theory. The differences can be explained by an isotopic scrambling mechanism, involving H - D exchange between the hydrogens of the methyl groups and the D-atoms in the ring in 2,3-dimethylsilirene-1,1-d(2). A detailed mechanism involving several intermediate species, which is consistent with the G3 energy surface, is proposed to account for this.

Supporting multi-organisational collaborative groups in the public sector

In this paper, the issues that arise in multi-organisational collaborative groups (MOCGs) in the public sector are discussed and how a technology-based group support system (GSS) could assist individuals within these groups. MOCGs are commonly used in the public sector to find solutions to multifaceted social problems. Finding solutions for such problems is difficult because their scope is outside the boundary of a single government agency. The standard approach to solving such problems is collaborative involving a diverse range of stakeholders. Collaborative working can be advantageous but it also introduces its own pressures. Conflicts can arise due to the multiple contexts and goals of group members and the organisations that they represent. Trust, communication and a shared interface are crucial to making any significant progress. A GSS could support these elements.

Mean flow and turbulence statistics over groups of urban-like cubical obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

A comparison of the reactivity of germylene and dimethylgermylene with some methylgermanes. Direct kinetic and quantum chemical studies

Time-resolved studies of germylene, GeH2, and dimethygermylene, GeMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to try to obtain rate coefficients for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas-phase. GeH2 + Me2GeH2 was studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 296-553 K. Only slight pressure dependences were found (at 386, 447 and 553 K). RRKM modelling was carried out to fit these pressure dependences. The high pressure rate coefficients gave the Arrhenius parameters: log(A/cm(3) molecule(-1)s(-1)) = -10.99 +/- 0.07 and E-a = -(7.35 +/- 0.48) kJ mol(-1). No reaction could be found between GeMe2 + Me2GeH2 at any temperature up to 549 K, and upper limits of ca. 10(-14) cm(3) molecule(-1)s(-1) were set for the rate coefficients. A rate coefficient of (1.33 +/- 0.04) x 10(-11)cm(3) molecule(-1)s(-1) was also obtained for GeH2 + MeGeH3 at 296 K. No reaction was found between GeMe2 and MeGeH3. Rate coefficient comparisons showed, inter alia, that in the substrate germane Me-for-H substitution increased the magnitudes of rate coefficients significantly, while in the germylene Me-for-H substitution decreased the magnitudes of rate coefficients by at least four orders of magnitude. Quantum chemical calculations (G2(MP2,SVP)// B3LYP level) supported these findings and showed that the lack of reactivity of GeMe2 is caused by a positive energy barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper.

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm(3) molecule(-1) s(-1)) = -13.25 +/- 0.16 and E-a = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.

An investigation of the germylene addition reaction, GeH2+C2H2: Time-resolved gas-phase kinetic studies and quantum chemical calculations of the reaction energy surface

Time resolved studies of germylene, GeH2, generated by laser flash photolysis of 3,4-dimethylgermacyclopentene-3, have been carried out to obtain rate constants for its bimolecular reaction with acetylene, C2H2. The reaction was studied in the gas-phase over the pressure range 1-100 Tort, with SF6 as bath gas, at 5 temperatures in the range 297-553 K. The reaction showed a very slight pressure dependence at higher temperatures. The high pressure rate constants (obtained by extrapolation at the three higher temperatures) gave the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) (-10.94 +/- 0.05) + (6.10 +/- 0.36 kJ mol(-1))/RTln10. These Arrhenius parameters are consistent with a fast reaction occurring at approximately 30% of the collision rate at 298 K. Quantum chemical calculations (both DFT and ab initio G2//B3LYP and G2//QCISD) of the GeC2H4 potential energy surface (PES), show that GeH2 + C2H2 react initially to form germirene which can isomerise to vinylgermylene with a relatively low barrier. RRKM modelling, based on a loose association transition state, but assuming vinylgermylene is the end product (used in combination with a weak collisional deactivation model) predicts a strong pressure dependence using the calculated energies, in conflict with the experimental evidence. The detailed GeC2H4 PES shows considerable complexity with ten other accessible stable minima (B3LYP level), the three most stable of which are all germylenes. Routes through this complex surface were examined in detail. The only product combination which appears capable of satisfying the (P-3) + C2H4.C2H4 was confirmed as a product by GC observed lack of a strong pressure dependence is Ge(P-3) + C2H4. C2H4 was confirmed as a product by GC analysis. Although the formation of these products are shown to be possible by singlet-triplet curve crossing during dissociation of 1-germiranylidene (1-germacyclopropylidene), it seems more likely (on thermochernical grounds) that the triplet biradical, (GeCH2CH2.)-Ge-., is the immediate product precursor. Comparisons are made with the reaction of SiH2 with C2H2.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.