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.

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

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 NO. 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 299-592 K. The second-order rate constants at 10 Torr fitted the Arrhenius equation log(k/cm(3) molecule(-1) s(-1)) = (- 11.66 +/- 0.01) + (6.20 +/- 0.10 kJ mol(-1))IRT In 10 The rate constants showed a variation with pressure of a factor of ca. 2 over the available range, almost independent of temperature. The data could not be fitted by RRKM calculations to a simple third body assisted association reaction alone. However, a mechanistic model with an additional (pressure independent) side channel gave a reasonable fit to the data. Ab initio calculations at the G3 level supported a mechanism in which the initial adduct, bent H2SiNO, can ring close to form cyclo-H2SiNO, which is partially collisionally stabilized. In addition, bent H2SiNO can undergo a low barrier isomerization reaction leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are NH2 + SiO. The rate controlling barrier for this latter pathway is only 16 kJ mol(-1) below the energy of SiH2 + NO. This is consistent with the kinetic findings. A particular outcome of this work is that, despite the pressure dependence and the effects of the secondary barrier (in the side reaction), the initial encounter of SiH2 with NO occurs at the collision rate. Thus, silylene can be as reactive with odd electron molecules as with many even electron species. Some comparisons are drawn with the reactions of CH2 + NO and SiCl2 + NO.

The addition reaction between silylene and ethyne: further isotope studies, pressure dependence studies, and quantum chemical calculations

Time-resolved kinetic studies of the reaction of dideutero-silylene, SiD2, generated by laser flash photolysis of phenylsilane-d(3), have been carried out to obtain rate constants for its bimolecular reaction with C2H2. 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 obtained by extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equation log(k(infinity)/cm(3) molecule(-1) s(-1)) = (-10.05 +/- 0.05) + (3.43 +/- 0.36 kJ mol(-1))/RT ln 10. The rate constants were used to obtain a comprehensive set of isotope effects by comparison with earlier obtained rate constants for the reactions of SiH2 with C2H2 and C2D2. Additionally, pressure-dependent rate constants for the reaction of SiH2 with C2H2 in the presence of He (1-100 Tort) were obtained at 300, 399, and 613 K. Quantum chemical (ab initio) calculations of the SiC2H4 reaction system at the G3 level support the initial formation of silirene, which rapidly isomerizes to ethynylsilane as the major pathway. Reversible formation of vinylsilylene is also an important process. The calculations also indicate the involvement of several other intermediates, not previously suggested in the mechanism. RRKM calculations are in semiquantitative agreement with the pressure dependences and isotope effects suggested by the ab initio calculations, but residual discrepancies suggest the possible involvement of the minor reaction channel, SiH2 + C2H2 - SWPO + C2H4. The results are compared and contrasted with previous studies of this reaction system.

Time-resolved gas-phase kinetic and quantum chemical studies of reactions of silylene with chlorine-containing species. 1. HCl

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 HCL The reaction was studied in the gas phase at 10 Torr total pressure in SF6 bath gas, at five temperatures in the range of 296-611 K. The second-order rate constants fitted the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.51 +/- 0.06) + (1.92 +/- 0.47 kJ mol(-1))/RTIn10 Experiments at other pressures showed that these rate constants were unaffected by pressure in the range of 10-100 Torr, but showed small decreases in value of no more than 20% ( +/- 10%) at I Toff, at both the highest and lowest temperatures. The data are consistent with formation of an initial weakly bound donor-acceptor complex, which reacts by two parallel pathways. The first is by chlorine-to-silicon H-shift to make vibrationally excited chlorosilane, SiH3Cl*, which yields HSiCl by H-2 elimination from silicon. In the second pathway, the complex proceeds via H-2 elimination (4-center process) to make chlorosilylene, HSiCl, directly. This interpretation is supported by ab initio quantum calculations carried out at the G3 level which reveal the direct H-2 elimination route for the first time. RRKM modeling predicts the approximate magnitude of the pressure effect but is unable to determine the proportions of each pathway. The experimental data agree with the only previous measurements at room temperature. Comparisons with other reactions of SiH2 are also drawn.

Wigner Transport models of the electron-phonon kinetics in quantum wires

Two quantum-kinetic models of ultrafast electron transport in quantum wires are derived from the generalized electron-phonon Wigner equation. The various assumptions and approximations allowing one to find closed equations for the reduced electron Wigner function are discussed with an emphasis on their physical relevance. The models correspond to the Levinson and Barker-Ferry equations, now generalized to account for a space-dependent evolution. They are applied to study the quantum effects in the dynamics of an initial packet of highly nonequilibrium carriers, locally generated in the wire. The properties of the two model equations are compared and analyzed.

On a non-autonomous difference equation

Abu-Saris and DeVault proposed two open problems about the difference equation x(n+1) = a(n)x(n)/x(n-1), n = 0, 1, 2,..., where a(n) not equal 0 for n = 0, 1, 2..., x(-1) not equal 0, x(0) not equal 0. In this paper we provide solutions to the two open problems. (c) 2004 Elsevier Inc. All rights reserved.

Gas-phase kinetics of chlorosilylene reactions II. ClSiH + C2H4: absolute rate measurements and quantum chemical and RRKM calculations for the prototype pi addition reaction

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1-silacyclopent-3-ene, are carried out to obtain rate constants for its bimolecular reaction with ethene, C2H4, in the gas-phase. The reaction is studied over the pressure range 0.13-13.3 kPa (with added SF6) at five temperatures in the range 296-562 K. The second order rate constants, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1))=(-10.55 +/- 0.10) + (3.86 +/- 0.70) kJ mol(-1)/RT ln10. The Arrhenius parameters correspond to a loose transition state and the rate constant at room temperature is 43% of that for SiH2 + C2H4, showing that the deactivating effect of Cl-for-H substitution in the silylene is not large. Quantum chemical calculations of the potential energy surface for this reaction at the G3MP2//B3LYP level show that, as well as 1-chlorosilirane, ethylchlorosilylene is a viable product. The calculations reveal how the added effect of the Cl atom on the divalent state stabilisation of ClSiH influences the course of this reaction. RRKM calculations of the reaction pressure dependence suggest that ethylchlorosilylene should be the main product. The results are compared and contrasted with those of SiH2 and SiCl2 with C2H4.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.

The reaction between silylene and ammonia: some gas-phase kinetic and quantum chemical studies

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by 193 nm laser flash photolysis of silacyclopent-3-ene, have been carried out in the presence of ammonia, NH3. Second order kinetics were observed. The reaction was studied in the gas phase at 10 Torr total pressure in SF6 bath gas at each of the three temperatures, 299, 340 and 400 K. The second order rate constants (laser pulse energy of 60 mJ/pulse) fitted the Arrhenius equation: log(k/cm3 molecule-1 s-1) = (-10.37 ± 0.17) + (0.36 ± 1.12 kJ mol-1)/RTln10 Experiments at other pressures showed that these rate constants were unaffected by pressure in the range 10-100 Torr, but showed small decreases in value at 3 and 1 Torr. There was also a weak intensity dependence, with rate constants decreasing at laser pulse energies of 30 mJ/pulse. Ab initio calculations at the G3 level of theory, show that SiH2 + NH3 should form an initial adduct (donor-acceptor complex), but that energy barriers are too great for further reaction of the adduct. This implies that SiH2 + NH3 should be a pressure dependent association reaction. The experimental data are inconsistent with this and we conclude that SiH2 decays are better explained by reaction of SiH2 with the amino radical, NH2, formed by photodissociation of NH3 at 193 nm. The mechanism of this previously unstudied reaction is discussed.